Hierarchical Bayesian estimation of population-level torque law parameters from anomalous pulsar braking indices
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| Formato: | Preprint |
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2025
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| _version_ | 1866913701599117312 |
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| author | Vargas, Andrés F. Carlin, Julian B. Melatos, Andrew |
| author_facet | Vargas, Andrés F. Carlin, Julian B. Melatos, Andrew |
| contents | Abridged. Stochastic fluctuations in the spin frequency $ν$ of a rotation-powered pulsar affect how accurately one measures the power-law braking index, $n_{\rm pl}$, defined through $\dotν=Kν^{n_{\rm pl}}$, and can lead to measurements of anomalous braking indices, with $\vert n \vert = \vert ν\ddotν/ \dotν^{2} \vert \gg1$, where the overdot symbolizes a derivative with respect to time. Previous studies show that the variance of the measured $n$ obeys the predictive, falsifiable formula $\langle n^{2} \rangle = n_{\rm pl}^{2}+σ^{2}_{\ddotν}ν^{2}γ_{\ddotν}^{-2}\dotν^{-4}T_{\rm obs}^{-1}$ for $\dot{K}=0$, where $σ_{\ddotν}$ is the timing noise amplitude, $γ_{\ddotν}^{-1}$ is a stellar damping time-scale, and $T_{\rm obs}$ is the total observing time. Here we combine this formula with a hierarchical Bayesian scheme to infer the population-level distribution of $n_{\rm pl}$ for a pulsar population of size $M$. The scheme is validated using synthetic data. For a plausible test population with $M=100$ and injected $n_{\rm pl}$ values drawn from a population-level Gaussian with mean $μ_{\rm pl}=4$ and standard deviation $σ_{\rm pl}=0.5$, intermediate between electromagnetic braking and mass quadrupole gravitational radiation reaction, the Bayesian scheme infers $μ_{\rm pl}=3.89^{+0.24}_{-0.23}$ and $σ_{\rm pl}=0.43^{+0.21}_{-0.14}$. The $M=100$ per-pulsar posteriors for $n_{\rm pl}$ and $σ^{2}_{\ddotν}γ_{\ddotν}^{-2}$ contain $87\%$ and $69\%$, respectively, of the injected values within their $90\%$ credible intervals. Comparable accuracy is achieved for (i) population sizes spanning the range $50 \leq M \leq 300$, and (ii) wide priors satisfying $μ_{\rm pl} \leq 10^{3}$ and $σ_{\rm pl} \leq 10^{2}$, which accommodate plausible spin-down mechanisms with $\dot{K}\neq0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15211 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hierarchical Bayesian estimation of population-level torque law parameters from anomalous pulsar braking indices Vargas, Andrés F. Carlin, Julian B. Melatos, Andrew High Energy Astrophysical Phenomena Abridged. Stochastic fluctuations in the spin frequency $ν$ of a rotation-powered pulsar affect how accurately one measures the power-law braking index, $n_{\rm pl}$, defined through $\dotν=Kν^{n_{\rm pl}}$, and can lead to measurements of anomalous braking indices, with $\vert n \vert = \vert ν\ddotν/ \dotν^{2} \vert \gg1$, where the overdot symbolizes a derivative with respect to time. Previous studies show that the variance of the measured $n$ obeys the predictive, falsifiable formula $\langle n^{2} \rangle = n_{\rm pl}^{2}+σ^{2}_{\ddotν}ν^{2}γ_{\ddotν}^{-2}\dotν^{-4}T_{\rm obs}^{-1}$ for $\dot{K}=0$, where $σ_{\ddotν}$ is the timing noise amplitude, $γ_{\ddotν}^{-1}$ is a stellar damping time-scale, and $T_{\rm obs}$ is the total observing time. Here we combine this formula with a hierarchical Bayesian scheme to infer the population-level distribution of $n_{\rm pl}$ for a pulsar population of size $M$. The scheme is validated using synthetic data. For a plausible test population with $M=100$ and injected $n_{\rm pl}$ values drawn from a population-level Gaussian with mean $μ_{\rm pl}=4$ and standard deviation $σ_{\rm pl}=0.5$, intermediate between electromagnetic braking and mass quadrupole gravitational radiation reaction, the Bayesian scheme infers $μ_{\rm pl}=3.89^{+0.24}_{-0.23}$ and $σ_{\rm pl}=0.43^{+0.21}_{-0.14}$. The $M=100$ per-pulsar posteriors for $n_{\rm pl}$ and $σ^{2}_{\ddotν}γ_{\ddotν}^{-2}$ contain $87\%$ and $69\%$, respectively, of the injected values within their $90\%$ credible intervals. Comparable accuracy is achieved for (i) population sizes spanning the range $50 \leq M \leq 300$, and (ii) wide priors satisfying $μ_{\rm pl} \leq 10^{3}$ and $σ_{\rm pl} \leq 10^{2}$, which accommodate plausible spin-down mechanisms with $\dot{K}\neq0$. |
| title | Hierarchical Bayesian estimation of population-level torque law parameters from anomalous pulsar braking indices |
| topic | High Energy Astrophysical Phenomena |
| url | https://arxiv.org/abs/2502.15211 |