Black hole mass estimations: Limitations and uncertainties

Mass scaling relations are a powerful tool for estimating virial masses of the central supermassive black holes that power distant quasars and active galactic nuclei owing in part to the relative ease with which they can be applied to large catalogs of spectral data. There is a large suite of mass scaling relations available in the literature, based on the three main broad emission lines: Hβ , Mg II, and C IV. We summarize some of the issues to be aware of when choosing and using these relations, including those of special interest to Narrow Line Seyfert 1 galaxy studies. In particular, we advocate using high-quality spectral data and multiple emission lines for the most accurate mass estimates. In the literature certain scaling relations, including that based on C IV, are claimed to be unreliable. We show results indicating that all of the three broad lines (Hβ , Mg II, or C IV) exhibit issues suggesting that none of them are more accurate mass estimators than the others. Only by using as many broad lines as possible can we hope to even out the slight deviations introduced by the individual lines. Denney et al. (these proceedings) provide convincing evidence against the use of low-quality data for mass estimates. We present additional evidence, including extensive simulations, that low-quality data is most likely to bias our mass estimates which can be quite significant for narrow-lined sources like NLS1s. Finally, we present results based on Bayesian statistical analysis of the SDSS DR3 luminosity and mass function sample which shows that the peak of the estimated Eddington luminosity ratios (L_BOL/L_Edd) distribution will be overestimated and the distribution width underestimated unless the intrinsic uncertainties in the mass estimates and survey incompleteness are accounted for.