Algorithms and Programs for Strong Gravitational Lensing In Kerr Spacetime Including Polarization
Abstract
Active galactic nuclei (AGNs) and quasars are important astrophysical objects to understand. Recently, microlensing observations have constrained the size of the quasar Xray emission region to be of the order of 10 gravitational radii of the central supermassive black hole. For distances within a few gravitational radii, light paths are strongly bent by the strong gravity field of the central black hole. If the central black hole has nonzero angular momentum (spin), then a photon’s polarization plane will be rotated by the gravitational Faraday effect. The observed Xray flux and polarization will then be influenced significantly by the strong gravity field near the source. Consequently, linear gravitational lensing theory is inadequate for such extreme circumstances. We present simple algorithms computing the strong lensing effects of Kerr black holes, including the effects on polarization. Our algorithms are realized in a program “KERTAP” in two versions: MATLAB and Python. The key ingredients of KERTAP are a graphic user interface, a backward raytracing algorithm, a polarization propagator dealing with gravitational Faraday rotation, and algorithms computing observables such as flux magnification and polarization angles. Our algorithms can be easily realized in other programming languages such as FORTRAN, C, and C++. The MATLAB version of KERTAP is parallelized using the MATLAB Parallel Computing Toolbox and the Distributed Computing Server. The Python code was sped up using Cython and supports full implementation of MPI using the “mpi4py” package. As an example, we investigate the inclination angle dependence of the observed polarization and the strong lensing magnification of AGN Xray emission. We conclude that it is possible to perform complex numericalrelativity related computations using interpreted languages such as MATLAB and Python.
 Publication:

The Astrophysical Journal Supplement Series
 Pub Date:
 May 2015
 DOI:
 10.1088/00670049/218/1/4
 arXiv:
 arXiv:1505.02714
 Bibcode:
 2015ApJS..218....4C
 Keywords:

 accretion;
 accretion disks;
 gravitational lensing: strong;
 methods: numerical;
 polarization;
 quasars: supermassive black holes;
 Astrophysics  High Energy Astrophysical Phenomena
 EPrint:
 11 pages, 7 figures