Statistical estimates of the pulsar glitch activity

TL;DR

This paper revisits the estimation of pulsar glitch activity, highlighting that traditional methods underestimate uncertainties and proposing bootstrap techniques to obtain more accurate error bounds, impacting neutron star models.

Contribution

It introduces alternative methods to estimate glitch activity, relaxing assumptions of linear regression and incorporating bootstrap techniques for better uncertainty quantification.

Findings

Bootstrap method yields larger uncertainty estimates.

Uncertainty affects the upper bound on neutron star moment of inertia.

Considering crust-only superfluid reservoir broadens the activity bounds.

Abstract

A common way to calculate the glitch activity of a pulsar is an ordinary linear regression of the observed cumulative glitch history. This method however is likely to underestimate the errors on the activity, as it implicitly assumes a (long-term) linear dependence between glitch sizes and waiting times, as well as equal variance, i.e., homoscedasticity, in the fit residuals, both assumptions that are not well justified from pulsar data. In this paper, we review the extrapolation of the glitch activity parameter and explore two alternatives: the relaxation of the homoscedasticity hypothesis in the linear fit and the use of the bootstrap technique. We find a larger uncertainty in the activity with respect to that obtained by ordinary linear regression, especially for those objects in which it can be significantly affected by a single glitch. We discuss how this affects the theoretical upper bound on the moment of inertia associated with the region of a neutron star containing the superfluid reservoir of angular momentum released in a stationary sequence of glitches. We find that this upper bound is less tight if one considers the uncertainty on the activity estimated with the bootstrap method and allows for models in which the superfluid reservoir is entirely in the crust.