Variable Magellanic HMXB Sources versus Variable ULX Sources: Nothing to Brag about the ULX Sources

We carry out a meta-analysis of ultraluminous X-ray (ULX) sources that show large variabilities (by factors of >10) between their highest and lowest emission states in the X-ray energy range of 0.3–10 keV. We are guided by a recent stringent compilation of 25 such X-ray sources by Song et al. We examine the relation of logN versus logSmax, where N is the number of sources radiating above the maximum-flux level Smax. We find a strong deviation from all previously determined slopes in various high-mass X-ray binary (HMXB) samples. In fact, the ULX data clearly show a slope of −0.91. Thus, ULX sources do not appear to be uniform and isotropic in our Universe. We compare the ULX results against the local X-ray luminosity function of HMXBs in the Small Magellanic Cloud (SMC) constructed from our latest library that includes 41 Chandra 0.3–8 keV sources and 56 XMM-Newton 0.2–12 keV sources. The ULX data are not drawn from the same continuous distribution as the SMC data (the ULX data peak at the low tails of the SMC distributions), and none of our data sets is drawn from a normal distribution or from a log-normal distribution (they all show marked excesses at both tails). At a significance level of α=0.05 (2σ), the two-sample p-value of the Kolmogorov–Smirnov (KS) test gives p=4.7×10−3 α, which tells us to accept H0.