Reflection Modeling of the Black Hole Binary 4U~1630$-$47: the Disk Density and Returning Radiation.

We present the analysis of X-ray observations of the black hole binary 4U~1630$-$47 using relativistic reflection spectroscopy. We use archival data from the RXTE, Swift, and NuSTAR observatories, taken during different outbursts of the source between $1998$ and $2015$. Our modeling includes two relatively new advances in modern reflection codes: high-density disks, and returning thermal disk radiation. Accretion disks around stellar-mass black holes are expected to have densities well above the standard value assumed in traditional reflection models (i.e., $n_{\rm e}\sim10^{15}~{\rm cm^{-3}}$). New high-density reflection models have important implications in the determination of disk truncation (i.e., the disk inner radius). This is because one must retain self-consistency in the irradiating flux and corresponding disk ionization state, which is a function of disk density and system geometry. We find the disk density is $n_{\rm e}\ge10^{20}~{\rm cm^{-3}}$ across all spectral states. This density, combined with our constraints on the ionization state of the material, implies an irradiating flux impinging on the disk that is consistent with the expected theoretical estimates. Returning thermal disk radiation -- the fraction of disk photons which bend back to the disk producing additional reflection components -- is expected predominantly in the soft state. We show that returning radiation models indeed provide a better fit to the soft state data, reinforcing previous results which show that in the soft state the irradiating continuum may be blackbody emission from the disk itself.