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Probing the near-horizon region of Cygnus X-1 with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mi>u</mml:mi><mml:mi>z</mml:mi><mml:mi>a</mml:mi><mml:mi>k</mml:mi><mml:mi>u</mml:mi></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi><mml:mi>u</mml:mi><mml:mi>S</mml:mi><mml:mi>T</mml:mi><mml:mi>A</mml:mi><mml:mi>R</mml:mi></mml:math>

Zuobin ZhangCenter for Field Theory and Particle Physics and Department of Physics, Fudan University, 200438 Shanghai, ChinaH. LiuCenter for Field Theory and Particle Physics and Department of Physics, Fudan University, 200438 Shanghai, ChinaAskar B. AbdikamalovCenter for Field Theory and Particle Physics and Department of Physics, Fudan University, 200438 Shanghai, ChinaDimitry AyzenbergTheoretical Astrophysics, Eberhard-Karls Universität Tübingen, D-72076 Tübingen, GermanyCosimo BambiCenter for Field Theory and Particle Physics and Department of Physics, Fudan University, 200438 Shanghai, ChinaMenglei ZhouInstitut für Astronomie und Astrophysik, Eberhard-Karls Universität Tübingen, D-72076 Tübingen, Germany
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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 ${\ensuremath{\alpha}}_{13}$. 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.

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