On the Nature of the mHz X-Ray Quasi-periodic Oscillations from Ultraluminous X-Ray Source M82 X-1: Search for Timing-Spectral Correlations

Using all the archival XMM-Newton X-ray (3-10 keV) observations of the ultraluminous X-ray source (ULX) M82 X-1, we searched for a correlation between its variable mHz quasi-periodic oscillation (QPO) frequency and its hardness ratio (5-10 keV/3-5 keV), an indicator of the energy spectral power-law index. When stellar-mass black holes (StMBHs) exhibit type-C low-frequency QPOs (~0.2-15 Hz), the centroid frequency of the QPO is known to correlate with the energy spectral index. The detection of such a correlation would strengthen the identification of M82 X-1's mHz QPOs as type-C and enable a more reliable mass estimate by scaling its QPO frequencies to those of type-C QPOs in StMBHs of known mass. We resolved the count rates and the hardness ratios of M82 X-1 and a nearby bright ULX (source 5/X42.3+59) through surface brightness modeling. We detected QPOs in the frequency range of 36-210 mHz during which M82 X-1's hardness ratio varied from 0.42 to 0.47. Our primary results are (1) that we do not detect any correlation between the mHz QPO frequency and the hardness ratio (a substitute for the energy spectral power-law index) and (2) similar to some accreting X-ray binaries, we find that M82 X-1's mHz QPO frequency increases with its X-ray count rate (Pearson's correlation coefficient = +0.97). The apparent lack of a correlation between the QPO centroid frequency and the hardness ratio poses a challenge to the earlier claims that the mHz QPOs of M82 X-1 are the analogs of the type-C low-frequency QPOs of StMBHs. On the other hand, it is possible that the observed relation between the hardness ratio and the QPO frequency represents the saturated portion of the correlation seen in type-C QPOs of StMBHs—in which case M82 X-1's mHz QPOs can still be analogous to type-C QPOs.