Constraining Orbital Eccentricity of a Supermassive Black Hole Binary Candidate PKS 2131-0211

Abstract

A detailed analysis of the decades-long radio light curve of blazar PKS 2131-021 showed epochs of sinusoidal variations in the radio flux density time-series as detailed in O'Neill et al. (2022). The observed sinusoidal flux modulation arises naturally from relativistic Doppler boosting of the jet when the jet-emitting supermassive black hole (SMBH) orbits its companion. For SMBHs in circular orbits, this scenario yields sinusoidal light curves, offering a simple kinematic explanation for the observed variability in PKS 2131-021. We present an approach that incorporates the effects of orbital eccentricity into the Kinematic Orbital model for PKS 2131-021, using the Keplerian parametric solution to describe the SMBH binary orbit. Using the available radio light curve data, we demonstrate that the proposed SMBH binary likely possesses a residual orbital eccentricity, which we constrain through detailed Bayesian parameter estimation studies to be 0.053 \pm 0.015 with a Bayes factor of 3.15 over the circular model. However, when the analysis accounts for the presence of red noise in the data using a Damped Random Walk (DRW) process, the circular model is preferred, giving an eccentricity upper limit of e < 0.15. Nevertheless, our efforts reveal that the Circular+DRW model is strongly favored. This model consistently recovers a coherent periodic signal across all datasets, with the orbital period remaining well-defined even when accounting for broader uncertainties. This analysis incorporated archival observations from the Haystack Observatory, the University of Michigan Radio Astronomy Observatory (UMRAO), and the Owens Valley Radio Observatory (OVRO), spanning the period from 1975 to 2021, compiled by O'Neill et al. (2022).