Recovering Pulsar Braking Index from a Population of Millisecond Pulsars

Abstract The braking index, n , of a pulsar is a measure of its angular momentum loss and the value it takes to correspond 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, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̈</mml:mo> </mml:mrow> </mml:mover> </mml:math> . 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 ms pulsars and extract the distribution using hierarchical Bayesian inference methods. We find that while possible, observation times of over 20 yr and rms noise of the order of 10 −5 ms are needed, which can be compared to the mean noise value of 3 × 10 −4 ms for the recent wide-band 12.5 yr NANOGrav sample, which provided the pulsar timing data used in this paper.