Black hole mass estimation using X-ray variability measurements in Seyfert galaxies

¹ Institute for Astronomy Astrophysics Space Applications and Remote Sensing (IAASARS), National Observatory of Athens, I. Metaxa & V. Pavlou, Penteli 15236, Greece
e-mail: aakylas@noa.gr
² Department of Physics and Institute of Theoretical and Computational Physics, University of Crete, 71003 Heraklion, Greece
³ Institute of Astrophysics – FORTH, N. Plastira 100, 70013 Vassilika Vouton, Greece

Received: 1 June 2022
Accepted: 4 August 2022

Abstract

Aims. Our objective is to critically assess the X-ray flux variability as a tool for measuring the black hole (BH) mass in active galactic nuclei (AGN). We aim to establish a prescription for estimating BH masses based on measurements of the normalised excess variance from X-ray data. We discuss the minimum requirements in terms of the light-curve duration and X-ray signal-to-noise ratio (S/N) to enable a reliable determination that is comparable to what can be derived from the continuum and emission line reverberation studies.

Methods. We used the light curves of local Seyfert from the Nuclear Spectroscopic Telescope Array hard X-ray mission (NuSTAR), to compute the normalised excess variance (σ_NXV²) in the 3–10 and 10–20 keV bands, thus extending the analysis to an energy band higher than 10 keV. The excess variance measurements were then combined with independent BH mass estimates from the literature to establish the M_BH vs. σ_NXV² relation for different samples and weigh its accuracy in terms of the light-curve duration and X-ray S/N.

Results. We find that it is possible to accurately measure the BH mass in AGN using excess variance measurements in the 3–10 and the 10–20 keV bands, however, strong quality requirements should be applied. The minimum necessary S/N and duration of the light curves used to compute the excess variance ought to be ∼3 and ∼80 − 100 ks, respectively. We provide a linear relationship between the normalised excess variance and the black hole mass that can be used to estimate the latter, with an average uncertainty of the order of 0.4 − 0.25 dex (depending on the adopted light-curve segment duration). In general, BH mass estimates from 3–10 keV and 10–20 keV band light curves are expected to be similar. The 10–20 keV band is preferred for sources that are heavily absorbed and the 3–10 keV band is preferred for sources that may be dominated by the X-ray reflection component at energies above 10 keV.