We present a comprehensive description of the population synthesis code StarTrack. The original code has been significantly modified and updated. Special emphasis is placed here on processes leading to the formation and further evolution of compact objects (white dwarfs, neutron stars, and black holes). Both single and binary star populations are considered. The code now incorporates detailed calculations of all mass transfer phases, a full implementation of orbital evolution due to tides, as well as the most recent estimates of magnetic braking. This updated version of StarTrack can be used for a wide variety of problems, with relevance to observations with many current and planned observatories, e.g., studies of X-ray binaries (Chandra, XMM-Newton), gravitational radiation sources (LIGO, LISA), and gamma-ray burst progenitors (HETE-II, Swift). The code has already been used in studies of Galactic and extragalactic X-ray binary populations, black holes in young star clusters, Type Ia supernova progenitors, and double compact object populations. Here we describe in detail the input physics, we present the code calibration and tests, and we outline our current studies in the context of X-ray binary populations.

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A commonly used measure to summarize the nature of a photon spectrum is the so-called hardness ratio, which compares the numbers of counts observed in different passbands. The hardness ratio is especially useful to distinguish between and categorize weak sources as a proxy for detailed spectral fitting. However, in this regime classical methods of error propagation fail, and the estimates of spectral hardness become unreliable. Here we develop a rigorous statistical treatment of hardness ratios that properly deals with detected photons as independent Poisson random variables and correctly deals with the non-Gaussian nature of the error propagation. The method is Bayesian in nature and thus can be generalized to carry out a multitude of source-populationYbased analyses. We verify our method with simulation studies and compare it with the classical method. We apply this method to real-world examples, such as the identification of candidate quiescent low-mass X-ray binaries in globular clusters and tracking the time evolution of a flare on a low-mass star.

High redshift galaxies permit the study of the formation and evolution of X-ray binary populations on cosmological timescales, probing a wide range of metallicities and star-formation rates. In this paper, we present results from a large scale population synthesis study that models the X-ray binary populations from the first galaxies of the universe until today. We use as input to our modeling the Millennium II Cosmological Simulation and the updated semi-analytic galaxy catalog by Guo et al. (2011) to self-consistently account for the star formation history and metallicity evolution of the universe. Our modeling, which is constrained by the observed X-ray properties of local galaxies, gives predictions about the global scaling of emission from X-ray binary populations with properties such as star-formation rate and stellar mass, and the evolution of these relations with redshift. Our simulations show that the X-ray luminosity density (X-ray luminosity per unit volume) from X-ray binaries in our Universe today is dominated by low-mass X-ray binaries, and it is only at z 2.5 that high-mass X-ray binaries become dominant. We also find that there is a delay of ∼ 1.1 Gyr between the peak of X-ray emissivity from low-mass Xray binaries (at z ∼ 2.1) and the peak of star-formation rate density (at z ∼ 3.1). The peak of the X-ray luminosity from high-mass X-ray binaries (at z ∼ 3.9), happens ∼ 0.8 Gyr before the peak of the star-formation rate density, which is due to the metallicity evolution of the Universe.