Long-term Spectral Variability of the Ultra-luminous X-ray source Holmberg IX X--1

We investigate the long-term spectral variability in the ultra-luminous X-ray source Holmberg IX X--1. By analyzing the data from eight {\it Suzaku} and 13 {\it XMM-Newton} observations conducted between 2001 and 2015, we perform a detailed spectral modeling for all spectra with simple models and complex physical models. We find that the spectra can be well explained by a disc plus thermal Comptonization model. Applying this model, we unveil correlations between the X-ray luminosity ($L_{\rm X}$) and the spectral parameters. Among the correlations, a particular one is the statistically significant positive correlation between $L_{\rm X}$ and the photon index ($\Gamma$), while at the high luminosities of $> 2\times10^{40}\,{\rm~erg\ s}^{-1}$, the source becomes marginally hard and that results a change in the slope of the $\Gamma - L_{\rm X}$ correlation. Similar variability behavior is observed in the optical depth of the source around $L_{\rm X} \sim 2\times10^{40}\,{\rm~erg\ s}^{-1}$ as the source becomes more optically thick. We consider the scenario that a corona covers the inner part of the disc, and the correlations can be explained as to be driven by the variability of seed photons from the disc input into the corona. On the basis of the disc-corona model, we discuss the physical processes that are possibly indicated by the variability of the spectral parameters. Our analysis reveals the complex variability behavior of Holmberg IX X--1 and the variability mechanism is likely related to the geometry of the X-ray emitting regions.