The following text briefly describes the equation of state (EOS) files found
in this directory and how to read them.  These files, also available
on the AAS CD-ROM Vol. 5, are meant to accompany Saumon, Chabrier and
Van Horn (1994, hereafter, SCVH) and provide complete equations of state
for hydrogen and helium.  Equations of state for mixtures of hydrogen
and helium can be obtained by compositional interpolation as described
in SCVH.

1)  DESCRIPTION OF THE FILES

There are seven ASCII files:

   File name               Contents

1) README.DOC           This text file.  Basic information on the tables.
2) READ.F               Short FORTRAN program which reads the above tables
                        (shows the format of the tables)
3) H_TAB_I.DAT          Interpolated hydrogen EOS table  2.10 < log T < 7.06
4) RHO_CRIT.DAT         Coexistence curve of the H plasma phase transition (PPT)
5) H_TAB_P1.DAT         Small table for the EOS near the plasma phase transition
                        (PPT) of hydrogen: Phase 1 (low density phase)
                        3.54 < log T < 4.82
6) H_TAB_P2.DAT         Small table for the EOS near the plasma phase transition
                        (PPT) of hydrogen: Phase 2 (high density phase)
                        3.54 < log T < 4.82
7) HE_TAB_I.DAT         Interpolated helium EOS table  2.10 < log T < 7.06

These files occupy about 970 Kbytes of disk space.
Files 3 to 6 are for the hydrogen EOS, and the last one is for helium.
Both equations of state are based on the free energy minimization method.
The Helmholtz free energy model for hydrogen is fully described in Saumon and
Chabrier (1991; 1992) and Chabrier (1990).  The model for the helium EOS is
found in SCVH.  The latter paper also shows both equations of state in graphic
form (thermodynamic surfaces), contains a critique of the present equations
of state, and compares these calculations with other EOS commonly used in
astrophysics.

2) CONTENT OF THE EOS TABLES

The equations of state are tabulated along isotherms.  As an example, these are
the first ten lines of H_TAB_I.A:

 2.10  30
  4.00  1.00000E+00  0.00000E+00  -5.7154   8.8910  10.1201  -1.0000   1.0000   0.1687  -0.0530   0.3142
  4.20  1.00000E+00  0.00000E+00  -5.5154   8.8803  10.1201  -1.0000   1.0000   0.1729  -0.0543   0.3144
  4.40  1.00000E+00  0.00000E+00  -5.3154   8.8693  10.1201  -1.0000   1.0000   0.1773  -0.0557   0.3144
  4.60  1.00000E+00  0.00000E+00  -5.1154   8.8580  10.1201  -1.0000   1.0000   0.1820  -0.0572   0.3144
  4.80  1.00000E+00  0.00000E+00  -4.9154   8.8464  10.1201  -1.0001   1.0000   0.1869  -0.0588   0.3144
  5.00  1.00000E+00  0.00000E+00  -4.7154   8.8345  10.1200  -1.0001   1.0000   0.1921  -0.0604   0.3144
  5.20  1.00000E+00  0.00000E+00  -4.5154   8.8222  10.1200  -1.0002   0.9999   0.1976  -0.0621   0.3145
  5.40  1.00000E+00  0.00000E+00  -4.3154   8.8096  10.1200  -1.0003   0.9999   0.2034  -0.0640   0.3145
  5.60  1.00000E+00  0.00000E+00  -4.1155   8.7966  10.1200  -1.0005   0.9999   0.2096  -0.0659   0.3145

