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%   - Acknowledgments

%   - Needed science cases:
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\chapter{Summary}

This document describes a series of ``Design-Reference'' programs that motivate the scientific scope, definition, and high-level requirements for the Keck-FOBOS instrument.  These are envisioned as public key programs, but their scientific reach is designed to be broad in order to drive capabilities and performance requirements for the wide array of science programs FOBOS will undertake.  Program and Science Requirements are developed here and flow down to requirements on the technical and data systems, as captured by our Requirements Table (\texttt{FOBOS.REQ}).

% To address this important spectroscopic need, we propose to advance the design of the FOBOS spectroscopic facility so that it is shovel-ready in 2024, ensuring 1st-light in 2029 as Rubin and Roman imaging surveys achieve their target depths. FOBOS, the Fiber-Optic Broadband Optical Spectrograph, would deploy on WMKO’s Keck II Telescope4 with 1800 fibers across a 20′ field and deep sensitivity from 310–1000 nm at R ∼ 3500. In several key ways, FOBOS is unique among near-term and proposed future instrument concepts in the next two decades(Bundy et al., 2019). It is the only instrument capable of reaching the necessary depths of LSST and Roman weak-lensing samples. Its sensitivity, field-of-view, and ability to target high on-sky source densities is ideally matched to dwarf galaxy kinematics in service of the search for dark matter. Its blue sensitivity and deployable integral-field units (IFUs) are wholly unique capabilities for accessing information-rich UV-optical transitions needed for studies ranging from stellar astrophysics and kilonovae to the high-z circumgalactic medium. And its targeting flexibility, including multiplexed IFU options, enables large and small programs to be interleaved, offering a powerful resource to the U.S. community of users.



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\mainmatter

\chapter{Introduction}

FOBOS (the Fiber Optic Broadband Optical Spectrograph) will be Keck's premiere spectroscopic instrument at optical wavelengths, providing users an unrivaled ability to collect deep, wide-band and especially blue-sensitive spectroscopy of both integrated and spatially-resolved sources at a data collection rate 20--40 times that of current instruments.  The instrument concept development is in response to the 2016 WMKO Scientific Strategic Plan (SSP) which recommended pursuit of ``highly multiplexed, highly sensitive spectroscopy'' as its top-priority design study.  

% Although largely cast as upgrades to existing instruments (e.g., adding a second DEIMOS channel), Appendix II of the SSP specifically notes recent improvements in the sophistication of fiber-based instruments that are ``improving throughput, increasing sky-subtraction accuracy, and increasing the density of fibers that can be stacked along the fiber pseudo-slit. All of these trends deepen the limiting magnitude attainable with fibers, as well as the number of objects than can be surveyed.''

% These considerations have lead to our concept for the \textbf{Fiber-Optic Broadband Optical Spectrograph, FOBOS,} scheduled to deploy on WMKO's Keck II Telescope in 2029, well-suited to immediately begin spectroscopic follow-up campaigns of the significant data sets delivered by various panoramic deep-imaging surveys by that time.  FOBOS emphasizes flexible and quickly configurable focal-plane sampling with high multiplex, UV sensitivity, and a stable spectral format that supports ultra-deep integrations of $\gtrsim$50 hours, thereby building from and expanding on traditional strengths of WMKO observations.

The broader U.S.\ community has also recognized this need, especially in light of the billions of faint sources that will soon be imaged by the Vera C.~Rubin Observatory Legacy Survey of Space and Time (LSST)\footnote{For the first ten years of operation, Vera C.~Rubin Observatory will perform the Rubin Observatory Legacy Survey of Space and Time (LSST). The National Science Foundation (NSF) and the US Department of Energy (DOE) are joint partners in the Rubin Observatory Project and Operations.} and NASA-supported missions like \euclid\footnote{\euclid\ is led by the European Space Agency with significant NASA involvement and will launch in 2022. Its primary mission is a 15,000 deg$^2$ imaging and grism survey in optical and near-IR wavebands.} and the Nancy Grace Roman Space Telescope.\footnote{Previously referred to as the Wide-Field Infrared Survey Telescope (WFIRST), the Nancy Grace Roman Space Telescope is expected to launch in the mid 2020's.}  Reports from the National Research Council in 2015 \citep{NAP21722} and from conferences organized by NOAO (now NOIRLab) in 2013 and 2016 note that a critical resource in need of prompt development is to, ``Develop or obtain access to a highly multiplexed, wide-field optical multi-object spectroscopic capability on an 8m-class telescope.''

% Particularly for the U.~S.\ astronomical community, the twin 10m telescopes of the W.~M.~Keck Observatory (WMKO) represent a compelling avenue to meet this need:  More than 60\% of the LSST footprint and three of its deep-drilling fields (COSMOS, XMM-LSS, and E-CDFS) are within the WMKO visibility window.  Compared to other ongoing efforts to meet upcoming spectroscopic needs \citep{mega2019, mse2019, spectel2019}, WMKO provides an \textit{existing} telescope infrastructure with a 10-m aperture, and, given its site and mirror coatings, is uniquely sensitive toward the atmospheric limit in the UV.  The limited multiplex capacity and sensitivity (compared to more modern equivalents) of its current instruments for optical spectroscopy motivates the need for a much more capable instrument.  Moreover, it is significantly more cost effective to invest in a new instrument for an existing facility than it would be to build an entirely new 10m-telescope$+$spectroscopic facility in the southern hemisphere.

Considering the historical strengths of Keck Observatory and the strategic landscape of astronomy in the 2030's, the FOBOS concept emerged from discussions within the Keck community in 2016--2019.  FOBOS is a high-multiplex optical spectrograph that will deploy on WMKO’s Keck II Telescope with 1800 fibers across a 20 arcmin diameter field and deep sensitivity from 310–1000 nm at $R \sim 3500$.  The focal plane is flexible in that it allows observers to configure the instrument with a combination of single-fiber apertures, multiplexed IFUs (integral field units), or a single, monolithic IFU.

\section{Key Science}

The design-reference programs described below define two broad science goals for FOBOS.  The first is \textbf{to provide a comprehensive view of the ‘cosmic ecosystem,’ the set of relationships between diffuse gas, galaxies, and stars.  By enabling us to \textit{follow the metals}, FOBOS will study kinematic and chemical signatures of the key physical processes driving these relationships across nearly all astronomical scales and cosmic epochs.}   These processes include the accretion and recycling of diffuse gas on large scales, star formation growth and processing through chemical enrichment, and feedback via stellar winds and AGN as measured on galactic and intergalactic scales.  FOBOS not only enables major advances in these sub-fields, but will connect them in powerful new ways.  

The second science goal is \textbf{providing critical follow up of national priority programs that probe fundamental physics and cosmology in the `dark sector.'}  FOBOS has unique and exciting contributions to make in the cross-discipline effort to understand the nature of dark energy and dark matter.  FOBOS represents the surest bet for obtaining the faint spectroscopic redshift samples needed to ensure that LSST/Roman cosmology analyses reach their full potential.  It is also well suited to detailed followup of nearby dwarf galaxies, a promising avenue for constraints on dark matter.


\section{Derivation of ``Requirements'' in this Document}

As a facility-class instrument, FOBOS will be used to pursue a wide range of scientific goals.  The purpose of this document is to encapsulate the breadth and depth of these goals in a way that flows down to the instrument-defining technical requirements.  This document enumerates and provides the justification for all high-level instrument requirements.  These are further developed at deeper levels of detail in associated design documents for each subsystem.

During its Conceptual Design Phase (CoDP), FOBOS science requirements have been developed by defining a set of \textbf{Design-Reference Programs} (Section \ref{sec:key}) that capture the core science that FOBOS \textit{must} enable.  The FOBOS Science Team has developed these programs with the view that they represent the most compelling FOBOS science within its first 5 years on-sky.  These programs are for reference only.  A competitive proposal process will determine the final makeup of approved, large-scale programs ahead of FOBOS commissioning. 

% \edit{section now removed, need to edit this} (2) \textbf{Additional Science Drivers} (Chapter \ref{chap:addsd}) are presented that have not (yet) led to large-scale observing programs, but also represent compelling science that FOBOS \textit{must} enable.

While we developed the Design-Reference Programs and associated requirements in order to explore the full range of required FOBOS capabilities, we constrained this exercise with a set of baseline assumptions.  FOBOS should:

\medskip
\begin{asparaenum}
\item Dramatically improve on the current DEIMOS multiplex of $\sim$100 targets,
\item Adopt a fiber-fed, modular spectrograph design (in order to do so),
\item Provide both single-aperture and integral-field capabilities,
\item Cover the near-UV to 1 $\mu$m wavelength range, and
\item Provide a spectral resolution of $R\sim 3000-5000$.
\end{asparaenum}
\medskip

\noindent It goes without saying that FOBOS should enable transformational science at a minimal total cost that is competitive with other modern instruments of a similar scale. With this context, we define four types of requirements in this document.  At the highest level:

\begin{itemize}
\item \textbf{Program Requirements (P)} define the final measurement fidelity, derived after all observations, that is required to make a given Design-Reference Program successful. For example, these requirements could specify the number of targets required, the number of fields, and the required S/N per target.
%``To measure a change in the slope of the initial mass function (IMF) of $X$ dex per ${\rm d}(\log\mathcal{M}_\ast)$ or larger, the equivalent width of the Wing-Ford band must be measured to better than $Y$ dex for $N$ galaxies evenly distributed over a mass range of $\mathcal{M}_1 < \mathcal{M}_\ast < \mathcal{M}_2$.''  

\item \textbf{Science Requirements (S)} define the \emph{instantaneous} ability of FOBOS to obtain observations that satisfy a program requirement.  For example, these requirements could specify the spectral range or spectral resolution required to enable measurements for each observed target.
%``The spectral range must include the Wing-Ford band (989 nm $< \lambda <$ 995 nm) for galaxies at $z \lesssim 0.1$.''  
\end{itemize}

\noindent Program Requirements (P) can flow to both Science Requirements (S) and Instrument Requirements.  Science Requirements (S) also flow to Instrument Requirements, but Science Requirements generally do not flow to Program Requirements.  

The Program and Science Requirements are used to construct Instrument and Data Requirements that translate science goals into technical specifications:

% A useful distinction is that program requirements can flow down to one or more science requirements, but not vice versa. Program and science requirements are signified by \textbf{P} (e.g., \ref{prog:photoz:sample}) and \textbf{S}, respectively.

\begin{itemize}
\item \textbf{Instrument Requirements} define technical capabilities, for example, ``The red spectral limit must be $\geq$ 0.95 $\mu$m.'' 

\item \textbf{Data Requirements} place requirements on software systems that manage the reduction, processing, and storage of data; i.e., they place requirements on the data-management systems (DMS).  For example, ``Across program fields observed over many nights, the reduction pipeline shall not introduce scatter greater than 10\% of the Poisson noise compared to a single-visit manual reduction.'' 
\end{itemize}

These requirements are maintained via a spreadsheet described in Section \ref{sec:instr}.

% This document consolidates the program and science requirements into a series of \textbf{instrument requirements} and \textbf{data requirements}.  Here, we distinguish between requirements that are primarily driven by the instrument hardware from those primarily driven by the software related to the data-management systems (DMS; Chapter \ref{chap:DMS}).  Following from the example above, a relevant instrument requirement would be: ``The red spectral limit must be $\geq$ 1.1 $\mu$m.''  A relevant data requirement would be: ``Systematic errors in the equivalent width of the Wing-Ford band introduced by sky subtraction and flux calibration must not be larger than 10\% of the Poisson error due to photon shot noise.''  

% \noindent Importantly, there is an obvious interplay between the hardware and software requirements that will evolve as the limitations of each are explored. Instrument and data requirements are signified by an \textbf{R} and \textbf{D}, respectively.

% In this SRD version, Data Requirements do not differentiate between requirements for the data-\textit{reduction} pipeline (the DMS \textit{Accountant}) versus the data-\textit{analysis} pipeline (the DMS \textit{Alchemist}).  In general, while FOBOS aims to deliver high-level data products for \textit{all} FOBOS data, the FOBOS software systems requirements will be driven by the Design-Reference Programs.

\section{Guiding Principles and Assumptions}

In discussing the science requirements, we distinguish between measurement ``precision'' and ``accuracy''. All of our quantitative requirements focus on measurement precision, which includes only uncertainty propagated from raw measurement uncertainties under a specific set of model assumptions. Assessments of the \textit{accuracy} of a given measurement are generally a model-dependent assessment and, therefore, beyond the scope of this document.

\section{Document Outline}

The Science Requirements Document is organized as follows:  Each of the Design-Reference Programs are motivated and presented in Section \ref{sec:key}, with each subsection motivating and describing each primary science program.  Many programs share a common discipline, and multiple programs are more efficiently executed simultaneously.  We close Section \ref{sec:key} by discussing possible observational synergies between programs. 

% TODO: We need a chapter devoted to machine-learning applications.

In Section \ref{sec:instr}, we consolidate the program and science requirements from Section \ref{sec:key} into a few high-level technical requirements for, e.g., patrol field, focal-plane sampling formats, and multiplex. 

%Chapter \ref{chap:DMS} mirrors Chapter \ref{chap:instr} but focuses on the data requirements and a discussion of the data management systems needed to meet these requirements.

%\newpage

\chapter{Design-Reference Programs}
\label{sec:key}

% Requirement redundancy in the science programs
%   - weigh this against overwhelming the reader

FOBOS is a facility-class instrument at Keck, emphasizing flexible and quickly configurable focal-plane sampling, UV sensitivity, and a stable spectral format that supports ultra-deep integrations of $\gtrsim$50 hours.  Multiple observing modes will be possible, including PI-led programs, survey-level campaigns, and queue-scheduled observations.  In combination, these modes will enhance overall science return by enabling human interaction/intervention while maximizing efficiency.  

While designed to support a broad range of science applications, the FOBOS concept is driven by a series of ``Design-Reference'' Programs centered on studies of metal enrichment and processing, from the high-redshift connection between the IGM/CGM and the galaxies hosted within, to internal galaxy processes revealed in the disk of M31, to nucleosynthesis at the sites of kilonovae.  We also present two dark sector programs highlighting the significant contribution FOBOS can make to our quest to understand dark energy and dark matter.  The sections below present the scientific motivation, execution details, program requirements, and success metrics for each program.

\noindent \textbf{Allocated Program Observing Time.}  To set requirements on capabilities like multiplex and sensitivity, we must often require that design-reference programs be completed with a given allocation of observing time, specified here as clear-weather nights (no weather factor) unless otherwise specified.  Following the history of past large-program campaigns at WMKO, we adopt a maximum program allocation of 130 nights over 5 years (about 15\% of total available dark time).  A five-year timescale is common among astronomical surveys and reflects the speed of scientific progress in the field and the timescales of graduate students and postdocs.  Keck is highly over-subscribed, with a large and diverse user pool carrying out an array of PI-led programs, so if they have any hope of being realized, most of the design-reference programs below should complete in \emph{far less} than 130 nights, with 5-10 nights anticipated per-year over a 5-year timespan.  

We assume an average of 9.5 hours of astronomically-useful (sun elevation $<$-18$^\circ$) time per night at Mauna Kea.  Unexpected telescope downtime is estimated at 13\%.\footnote{\url{https://www2.keck.hawaii.edu/inst/metrics/HistoricTimeLost.pdf}}  FOBOS observing overheads are estimated at 10\%.  A total clear night is therefore assumed to be 9.5 $\times$ 0.87 $\times$ 0.9 = 7.4 hours on average.  We note that lost time from weather at WMKO is 25--30\%.  

% To illustrate FOBOS's scientific potential, we present the science drivers and observing strategies for these design-reference programs.  Table \ref{tab:progreq} summarizes the details of each program and illustrates FOBOS's ability to interleave multiple programs with disparate scientific goals (\S \ref{sec:addsci}).  The final definition of FOBOS's design-reference programs, including detailed sample designs, scientific deliverables, and time requests, will be developed in the next phase through a community-wide competition organized jointly with NSF's NOIRLab and WMKO.

\section{IGM: Tomographic mapping of the Intergalactic Medium}

The fueling and regulation of galaxy growth during the peak formation epoch ($z \sim2$--3) is critically tied to the turbulent and gas-rich ecosystem in which early galaxies evolve. The James Webb Space Telescope (JWST) and upcoming 30-m class telescopes (ELTs) will marshal powerful infrared observations to study the stars and nebular gas at the heart of these early galaxies. But mapping the large-scale gaseous environments and filamentary networks that fuel and ultimately regulate galaxy evolution at these redshifts requires high multiplex absorption-line tomography and rest-frame UV spectral coverage.

% FOBOS enables an ambitious two-prong approach to characterizing galaxy ecosystems on all scales: a detailed tomographic study of the cosmic web at $z>1.5$ combined with an ultra-deep IFU survey of emission from the circumgalactic medium (CGM) of $\sim$180 galaxies at the peak of cosmic star formation.

