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
1) README.DOC
2) READ.F
tables
3) H_TAB_I.DAT
7.06
4) RHO_CRIT.DAT
transition (PPT)
5) H_TAB_P1.DAT
transition
6) H_TAB_P2.DAT
transition
7) HE_TAB_I.DAT
7.06
Contents
This text file. Basic information on the tables.
Short FORTRAN program which reads the above
(shows the format of the tables)
Interpolated hydrogen EOS table 2.10 < log T <
Coexistence curve of the H plasma phase
Small table for the EOS near the plasma phase
(PPT) of hydrogen: Phase 1 (low density phase)
3.54 < log T < 4.82
Small table for the EOS near the plasma phase
(PPT) of hydrogen: Phase 2 (high density phase)
3.54 < log T < 4.82
Interpolated helium EOS table 2.10 < log T <
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.
these are
the first ten lines of H_TAB_I.A:
As an example,
2.10 30
4.00 1.00000E+00 0.00000E+00
1.0000
0.1687 -0.0530
0.3142
4.20 1.00000E+00 0.00000E+00
1.0000
0.1729 -0.0543
0.3144
4.40 1.00000E+00 0.00000E+00
1.0000
0.1773 -0.0557
0.3144
4.60 1.00000E+00 0.00000E+00
1.0000
0.1820 -0.0572
0.3144
4.80 1.00000E+00 0.00000E+00
1.0000
0.1869 -0.0588
0.3144
5.00 1.00000E+00 0.00000E+00
1.0000
0.1921 -0.0604
0.3144
5.20 1.00000E+00 0.00000E+00
0.9999
0.1976 -0.0621
0.3145
5.40 1.00000E+00 0.00000E+00
0.9999
0.2034 -0.0640
0.3145
5.60 1.00000E+00 0.00000E+00
0.9999
0.2096 -0.0659
0.3145
-5.7154
8.8910
10.1201
-1.0000
-5.5154
8.8803
10.1201
-1.0000
-5.3154
8.8693
10.1201
-1.0000
-5.1154
8.8580
10.1201
-1.0000
-4.9154
8.8464
10.1201
-1.0001
-4.7154
8.8345
10.1200
-1.0001
-4.5154
8.8222
10.1200
-1.0002
-4.3154
8.8096
10.1200
-1.0003
-4.1155
8.7966
10.1200
-1.0005
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:
X(H2):
for
X(H):
helium).
log rho:
log S:
log U:
of
P is the pressure in dyn/cm**2.
The number concentration of H2 molecules (He atoms
helium).
The number concentration of H atoms (He+ ions for
rho is the mass density in g/cm**3.
S is the entropy in erg/g/K.
U is the internal energy in erg/g. The zero point
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:
to the
d log rho/d log P|T:
to the
d log S/d log T|P:
to the
d log S/d log P|T:
to the
Logarithmic derivative of the density with respect
temperature at constant P.
Logarithmic derivative of the density with respect
pressure at constant T.
Logarithmic derivative of the entropy with respect
temperature at constant P.
Logarithmic derivative of the entropy with respect
d log T/d log P|S
pressure at constant T.
The adiabatic gradient.
All logarithms are in base 10.
NOT
included.
The contribution from the photon gas is
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
Phase 1
log rho
Phase 2
3.540
3.620
3.700
3.780
3.860
3.940
4.020
4.100
4.180
12.360
12.345
12.330
12.289
12.210
12.143
12.054
11.952
11.800
-.098484
-.111784
-.126259
-.152205
-.195296
-.237227
-.293355
-.362653
-.437500
-.027440
-.029363
-.036724
-.055079
-.095751
-.132518
-.186550
-.259015
-.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
....
temperature by interpolating in the coexistence curve
....
rho_critical
this
table:
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,
Saumon, D. and Chabrier, G. 1991, Phys.
Saumon, D. and Chabrier, G. 1992, Phys.
Saumon, D., Chabrier, G., and Van Horn,
press.
1607.
Rev. A 44, 5122.
Rev. A 46, 2084.
H.M. 1994, Ap. J. Supp., in