Reflection Spectroscopy of the Black Hole Binary XTE J1752-223 in Its Long-stable Hard State

We present a detailed spectral analysis of the black hole binary XTE J1752-223. in the hard state of its 2009 outburst. Regular monitoring of this source by the Rossi X-ray Timing Explorer mission provided high signal-to-noise spectra along the outburst rise and decay. During one full month this source stalled at similar to 30% of its peak count rate at a constant hardness and intensity. By combining all the data in this exceptionally stable hard state, we obtained an aggregate proportional counter array spectrum (3-45 keV) with 100. million counts, and a corresponding high energy X-ray timing experiment spectrum (20-140 keV) with 5.8. million counts. Implementing a version of our reflection code with a physical model for Comptonization, we obtain tight constraints on important physical parameters for this system. In particular, the inner accretion disk is measured very close in, at R-in =1.7 +/- 0.4 R-g. Assuming R-in = R-ISCO, we find a relatively high black hole spin (a* = 0.92 +/- 0.06). Imposing a lamppost geometry, we obtain a low inclination (i = 35 degrees +/- 4 degrees), which agrees with the upper limit found in the radio (i < 49 degrees). However, we note that this model cannot be statistically distinguished from a non-lamppost model with a free emissivity index, for which the inclination is markedly higher. Additionally, we find a relatively cool corona (57-70 keV) and large iron abundance (3.3-3.7 solar). We further find that properly accounting for Comptonization of the reflection emission improves the fit significantly and causes an otherwise low reflection fraction (similar to 0.2-0.3) to increase by an order of magnitude, in line with geometrical expectations for a lamppost corona. We compare these results with similar investigations reported for GX 339-4. in its bright hard state.