The PFS Strategic Survey Program on Subaru (running 2023--2027) \citep{Nagamine:2020_tomography} will complete an important first step in Ly$\alpha$ tomography of the intergalactic medium (IGM) by making a map of structure at $2.1 < z < 2.6$ over 14 deg$^2$.  This map will be relatively coarse, however, with a sight-line density of 1140 deg$^{-2}$.  Although this provides valuable statistical measures of cosmic-web structures, a detailed study of the interplay between the fueling and feedback mechanisms mediated by these structures requires chemical and kinematic diagnostics that are only possible with higher S/N observations at a more fine-grained spatial resolution that is not well-suited to Subaru-PFS.

% TODO:
%   - Need some examples of how these data would be used.
%   - Describe overlap with cosmology program.

An observing program with FOBOS can meet these needs by building a high-resolution map of the IGM via a dense network of Ly-$\alpha$ absorbers associated with targeted structures at $1.6 < z < 2.5$ \citep[see][]{lee16}.  If the PFS survey is completed and distributed in time, this program should prioritize follow-up targets between $1.6 < z < 2.1$ (not accessible to PFS, but where sources are brighter) in these fields, such as protoclusters and galaxy overdensities.  This higher density yields statistical insight at 1 Mpc separations (the scale of individual massive halos) and the ability to stack sightlines to gain further in S/N so that various heavy-element ion transitions can be studied.  The FOBOS IGM program to acquire these data would need to meet the following requirements:

\subsection{FOBOS IGM Program Definition \& Requirements}

\medskip
\begin{itemize}[leftmargin=0.3in, itemsep=0pt]
	\item[] \textbf{Clear nights: 25}
	\item[] \textbf{Program Duration: 3 years}
\end{itemize}


\begin{programrequirement}
% KBW 16 Apr 2021: Break this into two requirements?  Requirement on the number of detected protocluster structures (if there's 3 per 0.1deg^2 FOBOS pointing, is the requirement that we detect 180?), and the follow-on requirement for the total survey area?
\reqitem The total survey area should be greater than 6 deg$^2$ to survey sufficient volume to detect multiple rare, proto-cluster structures that will evolve into $z=0$ halos with $M_{\rm halo} = 10^{14}$ \msun{}.  This total area will be divided into 12 sub-fields for ease of scheduling.  Each sub-field should be at least $\sim$0.5 deg$^2$ in order to span large-scale structures \citep[10 Mpc; see][]{lee16}.  Based on the halo mass function from \citet{Lukic:2007_highZhaloMassFunc}, we anticipate detecting 3 protoclusters with $M_{\rm halo} > 10^{14}$ \msun{} per FOBOS pointing.

\reqitem For sufficient spatial resolution in the reconstructed IGM tomography (\ref{prog:igm:dens}), each field should include $\sim$5000 targets between $1.6 < z < 2.5$. 
\reqitem Each field should also contain $\sim$3000 galaxies embedded in the cosmic web for comparison of the intergalactic and interstellar media.

% KBW 16 Apr 2021: This assumes a point source!  The S/N per angstrom is 2.7 for a constant surface brightness of 24.6 mag/arcsec^2, and 2.2 for a de Vaucouleur's profile with 0.5 ellipticity.
\reqitem To detect a minimum \ion{H}{1} column density of $10^{13}$ cm$^{-2}$ with a statistical error of no more than 0.1 dex (25\%), 3-hour integrations must reach a ${\rm S/N} \sim 3.5$ per angstrom at $r_{\rm AB} \approx 24.6$. 

\end{programrequirement}

\medskip
\begin{sciencerequirement}
\reqitem The FOBOS single-aperture sampling density shall deliver efficient ($>70$\% completeness), single-visit target allocation for on-sky source densities of $>$4 arcmin$^{-2}$.  This is commensurate with sampling the scales of massive halos, i.e., $\sim$1 Mpc for massive galaxy clusters at $z\sim 2$, with 3 sightlines. \label{prog:igm:dens}

% K. Bundy (2021-04-05): The 4 per arcmin^2 comes from 5000 sight-lines plus 3000 embedded galaxies per 0.5 deg^2.  The 70\% is a WAG.

\reqitem FOBOS shall cover the observed wavelength of Ly$\alpha$ (1216 \AA{}) at a redshift of $z=1.6$.  

\end{sciencerequirement}

%{Baseline source density goals for PFS: 1600/deg$^2$ over 15 deg$^2$.  This sightline density translates to 100 sources over the FOBOS FOV.  From the luminosity function of LBGs, going to a depth of R = 24.5 affords 400 possible $z=2.0-3.0$ sources within a single FOBOS pointing.  A 3-hr observation delivers S/N$\sim4$ per pixel in the g band.  Going to R = 24.6 means 1000 possible sources per FOV at S/N$\sim3.5$.  If we improve on source density over PFS by a factor of 4, we reduce the average sightline separation to $\sim1$ per comoving Mpc, or resolving scales of most massive individual halos!  This leaves 1400 fibers for `embedded' galaxies in the foreground. }

% \note{Joe/Dan/Kyle: play-out the combination of the 2nd program above and the Cosmology program as a practical illustration of what a series of observing nights devoted to these programs might look like. }


\section{CGM: Chemistry and Dynamics of the Circumgalactic Medium at $z\sim2$}

High- and intermediate-ionization transitions, such as \ion{O}{6} ($\lambda_{\rm rest} = 1032, 1037$ \AA) and \ion{C}{4} ($\lambda_{\rm rest} = 1548, 1550$ \AA), probe $10^{5-6}$ K and $10^4$ K gas, respectively.  This temperature range marks the peak in gas cooling and therefore constrains how gas rains onto galaxies to fuel star-formation, as well as tracks feedback processes that establish and regulate the circumgalactic medium (CGM).  Observations of this gas has largely hinged on detection via \textit{absorption} measurements against a background source \citep{Bahcall:1969qy,tumlinson17}.  The ability of these observations to probe the chemodynamical state of the CGM is therefore limited by the number of viable targets through each halo, and stacking of sightlines through many halos is generally required to provide a statistical view of their properties.  If the CGM is instead observed in \textit{emission}, each galaxy halo can be studied individually.

Current Keck instrumentation, namely KCWI, enables the mapping of Ly$\alpha$ emission for individual galaxy halos at $z\sim2$, and metal-line emission has already been studied in some extreme objects. However, significant progress in the field requires deeper observations of a significant sample ($\sim$100 objects) of relatively ``normal'' galaxies (Fig.~\ref{fig:cgmsample}).  Such a sample will allow us to explore correlations between host-galaxy and local CGM properties and will provide key observational constraints for cosmological hydrodynamical simulations \citep{Nelson:2019_outflows,Oppenheimer:2018aa}.  In fact, existing predictions of CGM emission remain virtually untested, particularly with respect to relationships to galaxy mass and SFR.  Thus, sampling a wide range of this parameter space is critical to progress on the theoretical front to connect gas physical conditions to emission properties, even to first order.  Based on the state-of-the-art predictions from a high-resolution galaxy-CGM simulation \citep{Corlies:2018aa}, we have set our minimum detection limit for emission lines according to the bright tail of the flux distribution in a fairly low-SFR, low-mass galaxy (green star in Figure \ref{fig:cgmsample}).  We expect our limit to sample down to the peak of the flux distribution for `main-sequence' and above galaxies, enabling kinematic analysis of individual spaxels.  Detections and line ratios may be obtained for less-massive, low-SFR galaxies and the outer, fainter CGM regions through spatially binning spaxels.


\begin{figure}
\includegraphics[width=\textwidth]{figs/msipProposalCgmCombo.pdf} 
\caption[CGM simulation examples and proposed sample]{\textit{Left}: Simulations of the density and temperature of the CGM at $z=2-2.5$ based on \citet{Corlies:2018aa}. \textit{Center}: Predicted observations of CGM emission sampled by the FOBOS IFUs, providing kinematic maps that trace gas flows using UV tracers (C IV and O VI).  \textit{Right}: The \textit{FOBOS Galaxy Ecosystem Program} will map these features for hundreds of galaxies sampling a large range physical parameters.  This panel shows a mock sample of program galaxies (star-forming in blue; passive in red) in the stellar mass-star formation rate ($M_*$-SFR) parameter space; the example simulation shown to the left is marked by a green star. The $M_*$-SFR ``main sequence'' from \citet{Whitaker:2012} is shown as the underlying gray 2D histogram.}
\label{fig:cgmsample}
\end{figure}


\subsection{FOBOS CGM Program Definition \& Requirements}
% FOBOS CGM: 
%   Could be done with 2 multi-IFU fields or visits: 45 IFUs per visit to get to 90 sources
%   Observing time of 50 hours per visit x 2 visits = 100 hours / 7.4 = 13.5 nights

\medskip
\begin{itemize}[leftmargin=0.3in, itemsep=0pt]
	\item[] \textbf{Clear nights: 13.5}
	\item[] \textbf{Program Duration: 5 years (integrate into Dark Energy Program)}
\end{itemize}



\begin{programrequirement}
\reqitem Spatially-resolved spectroscopy for least 90 individual galaxy halos over a range of host mass and SFR, selecting from Milky-Way-like progenitor galaxies to the most massive brightest-cluster-galaxies today: $9.7 <$ log ($M_*/M_\odot$) $< 11.5$ and spanning quiescent to SFR $\sim 1000$ yr$^{-1}$ \citep{Papovich:2015_progenitorMasses,Conroy:2007_buildUpMassive}. \label{prog:cgm:sample}

\reqitem For the detection of \ion{O}{6} and \ion{C}{4} at $z\sim 2$, we require S/N$\sim$3 per resolution element for emission-line fluxes of 10$^{-19}$ erg s$^{-1}$ cm$^{-2}$ arcsec$^{-2}$ after an integration time of no more than 50 hours.

\reqitem The target density of viable targets is expected to be 21 per 0.1 deg$^2$ field-of-view.  Given the exposure-time requirements, multiplexing must be at least 10 objects observed per field to efficiently build the required sample (\ref{prog:cgm:sample}).
\end{programrequirement}

% ; i.e. $\lambda_{\rm obs} \lesssim 3100$ \AA
\medskip
\begin{sciencerequirement}
\reqitem Measure line emission from gas diagnostic transitions including \ion{H}{1} Ly$\alpha$ ($\lambda_{\rm rest} = 1215$ \AA),  \ion{O}{6} ($\lambda_{\rm rest} = 1032, 1037$ \AA), \ion{C}{4} ($\lambda_{\rm rest} = 1548, 1550$ \AA), \ion{C}{3} ($\lambda_{\rm rest} = 1908$ \AA), and \ion{Mg}{2} ($\lambda_{\rm rest} = 2796, 2802$ \AA) to detect and distinguish cool $10^4$ K and warm-hot $10^{5-6}$ K gas phases in the CGM at $z = 2$. 

\reqitem Observations must produce contiguous maps of the regions beyond galaxy disk and disk/halo interface, requiring a field-of-view of $\gtrsim$40 kpc (proper).
\reqitem Spatial sampling must be sufficient to enable stacking of weak emission $>15$~kpc out into the CGM ($1.75$ arcsec at $z=2$).
% if necessary to construct emission profiles revealing thermodynamic structure of gaseous halo.  

\reqitem Resolve high-velocity outflows from ``ambient'' CGM gas at galaxy systemic velocity, $\sigma_v \sim 100$ \kms.  
\reqitem Spectral resolution must be able to measure line centroids to better than 10 \kms\ and Doppler broadening of line widths to better than $\sigma \sim 100$ \kms. 
\end{sciencerequirement}


% The combination of single-fiber and multiplexed IFU observations therefore allows FOBOS to map the density and dynamical state of diffuse gas at all relevant scales from the IGM to the CGM, providing novel constraints on the next generation of cosmological simulations.

% FOBOS's unique UV sensitivity and IFU capabilities also open completely new territory: FOBOS will deliver the first significant samples of high-$z$ galaxies with circumgalactic gas mapped \textit{in emission}. UV sensitivity opens access to 

% In longer term, think through science that we should be proposing now-ish to do with JWST with the idea that we can follow-up with FOBOS.

% Billion galaxy survey?
%Field selection will take advantage of quasar-quasar pairs 
%at \note{range or exact number?} certain redshifts.

% In a joint observing scheme with the ultra-deep exposures of the \textit{FOBOS Cosmology Program}, the CGM study would use FOBOS's unique IFU multiplex capability (configuring one-third of FOBOS's fiber complement into into 15 37-fiber IFUs) to build an unprecedented sample of galaxies spanning respectively $\sim2$ and $>3$ orders of magnitude in $M_\ast$ and SFR, with maps of their CGM \textit{in emission}.  Each IFU will observe an on-sky diameter of 5.6 arcsec, sampling gaseous halos in each galaxy at 5 kpc scales out to a radius of 20--25 kpc (Fig.~\ref{fig:cgmsample}).  These observations require the equivalent of 12.5 dark nights per year.

% --------------------------------------------------------------------
\section{High-z Galaxies: The Ensemble Spectral Program}


\begin{figure}
\includegraphics[width=\textwidth]{figs/restUV_features.pdf} 
\caption[Stellar and ISM diagnostic features at 1200--2000 \AA{}]{A composite spectrum of 30 $z \sim 2$ galaxies from \citet{steidel16}.  A wealth of features is apparent with labels for stellar absorption (red), ISM absorption (dark green), nebular emission (blue), and fine structure emission (purple).  Full spectral modeling at these wavelengths is becoming increasingly mature \citep[e.g.,][]{cullen19}.}
\label{fig:restUV}
\end{figure}



In the `cosmic ecosystem' analogy, galaxies are, of course, a critical player.  Embedded in a network for diffuse gas on large scales, galaxies provide the sites of gas cooling and accretion, the conversion of gas into stars, and its chemical enrichment.  They also mark locations of feedback that, through stellar evolutionary processes and AGN, recycle processed material and send it back into the circumgalactic and intergalactic medium.  

The goal of this program is to gain insight on these growth, processing, and feedback mechanisms by studying the galaxies themselves and specifically the metals contained in their stars and ISM to establish their growth history in relationship to the diffuse gas in which they are embedded at $z \sim 2$ \citep[see the IGM and CGM programs above; for a review, see][]{maiolino19}.  We will make use of restframe UV wavelengths, in particular the 1200--2000 \AA{} region, which offers a rich set of stellar metallicity and ISM diagnostics, as illustrated in Figure \ref{fig:restUV} from \citet{steidel16}.  Spectral modeling of the stellar continuum at these wavelengths now makes derived stellar metallicity and stellar abundances increasingly robust \citep[e.g.,][]{cullen19}.  Meanwhile, the incidence of P-Cygni profiles in \ion{C}{4} and \ion{He}{2} stellar wind lines probe stellar feedback, while ISM metal absorption kinematics and Lyman-$\alpha$ profiles constrain the nature of galaxy-scale outflows \citep[see][]{pettini02}, ideally requiring spectra with $R > 3000$.  Recent progress in this area has centered on derived estimates of metallicity and alpha-enhancement (specifically, [O/Fe]) measured through combinations of both $Z_*$ estimates from UV continua and $Z_{\rm gas}$ constrained from strong lines in the restframe optical \citep[e.g.,][]{steidel16, cullen19, cullen21}.  These initial works have confirmed a high-$z$ mass-metallicity relation with non-solar abundances and strong alpha enhancement, already setting important constraints on formation models.

But given their distant redshifts and faint magnitudes (typically AB$ \approx 24.5$), samples at these redshifts are limited and require spectral stacking to reach a desired S/N (a bare minimum is S/N$ > 5$ \AA{}$^{-1}$).  \citet{cullen21}, for example, study just two composite spectral stacks, representing two bins of $M_*$ at $z \approx 3$, in order to reach S/N $\sim10$ per element.  

The FOBOS Ensemble Spectral Program (ESP) will deliver a reference sample of 15,000 high-$z$ galaxies, from which stacks of hundreds to a thousand galaxies will yield high-S/N composite spectra that may be binned by SFR, environment, emission-line characteristics, and other global properties.  The program design follows in the spirit of VANDELS ESO public survey \citep{mclure18}, which obtained 20--80 hour per-source integrations with VIMOS for 2100 high redshift galaxies with an eye towards stacked analyses \citep{cullen19}.  FOBOS ESP will go deeper for a sample 5--10 times larger, with 7 times higher spectral resolution and bluer wavelength coverage (VANDELS observed $0.48 < \lambda < 1.0$ $\mu$m at $R \sim 500$).  

\begin{figure}
\includegraphics[width=\textwidth]{figs/highz_spectral_stacks_cullen19.pdf} 
\caption[Ensemble spectral stacks from VANDELS]{Ensemble spectral stacks at $R \sim 500$ from the VANDELS sample in seven $M_*$ bins \citep{cullen19}.  Each stack reaches ${\rm S/N} \sim 10$ per resolution element and stellar metallicity derived from UV continuum spectral fitting are labeled in each panel.  The FOBOS ESP program would significantly expand the VANDELS concept, delivering a larger and deeper sample at 7$\times$ higher spectral resolution.   }
\label{fig:highzStacks}
\end{figure}

The sample selection for this program strongly overlaps with the FOBOS Dark Energy program, with the intention being that a single observing campaign could address requirements from both programs at the same time.  In fact, the program and observing requirements are largely shared with a magnitude limit of $i_{\rm AB} = 25.3$.  Including a fraction of ESP sources with magnitudes brighter than $i_{\rm AB} = 24$ may be necessary for building complete samples in $M_*$, SFR, and redshift, and fields with near-IR imaging (e.g., with Roman) will be important.  As in \citet{mclure18}, the expected redshift distribution ranges from $z = 2$--5.  

