eq2mod.f

EQ2MOD maps a change in specific angular momentum, computed on an equally spaced grid, back onto the model's own mass points. It is the last step of the angular momentum transport by rotational instabilities: the diffusion equation is solved on the equally spaced grid for each unstable region, and this routine applies the result to the run of $j = J/M$ in the model.

• Who calls it: only SECULR, after it has solved the diffusion equation for one unstable region (shells IBEG to IEND).
• Inputs: the change DJ and the angular momentum EJ before redistribution, both on the equally spaced grid; the shell masses HS2; the convective flags LCZ; the total change SUMDJ across the grid.
• What it calls: OSPLIN, a shape-preserving osculatory quadratic spline (ACM Algorithm 574).
• Output: the array HJM (specific angular momentum at each model point), updated in place.
• Modules: EGRID_MOD (formerly /EGRID/) holds the grids: CHI (the model points' coordinate, $\chi = \log m/\Delta_m + L/\Delta_L - \log P/\Delta_P$, where $\Delta_m$ = HPTTOL(2), $\Delta_L$ = HPTTOL(9)$\cdot L_\mathrm{surf}$, $\Delta_P$ = HPTTOL(11), as GETGRID forms it (its comment writes $L/(L_\mathrm{tot}\Delta L)$); here CHI(1..NMOD) are the region's points, from IBEG on), ECHI (the equally spaced points), NTOT; it is filled by GETGRID and shared with SECULR, ROTGRID, MIXGRID, MIXCOM and CHECKJ. SPLIN_MOD (formerly /SPLIN/) is scratch space for the spline, shared with MIXCOM, MIXGRID and ROTGRID.

1. If a convection zone adjoins the region's first or last shell (whether or not that shell is itself convective), the region is extended (indices I0, I1) to the far edge of that zone, the test ROTGRID's sums use.
2. The fractional change $y = \Delta j / j$ (DJ/EJ) is interpolated with OSPLIN from the equally spaced points ECHI to the model points CHI, giving YVAL.

3. Each shell's $j$ is multiplied by $(1 + y_i)$. Shells in the extended convective parts take the value at the nearest edge (YVAL(1) or YVAL(NMOD)).

4. Conservation check. With $m_i$ the shell mass (HS2), $$S_J = \sum_i j_i m_i, \qquad S_{\Delta} = \sum_i y_i\, j_i m_i .$$ If $|S_\Delta - \Delta J| > 10^{-5}|\Delta J|$, where $\Delta J$ is SUMDJ, every shell from I0 to I1 is rescaled by $$\frac{S_J + \Delta J}{S_J + S_\Delta},$$ so that the region's total angular momentum changes by exactly $\Delta J$. When $\Delta J = 0$ (no surface loss), any mismatch triggers the rescaling, which then conserves the region's angular momentum exactly; this is what the comment asks for ("CARE IS USED HERE BECAUSE DUMDJ SHOULD BE ZERO IN MODELS WITHOUT LOSS," where DUMDJ is SUMDJ; lines 120–124↗, lines 131–136↗; settled from the code, Nov 9, 2026).