A Limit Relation between Black Hole Mass and H Width: Testing Super-Eddington Accretion in Active Galactic Nuclei

Abstract

We show that there is a limit relation between the black hole mass (MBH) and the width at half-maximum (υFWHM) of Hβ for active galactic nuclei (AGNs) with super-Eddington accretion rates. When a black hole has a super-Eddington accretion rate, the empirical relation derived from reverberation mapping can be applied in two possible ways. First, it reduces to a relation between the black hole mass and the size of the broad-line region because of photon-trapping effects inside the accretion disk. For the empirical reverberation relation of Kaspi et al., we obtain the limit relation MBH = (2.9–12.6) × 106 [vFWHM/(103 km s-1)]6.67M⊙, called the Eddington limit. Second, the Eddington limit luminosity will be relaxed if the trapped photons can escape from the magnetized super-Eddington accretion disk via the photon bubble instability, and the size of the broad-line region will be enlarged according to the empirical reverberation relation, leading to a relatively narrow Hβ width. We call this the Begelman limit. Using this limit relation, we searched 164 AGNs for super-Eddington accretion. We find that most of them are well confined by the Eddington limit relation—that is, most have sub-Eddington accretion rates—but there are a handful of objects located between the Eddington and Begelman limit lines; they may be candidate super-Eddington accretors in a hybrid structure of photon trapping and photon bubble instability. The maximum Hβ width is in the range (3.0–3.8) × 10 3 km s-1 for the most massive black holes with super-Eddington accretion rates among AGNs. We suggest that the FWHM(Hβ)-MBH relation is a reliable and convenient method to test whether a source is super-Eddington and useful to probe the structure of the super-Eddington accretion process.