Black hole mass estimations: limitations and uncertainties

Abstract

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. Narrow-Line Seyfert 1 Galaxies and their place in the Universe

Is MgIIλ2800 a reliable virial broadening estimator for quasars?

“…radio-quiet vs. radio-loud). This situation has led to claims that FWHM measures contain little or no information about black hole mass (Croom 2011) and others arguing that FWHM measures for different lines are equally valid M BH estimators (Vestergaard et al 2011). We argue that neither of these claims is valid and that the path to a clearer picture lies within the concept of a quasar parameter space like 4DE1.…”

Systematically smaller single-epoch quasar black hole masses using a radius-luminosity relationship corrected for spectral bias

“…It is worth noting that the RM mass has an inherent uncertainty of 0.3-0.5 dex due to its calibration against the 𝑀 − 𝜎 ★ relation (Peterson 2010; Vestergaard et al 2011;Shen 2013;Ho & Kim 2014). The SE mass estimates have a 0.5-0.6 dex relative uncertainty and 0.7 dex absolute uncertainty (e.g., Table 5, .…”

The Hα Broadband Photometric Reverberation Mapping of Four Seyfert 1 Galaxies

“…RM has established an empirical relationship between the BLR size and the AGN continuum luminosity (Kaspi et al 1996(Kaspi et al , 2000Bentz et al 2006Bentz et al , 2009, R BLR ∝ L α . The theoretical prediction from the photoionization model gives α = 0.5 (Netzer 1990), which has been examined extensively by many observational campaigns (Koratkar & Gaskell 1991;Kaspi et al 1996;Wandel et al 1999;McGill et al 2008;Vestergaard et al 2011;Shen et al 2015;Grier et al 2017). However, a large number of accurate measurements of R BLR are required to reduce the scatter of the current R − L relation.…”