Population Synthesis of Normal Radio and Gamma-ray Pulsars Using Markov Chain Monte Carlo Techniques

Abstract

We present preliminary results of a pulsar population synthesis of normal pulsars from the Galactic disk using a Markov Chain Monte Carlo method to better understand the parameter space of the assumed model. We use the Kuiper test, similar to the Kolmogorov-Smirnov test, to compare the cumulative distributions of chosen observables of detected radio pulsars with those simulated for various parameters. Our code simulates pulsars at birth using Monte Carlo techniques and evolves them to the present assuming initial spatial, kick velocity, magnetic field, and period distributions. Pulsars are spun down to the present, given radio and gamma-ray emission characteristics, filtered through ten selected radio surveys, and a {\it Fermi} all-sky threshold map. Each chain begins with a different random seed and searches a ten-dimensional parameter space for regions of high probability for a total of one thousand different simulations before ending. The code investigates both the "large world" as well as the "small world" of the parameter space. We apply the K-means clustering algorithm to verify if the chains reveal a single or multiple regions of significance. The outcome of the combined set of chains is the weighted average and deviation of each of the ten parameters describing the model. While the model reproduces reasonably well the detected distributions of normal radio pulsars, it does not replicate the predicted detected $\dot P - P$ distribution of {\it Fermi} pulsars. The simulations do not produce sufficient numbers of young, high-$\dot E$ pulsars in the Galactic plane.