Estimating Black Hole Masses in Hundreds of Quasars

TL;DR

This paper demonstrates a method for estimating black hole masses in quasars using broad-band reverberation mapping, applying it to SDSS data to measure time delays and infer BLR sizes and black hole masses.

Contribution

It introduces a rigorous stochastic reverberation mapping approach for unevenly sampled multi-band flux data, enabling delay estimation and black hole mass inference from large quasar samples.

Findings

Estimated BLR sizes suggest they are 1.7 times larger than previous models.

Method successfully constrains time delays in simulated data.

Application to SDSS data yields black hole mass estimates for 323 quasars.

Abstract

We explore the practical feasibility of AGN broad-band reverberation mapping and present first results. We lay out and apply a rigorous approach for stochastic reverberation mapping of unevenly sampled multi-broad-band flux measurements, assuming that the broad-line region (BLR) line flux is contributing up to 15 % in some bands, and is directly constrained by one spectroscopical epoch. The approach describes variations of the observed flux as the continuum, modeled as a stochastic Gaussian process, and emission line contribution, modeled as a scaled, smoothed and delayed version of the continuum. This approach is capable not only to interpolate in time between measurements, but also to determine confidence limits on continuum -- line emission delays. This approach is applied to SDSS observations in 'Stripe 82' (S82) providing flux measurements precise to 2 % at $\sim$ 60 epochs over $\sim$ 10 years. The strong annual variations in the epoch sampling prove a serious limitation in practice. Also, suitable redshift ranges must be identified, where strong broad emission line contribute to one filter, but not to another. Through generating and evaluating problem-specific mock data, we verify that S82-like data can constrain $\tau_{\mathrm{delay}}$ for a simple transfer function model. In application to real data, we estimate $\tau_{\mathrm{delay}}$ for 323 AGN with $0.225 < z < 0.846$, combining information for different objects through the ensemble-scaling relationships for BLR size and BH mass. Our analysis tentatively indicates a 1.7 times larger BLR size of H$\alpha$ and MgII compared to Kaspi2000 and Vestergaard2002, but the seasonal data sampling casts doubt on the robustness of the inference.