The large ESP sample will provide many options for defining bins in which the ensemble or composite spectra would be computed (an example of seven spectral stacks is shown in Figure \ref{fig:highzStacks}).  These include bins based on information from individual source spectra themselves (redshifts, environment, emission line properties).  If aiming for high-S/N, a set of 15 bins (e.g., 5 $M_*$ bins at three different redshifts) at $i_{\rm AB} \sim 25$ with 1000 galaxies per bin would yield composite spectra with ${\rm S/N} \sim 67$ \AA{}$^{-1}$ at $R \sim 3500$, according to the FOBOS exposure time calculator.  A broad sampling of the galaxy population, for example, a total of 150 bins (100 galaxies per bin), would yield ensemble spectra with ${\rm S/N} \sim 20$ \AA{}$^{-1}$.  While these will be ensemble averages, spectra at such faint magnitudes with such high S/N can be achieved by ``converting'' FOBOS multiplexing capacity into spectral depth, enabling statistically powerful samples and studies typically associated with Extremely Large Telescopes like TMT/GMT.

% 2/sqrt(2) *sqrt(1000)*1.5


% $ = 20$--80 \AA$^{-1}$ at $i_{\rm AB} \approx 25$ for sets of 50--100 composites, defined in bins of $M_*$, , in particular the 1200--2000 \AA{} region, offer rich stellar metallicity and ISM diagnostics and the opportunity to compare the enrichment history of stellar populations at these redshifts with the nature of their CGM and large-scale IGM environment (see above).  While these will be ensemble averages, spectra at such faint magnitudes with such high S/N are typically thought to only be possible with TMT/GMT.\footnote{The E-ELT is not planning an early-light optical spectrometer.}  Capitalizing on FOBOS's sensitivity and multiplex allows us to reach these depths for statistically powerful samples well in advance of US-ELTs. 



\subsection{FOBOS Ensemble Spectral Program Definition \& Requirements}

% FOBOS Dark Energy Program:
%  - It's a little hard to get a better estimate on total nights because we imagine re-assigning once a S/N (or redshift) is obtained.  Could try to improve the estimate later if desired.

\medskip
\begin{itemize}[leftmargin=0.3in, itemsep=0pt]
	\item[] \textbf{Clear nights: 81}
	\item[] \textbf{Program Duration: 5 years}
\end{itemize}


\begin{programrequirement}
\reqitem Sample size of at least 15,000 high-quality spectra in the magnitude range $24 < i_{\rm AB} < 25.3$.

% , populating the region of the galaxy color/magnitude space relevant to the LSST-\euclid-Roman photometric samples, which is largely unconstrained by existing spectroscopic surveys. 

\reqitem At least 12 independent fields to limit cosmic variance, with field centers that span a large range in right ascension for efficient program scheduling. \label{prog:photoz:fields}

\reqitem Each field must be at least 20\arcmin\ in diameter and contain roughly 1700 viable targets.  This number assumes 15,000 galaxies observed over the number of independent fields.


% \reqitem At least 10 fields must also overlap with the LSST footprint and be within the visibility window of Keck II for no less than two consecutive hours.

% \reqitem At least one field must be in the NEP for overlap with \euclid\ and (Subaru) Hyper Suprime-Cam observations.
\reqitem Fields must have near-IR imaging to $H_{\rm AB} = 26.5$ to enable selection of $M_*$-limited samples \citep[e.g.,][]{mclure18}.

\reqitem Objects observed must achieve an $i$-band-weighted signal-to-noise of 2 per angstrom at $R \sim 1500$.

% KBundy 2021-04-04:  Newman+13 Fig 47 shows 75% redshift success at S/N = 0.75 per DEIMOS 0.33 A pixel (with 1200 line grating).  Multiply by sqrt(3) and S/N per angstrom is 1.3.  But this is for "all" galaxies and r-band, so until we do simulations, let's adopt S/N = 2 per angstrom.

% \reqitem No target should require more than 50 hours of integration time under dark, spectrophotometric conditions to maintain observing efficiency.  Given requirement \ref{prog:photoz:snperspec}, this means the continuum S/N per object after one hour of observing must be no less than 0.4 per angstrom at $i$-band.  \label{prog:photoz:snperhr}

\reqitem To efficiently build the sample, the program must be able to reconfigure individual fibers in a field to new targets either as targets acquire sufficient S/N.
\end{programrequirement}

\medskip
\begin{sciencerequirement}
% \reqitem At least 75\% of FOBOS spectra for galaxies at $z<2.5$ with a continuum S/N of 2 per angstrom must result in accurate spectroscopic redshifts. \label{prog:photoz:zcomplete}

\reqitem FOBOS should be sensitive from 310--1000 nm in order to have no ``redshift desert.''  Specifically, the wavelength range should permit line-center measurements of either \ion{O}{2} 3727\AA{} or Ly$\alpha$ 1216 \AA{} for any source with $z < 7.0$.  

\reqitem Systematic errors resulting from the combination of spectroscopic observations over 50 hours shall degrade the final signal-to-noise ratio by no more than 30\%.  

\end{sciencerequirement}



\section{Andromeda: The Chemodynamical Evolution of the M31 Disk}
\label{sec:m31disk}

\begin{figure}
\begin{center}
\includegraphics[width=0.58\textwidth]{figs/M31_footprint_v3.jpg}
\end{center}
\caption[M31 pointing distribution]{A Subaru HSC image (lower right) superposed on a larger background image of M31 (credit: Adam Evans).  Keck II Nasmyth pointings (white circles) can be arranged to span the PHAT area (magenta) and NGC 205.  The Subaru-PFS FOV (green circle; similar to MSE) and single-pointing WFIRST imaging footprint (blue squares) are also shown.}
\label{fig:M31}    
\end{figure}

Galaxy groups like the Local Group, with two L$^*$ galaxies, dominate the nearby universe \citep{kourkchi17}.  We expect galaxies in such groups to share common assembly histories, and yet, the Milky Way and Andromeda galaxies (M31) appear to have evolved in significantly divergent ways.  Differences from their star-cluster populations to their dwarf-galaxy properties remain poorly understood, limiting progress towards building a complete picture for how the Local Group formed and evolved.

For the Milky Way, stellar properties (e.g., age, metallicity, $\alpha$ abundance) and kinematics from large-scale spectroscopic surveys (e.g., APOGEE, Galah, LAMOST) are now being combined with exquisite astrometric data from \textit{Gaia} to provide a revolutionary view of its evolution.  For example, these data reveal a clear bimodality in $\alpha$ abundance, indicating that stars at relatively greater distances from the disk plane (i.e., ``thick-disk'' stars) were formed in environments with much shorter star-formation timescales, likely due to a merger event that truncated star formation for a time. This is further confirmed by spectroscopic ages of the stars derived via data-driven methods that tie spectral CN features to their asteroseismic ages \citep[e.g.][]{Martig16}.  Isolating chemically similar groups of stars in this way to reveal their common structural and dynamical properties is now fundamental to our understanding of the Milky Way.  This ``chemical tagging'' offers greater insights than studies of stars selected by their structural or dynamical associations alone \citep[e.g.,][]{Ting15}.  FOBOS will advance our understanding of the Local Group by enabling such chemical tagging studies of M31.

The FOBOS Andromeda program requires large samples ($\gtrsim 10^5$) of resolved stars in the disk of M31 in order to map the velocity dispersion of populations of different ages and metallicities.  Detailed quantitative comparisons to simulations will diagnose M31's interaction and merger history.  Although chemical tagging with M31 benefits from our outside view (compared to our inside view of the Milky Way), it also faces the challenge of obtaining precise stellar parameter measurements for very large samples.  First steps were made by SPLASH,\footnote{Spectroscopic and Photometric Landscape of Andromeda’s Stellar Halo \citep[e.g.][]{splash}} which obtained $\sim$1hr Keck-DEIMOS exposures for $\sim$10,000 RGB stars in the disk, stellar streams, and halo of M31.  \citet{dorman15} used SPLASH to study the stellar age and velocity dispersion of disk stars and found that M31 features a much thicker, high-dispersion component compared to the Milky Way.  More recently, \citet{escala20} explored metallicity and $\alpha$ abundance trends in 70 RGB stars ($\sim$6hr Keck-DEIMOS integrations) in the outer disk, inner halo, and Giant Stellar Stream of M31.  These trends also suggest a significant, merger-induced star-formation event in M31.  However, without more precise stellar parameters and larger samples --- beyond the limits of what one can expect to achieve with DEIMOS --- we can only determine general trends in the overall populations.  FOBOS will deliver an order-of-magnitude increase in sample size with excellent precision in stellar parameter and velocity measurements.  The goal is to make clear distinctions between populations with different metallicity and spatial distributions that contrast the evolutionary histories of the Milky Way and M31 disks.  We will address two key questions for the first time: Does M31, like the Milky Way, exhibit its own [$\alpha$/Fe] bimodality?  If so, were the ancient merger histories of the two galaxies linked or largely independent? 


\begin{figure}
\includegraphics[width=1.0\textwidth]{figs/abundances_snr_v6.png}
\caption[Simulated M31 RGB spectra and abundance forecasts]{Simulated observations demonstrating FOBOS's ability to perform ``chemical tagging'' in M31. \textit{Left:} Expected S/N for an $i=21.5$ RGB star in M31 observed for 10hr using FOBOS, PFS, and DEIMOS. \textit{Right:}  Forecasted abundance precision for these observations (filled circles), including both statistical uncertainty ($\sigma_{\rm stat}$; predicted by the Cram\'er-Rao Lower Bound) and a 0.1-dex systematic uncertainty \citep[$\sigma_{\rm syst}$; cf.,][]{kirby18, xiang2019}. Elements are ordered along the ordinate by decreasing precision (limited to $\lesssim$0.3 dex) and color-coded by their primary nucleosynthetic origin. Although these forecasts are optimistic, the indicated \textit{relative} precision between instruments is robust. For reference, we show abundance uncertainties reported by \citet[][purple squares]{kirby18} from DEIMOS spectra of $-1.0<\text{[Fe/H]}<-0.6$ RGB stars in MW satellites with comparable S/N to our simulations; their measurement precision is worse than our DEIMOS predictions primarily because of their lower metallicity targets.  We also show abundance uncertainties reported by \citet[][yellow squares]{xiang2019} from LAMOST spectra of MW RGB stars, scaled to the S/N and resolution of the proposed FOBOS  observations.}
\label{fig:abundances_snr}
\end{figure}

\begin{figure}
\includegraphics[width=1.0\textwidth]{figs/BlueFeatures_Sandford_2020_fig18.pdf}
\caption[Importance of blue abundance-indicating spectral features]{Reproduced from \citet{Sandford20}, this figure shows the spectrum of a $\log{Z} = -1.5$ RGB star at $R \sim 2000$ (top panel) and the associated response functions for a variety of elemental abundances (below).  Many elements—--especially heavier neutron-capture (r- and s-process) elements—--have most, if not all, of their absorption features at wavelengths shorter than 4500 \AA{}.}
\label{fig:abundances_blue}
\end{figure}


\subsection{FOBOS M31 Program Definition \& Requirements}

% FOBOS Andromeda Program:
%  - 6 fields in M31 disk visited 10 times = 60 visits, plus 2 outer fields visited twice.  Total = 64 visits
%  - 64 visits x 10-hours per-visit = 640 hours for M31 disk alone.  (640/7.4 = 86 nights)
%  - M33: 3 fields, each visited twice, 10 hours per visit: 3 x 2 x 10 = 60 hours for M33
%  - 640 + 60 = 700 hours / 7.4 = 94.5 nights (too many)
\medskip
\begin{itemize}[leftmargin=0.3in, itemsep=0pt]
	\item[] \textbf{Clear nights: 86}
	\item[] \textbf{Program Duration: 5 years}
\end{itemize}


\begin{programrequirement}
\reqitem To create 5 bins in age, abundance, and velocity pattern, the stellar sample should be $\sim 10^5$ stars in the M31 disk. \label{prog:lgdisks:sample} 

% KBW 16 Apr 2021: Will there be other relevant survey data for target selection by 2029, e.g., from Roman?
\reqitem Six M31 disk fields at radii between 5--20 kpc with two additional fields beyond 20 kpc should be drawn from the PHAT\footnote{Panchromatic Hubble Andromeda Treasury \citep{phat} is a multi-cycle HST program that maps $\sim1/3$ M31's star-forming disk in 6 filters.} HST footprint.  

\reqitem The program should be accomplished with fewer than 64 FOBOS-visits in the M31 disk, with 10-hour integrations required per visit.  Given rejections due to crowding \citep{dorman12} of RGBs at $i_{\rm Vega} < 22.5$, a science-fiber multiplex of at least 1600 per pointing is required to build the M31 disk sample of $\sim$10$^5$ stars.

% K. Bundy (2021-04-07): Commenting these out because they don't impact FOBOS instrument design.
% \reqitem All stars should be observed over a region with high resolution photometry for targeting fidelity.
% \reqitem Target selection should account for precursor/coincident surveys planned with Subaru PFS and the Maunakea Spectroscopic Explorer (MSE).


% \reqitem To build the necessary M33 disk sample (\ref{prog:lgdisks:sample}), we require 3 fields each visited twice.
% \reqitem To build the necessary M31 satellite sample (\ref{prog:m31halo:sample}), we require 3 fields in the region including NGC 147, NGC 185, and And II, each visited once, and 1 pointing in NGC 205, visited twice.  
% \reqitem To enable robust and informative modeling of the M31 satellite system's chemodynamical evolution, the stellar sample should be $\sim10^{4}$ RGB stars across multiple M31 satellite galaxies.  \label{prog:m31halo:sample}


\reqitem To maximize observing efficiency, each disk field visit should achieve $\sim$95\% efficiency of allocated spectrograph (single-fiber) apertures.


\end{programrequirement}

\medskip
\begin{sciencerequirement}

\reqitem A field diameter of 20\arcmin\ is required to span the width of the M31 disk, and the core of M33 and other Andromeda satellite galaxies.  Note, much larger fields of view are not beneficial for M31 disk science.

\reqitem Must be able to observe an on-sky target density greater than 5 arcmin$^{-2}$ to efficiently observe extremely high-density source distributions (60 arcmin$^{-2}$ is surpassed in the M31 disk).

\reqitem The velocity precision of each star observed should be $\lesssim 5$ \kms.  

\reqitem Sensitivity to 310 nm is required to capture prominent stellar age and abundance features \citep[Fig.~\ref{fig:abundances_blue}; cf.][]{Sandford20}.  Blue sensitivity is also generally valuable for studying young stars whose broadband flux peaks at blue wavelengths.

\reqitem The abundance precision must be $<$0.15 dex for both [Fe/H] and [$\alpha$/Fe]; additional abundances for individual elements produced via Type Ia SNe (e.g., Cr, Ti, Ni), core-collapse SNe (e.g., Mg, Ca, Si), and various proposed neutron-capture channels (e.g., Nd, Y, Ba) should be measured to $<$0.25 dex \citep[Fig.~\ref{fig:abundances_snr}; cf.][]{Sandford20}. \label{prog:lgdisks:precision}

% \reqitem In M31 satellites, the abundance precision must be $<$0.25 dex for both [Fe/H] and [$\alpha$/Fe].
\reqitem Stellar age precision must $<$0.1 dex as inferred via, e.g., use of the blue CN absorption features \citep[e.g.][]{Martig16,Ting19}.  %This typically requires S/N $\approx$ 30 per pixel at $R=1800$.
\label{prog:age:precision}

\reqitem To achieve the required measurement precision (\ref{prog:lgdisks:precision}, \ref{prog:age:precision}), we must reach an $i$-band ${\rm S/N} \approx 40$ \AA$^{-1}$ and $\approx 20$ \AA$^{-1}$ at the  ``sweet-spot'' of the RGB ($i_{Vega} = 21.5$) and a magnitude fainter, respectively, in $\sim$10 hours.  This assumes a resolution of $R\sim3000$ and a wavelength coverage from 0.3 -- 1$\mu$m.
\end{sciencerequirement}


\section{Young Star Clusters in the Disk of M31}

The M31 disk contains thousands of young star clusters.  These clusters probe the process of star formation throughout the many environments present in the disk, including the clusters' dynamics and chemistry, as well as the conditions under which stars are formed and dispersed throughout the disk.  Although insights into the recent evolution of the M31's disk have already been possible through their photometric properties \citep[e.g.,][]{johnson16}, FOBOS will provide abundance, velocity, and mass information that is currently unavailable, allowing both confirmation of the inferences from photometry as well as large samples of spectroscopic masses and abundances to track the recent formation of stars and metals in clusters across the disk. 

