The Disk-Corona Model and Mass Estimates of the Ultraluminous X-ray Source Holmberg IX X-1

Abstract

The origin of the variable X-ray emission in the $(0.3-30)\,$keV energy range of ultraluminous X-ray sources (ULXs) remains unclear, making it difficult to constrain the mass of the central compact object. X-ray luminosities of bright ULXs can be explained with sub-critical accretion ($L<L_{\rm Edd}$) on to an intermediate-mass BH, with the alternative being super-critical accretion on to a stellar-mass BH. Broadband X-ray emission in the former scenario can be explained using the canonical disk plus Comptonizing corona model, whereas in the latter scenario radiation pressure driven massive winds lead to complex spectra that are inclination angle dependent. Here we fit the broadband (optical/UV to X-ray) spectrum of the persistently bright ULX Holmberg IX X-1 with the disk-corona plus irradiated outer disk model in an effort to constrain the BH mass. We use a one-zone time-dependent numerical code to exactly solve for the steady-state properties of the optically thick coronal photon-electron-positron plasma. Our modelling suggests that Holmberg IX X-1 hosts a stellar mass BH, with mass $4\lesssim(\hat M_{\rm BH}\equiv\alpha M_{\rm BH}/M_\odot)\lesssim10$ where $1/6\leq\alpha<1$ for a spinning (Kerr) BH, undergoing super-critical accretion ($L_{\rm Bol}/L_{\rm Edd}\sim20\alpha$). In our model, the X-ray spectrum below $10\,$keV is explained with an absorbed multi-colour disk spectrum having inner disk temperature $k_BT_{\rm in}\sim(2.2-2.9)\,$keV. An additional cooler thermal spectral component, as found in many works and not included in our modeling, is required. The hard excess above $10\,$keV, as seen by NuSTAR, arises in a photon-rich optically-thick Comptonizing spherical corona with optical depth $\tau_T\sim3.5$ and particle temperature $k_BT_e\sim14\,$keV.