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Next-generation gravitational-wave instruments are expected to constrain the equation of state of dense nuclear matter by observing binaries involving neutron stars. We highlight a problematic systematic error in finite-temperature merger simulations, where shock heating associated with the neutron-star surface gives rise to elevated temperatures. We demonstrate the severe implications of this artificial heating by computing static and dynamical tidal parameters for neutron stars immersed in simulation temperature profiles. The induced systematic errors must be addressed if we want to build robust gravitational-wave signal models for neutron-star, or indeed neutron star-black hole, binaries., Comment: 10 pages, 5 figures, 1 table

Qualitative properties such as convexity and monotonicity of the heat content in Riemannian manifolds and in Euclidean space in particular are obtained., Comment: 14 pages

The oscillation spectrum of a neutron star is notably rich and intrinsically dependent on the equation of state of nuclear matter. With recent advancements in gravitational-wave and electromagnetic astronomy, we are nearing the capability to perform neutron-star asteroseismology and probe the complex physics of neutron stars. With this in mind, we explore the implementation of three-parameter finite-temperature matter models in the computation of neutron-star oscillations. We consider in detail the thermodynamics of nuclear matter and show how this information enters the problem. Our realistic treatment takes into account entropy and composition gradients that exist in the nuclear matter, giving rise to buoyant g-mode oscillations. To illustrate the implementation, we determine the oscillation spectrum of a low-temperature neutron star. In addition to the expected compositional and thermal g-modes, we find perturbations sourced by phase transitions in the equation of state. We also examine the thermal evolution of the oscillation spectrum of a neutron star with constant redshifted temperature., Comment: 14 pages, 6 figures, 1 table

We investigate upper bounds for the spectral ratios and gaps for the Steklov eigenvalues of balls with revolution-type metrics. We do not impose conditions on the Ricci curvature or on the convexity of the boundary. We obtain optimal upper bounds for the Steklov spectral ratios in dimensions 3 and higher. In dimension 3, we also obtain optimal upper bounds for the Steklov spectral gaps. By imposing additional constraints on the metric, we obtain upper bounds for the Steklov spectral gaps in dimensions 4 and higher., Comment: Several ideas of proof from the first version could also be used to obtain Theorems 1.3 and 1.4 from the preprint arXiv:2403.13620 [math.SP] by J. Brisson and B. Colbois so we have incorporated these two theorems in this replacement

Rotating neutron stars that support long-lived, non-axisymmetric deformations known as mountains have long been considered potential sources of gravitational radiation. However, the amplitude from such a source is very weak and current gravitational-wave interferometers have yet to witness such a signal. The lack of detections has provided upper limits on the size of the involved deformations, which are continually being constrained. With expected improvements in detector sensitivities and analysis techniques, there is good reason to anticipate an observation in the future. This review concerns the current state of the theory of neutron-star mountains. These exotic objects host the extreme regimes of modern physics, which are related to how they sustain mountains. We summarise various mechanisms that may give rise to asymmetries, including crustal strains built up during the evolutionary history of the neutron star, the magnetic field distorting the star's shape and accretion episodes gradually constructing a mountain. Moving beyond the simple rotating model, we also discuss how precession affects the dynamics and modifies the gravitational-wave signal. We describe the prospects for detection and the challenges moving forward., Comment: 29 pages, 6 figures; Topical Review in Classical and Quantum Gravity

In \cite{GGKM-SSS} we examined the relationship between the singular set of a compact Riemannian orbifold and the spectrum of the Hodge Laplacian on $p$-forms by computing the heat invariants associated to the $p$-spectrum. We showed that the heat invariants of the $0$-spectrum together with those of the $1$-spectrum for the corresponding Hodge Laplacians are sufficient to distinguish orbifolds from manifolds as long as the singular sets have codimension $\le 3.$ This is enough to distinguish orbifolds from manifolds for dimension $\le 3.$ Here we give both positive and negative inverse spectral results for the individual $p$-spectra considered separately. For example, we give conditions on the codimension of the singular set which guarantee that the volume of the singular set is determined, and in many cases we show by providing counterexamples that the conditions are sharp., Comment: Small corrections made to previous arXiv submission. arXiv admin note: substantial text overlap with arXiv:2106.07882