The M31 Cluster Program would acquire IFU observations ($\sim$5.6\arcsec{} diameter), comparable to the sizes of $\sim$500 young star clusters in the M31 disk classified by the Panchromatic Hubble Andromeda Treasury \citep[PHAT;][]{johnson15}.  This legacy campaign would dwarf even Milky Way samples of young star clusters \citep{johnson15}.  In particular, observations of young stellar clusters require blue sensitivity and IFU capabilities to produce integrated-light spectra of these objects. Many of these star clusters are loose enough that the massive stars they contain can be resolved individually or in small very compact groups within the cluster.  IFU spectroscopy will provide optimal spatial resolution to separate these components.  On individual clusters or stacked ensembles, a goal  is to measure velocity dispersions (at a precision of 10 km/s) in addition to cluster metallicities.  Moreover, as the ages of these clusters are well-constrained from PHAT resolved stellar photometry, we can tie measurements of the cluster velocity dispersion to its age to constrain their dynamical evolution.  Finally, we can also integrate the IFU spectra to test our ability to measure ages and metallicities of young clusters with integrated light FOBOS spectra in more distant galaxies.



\subsection{FOBOS M31 Cluster Program Definition \& Requirements}

% M31 Cluster Program:
%   - 500 star clusters / 45 IFUs = 11.1 visits (using all IFU mode)
%   - 11.1 visit x 10 hours = 110 hours / 7.4 = 15 nights
\medskip
\begin{itemize}[leftmargin=0.3in, itemsep=0pt]
	\item[] \textbf{Clear nights: 15}
	\item[] \textbf{Program Duration: 3 years or integrate within M31 Program}
\end{itemize}


\begin{programrequirement}

\reqitem Acquire a sample of 500 young stellar clusters to probe different regions of the M31 disk and different cluster properties.
\reqitem Sensitivity from 310--600 nm is required to detect bright continuum and absorption features from young main-sequence stars.
\reqitem IFU observations are required to differentiate the integrated cluster light from the background of M31's disk and to measure velocity dispersions.
\end{programrequirement}

\medskip
\begin{sciencerequirement}
% Multiplex: 
%  - Assume "thousands" of clusters in the M31 disk = 6000 clusters over 6 non-overlapping FOBOS pointings (I'm assuming that "disk" means the SW side without PHAT coverage.
%  - So 1000 clusters per 20-arcmin diameter FOBOS pointing = 1000 / 300 sq.arcmin = 3 per sq.arcmin
%  - Let's say brightest third are 1 per square arcmin
%  - FOBOS IFU multiplex is max of 45 per pointing = 45 / 300 = 0.15 arcmin
\reqitem Given the priority star-cluster target density in M31 is $>$1.5 arcmin$^{-2}$, efficient surveying demands an IFU source density of at least 0.15 arcmin$^{-2}$.  IFUs could be more closely packed (by an order of magnitude) at the field center, but it is desirable to spread them over the full FOBOS field to more sparsely sample the M31 disk.

\reqitem Each IFU should have an angular diameter of at least 3\arcsec{}.  Larger IFUs are valuable for evaluating background levels around the cluster edges.

\reqitem The IFU-derived datacubes should achieve a $>$97\% fill-factor.  This may be accomplished through dithering.  Note: a program that integrates IFUs and single-fiber targets may require dithering of IFUs while single-fiber apertures remain fixed.

\reqitem The IFU datacubes should provide spatial information (sampling) on scales no larger than 0.6\arcsec{}.  This translates into IFU fiber sizes no greater than 0.8\arcsec{}.

  

\end{sciencerequirement}

%the blue sensitivity of FOBOS, along with its ability to obtain many small IFU regions within each pointing, will provide detailed spectroscopic maps of $\sim$500 young star clusters, , portegies10.  These clusters probe

% , including its dynamics and chemistry, as well as the conditions under which stars are formed and dispersed throughout the disk.  Although insights into the recent evolution of the M31's disk have already been possible through their photometric properties \citep[e.g.,][]{johnson16}, FOBOS will provide abundance, velocity, and mass information that is currently unavailable, allowing both confirmation of the inferences from photometry as well as large samples of spectroscopic masses and abundances to track the recent formation of stars and metals in clusters across the disk. 

% Wide-field ($\sim$20 kpc at M31 distances) mapping of the M31 halo, using instruments like PFS and MSE,\footnote{The Maunakea Spectroscopic Explorer (MSE) is a concept being developed for a future telescope and instrument at the current Canada-France-Hawaii Telescope site.} will soon probe the chemodynamical history of its stellar substructures; however, FOBOS will provide unique capabilities particularly suited to the high-source-density M31 disk (see Fig.~\ref{fig:M31}).

% However, FOBOS's blue sensitivity, order-of-magnitude greater sampling density, and IFU modes offer  unique capabilities for obtaining a high-source-density census of M31's disk (see Fig.~\ref{fig:M31}), M33, and the cores of Andromeda's major satellites.  Such data enable the chemodynamical studies needed to address key questions about the structure and assembly of these objects. 

%These relations will determine whether M31's thicker disk is the result of dynamical ``heating'' of stars initially formed in a cold, thin disk versus the ``settling'' of a more turbulent primordial disk into the dynamically cold structures seen today.

%Our large sample size, more than an order of magnitude larger than currently available, will allow for the finer subdivision of the stellar populations and the more-detailed quantification of the chemodynamical structures in M31 and M33, needed for a robust comparison to similar structures in our Milky Way.  

%Currently, {\it only} the Milky Way disk has been measured with this kind of precision, and it required very large surveys with substantial resources to complte, such as LAMOST  \citep{xiang2017, Xiang2019} and APOGEE \citep{hayden2015}.  With FOBOS, we can add {\it two} more disks to this detailed sample as just one example program of the science enabled.

%\note{Yuan-Sen: Maybe a sentence or two summarizing the importance of age-velocity-dispersion relation: e.g., nature vs. nurture; upside down ISM cooling vs. secular evolution}

%\note{Yuan-Sen: PHAT CMD + FOBOS spectra should give pretty good spectroscopic-photometric constraints on stars}

%\note{note gains in RGB numbers by probing deeper down the sequence?} 

% Proof in the pudding:
%\note{ref; https://arxiv.org/abs/1908.09727 ?}.

%----------------------------------------------------------


%-----------------------------------------------------------------------
\section{Kilonovae astrophysics}
\label{sec:kne}

The joint detection of electromagnetic radiation and gravitational waves from GW170817 began a new era of multi-messenger astronomy.  This single binary neutron star merger and its associated kilonova have transformed our understanding of multiple branches of astrophysics, from the physical nature of mergers and explosion mechanisms to the origin of the heaviest elements in the universe.  By the late 2020s, gravitational wave detectors like LIGO,\footnote{The Laser Interferometer Gravitational-Wave Observatory} Virgo, and KAGRA\footnote{The Kamioka Gravitational Wave Detector, formerly the Large Scale Cryogenic Gravitational Wave Telescope (LCGT)} will routinely detect $\sim$30 binary neutron star mergers with kilonovae (KNe) annually \citep{abbott2018prospects}, providing the samples needed to understand how the physical properties and nucleosynthetic yields of KNe vary with environment.  Rapid spectroscopic follow-up of these events are critical to these studies, particularly for studying quickly decaying phases such as the Lanthanide-free ``blue" component of the KNe light curve that peaks within a day post-merger at $\lambda_\mathrm{peak}\sim0.35$ $\mu$m (Fig.~\ref{fig:kilonova}).

Rubin Observatory target-of-opportunity (ToO) observations will search for KNe within an hour after the gravitational wave alerts are issued \citep[assuming the strategy proposed by][]{margutti2018}. For a typical 50 deg$^2$ localization region, we expect $\sim$100 KNe candidates with $m_i\lesssim22.5$, the expected KNe brightness at a sensitivity distance of 200 Mpc \citep{cowperthwaite2017, goldstein2019}. Identifying and triggering spectroscopic investigations of the true KNe will require rapid and blue-sensitive follow-up capabilities. Such rapid follow-up of KNe candidates discovered by LSST will enable a systematic population study of KNe and their environments.

%, each with a typical localization region of $\Omega_\mathrm{90\%}<100$ deg$^2$ . 

\begin{figure}
\begin{center}
\includegraphics[width=0.8\textwidth]{figs/kn_fobos.pdf}
\end{center}
\caption[Model spectra of kilonovae]{\textit{Left:} Model kilonova spectra based on GW170817 taken 3.5 hours, 6 hours, 1 day and 2 days post-merger. \textit{Right:} Variations of ``blue" kilonovae, generated by varying the energy, mass and Lanthanide fraction of kilonova models. FOBOS's blue sensitivity is essential to discriminate between these early-time models. Models from \citet{kasen2017}.}
\label{fig:kilonova}    
\end{figure}

Building spectroscopy of many KNe can be an expensive endeavor, both because LSST only provides KNe \textit{candidates} that must be spectroscopically vetted and because of their low on-sky density.  It is worth noting, therefore, that a highly multiplexed instrument is beneficial in this case because the KNe spectroscopy can be obtained jointly with other programs; however, this capability is not strictly a requirement of this specific program.

The 12.5 night Kilonovoe Program will vet KNe candidates and ultimately build a sample of high-quality KNe spectra at multiple evolution phases.  

\subsection{FOBOS Kilonovae Program Definition \& Requirements}

\medskip
\begin{itemize}[leftmargin=0.3in, itemsep=0pt]
	\item[] \textbf{Clear nights: 12.5}
	\item[] \textbf{Program Duration: 2 years}
\end{itemize}



\begin{programrequirement}
% This doesn't really read like a requirement
\reqitem Adopting the forecast in \citet{margutti2018}, we expect $\sim4$ bona-fide $z < 0.1$ KNe to be detectable by LSST and Keck annually. Over the duration of the program, FOBOS will observe $\gtrsim50$ LSST-triggered KNe candidates in the accessible LSST footprint with short ($\sim$10 min), low-resolution ($R\sim1000$) spectroscopy.  This is nearly twice the total spectroscopic follow-up effort currently possible \citep{hosseinzadeh2019}.

\reqitem It should be possible to interrupt any FOBOS program (ToO) and switch to a new field and set of targets within 1 hour of an event trigger.  Efficient target allocation of unused fiber-apertures at the new field location should make use of pre-defined target catalogs, with priority assigned to background targets from the interrupted program.  A software mechanism should allow the ToO observers and the regularly scheduled observers to coordinate the optimal fiber assignment, if desired.


\reqitem Quick-look reductions requiring no more than 2 minutes of runtime should allow for identification of KNe with $m_i < 22.5$ AB.  The goal is 90\% completeness based on 10-minute spectroscopic integrations in average FOBOS conditions. 

\reqitem For confirmed KNe, the program should immediately transition to deeper ($\sim$1 hr) observations to potentially capture ``blue'' KNe (Fig.~\ref{fig:kilonova}).
\end{programrequirement}

%We would observe each candidate with FOBOS's central, fixed IFU to obtain a redshift and potential-host properties.  If our monitoring of real-time quick-look reductions identifies the KN, our strategy would immediately initiate deeper ($\sim1$ hour) observations to potentially capture ``blue" kilonovae   With four KNe annually, this FOBOS program requires $2.5$ nights per year; beyond the KNe observations, many fibers would be allocated to pre-assigned transient sources.

\medskip
\begin{sciencerequirement}

% KBW 16 Apr 2021: I don't think the current 0.8" IFU apertures will meet the requirement of 5 independent spatial samples for a galaxy at z~0.7...
\reqitem Observations should acquire spectroscopy of both the KNe and the host galaxy with an always-deployed integral-field unit (IFU) with an angular diameter greater than 3 arcsec.  This size mitigates modest localization errors.  The resulting datacubes from this IFU should provide spatial sampling that allows independent spectra to be extracted for at least 5 separate regions of a typical $L_*$ host galaxy at $z \approx 0.1$.

% KBW 16 Apr 2021: This is achievable at full spectral resolution, and even easier if the spectra are binned to R~1000.
\reqitem  To identify KNe at a limiting distance of $D_\mathrm{L}\sim300$ Mpc,
candidate vetting spectra must achieve S/N$\sim$3 per angstrom at a magnitude limit of $i_\mathrm{AB}=22.5$ with integrations of no longer than 10 minutes.

\end{sciencerequirement}

\section{Extragalactic LSST Transients and Host Galaxies}
\label{sec:lssttransients}

%Each DDF is roughly 9 sq deg

Beyond KNe, Rubin Observatory will discover well over 1 million extragalactic transients annually, including thousands of currently rare sources such as tidal-disruption events \citep{bricman2020}, superluminous supernovae \citep{villar2018} and changing look quasars.  The on-sky densities are such that we expect $\sim$5 LSST transient hosts per 20\arcmin\ field-of-view.  Within the LSST Deep Drilling Fields observed by FOBOS for the {\it FOBOS Cosmology} and {\it Galaxy-Ecosystem Programs}, we expect $\sim$150 total transients to be visible each year with $m_i<24$. For a highly multiplexed instrument with dynamic target allocation, a high-impact, low-cost strategy would be to follow-up \textit{every} LSST transient and transient host within any given Keck pointing. Currently, roughly 1,000 supernovae have spectroscopic observations each year, although essentially all are observed at $m_i<21$. By combining both single-aperture and IFU observations of transients, we would dramatically increase the database of transient spectroscopy for low-luminosity events.  In particular, IFU observations of this regularity would dramatically increase the resolved spectroscopy of extragalactic hosts \citep[see a recent review by][]{anderson2015} at little additional cost. A series of requirements follow for observations of these targets:


\subsection{FOBOS Transients Program Definition \& Requirements}

\medskip
\begin{itemize}[leftmargin=0.3in, itemsep=0pt]
	\item[] \textbf{Clear nights: Integrated into other programs}
	\item[] \textbf{Program Duration: ongoing}
\end{itemize}


\begin{programrequirement}
\reqitem This program would reserve 5--10 single-aperture fibers in specified FOBOS pointings within the LSST footprint that are to be observed by other FOBOS programs.  

\reqitem It should be possible to assign or adjust the on-sky targets for these reserved fibers in as little as 1 hour before acquiring a new field configuration.

\end{programrequirement}

\medskip
\begin{sciencerequirement}
\reqitem A central IFU with a minimum field-of-view of 3\arcsec\ should be continuously deployed in all FOBOS instrument configurations.

\reqitem UV sensitivity to the atmospheric limit (310 nm) as rest-frame $\lambda \lesssim 0.3$~nm is required for studying shock-driven (e.g., Type IIn supernovae) and relativistic events \citep[e.g., the atypically bright Type Ib supernova AT 2018cow;][]{margutti2019}.

\reqitem The widest possible simultaneous wavelength range is required to study a broad range of host galaxy redshifts and spectral features associated with transient phenomena.  
\end{sciencerequirement}

% By deploying the remaining single fibers and IFUs on separate, pre-assigned transient sources in each pointing, we will take maximum advantage of synergies with time-series data from the world-wide follow-up observations of these gravitational-wave fields. 

% When deployed as the Keck II instrument, FOBOS's always-ready IFU makes it ideal for instant target acquisition and host galaxy characterization, all while simultaneously observing serendipitous targets of interest in the same field-of-view. 



%-------------------------------------------------------------
\section{Dark Energy: Photometric Redshift Training}
\label{sec:photozs}

Stage-IV cosmology missions --- like the Vera C.~Rubin Observatory Legacy Survey of Space and Time (LSST), the ESA/NASA \euclid\ mission, and the NASA-led Nancy Grace Roman Space Telescope (Roman) --- will obtain multi-band imaging data with unprecedented depth and survey area in the coming decades.  Current survey baselines for LSST will provide \textit{ugrizy} optical imaging of $\sim$18,000~deg$^{2}$ with a detection limit 1,000 times fainter than the Sloan Digital Sky Survey (SDSS), complemented by deep near-IR imaging by Roman for an overlapping $\sim$2000~deg$^{2}$.  Measurements drawn from these data of galaxy positions and gravitational shear as a function of distance over vast cosmic volumes will be used to delineate cosmic expansion and the growth of large-scale structure. Critically, the distances used for these measurements must be estimated by photometric redshifts (photo-$z$s), given the infeasibility of obtaining spectroscopic redshifts (spec-$z$s) for the expected magnitude distribution of the billions of sources imaged by these surveys (see Figure \ref{fig:cosmos_magdist}).  This reliance on photo-$z$s has led to significant effort devoted to understanding their influence on the derived cosmological parameters \citep{huterer06, hearin10, newman15, LSSTDESCSRD}.  The consensus of these studies is that improving galaxy photo-$z$ estimates represents one of the most significant gains to be made in the precision of the cosmological parameters.

