dart_board: Binary Population Synthesis with Markov Chain Monte Carlo

Jeff J Andrews, Andreas Zezas, Tassos Fragos

Published 2017-10-30Version 1

By employing Monte Carlo random sampling, traditional binary population synthesis (BPS) offers a substantial improvement in efficiency over brute force, grid-based studies. Even so, BPS models typically require a large number of simulation realizations, a computationally expensive endeavor, to generate statistically robust results. In this work we describe our publicly available code dart_board which combines rapid binary evolution codes, typically used in traditional BPS, with modern Markov chain Monte Carlo methods. dart_board treats the initial binary conditions and the supernova kick vector as model parameters using the same prior distributions typically used in traditional BPS and a given set of observations as the likelihood function. This approach has several advantages such as the ability to trivially model either populations of systems or individual binaries, the natural inclusion of observational uncertainties, and the flexible addition of new constraints which are problematic to include using traditional BPS (such as star formation history maps). We test our code on three mock systems, finding excellent recovery of their input parameters. We then apply dart_board to three test cases to demonstrate how it can flexibly model a variety of stellar binary populations: (i) a generic population of high mass X-ray binaries (HMXBs), (ii) the population of HMXBs in the Large Magellanic Cloud (LMC) in which the spatially resolved star formation history is used as a prior, and (iii) one particular HMXB in the LMC, Swift J0513.4-6547. We find that spatially resolved star formation histories can add a powerful constraint on the formation of individual systems. Although this work focuses on HMXBs, dart_board can be applied to model a variety of stellar binary populations including the merging compact object binaries recently detected by gravitational wave observatories.