Hierarchical Bayesian estimation of population-level torque law parameters from 68 young radio pulsars observed with the Murriyang telescope

The measured braking index, n=ν ν ̈/ν ̇², of a rotation-powered pulsar with spin frequency ν (where an overdot symbolizes a time derivative) and braking torque K ν ^nₚₗ, features secular and stochastic anomalies arising from K̇ ≠ 0 and random torque noise respectively. Previous studies quantified the variance n² = (nₚₗ+K̇dim)²+σ dim², where the secular anomaly, K̇dim, is inversely proportional to the characteristic time-scale τK over which K varies; the stochastic anomaly, σ dim² = σ ν ̈²ν ²γ ν ̈⁻²ν ̇⁻⁴Tobs⁻¹, is a function of the timing noise amplitude σ ν ̈, a damping time-scale γ ν ̈⁻¹ and the total observing time Tobs; and the average is taken over an ensemble of random realizations of the noise process. Here, we use a hierarchical Bayesian scheme, based on the formula for 〈n2〉, to infer the population-level distribution of nₚₗ+K̇dim for a sample of 68 young radio pulsars, observed for ≳ 10 years with Murriyang, the 64-m Parkes radio telescope. Upon assuming that the nₚₗ+K̇dim values are drawn from a population-level Gaussian, N(μ ₚₗ, σ ₚₗ), the Bayesian scheme returns the mean μ ₚₗ = 9.95+5.58-5.26 and standard deviation σ ₚₗ=10.89+5.14-3.69. At a per-pulsar level it returns posterior medians satisfying -13.86 ≤ nₚₗ+K̇dim ≤ 30.38. The secular anomaly dominates the stochastic anomaly, with posterior medians satisfying |nₚₗ + K̇dim| ≥ σ dim in 10 out of 68 objects. The inference results imply that some mechanism other than electromagnetic or gravitational radiation reaction with K̇ = 0 operates in at least 66 out of 68 analyzed pulsars, in line with previous observational studies. The results are also consistent with τ K ν / ν ̇, with implications for the physical mechanism causing K̇ ≠ 0.