Limiting uncertainties in photo-$z$ estimates involves improving photo-$z$ \textbf{training} and \textbf{calibration} \citep{newman15}.  Training focuses on improving photo-$z$s by, e.g., ensuring that the underlying spectroscopic redshifts used to establish the relationship between galaxy color and redshift sample the relevant parameter space \citep{masters15, hemmati18}.  Photo-$z$ calibration involves quantification of the accuracy and precision with which photo-$z$s map to spec-$z$s for \textit{all} galaxies used to measure dark-energy parameters of interest.  Both pursuits are critical to improving the constraining power of and minimizing the biases in the resulting cosmological parameters \citep{LSSTDESCSRD}.

The specific needs for photo-$z$ training and calibration for Dark Energy have been laid out in series of Astro2020 white papers that detail required observing programs and advocate for new instruments like FOBOS \citep{newman19, hlovek19, mandelbaum19}.  In particular, \citet{newman15, newman19} outline an observing program that improves photo-$z$ training via spectroscopy of thousands of galaxies at very faint magnitudes ($i_{\rm AB} \lesssim 25.3$).  The combination of sample size and magnitude distribution is nearly impossible to achieve with current instrumentation.  Even so, \citet{masters19} describe the significant efforts underway to obtain Keck spectroscopy in service of \euclid\ photo-$z$ training; however, more ambitious programs will be needed for fainter LSST/Roman samples.


% LSST will provide a crucial extragalactic dataset in the late 2020s, providing deep \textit{ugrizy} optical imaging of $\sim$18,000~deg$^{2}$, while WFIRST will obtain deep near-IR imaging for $\sim$2000~deg$^{2}$, overlapping the LSST footprint. FOBOS will be well-positioned to contribute critical follow-up spectroscopy for both missions, with the ability to efficiently observe sources as far south as $-30^\circ$, comprising $\sim$60\% of the current baseline LSST footprint.

\begin{figure}
\begin{center}
\includegraphics[width=0.7\textwidth]{figs/fobos_cosmology_v2.pdf}
\end{center}
\caption[Magnitude distribution of spec-$z$ samples]{Magnitude distribution of secure spec-$z$ samples in existing deep fields from, e.g., DEEP2, VVDS, VIPERS, C3R2, and zCOSMOS (\textit{green}), compared with the anticipated distribution of the LSST/WFIRST weak-lensing sample derived in \citet[][\textit{blue}]{hemmati18}. Ultra-deep (50hr) exposures in the FOBOS cosmology program are designed to obtain spec-$z$s for $\sim$15k faint galaxies in the hatched region, representing roughly 50\% of the weak-lensing sample of these missions and weakly constrained by current spec-$z$ samples. The FOBOS cosmology program would operate over 12 independent regions to mitigate cosmic variance, employing a careful selection to explore the full color-magnitude parameter space efficiently, as in \cite{masters15}. }
\label{fig:cosmos_magdist}
\end{figure}

% KBW 16 Apr 2021: Below we again say "begin reaching the LSST target depth" by 2029, but the survey won't be over until 2032-2033.  We've gone back and forth on this sentence.  Is there a plot of point-source sensitivity as a function of survey time for LSST?

FOBOS will provide uniquely powerful spectroscopy capabilities for photo-$z$ training, until at least the second generation of instruments on ELTs (E-ELT, TMT, GMT).  It will excel for sources with spectral features too blue or fluxes too faint for other instruments, like PFS,\footnote{Subaru's Prime Focus Spectrograph (PFS) commissioning in 2022.} but that dominate by number (Fig.~\ref{fig:cosmos_magdist}).  For example, Rubin Observatory will begin reaching the LSST target 5$\sigma$ point-source depth of $i_{\rm AB} = 26.8$ in 2029.   FOBOS spectroscopic follow-up to $i_{AB} = 25.3$ for extended sources will provide a well-matched training sample\footnote{\citet{newman15} emphasize that photo-$z$ ``calibration'' can be accomplished by cross-referencing all-sky surveys of various low-density tracers like quasars and associated absorbers, luminous red galaxies, and emission-line galaxies.} that will \textit{increase LSST's dark energy figure-of-merit by 20--40\%} \citep{newman15}.

% KBW 16 Apr 2021: Where can we add the details regarding the improvement based on the work by Dan, Rachel, and Husni in late 2020/early 2021?

 Additionally, because FOBOS has no ``redshift desert'' (its blue wavelength coverage allows redshift determination at $1.5\lesssim z \lesssim2.5$ via Ly$\alpha$ or nearby UV absorption features), FOBOS observations will reduce the need for expensive, space-based\footnote{Ground-based near-IR spectroscopy is too contaminated by night-sky emission lines to provide spec-$z$s at the required level of completeness \citep{newman15}.} near-IR spectroscopy of galaxies with $z > 1.5$.  

 Beyond enhancing cosmological analyses, the resulting galaxy sample would have a major impact on galaxy-evolution studies by providing the spectroscopic coverage needed to fully leverage photometry for billions of galaxies.  % (see \S\ref{sec:ML}). 

% \edit{Can Dan M. update this with some of the work he did in the lead-up to the MsRI proposal?  I.e., SOM results and expected "no error" photo-z precision?  Also, add plot from Rachel and Husni?}

\subsection{FOBOS Dark Energy Program Definition \& Requirements}

% FOBOS Dark Energy Program:
%  - It's a little hard to get a better estimate on total nights because we imagine re-assigning once a S/N (or redshift) is obtained.  Could try to improve the estimate later if desired.

\medskip
\begin{itemize}[leftmargin=0.3in, itemsep=0pt]
	\item[] \textbf{Clear nights: 81}
	\item[] \textbf{Program Duration: 5 years}
\end{itemize}


\begin{programrequirement}
\reqitem Sample size of at least 15,000 high-confidence spectroscopic redshifts in the magnitude range $24 < i_{\rm AB} < 25.3$ to provide maximum statistical precision on the mapping of color-space to redshift-space. \label{prog:photoz:sample}

% , populating the region of the galaxy color/magnitude space relevant to the LSST-\euclid-Roman photometric samples, which is largely unconstrained by existing spectroscopic surveys. 

\reqitem At least 12 independent fields to limit cosmic variance \citep[see][]{newman15}, with field centers that span a large range in right ascension for efficient program scheduling. \label{prog:photoz:fields}

\reqitem Each field must be at least 20\arcmin\ in diameter and contain roughly 1700 viable targets.  This number assumes 15,000 galaxies observed (\ref{prog:photoz:sample}) over the number of independent fields (\ref{prog:photoz:fields}), and it accounts for the expected redshift completeness (75\%; \ref{prog:photoz:zcomplete}).


\reqitem At least 10 fields must also overlap with the LSST footprint and be within the visibility window of Keck II for no less than two consecutive hours.
\reqitem At least one field must be in the NEP for overlap with \euclid\ and (Subaru) Hyper Suprime-Cam observations.
\reqitem At least three of these fields must overlap LSST deep-drilling fields.

\reqitem Objects observed must achieve an $i$-band-weighted signal-to-noise of 2 per angstrom to ensure 75\% redshift completeness (see the appendix of \citealt{masters15} for details on the required S/N per resolution element after binning to $R~1500$ and as a function of galaxy type).  \label{prog:photoz:snperspec}

% KBundy 2021-04-04:  Newman+13 Fig 47 shows 75% redshift success at S/N = 0.75 per DEIMOS 0.33 A pixel (with 1200 line grating).  Multiply by sqrt(3) and S/N per angstrom is 1.3.  But this is for "all" galaxies and r-band, so until we do simulations, let's adopt S/N = 2 per angstrom.

\reqitem No target should require more than 50 hours of integration time under dark, spectrophotometric conditions to maintain observing efficiency.  Given requirement \ref{prog:photoz:snperspec}, this means the continuum S/N per object after one hour of observing must be no less than 0.4 per angstrom at $i$-band.  \label{prog:photoz:snperhr}

\reqitem To efficiently build the sample, the program must be able to reconfigure individual fibers in a field to new targets either as targets acquire sufficient S/N for redshift measurements or targets are found to not meet requirement \ref{prog:photoz:snperhr}.
\end{programrequirement}

\medskip
\begin{sciencerequirement}
\reqitem At least 75\% of FOBOS spectra for galaxies at $z<2.5$ with a continuum S/N of 2 per angstrom must result in accurate spectroscopic redshifts. \label{prog:photoz:zcomplete}

\reqitem FOBOS should be sensitive from 310--1000 nm in order to have no ``redshift desert.''  Specifically, the wavelength range should permit line-center measurements of either \ion{O}{2} 3727\AA{} or Ly$\alpha$ 1216 \AA{} for any source with $z < 7.0$.  

\reqitem Systematic errors resulting from the combination of spectroscopic observations over 50 hours shall degrade the final signal-to-noise ratio by no more than 30\%.  

\end{sciencerequirement}


%\begin{sciencerequirement}
%\reqitem Redshift precision of 150 \kms{} or better. Stage IV cosmology experiments need to constrain the mean redshift of shear bins to $\lesssim0.2\%$. Redshift samples used for calibration must achieve at least this level of precision per source, which sets this requirement. 
%%
%\reqitem Redshift success rate of 75\% measured in a magnitude bin of width 0.5 mag up to the magnitude limit.  Explanation...
%%
%\reqitem Magnitude limit of $i_{\rm AB} = 25.3$.  This limit corresponds to the expected depth of LSST lensing samples (REF).
%%
%\reqitem Minimum sample size of 15,000, required for sufficient coverage of the photometric color space and for training statistics (REF).
%%
%\reqitem 10 independent fields of minimum 20\arcmin{} diameter in order to average over systematics in the galaxy population owing to sample variance.
%%
%\reqitem Redshift range of $z = $[0.1, 3.5], spanning the distribution of LSST and WFIRST cosmology samples (REF).
%%
%\end{sciencerequirement}


% This program is designed to observe a set of twelve 0.1 deg$^2$ FOBOS pointings arranged evenly in right ascension and chosen to overlap with the LSST, \euclid, and WFIRST footprints.  At least three pointings would include LSST deep drilling fields (COSMOS, XMM-LSS, and E-CDFS).  The program satisfies the sample size, field variance, and depth requirements in \citet{newman15} by obtaining ultra-deep 50-hour integrations of $\sim$15,000 sources at $24 < i_{AB} < 25.3$, a magnitude range that covers the majority of LSST/WFIRST weak-lensing samples.  While near-Poisson performance with such extreme integration times has been demonstrated with fiber spectrographs \citep[e.g.,][]{gu17,childress17}, our team's investigation of critical design factors that enable such performance (Bundy et al., in prep) has defined FOBOS instrument requirements, including a multi-tier calibration system (\S \ref{sec:calib}).  Accounting for expected sensitivity and stability, our exposure-time calculator estimates a continuum S/N$\sim3.5$ ($i$-band) for the faintest sources at these depths, a level known to be sufficient for $>75$\% redshift success (e.g., \citealp{Newman13}, \citealp{masters19}). 

% With 1200 single fibers (per pointing) from two of FOBOS's three spectrographs assigned to cosmology program targets, parallel observations with IFUs fed to its 3rd spectrograph can leverage the ultra-deep exposures needed for targets in the \textit{FOBOS Galaxy Ecosystem Program} (\S \ref{sec:galaxies}).  Photo-$z$ calibrators targeted by single fibers will efficiently span color-magnitude space \citep{masters15, masters19} with dynamic re-allocation of fibers to new targets as successful redshifts are obtained.  This program would request 12.5 dark nights per year.

% TODO: **Move this somewhere relevant**:
% The source density of 40 arcmin$^{-2}$ far exceeds FOBOS's
% fiber density (6 arcmin$^{-2}$).
  

%----------------------------------------------------------


% KBW 16 Apr 2021: Probably because it was pulled directly from the MsRI proposal, this case reads more like a science case motivated by a pre-existing FOBOS, instead of a science case that FOBOS should be designed to tackle.
\section{Dark Matter from Dwarf Galaxy Dynamics}

Nearby dwarf galaxies ($<$ 1 Mpc) can be resolved into individual stars, providing great potential as laboratories for testing theories of galaxy formation and fundamental physics.  Deep-and-wide imaging from Rubin and Roman will open a new chapter in this field by detecting new dwarf galaxies and dramatically improving our census of member stars in known systems.  Once again, the addition of uniquely deep, high-multiplex FOBOS spectroscopy will allow the full potential of LSST/Roman dwarf galaxy observations to be realized.  This combination will have a major impact on the astrophysical search for dark matter in the next decade \citep{drlica-wagner19}.  Ideally suited as described by \citet{simon19} because of its FOV, sensitivity, and unrivaled efficiency at target separations down to 10\arcsec, FOBOS builds on the legacy of Keck-DEIMOS that has dominated dwarf galaxy spectroscopy over two decades.  Reaching 0.5 mag fainter than DEIMOS with twice the bandpass and 20 times the multiplex, FOBOS will play two important roles in the search for dark matter using dwarf galaxies.  First, FOBOS will spectroscopically confirm an anticipated $\sim$200 new low-luminosity dwarf candidates to constrain the ``minimum halo mass'' cutoff in the subhalo mass function as predicted by warm dark matter (WDM) models and other variants (e.g., `fluid', `fuzzy', `wave-like').  \citet{jethwa18}, for example, establish a WDM limit of $M_{\rm WDM} > 2.9$ keV based on the currently known Milky Way dwarf population while \citet{nadler19} extend a similar analysis to derive a 95\% upper bound of $6 \times 10^{-30}$ cm$^2$ for the DM-baryon cross section at 10 keV.  FOBOS confirmation of a highly complete LSST/Roman subhalo sample will deliver order-of-magnitude improvements in mass and cross-section limits by eliminating nuisance parameters on the galaxy-halo connection and subhalo disruption fraction.

Second, FOBOS will place tight limits on the cross section of self-interacting dark matter (SIDM) models by increasing the number of highly sampled dwarf galaxy density profiles by 1--2 orders of magnitude.  Currently, the best limit of $\sigma_{\rm SIDM}/m < 0.32$ cm$^2/$g (assuming velocity-independent SIDM) comes from a single dwarf galaxy, Draco, with 500 kinematic tracers \citep{read18}.  FOBOS will select targets from LSST/Roman imaging to go deeper down the RGB luminosity function and obtain $>$1,000 tracer stars at 1 km s$^{-1}$ precision for each of 50 Local Group dwarfs \citep[see][]{drlica-wagner19}, pushing the $\sigma_{\rm SIDM}/m$ bound to 0.05 cm$^2/$g and enabling exploration of more complex SIDM dynamics.  The sample will include both Milky Way satellites and M31 dSphs (with tracers selected from Roman), whose compact nature requires FOBOS's high sampling density.   

The FOBOS-derived dwarf galaxy density profiles are also critical to indirect detection searches for weakly interacting massive particle (WIMP) candidates such as Majorana fermions that produce pair annihilation gamma rays.  This is because the gamma-ray flux is proportional to the integral of the square of the density profile (the $J$-factor), in addition to its dependencies on particle cross section and mass.  Using a Fisher matrix approach, we estimate that our FOBOS program will improve existing $J$-factor measurements for classical dwarfs by a factor of 5.  Adding new FOBOS $J$-factors for additional dwarfs will bring further gains.  Even with existing Fermi LAT detection limits, our program would push current WIMP cross section upper bounds an order of magnitude lower to 10$^{-25}$ cm$^3$ s$^{-1}$ at 5 GeV.

% \medskip
% \noindent \emph{Impact Summary:} \textbf{FOBOS will yield order-of-magnitude improvements in cross-section and particle-mass limits across multiple, disparate regions of the proposed dark matter parameter space}.  The fact that state-of-the-art direct detection experiments offer such gains in just one part of parameter space, at a cost of \$60-100M each, demonstrates how powerful and cost-effective is FOBOS spectroscopy (combined with LSST/Roman imaging) in the search for dark matter.


