Testing the Kerr metric using X-ray reflection spectroscopy: spectral analysis of GX 339-4

Signatures of X-ray reprocessing (reflection) out of an accretion disk are commonly observed in the high-energy spectrum of accreting black holes, and can be used to probe the strong gravity region around these objects. In this paper, we extend previous work in the literature and we employ a full emission model for relativistic reflection in non-Kerr spacetime to demonstrate an approach that tests the Kerr black hole hypothesis. We analyze a composite spectrum obtained with the Proportional Counter Array in the Rossi X-ray Timing Explorer (RXTE), of the stellar-mass black hole GX 339-4 in its brightest hard state. With a remarkable sensitivity of ~0.1% and 40 million counts in the 3-45 keV band to capture the faint features in the reflection spectrum, we demonstrate that it is possible with existing data and an adequate model to place constraints on the black hole spin $a_*$ and the deformation parameter that quantifies the departure from the Kerr metric. Our measurement obtained with the best fit model, which should be regarded as principally a proof of concept, is $a_*=0.92^{+0.07}_{-0.12}$ and $\alpha_{13}=-0.76^{+0.78}_{-0.60}$ with a 90% confidence level and is consistent with the hypothesis that the compact object in GX 339-4 is a Kerr black hole. We also discuss how the physical model choice and the emissivity profile adopted could make an impact on the constraints of $\alpha_{13}$ and spin. To enable Kerr metric test using X-ray reflection spectroscopy, it is essential to improve our astrophysical understanding of accreting black holes, e.g., the natures of accretion flow and corona.