Testing the Kerr hypothesis using x-ray reflection spectroscopy with NuSTAR data of Cygnus X-1 in the soft state

We continue exploring the constraining capabilities of x-ray reflection spectroscopy to test the Kerr-nature of astrophysical black holes, and we present the results of our analysis of two NuSTAR observations of Cygnus X-1 in the soft state. We find that the final measurement can strongly depend on the assumption of the intensity profile. We conclude that Cygnus X-1 is not suitable for tests of general relativity using x-ray reflection spectroscopy, and we discuss the desired properties of a source to be a good candidate for our studies.

Figure 1

Constraints on the spin parameter $a_{*}$ and the Johannsen deformation parameters ${\alpha }_{13}$ (left panel) and ${\alpha }_{22}$ (right panel) from epoch 1. The emissivity profile is modeled with a power-law (top panels), a broken power-law with outer emissivity index frozen to 3 (central panels), and a broken power-law with both emissivity indices free (bottom panels). The red, green, and blue curves are, respectively, the 68%, 90%, and 99% confidence level boundaries for two relevant parameters.

Figure 2

Constraints on the spin parameter $a_{*}$ and the Johannsen deformation parameters ${\alpha }_{13}$ (left panel) and ${\alpha }_{22}$ (right panel) from epoch 4. The emissivity profile is modeled with a power-law (top panels), a broken power-law with outer emissivity index frozen to 3 (central panels), and a broken power-law with both emissivity indices free (bottom panels). The red, green, and blue curves are, respectively, the 68%, 90%, and 99% confidence level boundaries for two relevant parameters.

Figure 3

Ratio plots for epoch 1 (left panel) and epoch 4 (right panel). The emissivity profile is modeled with a power-law.

Figure 4

Best-fit models and ratio plots for epoch 1 (left panel) and epoch 4 (right panel), assuming ${\alpha }_{13}={\alpha }_{22}=0$ (Kerr metric, top panels), ${\alpha }_{13}$ free and ${\alpha }_{22}=0$ (central panels), and ${\alpha }_{13}=0$ and ${\alpha }_{22}$ free (bottom panels). The emissivity profile is modeled with a broken power-law with outer emissivity index frozen to 3.

Figure 5

Ratio plots for epoch 1 (left panel) and epoch 4 (right panel). The emissivity profile is modeled with a broken power-law with both emissivity indices free.

Figure 6

Output distribution of the MCMC analysis for epoch 1. The contours correspond to 1-, 2-, and $3\text{−}\sigma$ confidence level curves. Note that here $N_{\mathrm{H}}$ and $z$ refer, respectively, to the column density and the observed redshift of the absorber in xstar [$1+z=\sqrt{(1-\beta )/(1+\beta )}$, where $\beta =v_{\mathrm{out}}/c$].

Figure 7

Output distribution of the MCMC analysis for epoch 4. The contours correspond to 1-, 2-, and $3\text{−}\sigma$ confidence level curves. Note that here $N_{\mathrm{H}}$ and $z$ refer, respectively, to the column density and the observed redshift of the absorber in xstar [$1+z=\sqrt{(1-\beta )/(1+\beta )}$, where $\beta =v_{\mathrm{out}}/c$].

Figure 8

Constraints on the spin parameter $a_{*}$ and the deformation parameter ${\alpha }_{13}$ from the analysis with MCMC simulations for the spectra of epoch 1 (left panel) and epoch 4 (right panel). The red, green, and blue lines correspond to 1-, 2-, and $3\text{−}\sigma$ confidence level curves, respectively.