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Mature neutron stars are expected to exhibit gravity g-modes due to stratification caused by a varying matter composition in the high-density core. By employing the BSk equation of state family, and working within the relativistic Cowling approximation, we examine how subtle differences in the nuclear matter assumptions impact on the g-mode spectrum. We investigate the possibility of detecting individual g-mode resonances during a binary inspiral with current and next-generation ground-based detectors, like Cosmic Explorer and the Einstein Telescope. Our results suggest that these resonances may be within the reach of future detectors, especially for low mass stars with $M\lesssim1.4M_\odot$., Comment: 18 pages, 10 figures and 2 tables

The recent observation of the GW230529 event indicates that black hole-neutron star binaries can contain low-mass black holes. Since lower mass systems are more favourable for tidal disruption, such events are promising candidates for multi-messenger observations. In this study, we employ five finite-temperature, composition-dependent matter equations of state and present results from ten 3D general relativistic hydrodynamic simulations for the mass ratios $q = 2.6$ and $5$. Two of these simulations target the chirp mass and effective spin parameter of the GW230529 event, while the remaining eight contain slightly higher-mass black holes, including both spinning ($a_{BH} = 0.7$) and non-spinning ($a_{BH} = 0$) models. We discuss the impact of the equation of state, spin, and mass ratio on black hole-neutron star mergers by examining both gravitational-wave and ejected matter properties. For the low-mass ratio model we do not see fast-moving ejecta for the softest equation of state model, but the stiffer model produces on the order of $10^{-6}M_\odot$ of fast-moving ejecta, expected to contribute to an electromagnetic counterpart. Notably, the high-mass ratio model produces nearly the same amount of total dynamical ejecta, but yields $52$ times more fast-moving ejecta than the low-mass ratio system. In addition, we observe that the black-hole spin tends to decrease the amount of fast-moving ejecta while increasing significantly the total ejected mass. Finally, we note that the disc mass tends to increase as the neutron star compactness decreases., Comment: 9 pages, 8 Figures, 3 Tables

Nonlinear simulations of neutron star mergers are complicated by the need to represent turbulent dynamics. As we cannot (yet) perform simulations that resolve accurately both the gravitational-wave scale and the smallest scales at which magneto/hydrodynamic turbulence plays a role, we need to rely on approximations. Addressing this problem in the context of large-eddy models, we outline a coherent Lagrangian filtering framework that allows us to explore the many issues that arise, linking conceptual problems to practical implementations and the interpretation of the results. We develop understanding crucial for quantifying unavoidable uncertainties in current and future numerical relativity simulations and consider the implications for neutron-star parameter estimation and constraints on the equation of state of matter under extreme conditions., Comment: 15 pages, comments welcome

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

Previous theoretical works using the pre-merger orbital evolution of coalescing neutron stars to constrain properties of dense nuclear matter assume a gravitational wave phase uncertainty of a few radians, or about a half cycle. However, recent studies of the signal from GW170817 and next generation detector sensitivities indicate actual phase uncertainties at least twenty times better. Using these refined estimates, we show that future observations of nearby sources like GW170817 may be able to reveal neutron star properties beyond just radius and tidal deformability, such as the matter composition and/or presence of a superfluid inside neutron stars, via tidal excitation of g-mode oscillations. Data from GW170817 already limits the amount of orbital energy that is transferred to the neutron star to <2x10^47 erg and the g-mode tidal coupling to Qmode<10^-3 at 50 Hz (5x10^48 erg and 4x10^-3 at 200 Hz), and future observations and detectors will greatly improve upon these constraints. In addition, analysis using general parameterization models that have been applied to the so-called p-g instability show that the instability already appears to be restricted to regimes where the mechanism is likely to be inconsequential; in particular, we show that the number of unstable modes is <<100 at <~100 Hz, and next generation detectors will essentially rule out this mechanism (assuming that the instability remains undetected). Finally, we illustrate that measurements of tidal excitation of r-mode oscillations in nearby rapidly rotating neutron stars are within reach of current detectors and note that even non-detections will limit the inferred inspiralling neutron star spin rate to <20 Hz, which will be useful when determining other parameters such as neutron star mass and tidal deformability., Comment: 7 pages, 4 figures; accepted for publication in Physical Review D

