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Using all the archival XMM-Newton X-ray (3-10 keV) observations of theultraluminous X-ray source (ULX) M82 X-1 we searched for a correlation betweenits variable mHz quasi-periodic oscillation (QPO) frequency and its hardnessratio (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 theenergy spectral index. The detection of such a correlation would strengthen theidentification of M82 X-1's mHz QPOs as Type-C and enable a more reliable massestimate by scaling its QPO frequencies to those of Type-C QPOs in StMBHs ofknown mass. We resolved the count rates and the hardness ratios of M82 X-1 anda nearby bright ULX (source 5/X42.3+59) through surface brightness modeling. Wedetected QPOs in the frequency range of 36-210 mHz during which M82 X-1'shardness ratio varied from 0.42-0.47. Our primary results are: (1) we do notdetect any correlation between the mHz QPO frequency and the hardness ratio (asubstitute for the energy spectral power-law index) and (2) similar to someaccreting X-ray binaries, we find that M82 X-1's mHz QPO frequency increaseswith its X-ray count rate (Pearson's correlation coefficient = +0.97). Theapparent lack of a correlation between the QPO centroid frequency and thehardness ratio poses a challenge to the earlier claims that the mHz QPOs of M82X-1 are the analogs of the Type-C low-frequency QPOs of StMBHs. On the otherhand, it is possible that the observed relation between the hardness ratio andthe QPO frequency represents the saturated portion of the correlation seen inType-C QPOs of StMBHs -- in which case M82 X-1's mHz QPOs can still beanalogous to Type-C QPOs.

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