Recovering Pulsar Braking Index from a Population of Millisecond Pulsars

TL;DR

This paper explores the feasibility of inferring the distribution of pulsar braking indices for a population of millisecond pulsars using hierarchical Bayesian methods on simulated data, highlighting the observational challenges involved.

Contribution

It introduces a hierarchical Bayesian approach to estimate the pulsar braking index distribution from population data, which is novel compared to individual measurements.

Findings

Long observation times (>20 years) are required for accurate inference.

High precision timing noise levels (~10^{-5} ms) are necessary.

Current data (e.g., 12.5-year NANOGrav) may not suffice for precise population inference.

Abstract

The braking index, $n$, of a pulsar is a measure of its angular momentum loss and the value it takes corresponds to different spin-down mechanisms. For a pulsar spinning down due to gravitational wave emission from the principal mass quadrupole mode alone, the braking index would equal exactly 5. Unfortunately, for millisecond pulsars, it can be hard to measure observationally due to the extremely small second time derivative of the rotation frequency, $\ddot{f}$. This paper aims to examine whether it could be possible to extract the distribution of $n$ for a whole population of pulsars rather than measuring the values individually. We use simulated data with an injected $n=5$ signal for 47 millisecond pulsars and extract the distribution using hierarchical Bayesian inference methods. We find that while possible, observation times of over 20 years and RMS noise of the order of $10^{-5}$ ms are needed, which can be compared to the mean noise value of $3\times10^{-4}$ ms for the recent wideband 12.5-year NANOGrav sample, which provided the pulsar timing data used in this paper.