Constraining the Kerr parameters via x-ray reflection spectroscopy

In a recent paper [Ghasemi-Nodehi and Bambi, Eur. Phys. J. C 76, 290 (2016)], we have proposed a new parametrization for testing the Kerr nature of astrophysical black hole candidates. In the present work, we study the possibility of constraining the “Kerr parameters” of our proposal using x-ray reflection spectroscopy, the so-called iron line method. We simulate observations with the LAD instrument on board of the future eXTP mission assuming an exposure time of 200 ks. We fit the simulated data to see if the Kerr parameters can be constrained. If we have the correct astrophysical model, 200 ks observations with LAD/eXTP can constrain all the Kerr parameters with the exception of $b_{11}$, whose impact on the iron line profile is extremely weak and its measurement looks very challenging.

Figure 1

Impact of the parameters $b_2$ (top left panel), $b_4$ (top right panel), $b_5$ (central left panel), $b_7$ (central right panel), $b_8$ (bottom left panel), and $b_9$ (bottom right panel) on the shape of the iron line. The flux of the photon number is in arbitrary units. See the text for more details.

Figure 2

As in Fig. 1 for the parameters $b_{10}$ (left panel) and $b_{11}$ (right panel).

Figure 3

Folded spectrum (top panel) and ratio between the simulated data and the best fit (bottom panel) for the simulation of a Kerr black hole with spin parameter $a_{*}=0.8$ and observed from a viewing angle $i=55°$. The minimum of the reduced ${\chi }^2$ is about 0.99. See the text for more details.

Figure 4

Top left panel: As in Fig. 3 for a background metric with $b_2=1.2$ and all other Kerr parameters set to 1. The minimum of the reduced ${\chi }^2$ is about 1.63. Top right panel: As in Fig. 3 for a background metric with $b_4=1.2$ and all other Kerr parameters set to 1. The minimum of the reduced ${\chi }^2$ is about 2.16. Bottom left panel: As in Fig. 3 for a background metric with $b_5=1.2$ and all other Kerr parameters set to 1. The minimum of the reduced ${\chi }^2$ is about 1.16. Bottom right panel: As in Fig. 3 for a background metric with $b_7=1.2$ and all other Kerr parameters set to 1. The minimum of the reduced ${\chi }^2$ is about 1.90. See the text for more details.

Figure 5

Top left panel: As in Fig. 3 for a background metric with $b_8=1.2$ and all other Kerr parameters set to 1. The minimum of the reduced ${\chi }^2$ is about 1.17. Top right panel: As in Fig. 3 for a background metric with $b_9=1.2$ and all other Kerr parameters set to 1. The minimum of the reduced ${\chi }^2$ is about 2.19. Bottom left panel: As in Fig. 3 for a background metric with $b_{10}=1.2$ and all other Kerr parameters set to 1. The minimum of the reduced ${\chi }^2$ is about 2.57. Bottom right panel: As in Fig. 3 for a background metric with $b_{11}=5$ and all other Kerr parameters set to 1. The minimum of the reduced ${\chi }^2$ is about 1.06. See the text for more details.