\subsection{FOBOS Dark Matter Program Definition \& Requirements}

% Dark Matter Program:
%   - Confirmation of 200 new, faint dwarf galaxies - 1-hour each = 200 hours / 7.4 = 27 nights
%   - Dynamics: 50 dwarfs with 1000 stars each to 1 km/s.  8 hours per dwarf (average) = 400 hours / 7.4 = 54 nights
\medskip
\begin{itemize}[leftmargin=0.3in, itemsep=0pt]
	\item[] \textbf{Clear nights: 81}
	\item[] \textbf{Program Duration: 5 years}
\end{itemize}


\begin{programrequirement}

% KBW 16 Apr 2021: What mag stars and S/N are needed for spectroscopic confirmation?  S/N ~ 3 at i~24?
\reqitem Spectroscopic confirmation of $\sim$ 200 new dwarf galaxy candidates from LSST and Roman is required to constrain the existence of a ``minimum halo mass'' cutoff in the subhalo mass function.  Each confirmation must not take more than one hour of observing time.

\reqitem Densely sampled stellar kinematics of 50 dwarf galaxies is required to  constrain the $\sigma_{\rm SIDM}/m$ bound to 0.05 cm$^2/$g.

% \reqitem The program has two components: 1) Spectroscopically confirm 200 new dwarf galaxy candidates with 1-hour integrations per candidate; 2) 8-hour integrations on 50 known dwarf galaxies to obtain highly-sampled dynamical models.


% KBW 16 Apr 2021: S/N per angstrom for an 8-hr exposure of a point source at i=23.5 is ~10 in the i-band and about 20 in the g-band.  Scaling from MaNGA, 1 km/s might be tough, but 3 km/s shouldn't be a problem, but I'd want to do some better tests...
\reqitem To enable robust dynamical modeling, the velocity precision per star must be better than 1 km s$^{-1}$ at a magnitude of $i_{\rm AB} < 23.5$.  This precision must be achievable in a single observing night ($\sim$7.4 hr).

\end{programrequirement}

\medskip
\begin{sciencerequirement}

% Refers to Table 2 of Drlica-Wagner "Milky Way Satellite Census - I"
%  - To estimate "angular diameter" take the half-light semi-major axis, double it and double it again
% \reqitem The FOBOS field of view should be 20\arcmin{} to match the typical angular extent of dwarf galaxy targets whose diameters vary from 6--120 \arcmin{}.  
\reqitem The FOBOS field of view must be reach at least the median angular extent of dwarf galaxies in the Local Group (17\arcmin; this also allows coverage up to the half-light diameter for $>$70\% of LG dwarfs).

\reqitem Using single-fiber apertures, the science-fiber multiplex should be $>$1600 to enable spectroscopic measurements of $>$1,000 member stars per dwarf galaxy, after accounting for a 35\% contamination rate.

% KBW 16 Apr 2021: The current design fails this.
\reqitem The single-fiber collision radius should be no greater than 10\arcsec{} to allow for allocation to tightly packed targets.

% KBW 16 Apr 2021: I'd have to check in detail, but I think the current design also fails this one.
\reqitem Near the field center where source densities are highest, it should be possible to deploy 350 single apertures within a near-center region spanning a 3\arcmin{} diameter or 27 arcmin$^{2}$ (i.e., close packing of a subset of fibers to reach an on-sky density of 13 arcmin$^{-2}$).

\end{sciencerequirement}

\chapter{Programmatics and Upgrade Paths}

\section{Program Integration and Rare Targets}
\label{sec:synergy}

% KBW 21 Apr 2021: This is pulled directly from the 2020 MSIP with some edits to make it more appropriate for the SRD instead of a proposal.

Beyond the scope of our design-reference key programs, our discussions with the UC/Keck observing community have yielded a host of additional science programs that would be enabled by a new, highly multiplexed, mulit-format optical spectrograph.  We mention them here for completeness, but do not go into further detail, instead leaning on the design-reference programs above as the primary source of science requirements.  A glimpse of additional science cases for FOBOS includes: Milky Way and M31 halo stars and stellar streams; the Milky Way bulge and globular clusters; newly identified variable stars from cadenced LSST imaging; white dwarfs toward the faint end of the cooling sequence; dwarf-galaxy stellar populations and dynamics; the environments and spectra of sources producing fast-radio bursts;  the structure and dynamics of Coma and Virgo galaxies using globular-cluster and planetary nebulae (PNe) tracers; the kinematics and physical properties of gaseous winds expelled from galaxies; 2D emission-line kinematics and radial trends in stellar-population parameters from stacked spectra in galaxies up to $z \sim 1$; environmental metrics for groups and clusters at $z \sim 1$--2; galaxy cluster and proto-cluster dynamics; QSO light echos in the IGM; black-hole reverberation mapping; and the redshift calibration of LBG samples at $z = 1.5$--5 for CMB lensing cross-correlation.

% KBW 21 Apr 2021: Include "information gathering power" figure from MSIP?
All of these will be able to take advantage of FOBOS design capabilities following from those defined by our design-reference programs.  Importantly, they will all collectively benefit from FOBOS's flexible focal-plane sampling with a uniform spectral format.  While maintaining the important freedom of a PI-led observing mode, these design elements also facilitate new synergistic observing modes that capitalize on FOBOS's information gathering power. Indeed, the high density of future source catalogs ($\sim$40 arcmin$^{-2}$ at $i_{\rm AB} = 25$) in the era of deep-wide imaging will incentivize high-multiplex, facility-class instruments to simultaneously observe multiple programs that target varied source types for disparate science goals at virtually any accessible field location.

\begin{figure}[h!]
\centering
\captionof{table}{Design-Reference Program Summary}
\includegraphics[width=0.95\textwidth]{figs/key_program_summary_v3.pdf}
\label{tab:drprog}
\end{figure}

To illustrate this, Table~\ref{tab:drprog} collects salient program metrics for the nine design-reference programs in Section \ref{sec:key}.  From left to right, we provide the program name, the required aperture format, the expected source magnitude, the sample size to observe, the exposure time per target, the number of unique pointings, the fraction of fibers allocated to the program targets in each configuration, and the total number of nights that would be requested (assuming the entire instrument is dedicated to the program for the full night).  The ``allocation fraction'' assumes an instrument that meets the science requirements of all programs in terms of multiplex, and this column in the table illustrates specific combinations of design-reference programs that could be observed simultaneously.  For example, 70\% of the fiber complement could be configured as single-fiber apertures and 30\% in IFUs for simultaneous observations of the Dark Energy and CGM programs.

In a mode where multiple programs acquire spectra in the same field, we can apportion FOBOS usage in units of ``fiber-hours,'' instead of nights, in a way that maximizes observing efficiency.  This approach is, in fact, critical to meeting the needs of the KNe (Section \ref{sec:kne}) and LSST Transient programs (Section \ref{sec:lssttransients}).  In these cases specifically but also more generally, emphasizing a flexible, responsive, and multi-format focal plane grows the scientific pie by enabling even small programs with rare targets (low target densities) to be combined with other, high-density programs.  These design-reference programs are critical to this aspect of FOBOS, an aspect that facilitates U.S.\ community access via efficient allocation of a fraction of FOBOS apertures to a broadly sourced database of targets-of-interest.

% Serving as both a summary table and an illustration of how FOBOS enables program synergies, Table \ref{tab:progreq} collects salient details for the {\it FOBOS Cosmology} (blue), {\it Galaxy-Ecosystem} (green), {\it Time-Domain} (gold), and {\it Andromeda} (red) Programs.  From left to right, we provide the primary program targets, the required aperture format, the expected source magnitude, the observed sample size, the exposure time per target, the number of unique pointings, the fraction of fibers allocated to the program targets in each configuration, and the total number of nights that would be requested.  Bold entries in the last four columns highlight quantities that are {\it shared} between multiple programs; e.g., observations of photo-$z$ calibrators and CGM emission are completed {\it simultaneously} via a single 62.5-night request. This demonstrates the utility of allocating FOBOS time in terms of ``fiber hours'' given that programs may not require FOBOS's full fiber complement on a given observing night.  Indeed, no nights have been assigned to follow-up of LSST transients or their hosts given that these observations can be integrated with other (e.g., PI-led) observing programs in effectively any FOBOS field.  

% Optimized integration of observing programs is an exciting opportunity in terms of access (as described above), observing efficiency and science return.  It also presents an interesting challenge that the FOBOS team (in particular via our CMU partnership/sub-award) will begin to address during the preliminary design phase.

\section{Deep Learning with FOBOS}
\label{sec:ML}

% Think of this the other way around, as well.  Because Astronomy is data wealthy, that enables development of new machine learning tools/methods.

% Homogeneity and repeatibility.  Work it backwards to what development the machine learning applications need.

% Ease of access (things not only available as fits files), populate a database that is more accessible programmatically.  Cloud computing capabilities.  Avoid having multiple copies distributed across users.

% Machine learning application for operational part.

Even the high target-density requirements of our design reference programs would not lead to an instrument that would provide spectroscopic follow-up of a significant fraction of targets drawn from upcoming large-scale imaging surveys.  Indeed, {\it billions} of viable galaxy targets will be observable from Keck in the combined LSST, \euclid, and Roman photometric catalogs.  A spectroscopic survey of that scale requires techniques still in the early stages of development (e.g., high-throughput photonics).  Fortunately, however, advanced data-analysis methods, adapted from ongoing research in Machine Learning and Statistics, can leverage spectroscopic samples to infer properties of objects with only photometric measurements \citep[e.g.][]{hemmati19}. Recent years have seen significant progress in the development and application of such methods for this purpose; for example, redshift estimation with photometry (``photo-$z$ estimation’’) can now be addressed as a machine-learning problem. While spectroscopic surveys provide the crucial ``training sets’’ required to learn the relationship between colors and redshift, small samples are sufficient in order to build accurate prediction methods, as long as they are representative of the photometric population. Each problem presents unique challenges and requirements, but similar approaches could be taken to infer properties of objects, such as galaxy star-formation rate or stellar age \citep[e.g.][]{TingPayne19}. Hence, a moderate investment in the development of tailored methods of data analysis can yield scientific gains from photometric surveys, comparable to having significantly larger spectroscopic samples.

By combining the sensitivity and multiplex requirements of our design reference programs, we ensure that FOBOS on Keck will be ideally suited to such applications in three ways.  First, at least until the advent of 2nd-generation ELT instruments, FOBOS will be unparalleled in its ability to probe the faint end of, e.g., LSST's photometric catalogs. In fact, beyond its immediate application to photo-$z$ training, the 15,000 spectra obtained by our Dark Energy Program (Section \ref{sec:photozs}) would serve as an ideal training set for galaxy-evolution studies of the much larger galaxy samples with LSST/\euclid/Roman photometry.  Second, the information gathering power of FOBOS will significantly greater than similar instruments over the same wavelength range.  This allows FOBOS to efficiently build large samples that can be combined with training data of greater depth or higher spectral resolution to, e.g., produce high-level properties of galaxies at moderate redshift.  Finally, as discussed in Section \ref{sec:synergy}, the cost of observing rare targets --- critical to constructing training sets that span large volumes of parameter space --- is reduced because FOBOS can efficiently combine targets from multiple programs.

\section{Upgrade Paths: GLAO and Added Fiber Feeds}

We highlight here several important upgrade paths for FOBOS, including the general concept that FOBOS can serve as a ``platform'' for other fiber-based instruments in the near-IR or at higher spectral resolution and even enable simultaneous multi-instrument observations (``polyplex'').  Enabling these upgrade paths will necessitate additional technical requirements that may impact the FOBOS design.  As of the 2021 CoDR, we choose not include these requirements formally.  Instead, we will begin to sketch them here so that they may be considered for further development in future design phases.

\subsection{Ground-Layer Adaptive Optics}

New actuator technology shows great promise for enabling a more robust and less expensive Keck adaptive secondary design (Keck-ASM). See work by Hinz and collaborators.  A regular GLAO mode at Keck with a $\sim$10 arcmin corrected field may be easier to realize by 2030 than was previously thought.

From a technical standpoint, an adaptive secondary would provide a more elegant solution to the problem of extending the back-focal distance to fit FOBOS's horizontal focal plane.  The secondary mirror figure with the ASM translated forward to the ``FOBOS position'' could be reconfigured to provide optimal image quality, particularly given that the current image quality is limited by the rephasing of the primary mirror.  This figuring could also be done in concert with the ADC design for further improvements.  An ASM necessarily involves retrofitting the Keck II top-end which would address potential risks in the shifting the existing secondary mirror with the currently deployed motion systems.

Scientifically, observations in the red FOBOS channels would benefit dramatically from GLAO corrections, which would be expected to deliver 0.3\arcsec{} FWHM at 700 nm, although with a decreasing correction at bluer wavelengths.  The improved spatial resolution would open new scientific territory for multi-IFU resolved spectroscopy, especially for galaxies at $z \sim 1$.  It would also enable enhanced single-aperture observations in crowded regions such as the M31 bulge and improve sensitivity (by reducing the sky background) if smaller apertures could be deployed when targeting compact objects.

A number of considerations and requirements would be needed to enable GLAO with FOBOS:

\begin{itemize}
\item \textbf{Wave Front Sensors.} Approximately 4 pick-off mirrors or focal-plane wave front sensors (WFS) would be required to close the GLAO loop.  See EELT-MOSAIC for one solution to this problem.  While concepts exist for focal plane WFS, they have not been deployed.  The laser guide star (LGS) focal plane is significantly offset from the nominal focal plane; as a result, a large portion of the science focal plane is obscured by each laser spot.  This may be acceptable in GLAO mode if only the central few arcmin are corrected so that LGS spots can be positioned in the perimeter.  But the obscuring elements should be removable for non-GLAO observations.  It may also be possible to achieve GLAO without LGS if sufficient numbers of natural guide star WFS could be obtained, perhaps with a photonics based focal plane WFS.

\item \textbf{ADC Performance.} The delivered image quality requirements on the ADC at $\lambda > 600$ nm will be much tighter in order to prevent degradation of the GLAO-corrected 0.3\arcsec{} FWHM.  However, the tighter requirements are wavelength dependent and would only apply to the central portions of the field where the nominal ADC design performs best.  The ADC action (residual atmospheric dispersion) may also face tighter requirements if smaller single-fiber apertures are desired to limit sky contamination on compact sources.  However, the more limited wavelength range over which GLAO provides a correction would make tighter ADC residual requirements easier to meet.  Note that atmospheric dispersion residuals can be corrected when using IFU observations.

\item \textbf{Fiber sampling.} New fore-optics designs will be required to decrease the effective angular diameter sampled by fibers in single-apertures or within IFUs.  A spatial sampling less than the GLAO FWHM of 0.3\arcsec{} would be desired.  In principle, his can be accomplished with smaller-pitch lenslet arrays that simply underfill fibers that are otherwise identical (same core/cladding diameters) to the native FOBOS instrument.  Finer spatial sampling would be achieved but without any gains in spectral resolution so that the spectrograph architecture would remain fixed.  The performance of this approach needs to be understood and tested.

\end{itemize}


\subsection{Near-IR Instrumentation}

% KBW 21 Apr 2021: We may want to post the white paper somewhere that is generally accessible.

A particularly compelling addition to the FOBOS focal-plane module would be a fiber-fee for a set of near-IR spectrographs. Given the exciting possibility of such an instrument, a concept we refer to as IR-FOBOS, we have produced an initial sketch of this concept via a white paper and submitted it for consideration during a 2021 workshop to discuss new IR instrumentation for Keck.  The workshop resulted in a report submitted to and well-received by the Keck Science Steering Committee and the Observatory, which featured our IR-FOBOS concept.  The multiplexed IFU capabilities of our design were particularly well received as a complement to Liger.  Key challenges for our concept include (1) high throughput from 0.31 to 2.5 micron with a single ADC and (2) minimizing the effect of thermal emission from the telescope, particularly at K-band.  Given the competitive landscape and the desires of the Keck community, core metrics for success include (1) a bandpass that covers the full K-band, (2) overall sensitivity in the JHK bands that is competitive with MOSFIRE, and (3) an adaptive-optics correction, such as obtained with ground-layer AO (GLAO). A copy of our white paper is available by request.


\chapter{Instrument Requirements and Traceability References}
\label{sec:instr}

% Summary tables provide a mapping from each instrument/data requirement to all associated program/science requirements (Table \edit{x}) and vice versa (Table \edit{y}); each program/science requirement must lead to at least one instrument/data requirement.

The program and science requirements enumerated in Section \ref{sec:key} have been used to construct instrument requirements for FOBOS.  These requirements are part of a separate document (spreadsheet), \texttt{FOBOS.REQ}.  Here, we briefly comment on the content of the spreadsheet.

