Does the disk in the hard state of XTE J1752-223 extend to the innermost stable circular orbit?

The accreting black-hole binary XTE J1752--223 was observed in a stable hard state for 25 d by RXTE, yielding a 3--140 keV spectrum of unprecedented statistical quality. Its published model required a single Comptonization spectrum reflecting from a disk close to the innermost stable circular orbit. We studied that model as well as a number of other single-Comptonization models (yielding similarly low inner radii), but found they violate a number of basic physical constraints, e.g., their compactness is much above the maximum allowed by pair equilibrium. We also studied the contemporaneous 0.55--6 keV spectrum from the Swift/XRT and found it well fitted by an absorbed power law and a disk blackbody with the innermost temperature of 0.1 keV. The normalization of the disk blackbody corresponds to an inner radius of $gtrsim$20 gravitational radii and its temperature, to irradiation of the truncated disk by a hot inner flow. We have also developed a Comptonization/reflection model including the disk irradiation and intrinsic dissipation, but found that it does not yield any satisfactory fits. On the other hand, we found that the $leq$10 keV band from RXTE is much better fitted by a reflection from a disk with the inner radius $gtrsim$100 gravitational radii, which model then underpredicts the spectrum at $>$10 keV by $<$10%. We argue that the most plausible explanation of the above results is inhomogeneity of the source, with the local spectra hardening with the decreasing radius. Our results support the presence of a complex Comptonization region and a large disk truncation radius in this source.