Time-correlated structure in spin fluctuations in pulsars

Abstract

We study statistical properties of stochastic variations in pulse arrival times, timing noise, in radio pulsars using a new analysis method applied in the time domain. The method proceeds in two steps. First, we subtract low‐frequency wander using a high‐pass filter. Secondly, we calculate the discrete correlation function of the filtered data. As a complementary method for measuring correlations, we introduce a statistic that measures the dispersion of the data with respect to the data translated in time. The analysis methods presented here are robust and of general usefulness for studying arrival time variations over time‐scales approaching the average sampling interval. We apply these methods to timing data for 32 pulsars. In two radio pulsars, PSRs B1133+16 and B1933+16, we find that fluctuations in arrival times are correlated over time‐scales of 10–20 d with the distinct signature of a relaxation process. Though this relaxation response could be magnetospheric in origin, we argue that damping between the neutron star crust and interior liquid is a more likely explanation. Under this interpretation, our results provide the first evidence independent from pulsar spin glitches of differential rotation in neutron stars. PSR B0950+08 shows evidence for quasi‐periodic oscillations that could be related to mode switching.

Parameter estimation of a two-component neutron star model with spin wandering

“…Stochastic torques can excite deterministic dynamical modes in the star, such as relaxation processes. Thus the specific, random realization of the spin wandering we observe in a neutron star contains useful information about the star's structure (Baykal et al 1991;Price et al 2012;Melatos & Link 2014) or external influences on the star (Bildsten et al 1997;Mukherjee et al 2018). In the popular two-component, crust-superfluid model (Baym et al 1969), a stochastic driving torque acting on the crust is counteracted by the restoring torque from the coupling between the crust and the superfluid.…”

“…One common feature revealed by pulsar timing experiments is deviations from the long-term secular rotation and spin-down of the star known as 'spin-wandering.' When testing general relativity or seeking to detect a stochastic gravitational-wave background, spin wandering is treated as a nuisance, which needs to be characterized accurately and then subtracted in a statistical sense (Groth 1975;Cordes 1980;Arzoumanian et al 1994;Shannon & Cordes 2010;Price et al 2012; ★ E-mail: pat.meyers@unimelb.edu.au Namkham et al 2019;Parthasarathy et al 2019;Lower et al 2020;Parthasarathy et al 2020;Goncharov et al 2020). In this paper, we use 'spin wandering' to refer to the achromatic fluctuations in pulse times-of-arrival (TOAs) that are intrinsic to the pulsar, specifically the rotation of its crust and corotating magnetosphere.…”

“…Meyers et al (2021) showed with synthetic data that one can resolve the natural relaxation time-scale of the two-component sys-tem by using a Kalman filter to track the spin wandering of the crust without seeking to subtract or average out the "noisy" component of the signal. The relaxation time-scale has also been estimated by auto-correlating noise residuals (Price et al 2012). Meyers et al (2021) presented a maximum-likelihood method to solve for the parameters of the two-component model based on the expectation-maximization algorithm (Dempster et al 1977;Shumway & Stoffer 1982;Gibson & Ninness 2005).…”

Hidden Markov model tracking of continuous gravitational waves from a neutron star with wandering spin

“…Radio and X-ray timing of pulsating neutron stars reveal that spin wandering is a widespread phenomenon. In isolated objects, it manifests itself as timing noise [23][24][25], exhibits a red Fourier spectrum with an auto-correlation time-scale of days to years [26,27], and has been attributed variously to magnetospheric changes [28], superfluid dynamics in the stellar interior [27,[29][30][31], spin microjumps [32,33], and fluctuations in the spin-down torque [34][35][36]. In accreting objects, spin wandering results from fluctuations in the magnetized accretion torque [37][38][39], due to transient accretion disk formation [40,41] or disk-magnetospheric instabilities and reconnection events [42].…”

Long-term statistics of pulsar glitches triggered by a Brownian stress accumulation process

“…The secular braking of rotation-powered pulsars is perturbed by two phenomena: glitches and timing noise. Timing noise, or stochastic wandering of the spin frequency, shows up in timing residuals as a red-noise process with an autocorrelation time-scale of days to weeks (Cordes & Helfand 1980;Price et al 2012;Parthasarathy et al 2019). Glitches are impulsive spin-up events that recur erratically (Melatos et al 2008;Espinoza et al 2011;Fuentes et al 2019).…”