PyREC scaffolding (from YREC development, 7be4133)/ alex06tab.fGlossary

alex06tab.f

134 lines · 1 definitions · on GitHub (7be4133)

Python version: alex06tab.py, 125 lines, on the right (switch to Python above the code).

Variables on this page (12)

capalex06, captalex06, ishort, ix, numd, numt, numx, numz, xe, xxg06, ze, zzg06

Purpose

This file builds the table of the low-temperature opacities of Ferguson et al. (2005), called ALEX06 in the code (read by READALEX06), for one composition $(X, Z)$, by interpolating between the stored tables of the grid in $X$ and $Z$. The result is a single table of opacity against $\log T$ and $\log R$ that GETALEX06 then interpolates in.

How it fits

  • Inputs: the full set of tables, CAPTALEX06 in ALOT06ALL_MOD, read once by READALEX06, and the grid values XXG06, ZZG06 in GALOT06_MOD (initialized there); the requested composition XE, ZE in ALOT06_MOD.
  • Who calls it: only GETALEX06, whenever the $X$ or $Z$ of the point differs from the composition of the current table by more than $10^{-8}$. GETALEX06 sets XE, ZE before the call.
  • What it calls: INTRP2, 4-point Lagrange weights.
  • Output: CAPALEX06(NUMT,NUMD) in ALOT06_MOD, read by GETALEX06. It also sets the index IX in ALOT06_MOD.
  • Modules: GALOT06_MOD and ALOT06_MOD (with GETALEX06 and READALEX06), ALOT06ALL_MOD (with READALEX06); the formerly shared COMMON blocks /GALOT06/, /ALOT06/ and /ALOT06ALL/.

The grid. READALEX06 stores the tables as CAPTALEX06(JJ, T, R) with $JJ = (i_X - 1)\,N_Z + i_Z$, for $N_X = 9$ values of $X$ (eight from 0 to 0.9, then a ninth set at $X = 1 - Z$, which XXG06(9) = 1.0 stands for) and $N_Z = 16$ values of $Z$ (0 to 0.10): 143 tables in all, since there is no extra table at $X = 1 - Z$ for $Z = 0.10$ (the $X = 0.9$ table doubles for it). Each table has 85 temperatures and 19 values of $\log R$.

The method

  1. Check the composition: $0 \le X \le 1 - Z$, and $0 \le Z \le Z_{16} + (Z_{16} - Z_{15}) = 0.12$, an extrapolation by one grid step in $Z$ (lines 28–45↗; the comment: "PERMIT EXTRAPOLATION IN Z BY UP TO 1 TABLE ELEMENT"). Otherwise the run stops.

  2. Choose 4 neighboring grid values in $Z$ (starting index IZ) and in $X$ (IX). Above $X = 0.8$ the start is NUMX-3, or NUMX-4 if $Z \ge 0.1$.

  3. Interpolate in $Z$ for each of the 4 values of $X$, with the 4-point Lagrange weights $w_k(Z)$: $$\kappa_m(T,R) = \sum_{k=1}^{4} w_k(Z)\,\kappa(X_m, Z_{k}; T, R), \qquad w_k(Z) = \prod_{l \ne k} \frac{Z - Z_l}{Z_k - Z_l}.$$ The 4th value of $X$ needs its own indexing near the corner of the grid ($X = 1 - Z$, $Z = 0.1$).

  4. Interpolate in $X$ the same way over the 4 results (CAPTEMP), giving CAPALEX06. When IZ = NUMZ-3 ($Z > 0.06$), the 4th node in $X$ is placed at $1 - Z$, whatever IX is; otherwise at XXG06(IX+3), which is 1.0 for IX = NUMX-3 (lines 112–121↗; bug 1).

The tabulated quantity is $\log \kappa$, as GETALEX06 uses it (READALEX06 reads it with format F7.3); the interpolation is linear in $\log\kappa$.

Design

All state is in modules; the routine has no arguments. It stops the run on a bad composition (STOP 1), with a message that names "ALEX06," written to the terminal and the .short file (ISHORT, from IOUNITS_MOD).

Suspected bugs, checked by running the code

Each bug is marked by what running the code showed: (changes results, large) or (small), the fix moving a run clearly beyond a null change; (stops the run); (wrong output), the fix changing only what is written; (harmless in the runs), within the noise; (never occurred), the code ran but the fault did not; (not reached); (cannot be reached), a guard prevents it; (withdrawn), the suspicion was wrong.

1. (harmless in the runs) The 4th node in $X$ is tested on IZ, not on IX.

