Hierarchical Bayesian estimation of population-level torque law parameters from $68$ young radio pulsars observed with the Murriyang telescope
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914168612847616 |
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| author | Vargas, Andrés F. Melatos, Andrew Carlin, Julian B. Lower, Marcus E. Johnston, Simon Weltevrede, Patrick |
| author_facet | Vargas, Andrés F. Melatos, Andrew Carlin, Julian B. Lower, Marcus E. Johnston, Simon Weltevrede, Patrick |
| contents | Abridged. The measured braking index, $n=ν\ddotν/\dotν^2$, of a rotation-powered pulsar with spin frequency $ν$ and braking torque $K ν^{n_{\rm pl}}$, features secular and stochastic anomalies arising from $\dot{K} \neq 0$ and random torque noise respectively. Previous studies quantified the variance $\langle n^{2} \rangle = (n_{\rm pl}+\dot{K}_{\rm dim})^{2}+σ_{\rm dim}^{2}$, where the secular anomaly, $\dot{K}_{\rm dim}$, is inversely proportional to the characteristic time-scale $τ_{K}$ 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 $σ_{\ddotν}$, a damping time-scale $γ_{\ddotν}^{-1}$ and the total observing time $T_{\rm obs}$; 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 $\langle n^{2} \rangle$, to infer the population-level distribution of $n_{\rm pl}+\dot{K}_{\rm dim}$ for a sample of $68$ young radio pulsars, observed for $\gtrsim 10~{\rm years}$ with Murriyang, the 64-m Parkes radio telescope. Upon assuming that the $n_{\rm pl}+\dot{K}_{\rm dim}$ values are drawn from a population-level Gaussian, $N(μ_{\rm pl}, σ_{\rm pl})$, the Bayesian scheme returns the mean $μ_{\rm pl} = 9.95^{+5.58}_{-5.26}$ and standard deviation $σ_{\rm pl}=10.89^{+5.14}_{-3.69}$. At a per-pulsar level it returns posterior medians satisfying $-13.86 \leq n_{\rm pl}+\dot{K}_{\rm dim} \leq 30.38$. The secular anomaly dominates the stochastic anomaly, with posterior medians satisfying $|n_{\rm pl} + \dot{K}_{\rm dim}| \geq σ_{\rm dim}$ in 10 out of 68 objects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18744 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hierarchical Bayesian estimation of population-level torque law parameters from $68$ young radio pulsars observed with the Murriyang telescope Vargas, Andrés F. Melatos, Andrew Carlin, Julian B. Lower, Marcus E. Johnston, Simon Weltevrede, Patrick High Energy Astrophysical Phenomena Abridged. The measured braking index, $n=ν\ddotν/\dotν^2$, of a rotation-powered pulsar with spin frequency $ν$ and braking torque $K ν^{n_{\rm pl}}$, features secular and stochastic anomalies arising from $\dot{K} \neq 0$ and random torque noise respectively. Previous studies quantified the variance $\langle n^{2} \rangle = (n_{\rm pl}+\dot{K}_{\rm dim})^{2}+σ_{\rm dim}^{2}$, where the secular anomaly, $\dot{K}_{\rm dim}$, is inversely proportional to the characteristic time-scale $τ_{K}$ 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 $σ_{\ddotν}$, a damping time-scale $γ_{\ddotν}^{-1}$ and the total observing time $T_{\rm obs}$; 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 $\langle n^{2} \rangle$, to infer the population-level distribution of $n_{\rm pl}+\dot{K}_{\rm dim}$ for a sample of $68$ young radio pulsars, observed for $\gtrsim 10~{\rm years}$ with Murriyang, the 64-m Parkes radio telescope. Upon assuming that the $n_{\rm pl}+\dot{K}_{\rm dim}$ values are drawn from a population-level Gaussian, $N(μ_{\rm pl}, σ_{\rm pl})$, the Bayesian scheme returns the mean $μ_{\rm pl} = 9.95^{+5.58}_{-5.26}$ and standard deviation $σ_{\rm pl}=10.89^{+5.14}_{-3.69}$. At a per-pulsar level it returns posterior medians satisfying $-13.86 \leq n_{\rm pl}+\dot{K}_{\rm dim} \leq 30.38$. The secular anomaly dominates the stochastic anomaly, with posterior medians satisfying $|n_{\rm pl} + \dot{K}_{\rm dim}| \geq σ_{\rm dim}$ in 10 out of 68 objects. |
| title | Hierarchical Bayesian estimation of population-level torque law parameters from $68$ young radio pulsars observed with the Murriyang telescope |
| topic | High Energy Astrophysical Phenomena |
| url | https://arxiv.org/abs/2511.18744 |