### Supermassive Star

We consider a SMS model just prior to collapse, when it is described
by a uniformly rotating $\Gamma=4/3$ polytrope spinning at the mass-shedding
limit. The SMS is of arbitrary mass M and has an
angular momentum $J/M^2=0.96$ and a rotational-to-gravitational-binding-energy ratio $T/|W|=0.009$.
The equatorial radius of the star is
$R_{\rm eq}=626M\approx 9.25\times 10^6\,({M}/{10^6M_{\odot}})$km;
the polar radius satisfies $R_p/R_{eq}=2/3$.
This model is marginally unstable to radial collapse due
to GR, and this triggers the collapse. The SMS is seeded with a dipole magnetic field which extends from to stellar interior into the exterior. We choose the magnetic field strength such as the ratio of magnetic to the rotational kinetic energy
is $\mathcal{M}/T = 0.1$. The magnetic field strength is given by $B_{max} = 6.5\times{10^6}({10^6\,M_\odot}/{M})G$.