Constraining the Johannsen deformation parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>ε</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> with black hole x-ray data

We extend our previous work on tests of the Kerr black hole hypothesis using x-ray reflection spectroscopy and we infer observational constraints on the Johannsen deformation parameter ${\ensuremath{\epsilon}}_{3}$. We analyze a NuSTAR observation of the stellar-mass black hole in GS 1354--645, Suzaku data of the supermassive black holes in Ark 564, 1H0419--577, and PKS 0558--504, and some simultaneous XMM-Newton and NuSTAR observations of the supermassive black hole in MCG--6--30--15. All our measurements of ${\ensuremath{\epsilon}}_{3}$ are consistent with the Kerr metric and we find quite strong constraints from Ark 564 and MCG--6--30--15. We discuss the implications of our results and the next steps to improve our tests.

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