Quasi-periodic oscillations (QPOs) are an important key to understand the dynamic behavior of astrophysical objects during transient events like gamma-ray bursts, solar flares, and magnetar flares. Searches for QPOs often use the periodogram of the t
ime series and perform spectral density estimation using a Whittle likelihood function. However, the Whittle likelihood is only valid if the time series is stationary since the frequency bins are otherwise not statistically independent. We show that if time series are non-stationary, the significance of QPOs can be highly overestimated and estimates of the central frequencies and QPO widths can be overconstrained. The effect occurs if the QPO is only present for a fraction of the time series and the noise level is varying throughout the time series. This can occur for example if background noise from before or after the transient is included in the time series or if the low-frequency noise profile varies strongly over the time series. We confirm the presence of this bias in previously reported results from solar flare data and show that significance can be highly overstated. Finally, we provide some suggestions that help identify if an analysis is affected by this bias.
The orbital eccentricity of a merging binary black hole leaves an imprint on the associated gravitational-wave signal that can reveal whether the binary formed in isolation or in a dynamical environment, such as the core of a dense star cluster. We p
resent measurements of the eccentricity of 26 binary black hole mergers in the second LIGO--Virgo gravitational-wave transient catalog, updating the total number of binary black holes analysed for orbital eccentricity to 36. Using the texttt{SEOBNRE} waveform, we find the data for GW190620A is poorly explained by the zero-eccentricity hypothesis (frequentist $p$-value $lesssim 0.1%$). With a uniform eccentricity prior, the data prefer $e_{10} geq 0.11$ at $90%$ credibility, while assuming a uniform-in-log eccentricity prior yields a $90%$ credible lower eccentricity limit of $0.001$. Using the log-uniform prior, the eccentricity at $10$ Hz for GW190620A is constrained to $e_{10}geq0.05$ ($0.1$) at $74%$ ($65%$) credibility. This is the second measurement of a binary black hole system with statistical support for non-zero eccentricity; the intermediate-mass black hole merger GW190521 was the first. Interpretation of these two events is currently complicated by waveform systematics; we are unable to simultaneously model the effects of relativistic precession and eccentricity. However, if these two events are, in fact, eccentric mergers, then there are potentially many more dynamically assembled mergers in the LIGO--Virgo catalog without measurable eccentricity; $gtrsim 27%$ of the observed LIGO--Virgo binaries may have been assembled dynamically in dense stellar environments ($95%$ credibility).
Measuring the collapse time of a binary neutron star merger remnant can inform the physics of extreme matter and improve modelling of short gamma-ray bursts and associated kilonova. The lifetime of the post-merger remnant directly impacts the mechani
sms available for the jet launch of short gamma-ray bursts. We develop and test a method to measure the collapse time of post-merger remnants. We show that for a GW170817-like event at $sim!40,$Mpc, a network of Einstein Telescope with Cosmic Explorer is required to detect collapse times of $sim!10,$ms. For a two-detector network at A+ design sensitivity, post-merger remnants with collapse times of $sim!10,mathrm{ms}$ must be $lesssim 10,$Mpc to be measureable. This increases to $sim!18-26,$Mpc if we include the proposed Neutron star Extreme Matter Observatory (NEMO), increasing the effective volume by a factor of $sim!30$.
CDF-S XT1 is a fast-rising non-thermal X-ray transient detected by textit{Chandra} in the Deep-Field South Survey. Although various hypotheses have been suggested, the origin of this transient remains unclear. Here, we show that the observations of C
DF-S XT1 are well explained as the X-ray afterglow produced by a relativistic structured jet viewed off-axis. We measure properties of the jet, showing that they are similar to those of GRB170817A, albeit at cosmological distances. We measure the observers viewing angle to be $theta_{textrm{obs}} = 10^{circ}pm3^{circ}$ and the core of the ultra-relativistic jet to be $theta_{textrm{core}} = 4.4^{circ}pm0.9^{circ}$, where the uncertainties are the $68%$ credible interval. The inferred properties and host galaxy combined with Hubble, radio, and optical non detections favour the hypothesis that CDF-S XT1 is the off-axis afterglow of a binary neutron star merger. We find that other previously suggested hypotheses are unable to explain all properties of CDF-S XT1. At a redshift of $z=2.23$, this is potentially the most distant observed neutron star merger to date and the first orphan afterglow of a short gamma-ray burst. We discuss the implications of a binary neutron star merger at such a high redshift for the star-formation rate in the early Universe, the nucleosynthesis of heavy elements, and the prospect of identifying other off-axis afterglows.
Two neutron stars merge somewhere in the Universe approximately every 10 seconds, creating violent explosions observable in gravitational waves and across the electromagnetic spectrum. The transformative coincident gravitational-wave and electromagne
tic observations of the binary neutron star merger GW170817 gave invaluable insights into these cataclysmic collisions, probing bulk nuclear matter at supranuclear densities, the jet structure of gamma-ray bursts, the speed of gravity, and the cosmological evolution of the local Universe, among other things. Despite the wealth of information, it is still unclear when the remnant of GW170817 collapsed to form a black hole. Evidence from other short gamma-ray bursts indicates a large fraction of mergers may form long-lived neutron stars. We review what is known observationally and theoretically about binary neutron star post-merger remnants. From a theoretical perspective, we review our understanding of the evolution of short- and long-lived merger remnants, including fluid, magnetic-field, and temperature evolution. These considerations impact prospects of detection of gravitational waves from either short- or long-lived neutron star remnants which potentially allows for new probes into the hot nuclear equation of state in conditions inaccessible in terrestrial experiments. We also review prospects for determining post-merger physics from current and future electromagnetic observations, including kilonovae and late-time x-ray and radio afterglow observations.
