Methods for Estimating Neutron Star Parameters using Multiple Mechanisms for Gravitational Wave Emission Associated with Pulsar Glitches

TL;DR

This work tackles gravitational-wave emission from glitching pulsars and proposes a joint Bayesian framework to combine long-duration continuous waves (transient mountain) and short-duration f-mode bursts to constrain neutron-star mass and radius. It formalizes how non-detections map into a joint posterior by combining L(d|θ) and priors π(θ) via Bayes’ theorem, p(θ|d) ∝ L(d|θ) π(θ)/Z, and similarly converts CW and burst results into likelihoods for joint inference. The approach is demonstrated on the 2016 Vela glitch with targeted on-source and off-source burst searches and CW upper limits, yielding posterior constraints on M, R, and energy-fraction parameters that can become significantly tighter if energy-predictive models are available. The study discusses future detectability with next-generation detectors and argues that joint analyses are valuable when theoretical models make definite GW-energy predictions for multiple mechanisms.

Abstract

Several mechanisms for gravitational wave (GW) emission are believed to be associated with pulsar glitches. This emission may be split between long duration continuous waves and short duration bursts. In the Advanced LIGO era, searches for GWs associated with pulsar glitches have only considered continuous wave emission. The increasing sensitivity of the detectors and the prospects for future detectors suggest that astrophysically motivated analyses involving multiple mechanisms may be possible. Here, we present a framework for combining two simple models for GW emission - long duration continuous waves and short duration bursts - to derive more constraining astrophysical implications than a single model would allow. The best limits arise from using models that predict a specific amount of GW emission; however, there are relatively few models that make such predictions. We apply these methods to the December 2016 Vela pulsar glitch and make predictions for how well future observing runs and detectors would improve results. As part of this analysis, we performed a targeted search for GW bursts associated with this glitch and find no signal.

Figures (4)

• Figure 1: $90\%$ detection efficiency limits for the targeted X-Pipeline search. Ringdown injections were used to approximate sensitivity to f-mode waveforms. Upper limits are shown for damping times of $0.1\,\mathrm{s}$, $0.5\,\mathrm{s}$, and $1.0\,\mathrm{s}$. Note that for many of these points, the orange, cyan, and green dots are significantly overlapping. Background sensitivity for LIGO Hanford and LIGO Livingston are shown in red and blue, respectively.
• Figure 2: Mass, Radius, $\digamma_{\!\mathrm{fmode}}$, and $\digamma_{\!\mathrm{CW}}$ posterior distribution for the two-detector, off-source sensitivity. The different colors show how the prior space (blue) compares to the posterior (orange). Note that the $\digamma_{\!\mathrm{fmode}}$ and $\digamma_{\!\mathrm{CW}}$ terms are a fraction of the total glitch energy $E_\mathrm{Glitch}$, so values greater than $1$ would imply more energy than actually released in the glitch.
• Figure 3: $90\%$ confidence region on mass and radius for different analyses. $\digamma_{\!\mathrm{fmode}}$ and $\digamma_{\!\mathrm{CW}}$ are fixed to specific values for illustrative purposes. The blue contour shows the constraints placed when only considering the upper limits from the X-Pipeline search when assuming $\digamma_{\!\mathrm{fmode}}=100$ and without considering CW results. The red contour shows the constraints placed when only considering the upper limits from the CW search when assuming $\digamma_{\!\mathrm{CW}}=1$ and without considering burst results. The green contour shows the constraints when considering both burst and CW limits when assuming $\digamma_{\!\mathrm{fmode}}=100$ and $\digamma_{\!\mathrm{CW}}=1$. Dotted lines show the mass/radius curves for different sample equations of state for reference wiringa_equation_1988PhysRevC.58.1804douchin_unified_2001PhysRevD.73.024021. Notice, that in this hypothetical example, the H4 equation of state is consistent with the confidence intervals when considering either GW model on its own. However, when combining both models, H4 is no longer consistent. The black contour shows the constraints when an f-mode is detected. Here, an f-mode was injected into detector data for a $1.0 \, M_{\odot}$ neutron star with a $15.0\,\mathrm{km}$ radius at $\digamma_{\!\mathrm{fmode}}=100$. The line-like appearance of the contour is due to the tight constraints from the f-mode frequency.
• Figure 4: $90\%$ confidence interval for the distance-glitch size parameter space for a Vela-like pulsar. Glitches corresponding to values left of the lines would produce both CW transient mountain and burst f-mode GWs observable by those detectors. This assumes a $1.0 M_{\odot}$ neutron star with a $15.0\,\mathrm{km}$ radius with $\digamma_{\!\mathrm{CW}}=0.1$ and $\digamma_{\!\mathrm{fmode}}=0.9$. The purple star denotes the 2016 Vela pulsar glitch, showing that, under these assumptions, this glitch could have produced fully detectable burst and CW gravitational waves at the estimated sensitivity of O5.