hsolve.f

HSOLVE performs the last stage of the Henyey solution of the stellar-structure equations: it applies the surface boundary condition and back-substitutes through the shells, turning the forward-eliminated matrix into the corrections to the variables at every point.

Called only by CRRECT, which builds the Henyey system; the forward elimination is done shell by shell by REDUCE (called from COEFFT), whose page works out what HHA and HHB hold. Arguments: M (number of points), HHA(4,2,M) and HHB(4,M) (the eliminated coefficients and right-hand sides, overwritten), HSRF(6) (the surface boundary conditions). No modules but DIMENSIONS_MOD (for JSON), no calls.

Inferred from the code; the code has no comments. At the surface it solves a 2×2 system for the two corrections at point M, here written $\delta p$ and $\delta t$ (QQQP, QQQT; the corrections to $\log P$ and $\log T$ at point M, base 10, since CRRECT adds HHB(1,i) to HP and HHB(2,i) to HT):

$$\begin{pmatrix} s_1 - a_{31} & s_2 - a_{32}\\ s_4 - a_{41} & s_5 - a_{42}\end{pmatrix}\begin{pmatrix}\delta p\\ \delta t\end{pmatrix} = \begin{pmatrix} s_3 - b_3\\ s_6 - b_4\end{pmatrix},$$

with $s_k$ = HSRF(k) and $a_{ij}$, $b_i$ taken at point M.

Then, from the surface inward ($i = M, M-1, \dots, 2$), the rows stored at point $i$ give

$$\delta p(i-1) = b_1(i) - a_{11}(i)\,\delta p(i) - a_{12}(i)\,\delta t(i),\qquad \delta t(i-1) = b_2(i) - a_{21}(i)\,\delta p(i) - a_{22}(i)\,\delta t(i),$$

$$y_k(i) = b_k(i) - a_{k1}(i)\,\delta p(i) - a_{k2}(i)\,\delta t(i)\quad (k = 3, 4),$$

and the centre point is finished the same way. On return HHB(1..4, i) holds the four corrections at each point, $\delta\log P$, $\delta\log T$, $\delta\log r$ and $\delta L$ ($L_\odot$), in the order of REDUCE's rows. The six HSRF entries are the two surface conditions set by CRRECT: HSRF(1..3) the linearized $\log r$ relation of the envelope fit, HSRF(4..6) its $\log L$ relation, multiplied by $\ln 10\,L$ since $L$ is the unknown (CRRECT, step 4).

The code does not say what HHB and HSRF hold. The reading above is right: CRRECT adds HHB(1..4, i) after the call to HP, HT, HR, and HL as the corrections (crrect.f, lines 283–291↗), after finding their largest values (crrect.f, lines 212–236↗), the fourth tested also relative to HL, the luminosity (crrect.f, line 234↗); a comment in the code (lines 21–42↗) saying so, and which equations the six HSRF entries are, would help readers of CRRECT.