eqscve.f

EQSCVE interpolates the Saumon–Chabrier–Van Horn (SCV) equation of state in its table for the surface (envelope) composition. It returns the density, the thermodynamic derivatives and the ionization fractions of hydrogen and helium. For any other composition it hands the work to EQSCVG, which combines the pure-hydrogen, pure-helium and metal tables.

• Who calls it: only EQSTAT2, when LSCV is set and $\log T <$ TSCUT, right after EQSAHA. If the point is outside the table (LCALC false), the routine returns without touching its outputs, so the EQSAHA values stand.

• Inputs: TL, T, P, BETA, X, Z. It compares X, Z with XENV, ZENV from /COMP/.

• What it calls: KSPLINE and KSPLINT (a four-point natural spline), INTERP (four-point Lagrange) and EQSCVG.
• Outputs: DL, D, QDT, QDP, QCP, DELA, FXION, LCALC.
• Modules: SCVEOS_MOD holds the tables (TLOGX, TABLENV for the envelope mixture, TABLEX, TABLEY, TABLEZ, SMIX, NPTSX) and the last indices IDTSCV, IDP; it is filled by SETSCV and used also by EQSCVG and SETUPS. The flag LSCV is now in NMLPAR_MOD. COMP_MOD gives the envelope composition; CONSTANTS_MOD the constants.

1. The table is in $\log T$ and $\log P_\mathrm{gas}$, with $P_\mathrm{gas} = \beta P$. Out of table if $\log T$ is outside TLOGX, if $\log P_\mathrm{gas} < 4$, or if it is above the last pressure of the stencil's lowest-temperature row.

2. Find the 4×4 stencil (IDTSCV, IDP), starting from the last one. For each of the 4 temperatures, a natural spline in $\log P_\mathrm{gas}$ gives five quantities (columns 2–6 of TABLENV: $\log\rho$, $Q_{\rho T}$, $Q_{\rho P}$, $c_P$, $\partial U/\partial T$); a second spline in $\log T$ gives their values at the point. Column 5, the tabulated $c_P$ (TEMPT(4), QCP0), is interpolated but never used, since step 4 rebuilds $c_P$ from $\partial U/\partial T$: unused? (line 384↗).

   One pressure grid serves all four temperatures. The pressure abscissae are always taken from the row IDTSCV, the lowest temperature of the stencil, also for the other three rows (lines 102–103↗; lines 164–166↗), and the ionization step (5) uses TABLENV's pressures, which are TABLEX's (setscv.f, line 165↗), for TABLEX and TABLEY too (lines 407–409↗). That is right: In input/eos/scv, every row of h_tab_i.dat and he_tab_i.dat (63 temperatures) is a prefix of one grid, $\log P_\mathrm{gas} = 4.00$, $4.20$, …, its length growing with $T$ from 30 to 76 points, so the row IDTSCV is the shortest of the stencil and its pressures are those of the three hotter rows; the metal table z_tab_i.dat, read in reverse order (setups.f, lines 388–389↗), has the same pressures row by row (checked from the files, Nov 10, 2026).

3. Smoothing at stencil changes. When the point is within TOLST = 0.032 in $\log T$ (or TOLSP = 0.08 in $\log P$) of the edge of the middle interval, the routine also interpolates on the stencil shifted by one, and blends the two linearly (FST, FSP), so that the result does not jump when the stencil changes.

4. Radiation. The tables hold the gas alone. With $Q_{\rho P,0}$ and $Q_{\rho T,0}$ from the table, $$Q_{\rho P} = \frac{Q_{\rho P,0}}{\beta},\qquad \chi_T = \beta\left(-\frac{Q_{\rho T,0}}{Q_{\rho P,0}}\right) + 4(1-\beta),\qquad Q_{\rho T} = -\chi_T\,Q_{\rho P},$$ $$\frac{\partial U}{\partial T} \mathrel{+}= \frac{4}{T}\cdot\frac{3P_\mathrm{rad}}{\rho},\qquad c_P = \frac{\partial U}{\partial T} - \frac{P}{\rho T}Q_{\rho T}\chi_T,\qquad \nabla_\mathrm{ad} = -\frac{P\,Q_{\rho T}}{\rho T\,c_P}.$$

5. Ionization. From the pure-hydrogen table TABLEX and the pure-helium table TABLEY (columns 2 and 3, Lagrange interpolation on the same stencil and pressure abscissae as TABLENV), the particle fractions of H$_2$, H, He and He$^+$; charge and particle conservation give the rest, and $$x_{\mathrm{H}^+} = \frac{n_{\mathrm{H}^+}}{n_{\mathrm{H}_2} + n_\mathrm{H} + n_{\mathrm{H}^+}}, \quad x_{\mathrm{He}^+} = \frac{n_{\mathrm{He}^+}}{n_\mathrm{He} + n_{\mathrm{He}^+} + n_{\mathrm{He}^{++}}},$$ and likewise for He$^{++}$ (the code's formula for H$^+$; see bug 1).