The long-stable hard state of XTE J1752-223 and the disk truncation dilemma

The degree to which the thin accretion disks of black hole X-ray binaries are truncated during hard spectral states remains a contentious open question in black hole astrophysics. During its singular observed outburst in $2009\text{--}2010$, the black hole X-ray binary XTE J1752-223 spent $\sim 1$~month in a long-stable hard spectral state at a luminosity of $\sim 0.02\text{--}0.1L_{\mathrm{E}\mathrm{d}\mathrm{d}}$. It was observed with 56 RXTE pointings during this period, with simultaneous Swift-XRT daily coverage during the first 10 days of the RXTE observations. Whilst reflection modeling has been extensively explored in the analysis of these data, there is a disagreement surrounding the geometry of the accretion disk and corona implied by the reflection features. We re-examine the combined, high signal-to-noise, simultaneous Swift and RXTE observations, and perform extensive reflection modeling with the latest relxill suite of reflection models, including newer high disk density models. We show that reflection modeling requires that the disk be within $\sim 5R_{\mathrm{I}\mathrm{S}\mathrm{C}\mathrm{O}}$ during the hard spectral state, whilst weaker constraints from the thermal disk emission imply higher truncation ($R_{\mathrm{i}\mathrm{n}}=6\text{--}80R_{\mathrm{I}\mathrm{S}\mathrm{C}\mathrm{O}}$). We also explore more complex coronal continuum models, allowing for two Comptonization components instead of one, and show that the reflection features still require only a mildly truncated disk. Finally we present a full comparison of our results to previous constraints found from analyses of the same dataset.