YNOGK: A new public code for calculating null geodesics in the Kerr spacetime

TL;DR

YNOGK is a publicly available, fast computational tool that calculates null geodesics in Kerr spacetime using elliptic functions, simplifying complex calculations for astrophysical applications.

Contribution

It introduces a novel approach expressing coordinates and parameters as functions of a single integral parameter, eliminating the need for pre-specified turning points.

Findings

Fast computation of null geodesics achieved.

Validated against literature problems.

Handles arbitrary emitter and observer configurations.

Abstract

Following \cite{dexagol2009} we present a new public code for the fast calculation of null geodesics in the Kerr spacetime. Using Weierstrass' and Jacobi's elliptic functions, we express all coordinates and affine parameters as analytical and numerical functions of a parameter $p$, which is an integral value along the geodesic. This is a main difference of our code compares with previous similar ones. The advantage of this treatment is that the information about the turning points do not need to be specified in advance by the user, and many applications such as imaging, the calculation of line profiles or the observer-emitter problem, etc become root finding problems. All elliptic integrations are computed by Carlson's elliptic integral method as \cite{dexagol2009} did, which guarantees the fast computational speed of our code. The formulae to compute the constants of motion given by \cite{cunnbard1973} have been extended, which allow one readily to handle the situations, in which the emitter or the observer has arbitrary distance and motion state with respect to the central compact object. The validation of the code has been extensively tested by its application to toy problems from the literature. The source FORTRAN code is freely available for download on the web.