A Non-parametric Approach to Constrain the Transfer Function in Reverberation Mapping

Abstract

Broad emission lines of active galactic nuclei stem from a spatially extended region (broad-line region; BLR) that are composed of discrete clouds and photoionized by the central ionizing continuum. The temporal behaviors of these emission lines are blurred echoes of the continuum variations (i.e., reverberation mapping; RM) and directly reflect structures and kinematics information of BLRs through the so-called transfer function (also known as velocity-delay map). Based on the previous works of Rybicki & Press (1992) and Zu et al. (2011), we develop an extended, non-parametric approach to determine the transfer function for RM data, in which the transfer function is expressed as a sum of a family of relatively-displaced Gaussian response functions. As such, arbitrary shapes of transfer functions associated with complicated BLR geometry can be seamlessly included, enabling us to relax the presumption of a specified transfer function frequently adopted in previous studies and to let it be determined by observation data. We formulate our approach in the previously well-established framework that incorporates the statistical modeling of the continuum variations as a damped random walk process and takes into account the long-term secular variations which are irrelevant to RM signals. Application to reverberation mapping data shows fidelity of our approach.

Comment: 13 pages, 10 figures; accepted to the Astrophysical Journal; comments welcome