calc_flux_intrinsic_kerr
========================

.. py:function:: 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 :math:`1/(1+z)^4`

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

   .. math::

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

   where

   .. math::

      \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*}

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

   .. seealso:: :meth:`calc_f_kerr` for an algebraic expression of the :math:`f` function.