solve_for_impact_parameter

luminet.black_hole_math.solve_for_impact_parameter(radius, incl, alpha, bh_mass, order=0) → float

Calculate observer coordinates of a BH frame photon.

This method solves Equation 13 to get the photon periastron distance for a given coordinate on the black hole accretion disk \((r, \alpha)\). The observer coordinates \((b, \alpha)\) are then calculated from the periastron distance.

Attention

Photons that originate from close to the black hole, and the front of the accretion disk, have orbits whose periastron is below \(3M\) (and thus would be absorbed by the black hole), but still make it to the camera in the observer frame. These photons are not absorbed by the black hole, since they simply never actually travel the part of their orbit that lies below \(3M\)

Parameters:

  • radius (float) – radius on the accretion disk (BH frame)

  • incl (float) – inclination of the black hole

  • alpha – angle along the accretion disk (BH frame and observer frame)

  • bh_mass (float) – mass of the black hole

  • order (int) – Order of the image. Default is \(0\) (direct image).

Returns:

float – Impact parameter \(b\) of the photon