Evidence for High-Frequency QPOs with a 3:2 Frequency Ratio from a 5000 Solar Mass Black Hole

Following the discovery of 3:2 resonance quasi-periodic oscillations (QPOs) in M82X-1 (Pasham et al. 2014), we have constructed power density spectra (PDS) of all 15 (sufficiently long) {\it XMM-Newton} observations of the ultraluminous X-ray source NGC1313X-1 ($L_{X}$ $\approx$ 2$\times$10$^{40}$ erg/sec). We detect a strong QPO at a frequency of 0.29$\pm$0.01 Hz in data obtained on 2012 December 16. Subsequent searching of all the remaining observations for a 3:2/2:3 frequency pair revealed a feature at 0.46$\pm$0.02 Hz on 2003 Dec 13 (frequency ratio of 1.59$\pm$0.09). The global significance of the 0.29 Hz feature considering all frequencies between 0.1 and 4 Hz is $>$ 3.5 $\sigma$. The significance of the 0.46$\pm$0.02 Hz QPO is $>$ 3.5$\sigma$ for a search at 2/3 and 3/2 of 0.29 Hz. We also detect lower frequency QPOs (32.9$\pm$2.6 and 79.7$\pm$1.2 mHz). All the QPOs are super-imposed on a continuum consisting of flat-topped, band-limited noise, breaking into a power-law at a frequency of 16$\pm$3 mHz and white noise at $\gtrsim$ 0.1 Hz. NGC1313X-1's PDS is analogous to stellar-mass black holes' (StMBHs) PDS in the so-called steep power-law state, but with the respective frequencies (both QPOs and break frequencies) scaled down by a factor of $\sim$ 1000. Using the inverse mass-to-high-frequency QPO scaling of StMBHs, we estimate NGC1313X-1's black hole mass to be 5000$\pm$1300 $M_{\odot}$, consistent with an inference from the scaling of the break frequency. However, the implied Eddington ratio, L$_{Edd}$ $>$ 0.03$\pm$0.01, is significantly lower compared to StMBHs in the steep power-law state (L$_{Edd}$ $\gtrsim$ 0.2).