Hope
College Physics Department Research Experiences for Undergraduates Summer 2012Project Summary |

Project Title: |
A Probabilistic Approach Describing the Population
Statistics of Normal Radio Pulsars Detected by the Parkes Multibeam
Pulsar Survey |

Student Name: |
Caleb Billman |

Student's Home Institution: |
Hope College |

Research Advisor: |
Dr. Peter Gonthier |

Source of Support: |
This material is based upon work supported by the NSF-RUI-AST (1009731) and Hope College Department of Physics funds. |

We present a preliminary probabilistic approach that describes the measured
period-period derivative and radio flux-dispersion distributions of normal
radio pulsars detected in the Parkes Multibeam Pulsar Survey. We use 845 pulsars
from the survey with reported flux errors that have had scintillation effects
removed. Our approach finds the expected number of pulsars from the birth period
and magnetic field, viewing angle, and detection probabilities. This is normalized
to the present-day distribution of age, distance from the sun, and dispersion
measure of neutron stars in the Parkes Multibeam Survey region, which is obtained
from a Monte Carlo simulation for a set of birth characteristics. The birth
magnetic field and period probability is found by spinning up the period and
period derivate for a given age according to the assumed spin-down model and
calculating the probability as a bivariate Gaussian distribution of the initial
period and log magnetic field. For a given distance and set of viewing angles,
the radio flux is obtained assuming a radio beam geometry model. If the flux
is above the threshold flux, which is found assuming a constant sky temperature,
the detection probability equals one. Otherwise, it has an exponential probability
dependent on the flux and survey threshold flux. The log of the maximum likelihood
of the detected distribution is used to determine how well the models match
the data. We present several comparisons between the probabilistic approach
and the Monte Carlo-based approach that has been previously implemented.

**Publications and Presentations:**

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