Abstract
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 for the ULX versus the small Chandra sample and p=1.1×10−5<<α for the ULX versus the larger XMM-Newton sample, respectively. This adds to the evidence that ULX sources are not simply the higher end of the known local Be/X-ray pulsar distribution, but they represent a class of X-ray sources different from the young sources found in the SMC and in individual starburst galaxies. On the other hand, our two main SMC data sets are found to be statistically consistent, as they are drawn from the same continuous parent distribution (null hypothesis H0): at the α=0.05 significance level, the two-sample KS test shows an asymptotic p-value of 0.308>α, which tells us to accept H0.
Highlights
We revisit a new data set of strongly variable ultraluminous X-ray (ULX) sources that was produced by Song et al [1], and we compare these data (Table 1) statistically to the distribution ofBe/X-ray sources produced by our latest library for theSmall Magellanic Cloud (SMC) (Tables 1 and 2 below)
Table 3), we conclude that the flux/luminosity function of variable ULX sources with slope −0.91 is different than that of pure SMC XMHB sources and that the ULX sources do not appear to be the high end of known nearby high-mass X-ray binary (HMXB) with slopes of ≈ −0.4
Maximum X-ray fluxes (36 from XMM-Newton data and 22 from Chandra data; a combination of Tables 1 and 2) and the best-fit slope at intermediate flux values turns out to be −0.3939 ± 0.0195(1σ ), in better agreement with the findings of Reference [25] for pure HMXB sources. In this least-squares fit, we find that r = −0.9915 and that p = 0.0315 (Table 3), so our conclusions appear to be statistically solid for the combined SMC HMXB sample 4, and they are in good agreement with previous results from the SMC
Summary
We revisit a new data set of strongly variable ultraluminous X-ray (ULX) sources that was produced by Song et al [1], and we compare these data (Table 1) statistically to the distribution of. It has been argued by some groups that ULX sources appear to be so powerful because they are beaming in the direction of the observer [22,23,35,36,37], clearly a selection effect If this is the case, their log N-log S diagram should show a strong deviation from the theoretical Euclidean line with slope −3/2 and from the SMC log N-log S best-fit lines whose slopes fall consistently in the range of −(0.37–0.6) [25], where −0.37 is the slope of the securely identified SMC HMXBs and −0.6 is the mean slope of the examined “AGN-contaminated” samples.
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