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

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

Nuclear reactions may affect gravitational-wave signals from neutron-star mergers, but the impact is uncertain. In order to quantify the effect, we compare two numerical simulations representing intuitive extremes. In one case reactions happen instantaneously. In the other case, they occur on timescales much slower than the evolutionary timescale. We show that, while the differences in the two gravitational-wave signals are small, they should be detectable by third-generation observatories. To avoid systematic errors in equation of state parameters inferred from observed signals, we need to accurately implement nuclear reactions in future simulations., Comment: 6 pages, 2 figures

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

We study the tidal response of a superfluid neutron star in a binary system, focussing on Newtonian models with superfluid neutrons present throughout the star's core and the inner crust. Within the two-fluid formalism, we consider the main aspects that arise from the presence of different regions inside the star, with particular focus on the various interfaces. Having established the relevant theory, we determine the tidal excitation of the most relevant oscillation modes during binary inspiral. Our results suggest that superfluid physics has a negligible impact on the static tidal deformation. The overwhelming contribution to the Love number is given by, as for normal matter stars, the ordinary fundamental mode (f-mode). Strong entrainment, here described by a phenomenological expression which mimics the large effective neutron mass expected at the bottom of the crust, is shown to have significant impact on the superfluid modes, but our results for the dynamical tide are nevertheless similar to the static limit: the fundamental modes are the ones most significantly excited by the tidal interaction, with the ordinary f-mode dominating the superfluid one. We also discuss the strain built up in the star's crust during binary inspiral, showing that the superfluid f-mode may (depending on entrainment) reach the limit where the crust breaks, although it does so after the ordinary f-mode. Overall, our results suggest that the presence of superfluidity may be difficult to establish from binary neutron star gravitational-wave signals., Comment: 18 pages, 9 figures and 7 tables. Version accepted for publication in MNRAS

In order to extract maximal information from neutron-star merger signals, both gravitational and electromagnetic, we need to ensure that our theoretical models/numerical simulations faithfully represent the extreme physics involved. This involves a range of issues, with the finite temperature effects regulating many of the relevant phenomena. As a step towards understanding these issues, we explore the conditions for $\beta$-equilibrium in neutron star matter for the densities and temperatures reached in a binary neutron star merger. Using the results from our out-of-equilibrium merger simulation, we consider how different notions of equilibrium may affect the merger dynamics, raising issues that arise when attempting to account for these conditions in future simulations. These issues are both computational and conceptual. We show that the effects lead to, in our case, a softening of the equation of state in some density regions, and to composition changes that affect processes that rely on deviation from equilibrium, such as bulk viscosity, both in terms of the magnitude and the equilibration timescales inherent to the relevant set of reactions. We also demonstrate that it is difficult to determine exactly which equilibrium conditions are relevant in which regions of the matter due to the dependence on neutrino absorption, further complicating the calculation of the reactions that work to restore the matter to equilibrium., Comment: 26 pages, 11 figures

Models of turbulent flows require the resolution of a vast range of scales, from large eddies to small-scale features directly associated with dissipation. As the required resolution is not within reach of large scale numerical simulations, standard strategies involve a smoothing of the fluid dynamics, either through time averaging or spatial filtering. These strategies raise formal issues in general relativity, where the split between space and time is observer dependent. To make progress, we develop a new covariant framework for filtering/averaging based on the fibration of spacetime associated with fluid elements and the use of Fermi coordinates to facilitate a meaningful local analysis. We derive the resolved equations of motion, demonstrating how "effective" dissipative terms arise because of the coarse-graining, and paying particular attention to the thermodynamical interpretation of the resolved quantities. Finally, as the smoothing of the fluid-dynamics inevitably leads to a closure problem, we propose a new closure scheme inspired by recent progress in the modelling of dissipative relativistic fluids, and crucially, demonstrate the linear stability of the proposed model., Comment: Version as published on Phys. Rev. D

