Hierarchical Bayesian estimation of population-level torque law parameters from anomalous pulsar braking indices

Abstract

Abridged. Stochastic fluctuations in the spin frequency $\nu$ of a rotation-powered pulsar affect how accurately one measures the power-law braking index, $n_{\mathrm{pl}}$, defined through $\dot{\nu }=K{\nu }^{n_{\mathrm{pl}}}$, and can lead to measurements of anomalous braking indices, with $|n|=|\nu \ddot{\nu }/{\dot{\nu }}^2|\gg 1$, 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 $⟨n^2⟩=n_{\mathrm{pl}}^2+{\sigma }_{\ddot{\nu }}^2{\nu }^2{\gamma }_{\ddot{\nu }}^{-2}{\dot{\nu }}^{-4}{T}_{\mathrm{obs}}^{-1}$ for $\dot{K}=0$, where ${\sigma }_{\ddot{\nu }}$ is the timing noise amplitude, ${\gamma }_{\ddot{\nu }}^{-1}$ is a stellar damping time-scale, and $T_{\mathrm{obs}}$ is the total observing time. Here we combine this formula with a hierarchical Bayesian scheme to infer the population-level distribution of $n_{\mathrm{pl}}$ for a pulsar population of size $M$. The scheme is validated using synthetic data. For a plausible test population with $M=100$ and injected $n_{\mathrm{pl}}$ values drawn from a population-level Gaussian with mean ${\mu }_{\mathrm{pl}}=4$ and standard deviation ${\sigma }_{\mathrm{pl}}=0.5$, intermediate between electromagnetic braking and mass quadrupole gravitational radiation reaction, the Bayesian scheme infers ${\mu }_{\mathrm{pl}}=3.89_{-0.23}^{+0.24}$ and ${\sigma }_{\mathrm{pl}}=0.43_{-0.14}^{+0.21}$. The $M=100$ per-pulsar posteriors for $n_{\mathrm{pl}}$ and ${\sigma }_{\ddot{\nu }}^2{\gamma }_{\ddot{\nu }}^{-2}$ 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 $50\le M\le 300$, and (ii) wide priors satisfying ${\mu }_{\mathrm{pl}}\le 10^3$ and ${\sigma }_{\mathrm{pl}}\le 10^2$, which accommodate plausible spin-down mechanisms with $\dot{K}\ne 0$.

arXiv comment16 pages, 7 figures

References in corpus (50)

• The ATNF Pulsar Catalogue
• TEMPO2, a new pulsar timing package. I: Overview
• Birth and Evolution of Isolated Radio Pulsars
• A new class of unstable modes of rotating relativistic stars
• Switched magnetospheric regulation of pulsar spin-down
• Gravitational waves from hot young rapidly rotating neutron stars
• An analysis of the timing irregularities for 366 pulsars
• 45 Years of Rotation of the Crab Pulsar
• Assessing the Role of Spin Noise in the Precision Timing of Millisecond Pulsars
• TempoNest: A Bayesian approach to pulsar timing analysis
• The glitch-induced identity changes of PSR J1119-6127
• Pulsar timing analysis in the presence of correlated noise
• Revised Pulsar Spindown
• Relativistic MHD Winds from Rotating Neutron Stars
• Hyper-efficient model-independent Bayesian method for the analysis of pulsar timing data
• Pulsar braking and the P-Pdot diagram
• A High Braking Index for a Pulsar
• Pulsar Braking Indices Revisited
• Timing of young radio pulsars I: Timing noise, periodic modulation and proper motion
• Identifying and mitigating noise sources in precision pulsar timing data sets
• New Phase-coherent Measurements of Pulsar Braking Indices
• Post-outburst Observations of the Magnetically Active Pulsar J1846-0258: a new braking index, increased timing noise, and radiative recovery
• Radiative Precession of an Isolated Neutron Star
• Pulsar timing noise from superfluid turbulence
• Multipolar electromagnetic fields around neutron stars: exact vacuum solutions and related properties
• The impact of glitches on young pulsar rotational evolution
• The UTMOST pulsar timing programme II: Timing noise across the pulsar population
• Vortex Creep Against Toroidal Flux Lines, Crustal Entrainment, and Pulsar Glitches
• Torque Decay in the Pulsar (P,P_dot) Diagram. Effects of Crustal Ohmic Dissipation and Alignment
• Pulsar Braking Indices, Glitches and Energy Dissipation In Neutron Stars
• Rotational evolution of the Crab pulsar in the wind braking model
• Timing of young radio pulsars II. Braking indices and their interpretation
• Pulsar timing irregularities and the imprint of magnetic field evolution
• A strong $\ddot{\nu }-\dot{\nu }$ correlation in radio pulsars with implications for torque variations
• Long-Term X-ray Monitoring of the Young Pulsar PSR B1509-58
• Mode switching and oscillations in PSR B1828-11
• Are We Seeing Magnetic Axis Reorientation in the Crab and Vela Pulsars?
• The influence of nondipolar magnetic field and neutron star precession on braking indexes of radiopulsars
• The 2016 Vela glitch: a key to neutron star internal structure and dynamics
• Postglitch exponential relaxation of radio pulsars and magnetars in terms of vortex creep across flux tubes
• Stochastic processes for pulsar timing noise: fluctuations in the internal and external torques
• Time-Correlated Structure in Spin Fluctuations in Pulsars
• Multipolar electromagnetic fields around neutron stars: general-relativistic vacuum solutions
• Parameter estimation of a two-component neutron star model with spin wandering
• Rapid parameter estimation of a two-component neutron star model with spin wandering using a Kalman filter
• Non-Axisymmetric Precession of Magnetars and Fast Radio Bursts
• Impact of quasi-periodic and steep-spectrum timing noise on the measurement of pulsar timing parameters
• Spin Evolution of Pulsars with Weakly Coupled Superfluid Interiors
• Apparent dispersion in pulsar braking index measurements caused by timing noise
• Measuring the vortex-nucleus pinning force from pulsar glitch rates