The X-ray spectra of the most extreme ultra-luminous X-ray sources -- those with L > 1 E+40 erg/s -- remain something of a mystery. Spectral roll-over in the 5-10 keV band was originally detected in in the deepest XMM-Newton observations of the brightest sources; this is confirmed in subsequent NuSTAR spectra. This emission can be modeled via Comptonization, but with low electron temperatures (kT_e ~ 2 keV) and high optical depths (tau ~ 10) that pose numerous difficulties. Moreover, evidence of cooler thermal emission that can be fit with thin disk models persists, even in fits to joint XMM-Newton and NuSTAR observations. Using NGC 1313 X-1 as a test case, we show that a patchy disk with a multiple temperature profile may provide an excellent description of such spectra. In principle, a number of patches within a cool disk might emit over a range of temperatures, but the data only require a two-temperature profile plus standard Comptonization, or three distinct blackbody components. A mechanism such as the photon bubble instability may naturally give rise to a patchy disk profile, and could give rise to super-Eddington luminosities. It is possible, then, that a patchy disk (rather than a disk with a standard single-temperature profile) might be a hallmark of accretion disks close to or above the Eddington limit. We discuss further tests of this picture, and potential implications for sources such as narrow-line Seyfert-1 galaxies (NLSy1s) and other low-mass active galactic nuclei (AGN).
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