intmom.f

INTMOM returns the moment of inertia per unit mass of a rotationally distorted shell, and its derivative with respect to $\Omega$, at one point (the comment: "moment of inertia per unit mass at the specified point (HI) and dI/dΩ per unit mass (QIW)").

Called only by MOMI, at each zone centre. MOMI passes QR0R = 1, R0R $= r_0^5/r^3$ (with $r_0$ the equivalent radius R0 and $r$ the model's radius), ETA2X = $\eta_2$ (ETA2, from the Clairaut–Radau treatment of the distortion, as far as the names show) and $a = \dfrac{5}{3}\,\dfrac{\Omega^2 r_0^3}{G\,m\,(2+\eta_2)}$ (A; CON = $5/(3G)$ in MOMI). MOMI multiplies both results by the shell mass to get HI and QIW; it calls INTMOM only when WALPCZ = 0 (otherwise it uses $I = \tfrac23 \Delta m\, r^2$). Module: only CONSTANTS_MOD (for $2/3$, CC23).

With fixed coefficients $c_j$ (C: 0.6, 0.7286, 0.5088, 0.4973, 0.4285),

$$h = \tfrac{2}{3}\,q\,R,\qquad I/m = h\left(1 + 0.15\sum_{j=1}^{5} c_j\,(j\eta_2 + 5)\,a^j\right),\qquad \frac{dI/m}{d\ln a} = h\;0.15\sum_{j=1}^{5} j\,c_j\,(j\eta_2+5)\,a^j,$$

with $q$ = QR0R, $R$ = R0R; the two results are HIM and QIWM (lines 23–31↗). The series, with its coefficients C (lines 17–18↗) and the factor 0.15, is the method of Wai-Yuen Law's thesis (Yale, 1980), p. 61, which MOMI's comment cites (momi.f, lines 52–53↗) (settled from the code, Nov 9, 2026). The sum in QIWM is $a\,\partial(I/m)/\partial a$, a logarithmic derivative in $a \propto \Omega^2$, so $d(I/m)/d\Omega = (2/\Omega)\,$QIWM, while the comment (lines 21–22↗) calls it $dI/d\Omega$; SOLID's Newton step uses it as $dI/d\Omega$, a suspected bug (solid.f, suspected bug 2).