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 RXTE provided high signal-to-noise spectra along the outburst rise and decay .
During one full month this source stalled at \sim 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 PCA spectrum ( 3–45 keV ) with 100 million counts , and a corresponding HEXTE 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 _ { \mathrm { in } } = 1.7 \pm 0.4 R _ { g } .
Assuming R _ { \mathrm { in } } = R _ { \mathrm { ISCO } } , we find a relatively high black hole spin ( a _ { * } = 0.92 \pm 0.06 ) .
Imposing a lamppost geometry , we obtain a low inclination ( i = 35 \pm 4 deg ) , which agrees with the upper limit found in the radio ( i < 49 deg ) .
However , we note that this model can not be statistically distinguished from a non-lamppost model with 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 ( \sim 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 .