A note on black hole masses estimated by the second moment in Narrow Line Seyfert 1 Galaxies

The second moment of the Hβ emission line is calculated for 329 narrow line Seyfert 1 galaxies (NLS1s) selected from the Sloan Digital Sky Survey (SDSS), which is used to calculate the central supermassive black hole (SMBHs) mass of each. We find that the second moment depends strongly on the broader component of the Hβ line profile. We find that for the NLS1s requiring two Gaussians to fit the Hβ line the mean value of the SMBH mass from the Hβ second moment is larger by about 0.50 dex than that from the full width at half maximum (FWHM). Using the gas velocity dispersion of the core/narrow component of [O iii] λ 5007 to estimate the stellar velocity dispersion, σ∗, the new mass makes NLS1s fall very close to the MBH −σ∗ relation for normal AGNs. By using σ∗ measured directly from SDSS spectra with a simple stellar population synthesis method, we find that for NLS1s with mass lower than 107M⊙, they fall only marginally below the MBH − σ∗ relation considering the large scatter in the mass calculation.