For each instrument requirement, the table provides:
%
\begin{description}[itemindent=0pt, itemsep=2pt, parsep=0pt]
\item[Description] A descriptive name for the requirement.
\item[ID] An alphanumeric identifier.
\item[Requirement] The requirement that must be satisfied by FOBOS.
\item[Goal] A stretch goal for the requirement.
\item[2nd Light Goal] A stretch goal to relevant instrument upgrade paths.
\item[Derived From] The traceability of the requirement to other instrument requirements and, particularly, the program and/or science requirements from this document used to construct the instrument requirement.
\item[Justification] A brief justification for the requirement and its value.
\item[Status/Comments] The status of the requirement (e.g., if it has been deprecated or if the exact requirement value is still in development) and/or any further comments about the requirement.
\end{description}

Instrument requirements are grouped into top-level level requirements (\texttt{TOP.REQ}) and subsequent requirements for each subsystem according to the work breakdown structure (e.g., \texttt{FPM.REQ}).  All of the program and science requirements are directly linked to a top-level instrument requirement.



\chapter*{Acknowledgments}
\addcontentsline{toc}{chapter}{Acknowledgments}

FOBOS as a concept was originally developed by Khee-Ghan Lee (IPMU) and David Schlegel (LBNL).  We are deeply indebted to all the scientists that have contributed toward the development of science programs for FOBOS, including (but not limited to): A.~Alabi (UCSC), G.~Becker (UCR), J.~Brodie (Swinburne), Z.~Cai (Tsinghua), P.~Capak (Caltech), M.~Chun (IfA), A.~Coil (UCSD), M.~Cooper (UCI), P.~Guhathakurta (UCSC), J.~Hennawi (UCSB), K.~Gilbert (STScI), T.~Jones (UCD), J.~Larkin (UCLA), J.~Lu (UCB), M.~Malkan (UCLA), C.~Max (UCSC), R.~Mandelbaum (CMU), J.~Newman (Pitt), J.~O’Meara (WMKO), J.~X.~Prochaska (UCSC), M.~Rau (CMU), J.~Rhodes (JPL), C.~Rockosi (UCSC), A.~Romanowsky (SJSU/UCSC), L.~Sales (UCR), C.~Schafer (CMU), A.~Shapley (UCLA), B.~Siana (UCR), T.~Treu (UCLA), D.~Weisz (UCB), M.~White (UCB/LBNL), G.~Wilson (UCR), M.~Wilson (LBNL), R.~Yan (UK), \& K.~Zhang (LBL).

\chapter*{Revision History}
\addcontentsline{toc}{chapter}{Revision History}

\begin{table}[hp]{%
\begin{tabular}{l | l | l |  p{22pc}} \toprule
\textbf{Version} & \textbf{Date} & \textbf{Editor} & \textbf{Comments} \\ \midrule
% Insert your own version number with the date, your name, and a short
% description of this version of the document.
01 & 2021-04-22 & Kyle Westfall & CoDR Internal Review \\ \midrule
02 & 2021-05-17 & Kevin Bundy & External CoDR Version \\ \bottomrule
\end{tabular}}
\end{table}

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MAYBE KEEP THESE AS APPENDICES?
 
%-----------------------------------------------------------------------
% Cosmology
%-----------------------------------------------------------------------
\chapter{Additional Science Drivers}
\label{sec:addsd}

\edit{section to be substantially trimmed or removed}

\section{Redshift Distributions of CMB Lensing Cross-Correlation Photometric Samples}

High-S/N CMB maps from next-generation CMB observatories (e.g., Simons Observatory and CMB-S4) will provide a cosmic ``reference background'' for measurements of gravitational lensing induced by matter along the line of sight.  After cross-correlating with Lyman Break Galaxy (LBG) samples, a relatively flat lensing ``kernel'' with power at $z = 2$--5 enables powerful constraints on the Inflation-sensitive matter power spectrum, Horizon-scale General Relativity, cosmic curvature and neutrino masses, and early Dark Energy \citep{ferraro19}.  \citet{wilson19} explore these constraints in detail and highlight the need for spectroscopic determination of accurate redshift distributions for the employed LBG samples. FOBOS would address this need in two ways.  First, several deep-drilling fields targeting $\sim$1000 LBGs BX \YST{what is BX?}, $u$, $g$, and $r$ drop-out candidates per pointing ($\sim$10,000 deg$^{-2}$) would establish the interloper rate and intrinsic redshift distribution of LBG samples to sufficient precision (this program would likely overlap with the photo-$z$ program described above).  Second, $\sim$200 LBGs per pointing (2000 deg$^{-2}$) could be included as a background program when FOBOS observes other sources across the sky, eventually building a 50-100 deg$^2$ data set of sparse high-$z$ spectroscopy for LBG dN/d$z$ calibration via clustering redshifts \citep[see][]{wilson19}. 

\begin{sciencerequirement}
\reqitem Redshift precision of 150 \kms{} or better.  Explanation...
\reqitem Redshift success rate of 75\% measured in a magnitude bin of width 0.5 mag up to the magnitude limit.  Explanation...
\reqitem Photometric selections of various LBG samples...
\reqitem Minimum sample size of 
\reqitem 10 independent fields of minimum 20\arcmin{} diameter in order to average over systematics in the galaxy population owing to sample variance.
\reqitem Redshift range of $z = $[2, 5], spanning the peak power of the CMB lensing kernel.
\end{sciencerequirement}
%-----------------------------------------------------------------------

\newpage

\section{The 1B Galaxy Survey}
\label{sci:1Bgalaxies}

With both single-fiber and multiplexed IFU observations, FOBOS will produce rich and comprehensive data sets at faint source magnitudes.  Its blue sensitivity affords UV absorption studies down to $z \sim 1.5$, enabling detailed mapping of the baryonic environment at the peak formation epoch.  Samples at $z=1$--$2$ will not only characterize how this environment and its impact on galaxies evolves but will also provide large training sets that can be used to extract spectroscopic-like information from the billion-plus galaxy samples observed in all-sky surveys.  These data will be used in concert with large samples of spatially-resolved FOBOS observations (in IFU mode) to set the context for highly-detailed studies of targeted samples with James Webb Space Telescope and the U.S.~Extremely Large Telescopes.  Finally, FOBOS can tie evolutionary behavior seen at early times to the present day by observing faint sub-structure and dynamical tracers in nearby galaxies.

Apply deep-learning algorithms to infer physical properties of galaxies at $z$$\sim$2 using a combination of photometry and targetted spectroscopy. The range of observed spectral types is well-constrained by broad-band imaging, suggesting a far greater potential for imaging data to reveal physical properties with sufficient training than conventional modeling of spectral energy distributions (SEDs) would suggest.  Machine learning techniques will require training sets with well measured star-formation histories, stellar-population properties, dust content, inflow/outflow properties, and stellar masses --- and determine design parameters for future training sets that will enable such inferences for millions of imaged galaxies at $z$$\sim$2. \YST{I have a few ML colleagues who are actively working on this. If needed, I am happy to consult them in the future.}

\begin{sciencerequirement}
\reqitem Light-weighted stellar ages and metallicities with precision of 0.1 dex in appropriate bins of color space.
\reqitem Star formation rate uncertainties from strong emission lines of 0.1 dex in appropriate bins of color space.
\reqitem Redshift precision of at least 30 \kms{} to allow for accurate stacked spectra in specific color bins.
\end{sciencerequirement}

\section{The Galaxy Environment and Ecosystem}
\label{sci:ecosystem}

With publicly-accessible surveys like MOSDEF \citep{kriek15}, the Keck MOSFIRE instrument has provided powerful new insights into early galaxies at the $z$$\sim$2 peak-formation epoch \citep[also see KBSS,][]{steidel14}. However, a complete picture of the galaxy ``ecosystem'' at this key epoch must also consider the gas-filled environments. Using Ly$\alpha$ absorption in background galaxies, a tomographic map of the intergalactic medium (IGM) in regions surveyed by MOSDEF and KBSS is a key first step. The promise of this approach, demonstrated at Keck by \citet{lee14}, motivates FOBOS's UV sensitivity, target flexibility, and multiplex for tomographic mapping of large-scale structure, including protoclusters \citep{lee16,kartaltepe19}, voids \citep{krolewski18}, and filaments \citep{horowitz19}. \citet{2018arXiv181005156S} take IGM tomography in a new direction, demonstrating with simulated observations that quasar ``light echoes'' --- spatial signatures of the expanding ionization front of a newly activated quasar --- can be detected and used to infer opening angles and deconstruct the quasar's accretion history. The required FOBOS spectra can simultaneously constrain the CIV mass density (via $\lambda\lambda$1548,1550 \AA) and patterns of CIV enrichment on both IGM and circumgalactic scales, revealing the imprint of galaxy fueling and feedback processes \citep[e.g.,][]{tumlinson17}.

At later times, as IGM material becomes more confined to galaxies and their dark matter halos, these halos increasingly merge to form larger structures.  FOBOS will be particularly important for mapping out environmental effects at $z=1$--$2$ on galaxy evolution at the group scale ($\mathcal{M_\ast/M_\odot} \lesssim 10^{13}$) and statistically linking galaxies to their host dark matter halos \citep{behroozi19}.  Tens of thousands of satellites down to sub-L$^*$ luminosities will be mapped and characterized. Thanks to deep, wide-field imaging surveys, like LSST, a 1M-object environmental survey at $z=1$--$2$ may then be possible using improved photo-$z$s, strong priors on spectral types, and new machine-learning techniques to deliver \textit{ spectroscopic} redshifts (with $\lesssim$300 \kms\ accuracy) at the lowest signal-to-noise possible (exposure times reduced by factors of 4--5).

\begin{sciencerequirement}
\reqitem Detection of key IGM/ISM lines like... probing what densities.
\reqitem Redshift precision of at least 300 \kms{} to enable satellite membership
\reqitem Errors on the measured outflow velocity of less than 20~km~s$^{-1}$.  Outflows speeds of $\sim100 -- 200$~km~s$^{-1}$ are expected in most star forming galaxies where interstellar Na~I can be detected in absorption (Chen et al.~2010). 
\end{sciencerequirement}


\section{Internal Structure of Galaxies}
\label{sci:internal}

MaNGA \citep{bundy15} and other large IFU surveys are defining the $z=0$ benchmark for how internal structure is organized across the galaxy population. To understand and test ideas for how this internal structure emerged, we require spatially-resolved observations at $z = 1$--2, just after the peak formation epoch. Indeed, Keck has helped pioneer such observations \citep[e.g.,][]{erb04, miller11,law09}. With only one galaxy observed at a time, samples have so far been limited to a few hundred sources; however, FOBOS will obtain resolved spectroscopy for thousands of galaxies using its IFU-mode with a 25 deployed IFUs. Bright optical emission-line tracers for this unprecedented sample of galaxies will reveal their gas-phase and kinematic structure. Stacking restframe $\lambda \approx 4500$ spectra will enable radial stellar population analyses to constrain how stellar components formed and assembled. Although initially limited to coarse spatial scales, ground-layer adaptive optics (GLAO) in combination with FOBOS would be transformative for this science. A corrected FWHM of 0.2-0.3 arcsec would enable fine-sampling IFUs to probe smaller galaxies and study sub-structure on 1--2 kpc scales.

Environmental effects and evolutionary processes evident at higher redshift have consequences that can be tested in present-day galaxies.  Using globular cluster and planetary nebulae as tracers, FOBOS will dramatically advance dynamical studies of nearby galaxies with $\mathcal{M_\ast/M_\odot} \lesssim 10^{11}$, capturing the majority of the $\sim$1000 GCs located within $\sim$50 kpc of typical hosts \citep[see][]{2013ApJ...772...82H} and tightly constraining their dark matter halos. FOBOS's multi-IFU mode will additionally provide powerful insight on the origin of dwarf galaxies, both compact and ultra-diffuse (UDGs), in the field and in nearby clusters like Coma and Virgo.

Measurements of [O~II], [O~III], \Halpha, \Hbeta\, [N~II] and [S~II] will determine nebular gas metallicities, ionization parameter, and gas densities with high confidence. Measurements of \Halpha\ and \Hbeta\ yield estimates of the star formation rate over timescales of $\sim$$10^7$ years and dust extinction in \HII\ regions.  The combination of [O~III], \Hbeta, [N~II] and \Halpha\ allows us to place galaxies on the BPT diagram. [O~I] and [S~II] along with the BPT lines as a function of position within the galaxy differentiate between shocks in the interstellar medium, ionization by post-AGB stars, or the presence of a ``low-ionization'' active galactic nucleus.

One complication in placing requirements on nebular emission lines is that we expect a wide variation in line equivalent widths (EWs) in our sample. Obviously, we cannot guarantee determining, for example, 0.2 dex in SFR when the emission lines are too weak. Therefore, we set the requirements for a minimum peak amplitude of \Hbeta\ being 70\% of the continuum. This is equivalent to \Hbeta\ EW of 2.5\AA\ for an intrinsic line sigma of 50 \kms\ or EW of 5\AA\ for an intrinsic line sigma of 160 \kms. We chose \Hbeta\ because it is often the weakest emission line of all and is the limiting factor in determining extinction and SFR.

The stellar populations in a galaxy represent a record of the galaxy's star formation and chemical enrichment history.   For quiescent galaxies ages, metallicities, and abundances ratios are typically been measured using line indices \citep[e.g.][]{johansson12}.  More recently, methods have been developed that make use of the full spectrum \citep{conroy14}.  For late-type galaxies, constraints \YST{on?} the mean stellar age and the presence of recent bursts come from the 4000~\AA\ break and the high order Balmer lines \citep[e.g.][]{kauffmann03a}. 

FOBOS's wide spectral range (3500--10,000~\AA) captures a large range of absorption features, from blue indices such as D4000, Ca H$+$K, and higher-order Balmer lines, through classical optical absorption features such as \Hbeta, Mg\textit{ b}, and Fe5270/Fe5335, to red, gravity-sensitive features such as the Ca triplet at $8600$~\AA. These features encode a great deal of information about star formation histories and the IMF, and can be used to measure element abundance ratios like [Mg/Fe], [N/Fe], [C/Fe] and [Ca/Fe].

\begin{sciencerequirement}
\reqitem Gas ionization diagnostics ([N II]/H$\alpha$ vs.\ [O III]/H$\beta$) to separate gas that is photoionized from gas that is shocked or ionized by an AGN. The required precision in the log of the line ratios is $\pm$0.2 dex to minimize classification uncertainty.
\reqitem Spatial resolution of better than XXX kpc for a large fraction of the central galaxies in the sample in order to spatially resolve?
\reqitem Per-fiber S/N limits for dwarf galaxies, both compact and ultra-diffuse (UDGs), in the field and in nearby clusters like Coma and Virgo.
\reqitem A spectral resolution $R=\lambda/\Delta \lambda$ of at least 1,500 is needed to properly subtract the H$\beta$ stellar absorption from the corresponding nebular emission, to fully resolve the [NII] doublet from H$\alpha$, and to resolve the [SII] doublet.
\reqitem Stellar continuum $S/N > 7$ per pixel near \Hbeta\ per spatial resolution element so that we can constrain E(B-V) to 0.2 and achieve a $\Sigma_{\rm SFR}$ estimate of 0.2 dex. In the current baseline sample design and observing strategy, we can achieve this in half of the Primary sample. We expect that in most star forming galaxies, the H$\beta$ strength will be stronger than 70\% of the continuum at 1.5\Reff.Therefore, more than half of the galaxies will have $\Sigma_{\rm SFR}$ constrained to better than 0.2 dex per spatial resolution element.
\reqitem An \YST{amplitude-over-noise} A/N of $>7$ on the key nebular lines [O~II], H$\beta$, and [O~III] is needed to measure the gas metallicity with an accuracy better than 0.05~dex per elliptical annulus at 1.5\Reff. This translates to a continuum $S/N > 10$ per pixel near \Hbeta. An A/N of $>10$ on [N~II] is needed to locate galaxy sub-regions on the diagnostic diagrams with an accuracy better than 0.1 dex. Such S/N on [N~II] will also allow the determination of the [N/O] abundance ratio with an accuracy better than 0.1 dex.  % Individual fibers!
\reqitem Galaxies should be sampled by a minimum of 2.5 fibers per 1.5\Reff\ to enable measurements of metallicity gradients 
\reqitem For tracer studies, determine the dark matter fraction within 1.5\Reff\ and 2.5\Reff\ to 10\% (?)
\reqitem (\emph{From MaNGA, how close do we get to this with FOBOS?}) Resolve the bulk of the baryons by having at least 2 spatial resolution elements across the half-light radius.
\reqitem  Gas kinematics will use standard tracers such as the Balmer lines (\Hbeta, \Halpha), [OI], [OII], [OIII], [NII] and [SII], sometimes fitted simultaneously. 
\reqitem  Emission-line tracers will be continuum corrected to account for associated absorption lines, the kinematics of which will derived independently from absorption lines that are not heavily contaminated by emission.
\reqitem Gas velocity accuracy of 6-10 \kms\ and dispersion to ~30 \kms\ for lines with peak S/N $>$10.  Equivalently, $k_1$ (the kinemetric first moment) from emission-line tracers, will be determined to an accuracy of $<$ 5 \kms\ for amplitude-over-noise $A/N>5$ and $<$ 10 \kms\ for $A/N<5$. This applies only to galaxies with line-emission, that are rotation dominated, and have at least 5 spatial resolution elements across the major axis. 
\end{sciencerequirement}
%-----------------------------------------------------------------------

% In the description of straw-man observing programs, we don't have to follow the same thematic structure as we did in the science requirements.  For example, the \photoz{} survey and the 1B galaxy sample may be very similar and can be combined here.  So we could change the title of this key program to a more general ``The 1B Galaxy Inferrence'' or something...

