calc_flux_intrinsic_swarzschild
===============================

.. py:function:: luminet.black_hole_math.calc_flux_intrinsic_swarzschild(bh_mass, r, acc)

   Calculate the intrinsic flux of a photon.

   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`

   .. math::

      F_s = \frac{3 M \dot{M}}{8 \pi (r^* - 3) {r^*}^{5/2}} \left( \sqrt{r^*} - \sqrt{6} + \frac{\sqrt{3}}{2} \log \left( \frac{(\sqrt{r^*} + \sqrt{3})(\sqrt{6}-\sqrt{3})}{(\sqrt{6} + \sqrt{3})(\sqrt{r^*}-\sqrt{3})} \right) \right)

   where :math:`r^*=r/M`

   :Parameters: * **r** (*float*) -- radius on the accretion disk (BH frame)
                * **acc** (*float*) -- accretion rate
                * **bh_mass** (*float*) -- mass of the black hole

   :returns: *float* -- Intrinsic flux of the photon :math:`F_s`

   .. attention:: :cite:t:`Luminet_1979` has a mistake in Equation 15. The factor in fromt of the :math:`log` should be :math:`\sqrt{3}/2` instead of :math:`\sqrt{3}/3`. This can be verified by solving :cite:t:`Page_1974` Equation 15n. The resulting images of the paper are correct though.