The dependence of the estimated luminosities of ULX on spectral models

Data from {\it Chandra} observations of thirty nearby galaxies were analyzed and 365 X-ray point sources were chosen whose spectra were not contaminated by excessive diffuse emission and not affected by photon pile up. The spectra of these sources were fitted using two spectral models (an absorbed power-law and a disk blackbody) to ascertain the dependence of estimated parameters on the spectral model used. It was found that the cumulative luminosity function depends on the choice of the spectral model, especially for luminosities $> 10^{40}$ergs\mathrm{/}s\mathrm{.}Inaccordancewithpreviousresults,alargenumber($\sim 80$)ofthesourceshaveluminosities$> 10^{39}$ ergs/s (Ultra-Luminous X-ray sources) with indistinguishable average spectral parameters (inner disk temperature $\sim 1$ keV and/or photon index $\mathrm{\Gamma }\sim 2$) with those of the lower luminosities ones. After considering foreground stars and known background AGN,we identify four sources whose minimum luminosity exceed ${10}^{40}$ ergs/s, and call them Extremely Luminous X-ray sources (ELX). The spectra of these sources are in general better represented by the disk black body model than the power-law one. These ELX can be grouped into two distinct spectral classes. Two of them have an inner disk temperature of $<0.5$ keV and hence are called supersoft'' ELX, while the other two have temperatures $\gtrsim 1.3$ keV and are called hard’’ ELX. The estimated inner disk temperatures of the supersoft ELX are compatible with the hypothesis that they harbor intermediate size black holes, which are accreting at $\sim 0.5$ times their Eddington Luminosity. The radiative mechanism for hard ELX, seems to be Inverse Comptonization, which in contrast to standard black holes systems, is probably saturated.