(lines 56–68↗; lines 91–104↗; lines 117–121↗) The 4th table in $X$ is at $X = 1 - Z$ only when IX = NUMX-3 (lines 93–104 read it from the ninth set, or from $X = 0.9$ at $Z = 0.10$); otherwise it is the table at XXG06(IX+3). But its abscissa QR(4) is $1 - $ ZE whenever IZ = NUMZ-3, that is, for $Z > 0.06$, and XXG06(IX+3) otherwise. Two cases follow. (i) For $Z > 0.06$ and $X \le 0.8$ (IX ≤ NUMX-4), the 4th node is placed at $1 - Z$, between 0.88 and 0.94, instead of at its table's $X$ (for example 0.8 for $0.5 < X \le 0.7$, 0.9 for $0.7 < X \le 0.8$), so the Lagrange weights in $X$ are those of a wrong grid; this holds for any $X$ up to 0.8 (and, with an error of at most 0.02, for $X > 0.8$ at $Z \ge 0.10$, where IX = NUMX-4 and the table is at 0.9). (ii) For $Z \le 0.06$ and $X > 0.8$ (IX = NUMX-3), the 4th node is placed at XXG06(9) = 1.0, while its table is at $X = 1 - Z$, up to 0.06 lower. Only with LALEX06 (off by default in the code; recommended by YREC's User Guide), at $\log T \le$ TMOLMAX; case (i) only for $Z > 0.06$, case (ii) only for $X > 0.8$.

A possible fix:

alex06tab.f

@@ lines 114–120 @@
       DO I = 1,3
          QR(I) = XXG06(IX+I-1)
       END DO
-      IF(IZ.EQ.NUMZ-3)THEN
+C 11/09/26 KC via Claude
+C code changed to place the 4th node in X at 1-Z when the 4th table
+C is the X = 1-Z one (IX = NUMX-3), and at XXG06(IX+3) otherwise.
+      IF(IX.EQ.NUMX-3)THEN
          QR(4) = 1.0D0-ZE
       ELSE
          QR(4) = XXG06(IX+3)

Checked by running YREC (Nov 9, 2026; a line added at each suspected path counted how often it was taken, the outputs otherwise unchanged): 34 runs, 26 of YREC's cases (from a 0.04 $M_\odot$ brown dwarf and the solar models to 9 $M_\odot$, rotation, and helium burning) and 8 made-up ones (each one of YREC's cases with a few settings changed), of which one stopped in its first second. The interpolation in $X$ ran in all 33 others, 1 to 1,540 times a run, always at a surface $Z$ of 0.001 to 0.019, so case (i) was never reached. Case (ii) was: In testsuite/Test_m1p4feh+0p0GS98_dif_TAMS, diffusion drains helium from the surface, $X$ rises to 0.80–0.97, and the 4th node stood at 1.0 instead of $1 - Z$ in 363 calls. With the fix, that track moves by up to 0.0062 dex in $\log L$ and 0.013 dex in $\log T_c$ (819 models instead of 820, end age 3.40008 Gyr instead of 3.40039), within the noise: The null change used as a noise floor (nearly every opacity, all with $3 \le \log T \le 9$ and $-6 \le \log\rho \le 9.75$, times $1 + 10^{-10}$) moves $\log L$ by 0.057 dex and $\log T_c$ by 0.032 dex on that case. Case (i) needs a surface $Z$ above 0.06, which no run had, so it was not tested. Intent: none found; the comment at lines 91–92 places the $X = 1 - Z$ table by IX, as the fix does.

Definitions

subroutineALEX06TAB

lines 2–134 · GitHub

Interpolates the stored ALEX06 tables to the composition (XE, ZE) in ALOT06_MOD: first in $Z$, then in $X$, each with 4-point Lagrange weights from INTRP2. Writes CAPALEX06.

Uses modules ALOT06ALL_MOD, ALOT06_MOD, GALOT06_MOD, IOUNITS_MOD

Called by GETALEX06

Flowchart of its calls, in order (2)
INTRP275→INTRP2123

Change log

The changes since rp_1

Changed since rp_1. Declarations only: COMMON blocks to modules, IMPLICIT NONE (the unused NUMXZ parameter is now in ALOT06ALL_MOD).

Changed since a8a5950. The two stops on a bad composition now write their message to the .short file as well as the terminal (the routine now uses IOUNITS_MOD), and exit with status 1, the code for run-time errors, instead of a bare STOP (KNOWN_ISSUES.md, issue 38).