Population Synthesis of Radio & Gamma-Ray Millisecond Pulsars

In recent years, the number of known gamma-ray millisecond pulsars (MSPs) in the Galactic disk has risen substantially thanks to confirmed detections by Fermi Gamma-ray Space Telescope (Fermi). We have developed a new population synthesis of gamma-ray and radio MSPs in the galaxy which uses Markov Chain Monte Carlo techniques to explore the large and small worlds of the model parameter space and allows for comparisons of the simulated and detected MSP distributions. The simulation employs empirical radio and gamma-ray luminosity models that are dependent upon the pulsar period and period derivative with freely varying exponents. Parameters associated with the birth distributions are also free to vary. The computer code adjusts the magnitudes of the model luminosities to reproduce the number of MSPs detected by a group of ten radio surveys, thus normalizing the simulation and predicting the MSP birth rates in the Galaxy. Computing many Markov chains leads to preferred sets of model parameters that are further explored through two statistical methods. Marginalized plots define confidence regions in the model parameter space using maximum likelihood methods. A secondary set of confidence regions is determined in parallel using Kuiper statistics calculated from comparisons of cumulative distributions. These two techniques provide feedback to affirm the results and to check for consistency. Radio flux and dispersion measure constraints have been imposed on the simulated gamma-ray distributions in order to reproduce realistic detection conditions. The simulated and detected distributions agree well for both sets of radio and gamma-ray pulsar characteristics, as evidenced by our various comparisons.