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

• Main Authors: Dimitris M. Christodoulou, Silas G. T. Laycock, Rigel Cappallo, Ankur Roy, Sayantan Bhattacharya , Demosthenes Kazanas
• Format: Article
• Language: English
• Published: MDPI AG 2020-09-01
• Series: Galaxies
• Subjects: high-mass X-ray binary (HMXB); neutron star; pulsar; ultraluminous X-ray (ULX) source; X-rays
• Online Access: https://www.mdpi.com/2075-4434/8/4/70

We carry out a meta-analysis of ultraluminous X-ray (ULX) sources that show large variabilities (by factors of > 10<inline-formula><math display="inline"><semantics><mrow><mo>></mo><mn>10</mn></mrow></semantics></math></inline-formula>) 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 log <em>N </em><inline-formula><math display="inline"><semantics><mrow><mo form="prefix">log</mo><mi>N</mi></mrow></semantics></math></inline-formula>versus log <em>S</em>_max<inline-formula><math display="inline"><semantics><mrow><mo form="prefix">log</mo><msub><mi>S</mi><mi>max</mi></msub></mrow></semantics></math></inline-formula>, where <i>N</i> is the number of sources radiating above the maximum-flux level <em>S</em>_max<inline-formula><math display="inline"><semantics><msub><mi>S</mi><mi>max</mi></msub></semantics></math></inline-formula>. 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<inline-formula><math display="inline"><semantics><mrow><mo>−</mo><mn>0</mn><mo>.</mo><mn>91</mn></mrow></semantics></math></inline-formula>. Thus, ULX sources do not appear to be uniform and isotropic in our Universe. We compare the ULX results against the local X-raud (SMC) constructed from our latest library that includes 41 <i>Chandra</i> 0.3–8 keV sources and 56 <i>XMM-Newton</i> 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<inline-formula><math display="inline"><semantics><mrow><mi>α</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>05</mn></mrow></semantics></math></inline-formula> (2σ<inline-formula><math display="inline"><semantics><mrow><mn>2</mn><mi>σ</mi></mrow></semantics></math></inline-formula>), the two-sample <i>p</i>-value of the Kolmogorov–Smirnov (KS) test gives <em>p</em> = 4.7 × 10^-3< α<inline-formula><math display="inline"><semantics><mrow><mi>p</mi><mo>=</mo><mn>4</mn><mo>.</mo><mn>7</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup><mo><</mo><mi>α</mi></mrow></semantics></math></inline-formula> for the ULX versus the small <i>Chandra</i> sample and <em>p </em>= 1.1 × 10^-5<< α <inline-formula><math display="inline"><semantics><mrow><mi>p</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup><mo><</mo><mo><</mo><mi>α</mi></mrow></semantics></math></inline-formula>for the ULX versus the larger <i>XMM-Newton</i> 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 <em>H</em>₀<inline-formula><math display="inline"><semantics><msub><mi>H</mi><mn>0</mn></msub></semantics></math></inline-formula>): at the <inline-formula><math display="inline"><semantics><mrow><mi>α</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>05</mn></mrow></semantics></math></inline-formula> significance level, the two-sample KS test shows an asymptotic <i>p</i>-value of 0.308 > α<inline-formula><math display="inline"><semantics><mrow><mn>0</mn><mo>.</mo><mn>308</mn><mo>></mo><mi>α</mi></mrow></semantics></math></inline-formula>, which tells us to accept <em>H</em>₀<inline-formula><math display="inline"><semantics><msub><mi>H</mi><mn>0</mn></msub></semantics></math></inline-formula>.