calc_flux_intrinsic_kerr¶

luminet.black_hole_math.calc_flux_intrinsic_kerr(bh_mass, a, r, acc)¶

Calculate the intrinsic flux of the accretion disk of a Kerr black hole, in function of the accretion rate, specific angular momentum, and radius of emission.

The intrinsic flux is not redshift-corrected. Observed photons will have a flux that deviates from this by a factor of \(1/(1+z)^4\)

The intrinsic flux in function of the radius is defined as:

\[\begin{split}F_s(r) &= \frac{\dot{M_0}}{4\pi}e^{-(\nu+\psi+\mu)}f \\\end{split}\]

where

\[\begin{split}\begin{align*} e^{\nu+\psi+\mu} &= r \\ f &= -\Omega_{,r}(E^{\dagger}-\Omega L^\dagger)^{-2}\int_{r_{ms}}^r(E^\dagger \ - \Omega L^\dagger)L^\dagger_{,r}dr \end{align*}\end{split}\]

Parameters:

bh_mass (float) – Mass of the black hole.
a (float) – Specific angular momentum of the black hole. Should always be between \(-1\) and \(1\). \(a > 0\) if the accretion disk orbits in the same direction as the hole rotates; \(a < 0\) if it orbits in the opposite direction.
r (float) – Radius of the orbit.
acc (float) – (initial) accretion rate of the black hole \(\dot{M}_0\)