June 2021 ('v1' version)
Requests should be sent to chabrier@ens-lyon.fr
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These EOS tables for H/He interacting mixtures correspond to the following paper:
  "A new equation of state for dense hydrogen-helium mixtures:
    II: taking into account hydrogen-helium interactions"
          Chabrier & Debras, 2021, ApJ
  This paper is the extension of the previous one (Chabrier et al., 2019, ApJ, 872, 51)
  which is based on the Ideal (Additive) Volume Law (IVL) for the H/He mixture.
 The Tables for the IVL approximation can be found in: http://perso.ens-lyon.fr/gilles.chabrier/DirEOS/DirEOS2019
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Units for the tables are:
 T[K], P[GPa=0.1 Mbar], rho [g/cm3], U[MJ/kg], S[MJ/kg/K]

Tables for the H/He mixture:
 TABLEEOS_2021_TP_Y****_v1
 TABLEEOS_2021_Trho_Y***_v1

Also included is an 'effective' pure H EOS to be used to compute H/HE mixtures beyond the IVL with different values of Y (see Chabrier & Debras 2021,CD21):
 TABLE_H_TP_effective
This can be done by following the procedure listed through eqns.(8)-(11) of Chabrier et al. (2019).
>>>CAUTION: this 'effective' H EOS must be used *only* for this purpose. It must NOT be used as a pure H EOS by itself (see details in CD21).

- The (log T, log P) tables include NT=121 isotherms
  between logT=2.0 and logT=8.0 with a step dlogT=0.05.
  Each isotherm includes NP=441 pressures from
  logP=-9.0 to log P=+13.0 with a step dlogP=0.05.
- The (log T, log rho) tables include NT=121 isotherms
  between logT=2.0 and logT=8.0 with a step dlogT=0.05.
  *CAUTION*: Each isotherm includes now Nrho=241 densities (instead of 281 for the H/HE IVL tables) from
  log rho=-6.0 to log rho=+6.0 with a step dlog rho=0.05.
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The tables for the H/He mixture have been calculated for 3 different values of Y:
- TABLEEOS_HHE_Y0275: Y=0.275 (Z=0)
- TABLEEOS_HHE_Y0292: this corresponds to an 'effective' helium
  abundance Y'=0.275+Z_sol with Z_sol=0.017 the mean solar heavy element mass fraction
  This value is the one used in the DUSTY (Chabrier et al. 2000),
  COND (Baraffe et al. 2003) and Phillips et al. (2020) brown dwarf evolution models.
- TABLEEOS_HHE_Y0297: this corresponds to an 'effective' helium
  abundance Y'=0.280+Z_sol with Z_sol=0.017. 
  This value is the one used in the BHAC2015 (Baraffe et al. 2015) low-mass star models.
  Indeed, Y=0.28 is the helium abundance needed to recover the correct radius and luminosity
  for the Sun today with these models, with a mixing length l/H_p=1.6.
  It must be kept in mind that the exact helium abundance in the Sun remains undetermined:
  (i) it can not be determined observationnally, (ii) the helium abundance has evolved during
  the lifetime of the Sun because of the gravitational settling.
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                 *** Warning ! ***
For practical purposes, the tables are rectangular.
Therefore, some values at very low densities in the (log T, log P) table
or at very low pressure in the (log T, log rho) table might be unphysical.

Similarly, values in the solid phase or beyond the limit of
the first order quantum correction for the ions are unphysical
(see details and Figs. 1 and 16 in Chabrier et al. 2019).
                 *****************

A word of caution:
Due to the spline interpolation procedure, numerical
oscillations or flaws in the calculations of the various
thermodynamic quantities are expected. As these problems
will be revealed, the tables will be corrected accordingly. 
For a clear identification of the most recent
version of the tables, these latter will be labeled with
a '_vx' extension, as a reference to "version x". The date
corresponding to the version will be given at the top of the present
README file.
                ******************

          >>> FINAL WORD OF CAUTION <<<

- In the (low mass) *stellar* range, users should use the IVL (Chabrier et al. 2019) EOS tables.
  Indeed, non ideal H/He contributions are basically inconsequential in this domain. Therefore, in order
  to avoid unnecessary numerical oscillations due to interpolation procedures, it is strongly advised
  to use the IVL tables in this domain.
- In contrast, H/He interactions start to play a role in the *brown dwarf* domain (see Fig. 1 of Chabrier et al. 2021).
  The 2021 tables, which incorporate QMD simulations of Militzer & Hubbard (2013, ApJ, 774, 148), should thus be used in this domain. 
  However, given the limited temperature-density domain covered by these simulations, it must be kept in mind that
  uncertainties remain in these EOS calculations. Users must be aware of this issue.
  The situation will improve once further simulations will be conducted over a larger domain. See Chabrier et al., 2021, A&A for details.
        
