2010MNRAS.401..507B

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)x10⁶ M_☉ if it follows the well-known M_BH-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)x10⁶ M_☉ 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 the 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. For RE J1034+396, there is no relation between the Eddington ratio and the SSFR as suggested by Chen et al., despite a larger scatter in their relation. We also suggest that about 7.0 per cent of the total Hα luminosity and 50 per cent of the total [Oii] luminosity come from the star formation process.