Orbital Parameter Estimation from X-Ray/Optical Echo Mapping in X-Ray Binaries

Abstract Determination of X-ray binary system parameters informs a wide range of astrophysical investigations, including the formation and evolution of stellar populations, and the accretion/outflow process itself. However, interpretation of radial velocity signals is challenged by the complicated nature of the emission sites in the systems. X-ray/optical light echoes—in which X-ray emission from the vicinity of the compact object heats the surface of the donor, resulting in delayed optical emission—offers a separate route for establishing constraints on the system parameters. This method has already been employed to set limits on binary parameters in some systems. We present a practical Bayesian technique to constrain the credible ranges of X-ray binary orbital parameters, using observations of the time delay in these geometry-dependent X-ray/optical correlations. Parameters are conditioned on the data with the widely used and well-tested emcee Markov Chain Monte Carlo ensemble sampler to chart the joint posterior distribution of the system parameters. The potential of this echo-delay technique is demonstrated by recovering credible ranges of orbital parameters from synthetic test-case observations. Additionally, real echo delay and radial velocity data from the systems Sco X-1 and 4U 1636-536 are analyzed with our method, producing joint posterior probability distributions for the orbital parameters. We find that in certain cases our echo-delay method is able to break the mass–inclination degeneracy intrinsic to investigations using radial velocity data alone. We release our software to the community, and include a replication module so that the interested reader may reproduce our findings.