The first line gives log T (K) and the number of pressure points along that
isotherm.  The lowest value of the pressure is log P = 4, and it increases in
steps of 0.2 for all isotherms, but the maximum pressure is not the same for
all isotherms (see Figs 18 and 20 of SCVH).  Note that the (log T, log P)
coverage of H_TAB_I.A and HE_TAB_I.A are identical.  Each row then provides:

log P:                P is the pressure in dyn/cm**2.
X(H2):                The number concentration of H2 molecules (He atoms for
                      helium).
X(H):                 The number concentration of H atoms (He+ ions for helium).
log rho:              rho is the mass density in g/cm**3.
log S:                S is the entropy in erg/g/K.
log U:                U is the internal energy in erg/g.  The zero point of
                      energy is the ground state of the H2 molecule for
                      hydrogen, and the ground state of the He atom for helium.
d log rho/d log T|P:  Logarithmic derivative of the density with respect to the
                      temperature at constant P.
d log rho/d log P|T:  Logarithmic derivative of the density with respect to the
                      pressure at constant T.
d log S/d log T|P:    Logarithmic derivative of the entropy with respect to the
                      temperature at constant P.
d log S/d log P|T:    Logarithmic derivative of the entropy with respect to the
                      pressure at constant T.
d log T/d log P|S     The adiabatic gradient.

All logarithms are in base 10.  The contribution from the photon gas is NOT
included.

3) INTERPOLATION NEAR THE PLASMA PHASE TRANSITION

The file RHO_CRIT contains the coexistence curve for the plasma phase
transition (PPT) of hydrogen.  It allows the determination of the phase of the
system when this is of concern in a particular application of the hydrogen EOS.
The file is reproduced below, with column headings added:

  log T   log P      log rho      log rho
                     Phase 1      Phase 2

  3.540   12.360     -.098484     -.027440
  3.620   12.345     -.111784     -.029363
  3.700   12.330     -.126259     -.036724
  3.780   12.289     -.152205     -.055079
  3.860   12.210     -.195296     -.095751
  3.940   12.143     -.237227     -.132518
  4.020   12.054     -.293355     -.186550
  4.100   11.952     -.362653     -.259015
  4.180   11.800     -.437500     -.437500

Columns 3 and 4 define the extent of the metastable region and yield the
associated density discontinuity.  The last entry of the table corresponds to
the critical point of the PPT.

The tables H_TAB_P1.A and H_TAB_P2.A are intended to facilitate interpolation
near the PPT, if this feature of the EOS is desired.  To interpolate as
accurately as possible in the vicinity of the discontinuities associated with
the PPT, the following procedure should be used:

                    **** Skeletal FORTRAN Program ****

C  First check that the requested (log T, log P) point, given by TEMP and PG,
C  falls in the pressure ionization region covered by these two tables:
      IF(TEMP.LT.4.82 .AND. TEMP.GE.3.54 .AND. PG.GT.10.5 .AND. PG.LT.14.1) THEN
          IF(TEMP.GE.4.18) THEN
C  This is for an isotherm above the critical temperature of the PPT
              PTRANS=11.75
          ELSE
C  And now for an isotherm below the critical temperature

        ....   Determine the transition pressure (PTRANS) of the PPT at this
        ....   temperature by interpolating in the coexistence curve table:
        ....   rho_critical

          ENDIF
          IF(PG.LT.PTRANS) THEN

        ....   Interpolate in the Phase 1 table: H_tab_P1.a

          ELSE

        ....   Interpolate in the Phase 2 table: H_tab_P2.a

          ENDIF


4) ADDITIONAL ASSISTANCE

Please direct any questions and comments about the tables to Didier Saumon
at dsaumon@lpl.arizona.edu.  If you copy and use these EOS tables, please
send an e-mail message to the same address stating that you have done so.
This will allow us to compile a list of users for announcing future upgrades
in the EOS.

Didier Saumon
Lunar and Planetary Laboratory
University of Arizona
Tucson, AZ 85721
USA

Phone: (602) 621-6362
e-mail: dsaumon@lpl.arizona.edu


5) REFERENCES

Chabrier, G. 1990, J. Phys. (Paris) 51, 1607.
Saumon, D. and Chabrier, G. 1991, Phys. Rev. A 44, 5122.
Saumon, D. and Chabrier, G. 1992, Phys. Rev. A 46, 2084.
Saumon, D., Chabrier, G., and Van Horn, H.M. 1994,  Ap. J. Supp., in press.