calc_innermost_stable_orbit
===========================

.. py:function:: luminet.black_hole_math.calc_innermost_stable_orbit(bh_mass, a)

   Calculcate the innermost stable orbit :math:`r_{ms}` for a Kerr black hole.

   A larger specific angular momentum :math:`a` will yield innermost orbits closer to the black hole.

   .. math::

      \begin{align*}
      r_{ms} &= Mx_0^2 \\
      x_0^2 &= 3 + Z_2 - sgn(a_*)\sqrt{(3-Z_1)(3+Z_1+2Z_2) }
      \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.

   .. seealso:: :cite:t:`Page_1974`

   .. seealso:: :meth:`calc_Z1` and :meth:`calc_Z2`.