% There are at least two Cosmology programs: a \photoz{} training program a la \citet{newman15} and \citet{hemmati18} and a LBG dN/d$z$ program motivated by \citet{wilson19}.  We should have defined their top-level requirements in Section \ref{sci:cosmology}, but can we combine the observing needs into a single program here with multiple target classes?  Or do we break them out?


%\section{MaNGA-like observations at $z\sim0.9$}
%\label{prog:galaxies-IFU}
%
%\begin{programrequirement}
%\reqitem A median S/N of $>33$ per pixel in the r-band continuum (spatially binned, if necessary) to achieve the required mean stellar age ($\pm0.12$~dex), metallicity ($\pm0.1$~dex), and abundance constraints ($\pm0.1$~dex) in quiescent galaxies. This S/N constraint comes from the analysis of absorption indices in SDSS-I spectra presented by \cite{johansson12} and from the analysis of the test-run data (L. Coccato).  It is conceivable that this S/N threshold is conservative. Preliminary results from full spectral fitting suggests we could achieve $0.1$ dex in stellar age and abundance with a S/N per pixel of 10-20 (Choi \& Conroy, in prep).
%\reqitem For star-forming galaxies and newly quenched galaxies, a median S/N of $>10$ per pixel is required to constrain mean stellar ages to better than 0.1 dex using the 4000~\AA\ break and Balmer indices \citep{kauffmann03a}.  For populations older than 1~Gyr, age-metallicity degeneracies will increase the age uncertainty to 0.2 dex with this method.
%\reqitem To explore trends with galaxy physical parameters, the majority of the sample should reach the above S/N threshold (R1.2 for quiescent galaxies and R1.3 for star-forming galaxies) in the co-added spectra in at least three radial bins.
%\reqitem A median S/N of $>400$ in radially binned stacked spectra is required in order to probe IMF variations \citep{ferreras2013}. This will necessitate co-adding the radially binned spectra of 50 to 100 galaxies.  Thus, a total sample size of several thousand is desired for this analysis.
%\reqitem Relative spectrophotometry accurate to better than 7\% from [O~II]~$\lambda3727$ to H$\alpha$ and to better than 2.4\% between H$\beta$ and H$\alpha$ to ensure that calibration errors do not dominate the error budget on galaxy SFRs and nebular metallicities.
%\reqitem Poisson-limited sky subtraction, especially in the 8,000-10,000\AA\ range, in order to stack hundreds of galaxies together to analyze the weak IMF-sensitive stellar absorption features.
%\end{programrequirement}


%\noindent To meet these PSF requirements, while maintaining adequate S/N and coverage, requirements are placed on observing strategy, the IFU regularity, and the fiber fill-factor:
%
%\begin{programrequirement}
%
%\reqitem The individual observations shall be dithered by $\sim$1\arcsec\ offsets.
%
%\reqitem Fiber placement shall conform to a regular grid within a hexagonal ferrule.  
%
%\reqitem The tolerance of this spacing must be within 3 microns rms (and known to within 2 microns).
%
%\reqitem There shall be no non-functional fibers in the bundles, where non-functional is defined as having throughput less than 85\% when fed with a filled $f/5$ beam and measured through an $f/4$ aperture stop.
%
%\reqitem Bundle fill factor of live cores shall not be less than 50\%.
%
%\end{programrequirement}

%\subsection{IFU Program Science Justification}
%
%In typical observing conditions (seeing $\leq$ 2\arcsec), the image quality of the data cube is governed primarily by the fiber diameter and spacing. Observing efficiency (time to reach target S/N) is driven by the fill fraction of live fiber cores. 2-\arcsec\ fibers is a sweet spot, given by the characteristic seeing, the sample size, the desired spectral resolution and radial coverage, the desired S/N and the available detector space.  Better spatial and spectral resolution would be highly advantageous for our science goals, but decreasing fiber size provides little gain and several significant losses.  The gains for spatial resolution with small fibers is marginal because of seeing limits; the gains for spectral resolution is marginal because 2-\arcsec\ fibers are just critically exampled.  Further, smaller fibers would degrade S/N per unit exposure time and reduce the radial coverage limited by the available detector space. Larger fibers would degrade spatial resolution to be unusable for kinematics, and would require larger targets with surface densities not well matched to the Sloan 2.5m telescope 7 deg$^2$ field-of-view.
%
%In order to achieve kpc-scale resolution or better at $z\leq0.02$ (i.e., comparable to adaptive optics (AO)-assisted observations of high-z star forming galaxies to allow comparisons studies between MaNGA galaxies and high-z systems) the angular resolution of the reconstructed data cubes must have mean PSF FWHM $\sim 2.0$\arcsec\ or better. This PSF must be uniform across a given object and across a plate to within 10\% to permit accurate flux calibration of bright star forming knots at different wavelengths.  These requirements will necessitate dithering of the IFU in order to improve both the mean angular resolution and resolution uniformity of the reconstructed image. Each fiber bundle must be sufficiently regularly constructed that a single well-determined offset will suffice to uniformly sample each galaxy for all bundles on a plate simultaneously.
%
%Dead and/or broken fibers impinge significantly on the fidelity with which image reconstruction can be performed. We will not accept any dead fibers in our IFUs. While we initially considered allowing up to 1 dead fiber in our larger IFUs outside of the central 37-fiber core, proto-type development indicates the failure-rate for fibers during IFU fabrication is negligible, and our vendor (CTech) has accepted our requirement.
%
%\subsection{IFU Survey Success Metric and Completeness Metrics}
%
%To define a survey success metric, we concentrate on requirements relating to the {\em continuum} S/N distribution achieved for some number of galaxies.  Sample size arguments are presented in Section \ref{sec:sample_selection} where we motivate a {\em minimally} useful sub-sample size of 3000 galaxies and an {\em acceptable} size of 6000, where the sub-samples refer to the Primary (1.5\Reff) and Secondary (2.5 \Reff) samples.  An absolute minimum requirement on sample size that ensures MaNGA is worthwhile is therefore a total of 6000 galaxies, 3000 from each sub-sample. However, \textbf{success is defined by meeting the acceptable level of 6000 galaxies for the Primary sample, and the minimal level of 3000 for the Secondary sample}.  It should be stressed that the two samples are tightly coupled scientifically.  A significant loss to the Secondary sample would greatly degrade our understanding of the Primary sample simply because of the lack of information at radii beyond 1.5 \Reff.
%
%With the current tiling, 63.0\% of the bundles are assigned to the Primary+ sample, 35.5\% are assigned to the secondary sample, and 1.5\% of the bundles are left unallocated. We also plan to allocate 5\% of the bundles to ancillary programs. Therefore, to achieve the success-defining sample size above, we need to observe at least 590 plates ($6000/0.63/0.95/17.= 590$). Given the current master schedule in the repository and the plate completeness threshold defined below, simulation suggests that we will be able to complete 551 plates, which is 6.6\% short. Here we have assumed a 45\% open-dome time, with 10\% of the open-dome time lost on cloudy condition or bad seeing, and 10\% lost on orphaned exposures. The slight shortfall could be well within the uncertainty of the weather and other factors. 
%
%At what S/N do we define success? First, our focus on the stellar continuum does not invalidate the importance of science requirements for studies of the interstellar medium (Section \ref{sec:reqirements_ism}), but enables a metric that can be easily evaluated and compared to expectations from imaging data.  We define this metric using a spectral S/N threshold achieved for a given $r$-band surface brightness.  When this single, observational threshold is met by the data, we obtain a {\em distribution} of S/N values measured in the outer regions of galaxies in the target sample. We can likewise characterize that S/N distribution with a single number (e.g., a median) thus defining a requirement that ensures the science goals can be met for the full distrubtion.  In other words, galaxies with a S/N below the stated requirement will not be ``thrown out.''  They simply represent an acceptable subset of the sample with somewhat less precision.
%
%The two most stringent continuum S/N requirements both require a {\em median} $r$-band S/N per pixel of 33 to be achieved in annular spectral stacks in the outer regions of the Primary+ sample:
%
%\begin{programrequirement}
%\reqitem Stacked stellar continuum S/N of 33 per pixel in the outer annular ring between 1 \Reff\ and 1.5 \Reff\ to measure stellar age/metallicity gradients for quiescent galaxies.
%\reqitem Stacked stellar continuum S/N of 17 per pixel in one quadrant of the outer annular ring between 1\Reff\ and 1.5 \Reff, corresponding to 33 across the complete outer annulus.
%\end{programrequirement}
%
%\noindent The continuum requirement on star-forming galaxies and newly quenched galaxies is lower: 
%
%\begin{programrequirement}
%\reqitem Stacked stellar continuum S/N of 10 per pixel in the outer annular ring between 1\Reff\ and 1.5\Reff\ to measure stellar age to better than 0.1 dex in star-forming and newly-quenched galaxies. 
%\end{programrequirement}

%With 2.25 hour exposure time (3 sets of 3 dithered exposures), 70\% of the primary+ sample will achieve the S/N requirement above. Among ``blue'' primary+ galaxies that are centrally star-forming or newly-quenched ($D_n(4000) < 1.8$), 61\% will reach a stacked S/N of more than 10 per pxiel (R2.3).  In total, 92\% of the sample comfortably satisfy at least one of these two requirements.
%
%Using the empirical relation between S/N measured in raw spectra and that of fiber magnitudes, the 2.25 hour average exposure time corresponds to the following plate completeness metric. 

%\begin{programrequirement}
%\reqitem For galactic-extinction-corrected i-band fiber magnitude of 21, the summed $(S/N)^2$ in the i-band should be greater than 36.
%\reqitem For galactic-extinction-corrected g-band fiber magnitude of 22, the summed $(S/N)^2$ in the g-band should be greater than 19.
%\end{programrequirement}

%Both metrics have to be satisfied before a plate is considered done. With this metric, the majority of the plates will be finished with 9 exposures taken in good conditions, with a small fraction needing 12 or 15 good exposures. 

\begin{description}

\item [TOP.REQ.A01] Field of view (FoV) shall be 17\arcmin{} diameter with a goal of the full unvignetted 20\arcmin{} diameter.  A wider FoV increases the efficiency of targeting sources with lower on-sky densities, thus expanding FOBOS's science breadth.

\item [TOP.REQ.A02] Number of single fibers shall be at least 1800.  Over a 20\arcmin{} field, this number yields an average target density of 6 arcmin$^{-2}$ which matches the desired target density of our Design-Reference Programs.  Note that the on-sky density of sources brighter than i$_{AB}$ $\sim$25 is $\sim$40 arcmin$^{-2}$.

\item [TOP.REQ.A03] The Single-fiber on-sky aperture shall be between 0.7--1.2\arcsec{}.

\item [TOP.REQ.A10] In all instrument modes, FOBOS shall deploy 12 7-fiber bundles (4 per spectrograph) to achieve simultaneous spectrophotometry \citep[see][]{yan16}.  

\item [TOP.REQ.A04] In all instrument modes, FOBOS shall deploy a fixed, central fiber-bundle IFU with an on-sky aperture of 3\arcsec{} diameter.

\item [TOP.REQ.A05] For science and calibration IFUs, individual spatial sampling within the IFU shall correspond to size of 0.33\arcsec{} in order to adequately sample seeing of FWHM$ = 0.6$\arcsec.

\item [TOP.REQ.A06] The 1st-light IFU mode shall deploy 25 fiber-bundle IFUs each composed of 61 fibers.  The format is fixed because galaxy samples with $z > 0.4$ have a relatively confined apparent size distribution with a median of  $\sim$1.5\arcsec{} diameter.

\item [TOP.REQ.A07] The FOBOS 1st-light spectrographs shall span a wavelength range of 0.31-1.0 $\mu$m.  This ensures adequate coverage of spectral features for key program targets and makes sure that FOBOS has no ``redshift desert.''

\item [TOP.REQ.A08] The mid-channel spectral resolution in each spectrograph channel shall reach $R = 3500$

\item [TOP.REQ.A09] Excluding the telescope and atmosphere, the instrument throughput shall be greater than 30\% over 95\% of the full wavelength range.

\end{description}

\edit{need a scheme for translating P, S and R, D to things like TOP.REQ.A01 for the requirements tables}

Summaries of Science and Program requirements and how they flow down to technical requirements.

To be populated from Wiki Tables: \url{https://uco.atlassian.net/wiki/spaces/FOB/pages/15990810/Requirements}

\section{Spatial Sampling}
\label{sec:sampling}

\medskip
\noindent The main requirement on spatial resolution is that the delivered effective PSF shall not be degraded by more than 60\% from typical site conditions at all wavelengths:


\begin{requirement}

\reqitem The shape of the IFUs will be hexagonal as a best approximation of a circular aperture with natural fiber-packing and regular perimeter for mechanical mounting.

\reqitem The size and number of IFUs shall be determined by ...

\reqitem The FWHM of unresolved (stellar) objects in the reconstructed data cubes shall be 2.5\arcsec\ or less at $\lambda = 5400$ \AA\ in median observing conditions (1.5\arcsec\ seeing).

\reqitem The observational PSF of the reconstructed data cube must be circular at all locations to a tolerance of $b/a > 0.85$, with $b/a$ the observed axis ratio.

\reqitem The angular resolution of any spatial element within the reconstructed data cube shall not vary by more than 10\% from the average at any given wavelength, i.e., the effects of differential atmospheric refraction on the sampling must be wavelength-independent at this level.

\end{requirement}

\section{Spectrophotometry}
\label{sec:spectrophotometry}

The science requirements for spectrophotometry are driven by two considerations: (1) the need to derive accurate physical parameters from the widely-spaced nebular emission lines, e.g., SFR, dust attenuation, metallicity; (2) the need to derive accurate physical parameters from the stellar continuum through stellar population synthesis. This translates into the following requirements:

\begin{requirement}

\reqitem Relative spectrophotometry to 2.5\% between \Halpha\ and \Hbeta.
    
\reqitem Relative spectrophotometry to 7\% between [OII]$\lambda3727{\rm \AA}$ and [NII]$\lambda6584{\rm \AA}$. 
    
\end{requirement}

\subsection{Justification}

Following \citet{kennicutt1998} and \citet{calzetti01}, to achieve 5\% errors on the SFR from \Halpha\ we require a maximum 2.5\% error on the Balmer decrement. This ensures we are never dominated by spectrophotometric errors.

An important scientific goal is to measure nebular metallicity gradients. These are typically quite shallow, of order $\sim0.04$~dex/kpc \citep{vanzee1996}. It is thus desirable to have our spectrophotometry errors contribute no more than 0.01 dex to the error budget. The [N~II]6584~/~[O~II]3727 line ratio is one of the best lines for metallicity measurement in moderately metal-rich nebulae ($12 + \log(\mathrm{O/H}) > 8.5)$ due to its independence on the ionization parameter \citep{kewley02}. We can achieve a $\sim0.01$~dex error in metallicity with a less than 7\% error in the relative spectrophotometry between [OII] and [NII].

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Guiding
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Guiding and PSF Metrology}
\label{sec:guiding}

The high-level requirement is that guide errors should not dominate the positional error and image quality degradation of the target galaxies within the bundles. This leads to two specific requirements:

\begin{requirement}

\reqitem Guiding accuracy should be no worse than 0.2\arcsec.
    
\reqitem Knowledge of the PSF across the plate should be no worse than 0.2\arcsec.
    
\end{requirement}

\subsection{Justification}

The stack-up of mechanical tolerances in the ferrules, holes, and the plugging process, the plate shape errors, and the alignment of the bundles w.r.t.\ the chief ray leads to a guide accuracy requirement of 0.2\arcsec.

PSF metrology across the field is crucial for optimal data cube extraction. With our nominal 3-point dither pattern, the reconstructed PSF uniformity across a bundle is $\sim 0.15$\arcsec\ RMS. Mechanical tolerances in ferrule alignment and  the shape of the focal plane cause variations of the PSF of the order of 0.2\arcsec. Hence, for data quality to not be limited by PSF kernel mismatch (used in the extraction),  we require knowledge of the PSF across the field to a similar level.

\section{Program overlap and synergies}

\edit{This section highlights the overlap of the different programs and shows how they can be integrated.  Think Table 2 from the MSIP and the discussion around it.}

\section{Requirements tables}
\subsection{FOBOS.TOP: Top-Level Instrument Requirements}

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% Data Requirements and documentation : MOVED TO DATA MANAGEMENT SYSTEMS DOCUMENT
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