# Testing the Kerr Black Hole Hypothesis Using X-Ray Reflection Spectroscopy

## Abstract

We present the first X-ray reflection model for testing the assumption that the metric of astrophysical black holes is described by the Kerr solution. We employ the formalism of the transfer function proposed by Cunningham. The calculations of the reflection spectrum of a thin accretion disk are split into two parts: the calculation of the transfer function and the calculation of the local spectrum at any emission point in the disk. The transfer function only depends on the background metric and takes into account all the relativistic effects (gravitational redshift, Doppler boosting, and light bending). Our code computes the transfer function for a spacetime described by the Johannsen metric and can easily be extended to any stationary, axisymmetric, and asymptotically flat spacetime. Transfer functions and single line shapes in the Kerr metric are compared to those calculated from existing codes to check that we reach the necessary accuracy. We also simulate some observations with NuSTAR and LAD/eXTP and fit the data with our new model to show the potential capabilities of current and future observations to constrain possible deviations from the Kerr metric.

- Authors:

- Center for Field Theory and Particle Physics and Department of Physics, Fudan University, 200433 Shanghai (China)
- Programa de Matemática, Fundación Universitaria Konrad Lorenz, 110231 Bogotá (Colombia)
- Remeis Observatory and ECAP, Universität Erlangen-Nürnberg, D-96049 Bamberg (Germany)
- Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138 (United States)

- Publication Date:

- OSTI Identifier:
- 22663499

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Astrophysical Journal; Journal Volume: 842; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCRETION DISKS; ACCURACY; ASTROPHYSICS; AXIAL SYMMETRY; BLACK HOLES; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; EMISSION; GRAVITATION; HYPOTHESIS; KERR METRIC; RED SHIFT; REFLECTION; RELATIVISTIC RANGE; SPACE-TIME; SPECTRA; TRANSFER FUNCTIONS; VISIBLE RADIATION; X RADIATION

### Citation Formats

```
Bambi, Cosimo, Nampalliwar, Sourabh, Cárdenas-Avendaño, Alejandro, Dauser, Thomas, and García, Javier A., E-mail: bambi@fudan.edu.cn.
```*Testing the Kerr Black Hole Hypothesis Using X-Ray Reflection Spectroscopy*. United States: N. p., 2017.
Web. doi:10.3847/1538-4357/AA74C0.

```
Bambi, Cosimo, Nampalliwar, Sourabh, Cárdenas-Avendaño, Alejandro, Dauser, Thomas, & García, Javier A., E-mail: bambi@fudan.edu.cn.
```*Testing the Kerr Black Hole Hypothesis Using X-Ray Reflection Spectroscopy*. United States. doi:10.3847/1538-4357/AA74C0.

```
Bambi, Cosimo, Nampalliwar, Sourabh, Cárdenas-Avendaño, Alejandro, Dauser, Thomas, and García, Javier A., E-mail: bambi@fudan.edu.cn. Tue .
"Testing the Kerr Black Hole Hypothesis Using X-Ray Reflection Spectroscopy". United States.
doi:10.3847/1538-4357/AA74C0.
```

```
@article{osti_22663499,
```

title = {Testing the Kerr Black Hole Hypothesis Using X-Ray Reflection Spectroscopy},

author = {Bambi, Cosimo and Nampalliwar, Sourabh and Cárdenas-Avendaño, Alejandro and Dauser, Thomas and García, Javier A., E-mail: bambi@fudan.edu.cn},

abstractNote = {We present the first X-ray reflection model for testing the assumption that the metric of astrophysical black holes is described by the Kerr solution. We employ the formalism of the transfer function proposed by Cunningham. The calculations of the reflection spectrum of a thin accretion disk are split into two parts: the calculation of the transfer function and the calculation of the local spectrum at any emission point in the disk. The transfer function only depends on the background metric and takes into account all the relativistic effects (gravitational redshift, Doppler boosting, and light bending). Our code computes the transfer function for a spacetime described by the Johannsen metric and can easily be extended to any stationary, axisymmetric, and asymptotically flat spacetime. Transfer functions and single line shapes in the Kerr metric are compared to those calculated from existing codes to check that we reach the necessary accuracy. We also simulate some observations with NuSTAR and LAD/eXTP and fit the data with our new model to show the potential capabilities of current and future observations to constrain possible deviations from the Kerr metric.},

doi = {10.3847/1538-4357/AA74C0},

journal = {Astrophysical Journal},

number = 2,

volume = 842,

place = {United States},

year = {Tue Jun 20 00:00:00 EDT 2017},

month = {Tue Jun 20 00:00:00 EDT 2017}

}