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 ( \sim 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 0.42-0.47 .
Our primary results are : ( 1 ) 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 .