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

Abstract

Abridged. The measured braking index, $n=\hat{I}½\ddot{\hat{I}}½/\dot{\hat{I}}{½}^2$, of a rotation-powered pulsar with spin frequency $\hat{I}½$ and braking torque $K\hat{I}{½}^{n_{\mathrm{pl}}}$, features secular and stochastic anomalies arising from $\dot{K}\ne 0$ and random torque noise respectively. Previous studies quantified the variance $⟨n^2⟩=(n_{\mathrm{pl}}+{\dot{K}}_{\dim }{)}^2+\ddot{I}{ƒ}_{\dim }^2$, where the secular anomaly, ${\dot{K}}_{\dim }$, is inversely proportional to the characteristic time-scale $\ddot{I}{„}_K$ over which $K$ varies; the stochastic anomaly, $σ_{\rm dim}^{2} = σ_{\ddotν}^{2}ν^{2}γ_{\ddotν}^{-2}\dotν^{-4}T_{\rm obs}^{-1}$, is a function of the timing noise amplitude $\ddot{I}{ƒ}_{\ddot{\hat{I}}½}$, a damping time-scale $γ_{\ddotν}^{-1}$ and the total observing time $T_{\mathrm{obs}}$; 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 $⟨n^2⟩$, to infer the population-level distribution of $n_{\mathrm{pl}}+{\dot{K}}_{\dim }$ for a sample of $68$ young radio pulsars, observed for $\gtrsim 10\mathrm{years}$ with Murriyang, the 64-m Parkes radio telescope. Upon assuming that the $n_{\mathrm{pl}}+{\dot{K}}_{\dim }$ values are drawn from a population-level Gaussian, $N(\hat{I}{¼}_{\mathrm{pl}},\ddot{I}{ƒ}_{\mathrm{pl}})$, the Bayesian scheme returns the mean $\hat{I}{¼}_{\mathrm{pl}}=9.95_{-5.26}^{+5.58}$ and standard deviation $\ddot{I}{ƒ}_{\mathrm{pl}}=10.89_{-3.69}^{+5.14}$. At a per-pulsar level it returns posterior medians satisfying $-13.86\le n_{\mathrm{pl}}+{\dot{K}}_{\dim }\le 30.38$. The secular anomaly dominates the stochastic anomaly, with posterior medians satisfying $|n_{\mathrm{pl}}+{\dot{K}}_{\dim }|\ge \ddot{I}{ƒ}_{\dim }$ in 10 out of 68 objects.

20 pages, 6 figures