The I-Love-Q relations are approximate equation-of-state independent relations that connect the moment of inertia, the spin-induced quadrupole moment, and the tidal deformability of neutron stars. In this paper, we study the I-Love-Q relations for superfluid neutron stars for a general relativistic two-fluid model: one fluid being the neutron superfluid and the other a conglomerate of all charged components. We study to what extent the two-fluid dynamics might affect the robustness of the I-Love-Q relations by using a simple two-component polytropic model and a relativistic mean field model with entrainment for the equation-of-state. Our results depend crucially on the spin ratio $\Omega_{\rm n}/\Omega_{\rm p}$ between the angular velocities of the neutron superfluid and the normal component. We find that the I-Love-Q relations can still be satisfied to high accuracy for superfluid neutron stars as long as the two fluids are nearly co-rotating $\Omega_{\rm n}/\Omega_{\rm p} \approx 1$. However, the deviations from the I-Love-Q relations increase as the spin ratio deviates from unity. In particular, the deviation of the Q-Love relation can be as large as $O(10\%)$ if $\Omega_{\rm n}/\Omega_{\rm p}$ differ from unity by a few tens of percent. As $\Omega_{\rm n}/\Omega_{\rm p} \approx 1$ is expected for realistic neutron stars, our results suggest that the two-fluid dynamics should not affect the accuracy of any gravitational waveform models for neutron star binaries that employ the relation to connect the spin-induced quadrupole moment and the tidal deformability., Comment: Invited contribution to Universe's Special Issue "Superfluidity and Superconductivity in Neutron Stars" (Guest Editor: Nicolas Chamel)

We consider the dynamical tidal response of a neutron star in an inspiralling binary, focussing on the impact of the star's elastic crust. Within the context of Newtonian gravity, we add the elastic aspects to the theoretical formulation of the problem and quantify the dynamical excitation of different classes of oscillation modes. The results demonstrate the expectation that the fundamental mode dominates the tidal response and show how the usual tidal deformability (and the Love number) emerge in the static limit. In addition, we consider to what extent the different modes may be excited to a level where the breaking strain of the crust would be exceeded (locally). The results show that the fundamental mode may fracture the crust during the late stages of inspiral. This is also the case for the first gravity mode, which reaches the breaking threshold in strongly stratified stars. In our models with a fluid ocean, interface modes associated with the crust-ocean transition may also induce crust fracture. If this happens it does so earlier in the inspiral, at a lower orbital frequency., Comment: 23 pages, 12 figures and 6 tables. Version accepted for publication in MNRAS

Fully non-linear equations of motion for dissipative general relativistic multi-fluids can be obtained from an action principle involving the explicit use of lower dimensional matter spaces. More traditional strategies for incorporating dissipation-like the famous Mueller-Israel-Stewart model-are based on expansions away from equilibrium defined, in part, by the laws of thermodynamics. The goal here is to build a formalism to facilitate comparison of the action-based results with those based on the traditional approach. The first step of the process is to use the action-based approach itself to construct self-consistent notions of equilibrium. Next, first-order deviations are developed directly on the matter spaces, which motivates the latter as the natural arena for the underlying thermodynamics. Finally, we identify the dissipation terms of the action-based model with first-order "thermodynamical" fluxes, on which the traditional models are built. The description is developed in a general setting so that the formalism can be used to describe multi-fluid systems, for which causal and stable models are not yet available. As an illustration of the approach, a simple application of a single viscous fluid is considered and, even though the expansion is halted at first order, we sketch how a causal response can be implemented through Cattaneo-type equations., Comment: Final version as published on Classical and Quantum Gravity

The configuration of the magnetic field in the interior of a neutron star is mostly unknown from observations. Theoretical models of the interior magnetic field geometry tend to be oversimplified to avoid mathematical complexity and tend to be based on axisymmetric barotropic fluid systems. These static magnetic equilibrium configurations have been shown to be unstable on a short time scale against an infinitesimal perturbation. Given this instability, it is relevant to consider how more realistic neutron star physics affects the outcome. In particular, it makes sense to ask if elasticity, which provides an additional restoring force on the perturbations, may stabilise the system. It is well-known that the matter in the neutron star crust forms an ionic crystal. The interactions between the crystallized nuclei can generate shear stress against any applied strain. To incorporate the effect of the crust on the dynamical evolution of the perturbed equilibrium structure, we study the effect of elasticity on the instability of an axisymmetric magnetic star. In particular we determine the critical shear modulus required to prevent magnetic instability and consider the corresponding astrophysical consequences., Comment: 12 pages, accepted for publication in MNRAS