Mature neutron stars are expected exhibit gravity g-modes due to stratification caused by varying composition. These modes are affected by nuclear reactions, leading to complex (damped) mode frequencies and the suppression of high order g-modes, in contrast with the common non-dissipative analysis which leads to an infinite g-mode spectrum. Focusing on the transition between the fast and slow reaction regimes, we examine the impact of nuclear reactions on the g-mode spectrum. The general framework for the analysis is presented along with sample numerical results for the BSk21 equation of state and the standard Urca reactions., Comment: 11 pages, 3 figures

Objectives: To identify and quantify risk factors that contribute to clusters of COVID-19 in the workplace. Methods: We identified clusters of COVID-19 cases in the workplace and investigated the characteristics of the individuals, the workplaces, the areas they work, and the methods of commute to work, through data linkages based on Middle Layer Super Output Areas (MSOAs) in England between 20/06/2021 and 20/02/2022. We estimated associations between potential risk factors and workplace clusters, adjusting for plausible confounders identified using a Directed Acyclic Graph (DAG). Results: For most industries, increased physical proximity in the workplace was associated with increased risk of COVID-19 clusters, while increased vaccination was associated with reduced risk. Commuter demographic risk factors varied across industry, but for the majority of industries, a higher proportion of black/african/caribbean ethnicities, and living in deprived areas, was associated with increased cluster risk. A higher proportion of commuters in the 60-64 age group was associated with reduced cluster risk. There were significant associations between gender, work commute methods, and staff contract type with cluster risk, but these were highly variable across industries. Conclusions: This study has used novel national data linkages to identify potential risk factors of workplace COVID-19 clusters, including possible protective effects of vaccination and increased physical distance at work. The same methodological approach can be applied to wider occupational and environmental health research.

We re-visit the calculation of mode oscillations in the ocean of a rotating neutron star, which may be excited during thermonuclear X-ray bursts. Our present theoretical understanding of ocean modes relies heavily on the traditional approximation, commonly employed in geophysics. The approximation elegantly decouples the radial and angular sectors of the perturbation problem by neglecting the vertical contribution from the Coriolis force. However, as the implicit assumptions underlying it are not as well understood as they ought to be, we examine the traditional approximation and discuss the associated mode solutions. The results demonstrate that, while the approximation may be appropriate in certain contexts, it may not be accurate for rapidly rotating neutron stars. In addition, using the shallow-water approximation, we show analytically how the solutions that resemble r-modes change their nature in neutron-star oceans to behave like gravity waves. We also outline a simple prescription for lifting Newtonian results in a shallow ocean to general relativity, making the result more realistic., Comment: 16 pages, 2 figures. Missing text in Sec. III discovered in press

We report results from a study of XTE J1739-285, a transient neutron star low mass X-ray binary observed with AstroSat and NuSTAR during its 2019-2020 outburst. We detected accretion-powered X-ray pulsations at 386 Hz during very short intervals (0.5--1 s) of X-ray flares. These flares were observed during the 2019 observation of XTE J1739-285. During this observation, we also observed a correlation between intensity and hardness ratios, suggesting an increase in hardness with the increase in intensity. Moreover, a thermonuclear X-ray burst detected in our AstroSat observation during the 2020 outburst revealed the presence of coherent burst oscillations at 383 Hz during its decay phase. The frequency drift of 3 Hz during X-ray burst can be explained with r modes. Thus, making XTE J1739-285 belong to a subset of NS-LMXBs which exhibit both nuclear- and accretion-powered pulsations. The power density spectrum created using the AstroSat-LAXPC observations in 2020 showed the presence of a quasi-periodic oscillation at ~ 0.83 Hz. Our X-ray spectroscopy revealed significant changes in the spectra during the 2019 and 2020 outburst. We found a broad iron line emission feature in the X-ray spectrum during the 2020 observation, while this feature was relatively narrow and has a lower equivalent width in 2019,~when the source was accreting at higher rates than 2020., Comment: Accepted for publication in MNRAS, 13 pages