The no-hair theorem states that astrophysical black holes are fully characterised by just two numbers: their mass and spin. The gravitational-wave emission from a perturbed black-hole consists of a superposition of damped sinusoids, known as textit{q
uasi-normal modes}. Quasi-normal modes are specified by three integers $(ell,m,n)$: the $(ell, m)$ integers describe the angular properties and $(n)$ specifies the (over)tone. If the no-hair theorem holds, the frequencies and damping times of quasi-normal modes are determined uniquely by the mass and spin of the black hole, while phases and amplitudes depend on the particular perturbation. Current tests of the no-hair theorem, attempt to identify these modes in a semi-agnostic way, without imposing priors on the source of the perturbation. This is usually known as textit{black-hole spectroscopy}. Applying this framework to GW150914, the measurement of the first overtone led to the confirmation of the theorem to $20%$ level. We show, however, that such semi-agnostic tests cannot provide strong evidence in favour of the no-hair theorem, even for extremely loud signals, given the increasing number of overtones (and free parameters) needed to fit the data. This can be solved by imposing prior assumptions on the origin of the perturbed black hole that can further constrain the explored parameters: in particular, our knowledge that the ringdown is sourced by a binary black hole merger. Applying this strategy to GW150914 we find a natural log Bayes factor of $sim 6.5$ in favour of the Kerr nature of its remnant, indicating that the hairy object hypothesis is disfavoured with $<1:600$ with respect to the Kerr black-hole one.
We infer the collapse times of long-lived neutron stars into black holes using the X-ray afterglows of 18 short gamma-ray bursts. We then apply hierarchical inference to infer properties of the neutron star equation of state and dominant spin-down me
chanism. We measure the maximum non-rotating neutron star mass $M_mathrm{TOV} = 2.31 ^{+0.36}_{-0.21} M_{odot}$ and constrain the fraction of remnants spinning down predominantly through gravitational-wave emission to $eta = 0.69 ^{+0.21}_{-0.39}$ with $68 %$ uncertainties. In principle, this method can determine the difference between hadronic and quark equation of states. In practice, however, the data is not yet informative with indications that these neutron stars do not have hadronic equation of states at the $1sigma$ level. These inferences all depend on the underlying progenitor mass distribution for short gamma-ray bursts produced by binary neutron star mergers. The recently announced gravitational-wave detection of GW190425 suggests this underlying distribution is different from the locally-measured population of double neutron stars. We show that $M_mathrm{TOV}$ and $eta$ constraints depend on the fraction of binary mergers that form through a distribution consistent with the locally-measured population and a distribution that can explain GW190425. The more binaries that form from the latter distribution, the larger $M_mathrm{TOV}$ needs to be to satisfy the X-ray observations. Our measurements above are marginalised over this unknown fraction. If instead, we assume GW190425 is not a binary neutron star merger, i.e the underlying mass distribution of double neutron stars is the same as observed locally, we measure $M_mathrm{TOV} = 2.26 ^{+0.31}_{-0.17} M_{odot}$.
The origin of the X-ray afterglows of gamma-ray bursts has regularly been debated. We fit both the fireball-shock and millisecond-magnetar models of gamma-ray bursts to the X-ray data of GRB 130603B and 140903A. We use Bayesian model selection to ans
wer the question of which model best explains the data. This is dependent on the maximum allowed non-rotating neutron star mass $M_{textrm{TOV}}$, which depends solely on the unknown nuclear equation of state. We show that the data for GRB140903A favours the millisecond-magnetar model for all possible equations of state, while the data for GRB130603B favours the millisecond-magnetar model if $M_{textrm{TOV}} gtrsim 2.3 M_{odot}$. If $M_{textrm{TOV}} lesssim 2.3 M_{odot}$, the data for GRB130603B supports the fireball-shock model. We discuss implications of this result in regards to the nuclear equation of state and the prospect of gravitational-wave emission from newly-born millisecond magnetars.
Gravitational waves have been detected from the inspiral of a binary neutron-star, GW170817, which allowed constraints to be placed on the neutron star equation of state. The equation of state can be further constrained if gravitational waves from a
post-merger remnant are detected. Post-merger waveforms are currently generated by numerical-relativity simulations, which are computationally expensive. Here we introduce a hierarchical model trained on numerical-relativity simulations, which can generate reliable post-merger spectra in a fraction of a second. Our spectra have mean fitting factors of 0.95, which compares to fitting factors of 0.76 and 0.85 between different numerical-relativity codes that simulate the same physical system. This method is the first step towards generating large template banks of spectra for use in post-merger detection and parameter estimation.
X-ray observations of some short gamma-ray bursts indicate that a long-lived neutron star can form as a remnant of a binary neutron star merger. We develop a gravitational-wave detection pipeline for a long-lived binary neutron star merger remnant gu
ided by these counterpart electromagnetic observations. We determine the distance out to which a gravitational-wave signal can be detected with Advanced LIGO at design sensitivity and the Einstein Telescope using this method, guided by X-ray data from GRB140903A as an example. Such gravitational waves can in principle be detected out to $sim$ 20 Mpc for Advanced LIGO and $sim$ 450 Mpc for the Einstein Telescope assuming a fiducial ellipticity of $10^{-2}$. However, in practice we can rule out such high values of the ellipticity as the total energy emitted in gravitational waves would be greater than the total rotational energy budget of the system. We show how these observations can be used to place upper limits on the ellipticity using these energy considerations. For GRB140903A, the upper limit on the ellipticity is $10^{-3}$, which lowers the detectable distance to $sim$ 2 Mpc and $sim$ 45 Mpc for Advanced LIGO and the Einstein Telescope, respectively.