Using nonlinear, fully relativistic, simulations we investigate the dynamics and gravitational-wave signature associated with instabilities in neutron star postmerger remnants. For simplified models of the remnant we establish the presence of an instability in stars with moderate $T/|W|$, the ratio between the kinetic and the gravitational potential energies. Detailed analysis of the density oscillation pattern reveals a \emph{local} instability in the inner region of the more realistic differential rotation profile. We apply Rayleigh's inflection theorem and Fj{\o}rtoft's theorem to analyze the stability criteria concluding that this \emph{inner local} instability originates from a shear instability close to the peak of the angular velocity profile, and that it later evolves into a fast-rotating m=2 oscillation pattern. We discuss the importance of the presence of a corotation point in the fluid, its connection with the shear instability, and comparisons to the Rossby wave and Papaloizou Pringle instabilities considered in the wider literature., Comment: 17 Figures. Accepted for publication in Phys. Rev. D

During their most recent observing run, LIGO/Virgo reported the gravitational wave (GW) transient S191110af, a burst signal at a frequency of 1.78 kHz that lasted for 0.104 s. While this signal was later deemed non-astrophysical, genuine detections of uncertain origin will occur in the future. Here we study the potential for detecting GWs from neutron star fluid oscillations, which have mode frequency and duration matching those of S191110af and which can be used to constrain the equation of state of nuclear matter. Assuming that such transient oscillations can be excited to energies typical of a pulsar glitch, we use measured properties of known glitching pulsars to estimate the amplitude of GWs produced by such events. We find that current GW detectors may observe nearby pulsars undergoing large events with energy similar to Vela pulsar glitch energies, while next generation detectors could observe a significant number of events. Finally, we show that it is possible to distinguish between GWs produced by rapidly rotating and slowly rotating pulsars from the imprint of rotation on the f-mode frequency., Comment: 6 pages, 5 figures; accepted for publication in Physical Review D

Gravitational wave astronomy is expected to provide independent constraints on neutron star properties, such as their dense matter equation of state. This is possible with the measurements of binary components' tidal deformability, which alter the point-particle gravitational waveforms of the late inspiral phase of neutron-star binaries. Although current gravitational wave detectors are not sensitive enough for a precise determination of the individual tidal deformations of the components, a large number of combined observations with future detectors will decrease uncertainties in this quantity. Here we provide a first study of the tidal deformability effects due to the elasticity/solidity of the crust (hadronic phase) in a hybrid neutron star, as well as the influence of a quark-hadronic phase density jump on tidal deformations. We employ the framework of nonradial perturbations with zero frequency and study hadronic phases presenting elastic aspects when perturbed (with the shear modulus approximately $1\%$ of the pressure). We find that the relative tidal deformation change in a hybrid star with a perfect-fluid quark phase and a hadronic phase presenting an elastic part is never larger than about $2-4\%$ (with respect to a perfect-fluid counterpart). These maximum changes occur when the elastic region of a hybrid star is larger than approximately $60\%$ of the star's radius, which may happen when its quark phase is small and the density jump is large enough, or even when a hybrid star has an elastic mixed phase. For other cases, the relative tidal deformation changes due to an elastic crust are negligible ($10^{-5}-10^{-1}\%$), therefore unlikely to be measured even with third generation detectors. Thus, only when the size of the elastic hadronic region of a hybrid star is over half of its radius, the effects of elasticity could have a noticeable impact on tidal deformations., Comment: 11 pages, 3 figures. Minor changes to the abstract. Accepted for publication in ApJ

Implementing a family of differential rotation laws inspired by binary neutron-star merger remnants, we consider the impact of the rotation profile on the low-T/W instability. We use time evolutions of the linearised dynamical equations, in Newtonian gravity, to study non-axisymmetric oscillations and identify the unstable modes. The presence and evolution of the low-T/W instability is monitored with the canonical energy and angular momentum, while the growth time is extracted from the evolved kinetic energy. The results for the new rotation laws highlight similarities with the commonly considered j-constant law. The instability sets in when an oscillation mode co-rotates with the star (i.e. whenever there is a point where the mode's pattern speed matches the bulk angular velocity) and grows faster deep inside the co-rotation region. However, the new profiles add features, like an additional co-rotation point to the problem, which affect the onset of instability. The rotation laws influence more drastically the oscillation frequencies of the l=m=2 f-mode in fast rotating models, but affect the instability growth time at any rotation rate. We also identify models where the low-T/W instability appears to be triggered by inertial modes. We discuss to what extent the inferred qualitative behaviour is likely to be of observational relevance., Comment: 12 pages, 8 figures and 4 tables. Version accepted for publication in MNRAS