The only r-modes that exist in a globally barotropic, rotating, Newtonian star are the fundamental $l = |m|$ solutions, where $l$ and $m$ are the indices of the spherical harmonic $Y_l^m$ that describe the mode's angular dependence. This is in stark contrast to a stellar model that is non-barotropic throughout its interior, which hosts all the $l \geq |m|$ perturbations including radial overtones. In reality, neutron stars are stratified with locally barotropic regions. Therefore, we explore how stratification alters a star's ability to support r-modes. We consider the globally stratified case and examine the behaviour of the modes as the star gets close to barotropicity. In this limit, we find that all but the fundamental $l = |m|$ perturbations change character and become generic inertial modes. Restricting the analysis to $l = |m|$ perturbations, we develop the r-mode equations in order to consider stellar models that exhibit local barotropicity. Our results for such models show that the r-mode overtones diverge and join the inertial modes. In order to see which r-modes persist and retain their character in realistic neutron stars, these calculations will need to be brought into full general relativity., Comment: 15 pages, 8 figures. Accepted for publication in MNRAS

We revisit the problem of inertial r-modes in stratified stars, drawing on a more precise description of the composition stratification in a mature neutron star. The results highlight issues with the traditional approach to the problem, leading us to rethink the computational strategy for r-modes of non-barotropic neutron stars. We outline two strategies for dealing with the problem. For moderate to slowly rotating neutron stars the only viable alternative may be to approach the problem numerically from the outset, while a meaningful slow-rotation calculation can be carried out for the fastest known spinning stars (which may be close to being driven unstable by the emission of gravitational waves). We demonstrate that the latter approach leads to a problem close, but not identical, to that for barotropic inertial modes. We also suggest that these reformulations of the problem likely resolve the long-standing problem of singular behaviour associated with a co-rotation point in rotating relativistic neutron stars. This issue needs to be resolved in order to guide future gravitational-wave searches., Comment: 22 pages, 1 figure. Accepted for publication in ApJ

In this paper we introduce the magnetic Hodge Laplacian, which is a generalization of the magnetic Laplacian on functions to differential forms. We consider various spectral results, which are known for the magnetic Laplacian on functions or for the Hodge Laplacian on differential forms, and discuss similarities and differences of this new ``magnetic-type'' operator.

We investigate the heat flow in an open, bounded set $D$ in $\mathbb{R}^2$ with polygonal boundary $\partial D$. We suppose that $D$ contains an open, bounded set $\widetilde{D}$ with polygonal boundary $\partial \widetilde{D}$. The initial condition is the indicator function of $\widetilde{D}$ and we impose a Neumann boundary condition on the edges of $\partial D$. We obtain an asymptotic formula for the heat content of $\widetilde{D}$ in $D$ as time $t\downarrow 0$., Comment: 28 pages, 6 figures

Owed to their compactness, neutron stars involve strong gravity and extreme density physics. Nevertheless, at present, there are a variety of problems where progress (at least conceptually) can be made in the context of weak gravity. Motivated by this we examine how accurately one can model neutron stars using the post-Newtonian approximation to general relativity. In general, we find there is a significant degree of freedom in how the post-Newtonian equations of stellar structure can be formulated. We discuss this flexibility in the formulation and provide examples to demonstrate the impact on stellar models. We also consider the (closely related) problem of building neutron stars using isotropic coordinates. In this context, we provide a new strategy for solving the equations (based on a scaling argument) which significantly simplifies the problem., Comment: 23 pages, 7 figures, RevTeX format. Published in CQG

We carefully develop the framework required to model the dynamical tidal response of a spinning neutron star in an inspiralling binary system, in the context of Newtonian gravity, making sure to include all relevant details and connections to the existing literature. The tidal perturbation is decomposed in terms of the normal oscillation modes, used to derive an expression for the effective Love number which is valid for any rotation rate. In contrast to previous work on the problem, our analysis highlights subtle issues relating to the orthogonality condition required for the mode-sum representation of the dynamical tide and shows how the prograde and retrograde modes combine to provide the overall tidal response. Utilising a slow-rotation expansion, we show that the dynamical tide (the effective Love number) is corrected at first order in rotation, whereas in the case of the static tide (the static Love number) the rotational corrections do not enter until second order., Comment: 19 pages, 1 figure