# ALGORITHMS AND PROGRAMS FOR STRONG GRAVITATIONAL LENSING IN KERR SPACE-TIME 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 X-ray 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 X-ray 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 ray-tracing 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 ofmore »

- Authors:

- Research Computing Center, Department of Scientific Computing, Florida State University, Tallahassee, FL 32306 (United States)
- Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, OK 73019 (United States)

- Publication Date:

- OSTI Identifier:
- 22520225

- Resource Type:
- Journal Article

- Journal Name:
- Astrophysical Journal, Supplement Series

- Additional Journal Information:
- Journal Volume: 218; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0067-0049

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCRETION DISKS; ALGORITHMS; ASTROPHYSICS; BLACK HOLES; CALCULATION METHODS; COMPUTERIZED SIMULATION; COSMIC X-RAY SOURCES; FARADAY EFFECT; FORTRAN; GALAXY NUCLEI; GRAVITATION; GRAVITATIONAL LENSES; M CODES; P CODES; POLARIZATION; QUASARS; SPACE-TIME; SPIN; VISIBLE RADIATION

### Citation Formats

```
Chen, Bin, Maddumage, Prasad, Kantowski, Ronald, Dai, Xinyu, and Baron, Eddie, E-mail: bchen3@fsu.edu.
```*ALGORITHMS AND PROGRAMS FOR STRONG GRAVITATIONAL LENSING IN KERR SPACE-TIME INCLUDING POLARIZATION*. United States: N. p., 2015.
Web. doi:10.1088/0067-0049/218/1/4.

```
Chen, Bin, Maddumage, Prasad, Kantowski, Ronald, Dai, Xinyu, & Baron, Eddie, E-mail: bchen3@fsu.edu.
```*ALGORITHMS AND PROGRAMS FOR STRONG GRAVITATIONAL LENSING IN KERR SPACE-TIME INCLUDING POLARIZATION*. United States. doi:10.1088/0067-0049/218/1/4.

```
Chen, Bin, Maddumage, Prasad, Kantowski, Ronald, Dai, Xinyu, and Baron, Eddie, E-mail: bchen3@fsu.edu. Fri .
"ALGORITHMS AND PROGRAMS FOR STRONG GRAVITATIONAL LENSING IN KERR SPACE-TIME INCLUDING POLARIZATION". United States. doi:10.1088/0067-0049/218/1/4.
```

```
@article{osti_22520225,
```

title = {ALGORITHMS AND PROGRAMS FOR STRONG GRAVITATIONAL LENSING IN KERR SPACE-TIME INCLUDING POLARIZATION},

author = {Chen, Bin and Maddumage, Prasad and Kantowski, Ronald and Dai, Xinyu and Baron, Eddie, E-mail: bchen3@fsu.edu},

abstractNote = {Active galactic nuclei (AGNs) and quasars are important astrophysical objects to understand. Recently, microlensing observations have constrained the size of the quasar X-ray 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 X-ray 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 ray-tracing 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 X-ray emission. We conclude that it is possible to perform complex numerical-relativity related computations using interpreted languages such as MATLAB and Python.},

doi = {10.1088/0067-0049/218/1/4},

journal = {Astrophysical Journal, Supplement Series},

issn = {0067-0049},

number = 1,

volume = 218,

place = {United States},

year = {2015},

month = {5}

}