The application of standard accretion theory to observations of X-ray binaries provides valuable insights into neutron star properties, such as their spin period and magnetic field. However, most studies concentrate on relatively old systems, where the neutron star is in its late propeller, accretor, or nearly spin equilibrium phase. Here we use an analytic model from standard accretion theory to illustrate the evolution of high-mass X-ray binaries early in their life. We show that a young neutron star is unlikely to be an accretor because of the long duration of ejector and propeller phases. We apply the model to the recently discovered ~4000 yr old high-mass X-ray binary XMMU J051342.6-672412 and find that the system's neutron star, with a tentative spin period of 4.4 s, cannot be in the accretor phase and has a magnetic field B > (a few)x10^13 G, which is comparable to the magnetic field of many older high-mass X-ray binaries and is much higher than the spin equilibrium inferred value of (a few)x10^11 G. The observed X-ray luminosity could be the result of thermal emission from a young cooling magnetic neutron star or a small amount of accretion that can occur in the propeller phase., Comment: 7 pages, 4 figures; accepted for publication in MNRAS

With the first detections of binary neutron star mergers by gravitational-wave detectors, it proves timely to consider how the internal structure of neutron stars affects the way in which they can be asymmetrically deformed. Such deformations may leave measurable imprints on gravitational-wave signals and can be sourced through tidal interactions or the formation of mountains. We detail the formalism that describes fully-relativistic neutron star models with elastic crusts undergoing static perturbations. This formalism primes the problem for studies into a variety of mechanisms that can deform a neutron star. We present results for a barotropic equation of state and a realistic model for the elastic crust, which enables us to compute relevant quantities such as the tidal deformability parameter. We find that the inclusion of an elastic crust provides a very small correction to the tidal deformability. The results allow us to demonstrate when and where the crust starts to fail during a binary inspiral and we find that the majority of the crust will remain intact up until merger., Comment: 34 pages, 7 figures. Accepted by Phys. Rev. D

Two coupled, interpenetrating fluids suffer instabilities beyond certain critical counterflows. For ideal fluids, an energetic instability occurs at the point where a sound mode inverts its direction due to the counterflow, while dynamical instabilities only occur at larger relative velocities. Here we discuss two relativistic fluids, one of which is dissipative. Using linearized hydrodynamics, we show that in this case the energetic instability turns dynamical, i.e., there is an exponentially growing mode, and this exponential growth only occurs in the presence of dissipation. This result is general and does not rely on an underlying microscopic theory. It can be applied to various two-fluid systems for instance in the interior of neutron stars. We also point out that under certain circumstances the two-fluid system exhibits a mode analogous to the r-mode in neutron stars that can become unstable for arbitrarily small values of the counterflow., Comment: 20 pages, 4 figures, v2: minor changes in the text, references added, version accepted for publication

In this White Paper we present the potential of the enhanced X-ray Timing and Polarimetry (eXTP) mission for studies related to Observatory Science targets. These include flaring stars, supernova remnants, accreting white dwarfs, low and high mass X-ray binaries, radio quiet and radio loud active galactic nuclei, tidal disruption events, and gamma-ray bursts. eXTP will be excellently suited to study one common aspect of these objects: their often transient nature. Developed by an international Consortium led by the Institute of High Energy Physics of the Chinese Academy of Science, the eXTP mission is expected to be launched in the mid 2020s., Comment: Accepted for publication on Sci. China Phys. Mech. Astron. (2019)

In this paper we describe the potential of the enhanced X-ray Timing and Polarimetry (eXTP) mission for studies related to accretion flows in the strong field gravity regime around both stellar-mass and supermassive black-holes. eXTP has the unique capability of using advanced 'spectral-timing-polarimetry' techniques to analyze the rapid variations with three orthogonal diagnostics of the flow and its geometry, yielding unprecedented insight into the inner accreting regions, the effects of strong field gravity on the material within them and the powerful outflows which are driven by the accretion process., Comment: Accepted for publication on Sci. China Phys. Mech. Astron. (2019)

