The host galaxy of a narrow-line Seyfert 1 galaxy RE J1034+396 with X-ray quasi-periodic oscillations

Using simple stellar population synthesis, we model the bulge stellar contribution in the optical spectrum of a narrow-line Seyfert 1 galaxy RE J1034+396. We find that its bulge stellar velocity dispersion is 67.7± 8 km s . The supermassive black hole (SMBH) mass is about (1−4)×106M⊙ if it follows the well-known MBH−σ∗ relation found in quiescent galaxies. We also derive the SMBH mass from the Hβ second moment, which is consistent with that from its bulge stellar velocity dispersion. The SMBH mass of (1 − 4) × 106M⊙ implies that the X-ray quasi-periodic oscillation (QPO) of RE J1034+396 can be scaled to a high-frequency QPO at 27-108 Hz found in Galactic black hole binaries with a 10 M⊙ black hole. With the mass distribution in different age stellar populations, we find that the mean specific star formation rate (SSFR) over past 0.1 Gyr is 0.0163 ± 0.0011 Gyr, the stellar mass in the logarithm is 10.155± 0.06 in units of solar mass, and the current star formation rate is 0.23 ± 0.016 M⊙ yr . RE J1034+396 does not follow the relation between the Eddington ratio and the SSFR suggested by Chen et al., although a larger scatter in their relation. We also suggest that about 7.0% of the total Hα luminosity and 50% of the total [O ii] luminosity come from the star formation process.