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      <td style="vertical-align: top;">&nbsp; </td>
      <td>
      <h2 style="text-align: center;">Hipparcos star dataset</h2>
      <h3>The CASt dataset</h3>
      <a href="HIP_star.dat" target="_blank">HIP_star.dat</a><br>
      <br>
      <p><span style="font-weight: bold;">Astronomical background
      </span></p>
<p>The key to understanding the properties and evolution of stars
is the Hertzsprung-Russell diagram, first studied around 1910.&nbsp; It
plots the luminosity of stars along the ordinate, and the color of
stars along the abscissa.&nbsp; When a random selection of bright stars
is plotted, one sees the "main sequence" of hydrogen-burning stars and
the later "red giant" stars burning helium and other nuclei.&nbsp; The
main sequence is most clearly seen when the stars in a coeval (= born
together), codistant "open cluster" of stars are plotted.&nbsp; The
nearest open cluster is the Hyades cluster and its HR diagram has been
carefully studied for many years (e.g. <a
href="http://www.journals.uchicago.edu/ApJ/journal/issues/ApJ/v504n1/37753/37753.pdf">Pinsonneault
et al. 1998</a>).  </p>

<p>The main difficulty in establishing the HR diagram for a sample of
stars is determining their distances.&nbsp; For nearby stars, this can
be done with extremely precise measurements of their positional motion
every year as the Earth orbits the Sun.&nbsp; This is called the
parallax.&nbsp; In the 1990s, the European Space Agency launched a
satellite called Hipparcos that measured stellar parallaxes with more
precision than previously achieved for ~100,000 stars.&nbsp; The
Hipparcos catalog is thus often used for HR diagram studies. Bright
Hyades members have a mean parallax of 22 mas in the Hipparcos database
corresponding to a distance of 45 pc.&nbsp; A famous study of the
Hyades cluster using Hipparcos data has been made by <a
 href="http://aa.springer.de/papers/8331001/2300081.pdf">Perryman et
al. (1998)</a>. </p>
      <br>
      <p><span style="font-weight: bold;">Dataset</span></p>
<p>We have extracted a subset of 2719 Hipparcos stars which include many
Hyades members with the selection criterion that the parallax lie
between 20 and 25 mas (i.e. Hipparcos stars with distances 40-50
pc).&nbsp; The extraction was made using the <a
 href="http://vizier.u-strasbg.fr/viz-bin/VizieR?-source=I/239/hip_main">Vizier catalog</a>  service.&nbsp;
The file was manually edited a bit to give a convenient format &amp;
header resulting in the tab-separated ASCII file <a href="HIP_star.dat">HIP_star.dat</a>.&nbsp;
      </p>
      <p>This dataset has the following columns:<br>
      <ol>
        <li>HIP = Hipparcos star number</li>
        <li>Vmag = Visual band magnitude.&nbsp; This is an
inverted logarithmic measure of brightness&nbsp;</li>
        <li>RA = Right Ascension (degrees), positional
coordinate in the sky equivalent to longitude on the Earth</li>
        <li>DE = Declination (degrees), positional coordinate in
the sky equivalent to latitude on the Earth</li>
        <li>Plx = Parallactic angle (mas = milliarcsseconds).&nbsp;
1000/Plx gives the distance in parsecs (pc)</li>
        <li>pmRA = Proper motion in RA (mas/yr).&nbsp; RA
component of the motion of the star across the sky&nbsp;</li>
        <li>pmDE = Proper motion in DE (mas/yr). DE component of
the motion of the star across the sky</li>
        <li>e_Plx = Measurement error in Plx (mas)</li>
        <li>B-V = Color of star (mag)<br>
        </li>
      </ol>
</p>
<p>The HR diagram can be plotted by plotting logL vs. B-V where (roughly)
the log-luminosity in units of solar luminosity is constructed logL=(15
- Vmag - 5logPlx)/2.5.&nbsp; All logs are base-10.&nbsp; </p>
      <div style="text-align: center;"><img alt="Hyades HR diagram"
 src="Perryman.jpg" style="width: 576px; height: 439px;">
      </div>
<p>The plot above from <a
 href="http://aa.springer.de/papers/8331001/2300081.pdf">Perryman et
al. (1998)</a> shows the HR diagram of the Hyades from Hipparcos data
once Hyades members are discriminated from background stars.&nbsp; It
is tricky to select out Hyades members in a reliable and complete
fashion.&nbsp; Their sky positions are centered around RA=67 degrees
&amp; DE=+16 degrees, but they also share converging proper motions
with vector components pmRA and pmDE.  </p>

      <p><span style="font-weight: bold;">Statistical exercises
      </span><p>
      <ul>
        <li>Find Hyades cluster members, and possibly Hyades
supercluster
members, by multivariate clustering.
        </li>
        <li> Validate the sample, and reproduce other results of <a
 href="http://aa.springer.de/papers/8331001/2300081.pdf">Perryman et
al. (1998)</a> </li>
        <li> Construct the HR diagram, and discriminate the main
sequence and red giant branch in the full database and Hyades subset.&nbsp; Can anything be learned about the `red clump' subgiants?
        </li>
        <li> Isolate the Hyades main sequence and fit with
nonparametric local regressions and with parametric regressions.
        </li>
        <li> Use the heteroscedastic measurement error values e_Plx to
weight the points in all of the above operations.
        </li>
        <li>Can any unusual outliers be found? (white dwarfs, halo
stars, runaway stars, ...)<br>
        </li>
      </ul>
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