High values for the thermodynamic consistency metric dsp in blending involving FreeEOS, and as well in OPAL/SCVH tables

[JRGarza]

Hi,

Context: In my scientific problem, I am evolving the envelope of very massive stars as they expand due to the injection of additional heat. During the course of this evolution, as the outer part of the envelope expands and cools, the model began closing the blending zone at the lower temperature limit of FreeEOS. This led to abnormal behavior in the reported values of temperature and density.

Upon closer inspection, I found that this behavior correlates with unusually high values of the thermodynamic consistency metric dsp, which is defined as:

$$ \text{dsp} = -\rho \left( \frac{ds}{d\ln \rho} \right) \bigg/ \left( \frac{dp}{dT} \right) - 1 $$

This metric quantifies the consistency of the thermodynamic derivatives. Large deviations from zero may indicate that the EOS is no longer self-consistent in that regime.

My eos controls for this run are:

      use_simple_Skye_blends = .true.
      
      logT_min_for_any_Skye = 7.9
      logT_min_for_all_Skye = 8.0
      
      !logQ_max_FreeEOS_hi = 5.6d0
      !logQ_max_FreeEOS_lo = 4.0d0

      
      logT_max_FreeEOS_hi = 8.2d0 ! FreeEOS tabulations go up to here
      logT_max_FreeEOS_lo = 8.1d0

      logT_min_FreeEOS_hi = 3.0d0
       logT_min_FreeEOS_lo = 2.7d0
       logQ_min_FreeEOS_hi = -8.0d0
       logQ_min_FreeEOS_lo = -10.0d0
      
      logT_low_all_HELM = 2.2d0 ! HELM for lgT <= this
      logT_low_all_SCVH = 2.3d0 ! SCVH for lgT >= this

For the default EOS blending limits one still find inconsistent values for dsp in similar regions:

Similarly if one sets the lower T blending for freeEOS higher as:

      logT_min_FreeEOS_hi = 3.6d0
      logT_min_FreeEOS_lo = 3.5d0

Or if one removes the OPAL/SCVH tables:

     use_OPAL_SCVH = .false.

Given this, I am unable to set arrangement of the EOS that won't produce any weird behaviour while crossing that region of low T and low Rho. I'm opening this issue to better understand why dsp becomes large in this part of the envelope and whether this behavior is expected at the edge of FreeEOS's valid temperature range.