Probing the near-horizon region of Cygnus X-1 with $Suzaku$ and $NuSTAR$

Astrophysical black holes are ideal laboratories for testing Einstein’s theory of general relativity in the strong field regime. In this manuscript, we present an analysis of $Suzaku$ and $NuSTAR$ spectra of the black hole binary Cygnus X-1 using relxill_nk. Unlike our previous study on Cygnus X-1 with $NuSTAR$ data, here we are able to constrain the Johannsen deformation parameter ${\alpha }_{13}$. However, despite the high energy resolution near the iron line provided by $Suzaku$, our constraints on the Kerr metric from Cygnus X-1 are not very stringent in comparison with those that have been obtained from other sources, confirming that Cygnus X-1 is quite a complicated source.

Figure 1

The upper quadrant shows the spectrum of Cygnus X-1 in epoch 1 as seen by $\mathrm{XIS}0+\mathrm{XIS}3$ (black), PIN (red) and GSO (green). The spectrum is fitted with an absorbed power law ignoring the data below 3 keV, the 5–7 keV band, and the 15–45 keV band. The data to the best-fit model ratio is shown in the lower quadrant. The data have been rebinned for visual clarity.

Figure 2

Data to best-fit model ratios for models 1A and 1B (top panels), models 2A and 2B (central panels), and models 3A and 3B (bottom panels). For every model, we show the results from the fit with ${\alpha }_{13}=0$ and from the fit with ${\alpha }_{13}$ free.

Figure 3

Constraints on the spin parameter $a_{*}$ and the Johannsen deformation parameters ${\alpha }_{13}$ for models 1A and 1B (top panels), models 2A and 2B (central panels), and models 3A and 3B (bottom panels). The red, green, and blue curves are, respectively, the 68%, 90%, and 99% confidence level boundaries for two relevant parameters. The gray region is ignored in our analysis because the spacetime is not regular there.

Figure 4

Data to best-fit model ratios for models 4A and 4B ($NuSTAR$ data of epoch 2). For every model, we show the results from the fit with ${\alpha }_{13}=0$ and from the fit with ${\alpha }_{13}$ free.

Figure 5

Constraints on the spin parameter $a_{*}$ and the Johannsen deformation parameters ${\alpha }_{13}$ for models 4A and 4B ($NuSTAR$ data of epoch 2). The red, green, and blue curves are, respectively, the 68%, 90%, and 99% confidence level boundaries for two relevant parameters. The gray region is ignored in our analysis because the spacetime is not regular there.

Figure 6

Data to best-fit model ratios for models 5A and 5B ($Suzaku$ data of epoch 2). For every model, we show the results from the fit with ${\alpha }_{13}=0$ and from the fit with ${\alpha }_{13}$ free.

Figure 7

Constraints on the spin parameter $a_{*}$ and the Johannsen deformation parameters ${\alpha }_{13}$ for models 5A and 5B ($Suzaku$ data of epoch 2). The red, green, and blue curves are, respectively, the 68%, 90%, and 99% confidence level boundaries for two relevant parameters. The gray region is ignored in our analysis because the spacetime is not regular there.

Figure 8

Data to best-fit model ratios for model 6 ($NuSTAR+Suzaku$ data of epoch 2). The emissivity profile is modeled with broken power law with $q_{\mathrm{out}}=3$.

Figure 9

Constraints on the spin parameter $a_{*}$ and the Johannsen deformation parameters ${\alpha }_{13}$ for model 6 ($NuSTAR+Suzaku$ data of epoch 2). The emissivity profile is modeled with a broken power law with outer emissivity index frozen to 3. The red, green, and blue curves are, respectively, the 68%, 90%, and 99% confidence level boundaries for two relevant parameters.