Hierarchical Bayesian estimation of population-level torque law parameters from anomalous pulsar braking indices

Abstract

Stochastic fluctuations in the spin frequency of a rotation-powered pulsar affect how accurately one measures the power-law braking index,, defined through, and can lead to measurements of anomalous braking indices, with, where the overdot symbolizes a derivative with respect to time. Previous studies show that the variance of the measured n obeys the predictive, falsifiable formula for, where is the timing noise amplitude, is a stellar damping time-scale, and is the total observing time. Here, we combine this formula with a hierarchical Bayesian scheme to infer the population-level distribution of for a pulsar population of size M. The scheme is validated using synthetic data to quantify it..