On the Relaxation Behaviors of Slow and Classical Glitches: Observational Biases and Their Opposite Recovery Trends

TL;DR

This paper investigates biases in pulsar glitch recovery analysis, proposes a phenomenological model for glitch behavior, and recommends a high-order polynomial fitting method to improve parameter estimation accuracy.

Contribution

It introduces a new phenomenological model for glitch recovery and demonstrates an optimal fitting procedure to reduce biases in pulsar timing analysis.

Findings

Biases occur when fitting pulsar data with typical observation intervals.

A phenomenological model can reproduce slow and classical glitches.

High-order polynomial fitting yields more accurate glitch parameters.

Abstract

We study the pulsar timing properties and the data analysis methods during glitch recoveries. In some cases one first fits the time-of-arrivals (TOAs) to obtain the "time-averaged" frequency $\nu$ and its first derivative $\dot\nu$, and then fits models to them. However, our simulations show that $\nu$ and $\dot\nu$ obtained this way are systematically biased, unless the time intervals between the nearby data points of TOAs are smaller than about $10^4$ s, which is much shorter than typical observation intervals. Alternatively, glitch parameters can be obtained by fitting the phases directly with relatively smaller biases; but the initial recovery timescale is usually chosen by eyes, which may introduce a strong bias. We also construct a phenomenological model by assuming a pulsar's spin-down law of $\dot\nu\nu^{-3} =-H_0 G(t)$ with $G(t)=1+\kappa e^{-t/\tau}$ for a glitch recovery, where $H_0$ is a constant and $\kappa$ and $\tau$ are the glitch parameters to be found. This model can reproduce the observed data of slow glitches from B1822--09 and a giant classical glitch of B2334+61, with $\kappa<0$ or $\kappa>0$, respectively. We then use this model to simulate TOA data and test several fitting procedures for a glitch recovery. The best procedure is: 1) use a very high order polynomial (e.g. to 50th order) to precisely describe the phase; 2) then obtain $\nu(t)$ and $\dot\nu(t)$ from the polynomial; and 3) the glitch parameters are obtained from $\nu(t)$ or $\dot\nu(t)$. Finally, the uncertainty in the starting time $t_0$ of a classical glitch causes uncertainties to some glitch parameters, but less so to a slow glitch and $t_0$ of which can be determined from data.