The fastest-spinning neutron stars in low-mass X-ray binaries, despite having undergone millions of years of accretion, have been observed to spin well below the Keplerian break-up frequency. We simulate the spin evolution of synthetic populations of accreting neutron stars in order to assess whether gravitational waves can explain this behaviour and provide the distribution of spins that is observed. We model both persistent and transient accretion and consider two gravitational-wave-production mechanisms that could be present in these systems: thermal mountains and unstable $r$-modes. We consider the case of no gravitational-wave emission and observe that this does not match well with observation. We find evidence for gravitational waves being able to provide the observed spin distribution; the most promising mechanisms being a permanent quadrupole, thermal mountains and unstable $r$-modes. However, based on the resultant distributions alone it is difficult to distinguish between the competing mechanisms., Comment: 12 pages, 12 figures. Accepted for publication in MNRAS

Pulsar glitches provide a unique way to study neutron star microphysics because short post-glitch dynamics are directly linked to strong frictional processes on small scales. To illustrate this connection between macroscopic observables and microphysics, we review calculations of vortex interactions focusing on Kelvin wave excitations and determine the corresponding mutual friction strength for realistic microscopic parameters in the inner crust. These density-dependent crustal coupling profiles are combined with a simplified treatment of the core coupling and implemented in a three-component neutron star model to construct a predictive framework for glitch rises. As a result of the density-dependent dynamics, we find the superfluid to transfer angular momentum to different parts of the crust and the core on different timescales. This can cause the spin frequency change to become non-monotonic in time, allowing for a maximum value much larger than the measured glitch size, as well as a delay in the recovery. The exact shape of the calculated glitch rise is strongly dependent on the relative strength between the crust and core mutual friction, providing the means to probe not only the crustal superfluid but also the deeper neutron star interior. To demonstrate the potential of this approach, we compare our predictive model with the first pulse-to-pulse observations recorded during the December 2016 glitch of the Vela pulsar. Our analysis suggests that the glitch rise behavior is relatively insensitive to the crustal mutual friction strength as long as $\mathcal{B} \gtrsim 10^{-3}$, while being strongly dependent on the core coupling strength, which we find to be in the range $3 \times 10^{-5} \lesssim \mathcal{B}_{\rm core} \lesssim 10^{-4}$., Comment: 12 pages, 2 tables, 5 figures, accepted for publication in ApJ

A superconductor of paired protons is thought to form in the core of neutron stars soon after their birth. Minimum energy conditions suggest magnetic flux is expelled from the superconducting region due to the Meissner effect, such that the neutron star core is largely devoid of magnetic fields for some nuclear equation of state and proton pairing models. We show via neutron star cooling simulations that the superconducting region expands faster than flux is expected to be expelled because cooling timescales are much shorter than timescales of magnetic field diffusion. Thus magnetic fields remain in the bulk of the neutron star core for at least 10^6-10^7 yr. We estimate the size of flux free regions at 10^7 yr to be <~ 100 m for a magnetic field of 10^11 G and possibly smaller for stronger field strengths. For proton pairing models that are narrow, magnetic flux may be completely expelled from a thin shell of approximately the above size after 10^5 yr. This shell may insulate lower conductivity outer layers, where magnetic fields can diffuse and decay faster, from fields maintained in the highly conducting deep core., Comment: 6 pages, 5 figures; accepted for publication in Physical Review C

Pulsars are rotating neutron stars that are renowned for their timing precision, although glitches can interrupt the regular timing behavior when these stars are young. Glitches are thought to be caused by interactions between normal and superfluid matter in the star. We update our recent work on a new technique using pulsar glitch data to constrain superfluid and nuclear equation of state models, demonstrating how current and future astronomy telescopes can probe fundamental physics such as superfluidity near nuclear saturation and matter at supranuclear densities. Unlike traditional methods of measuring a star's mass by its gravitational effect on another object, our technique relies on nuclear physics knowledge and therefore allows measurement of the mass of pulsars which are in isolation., Comment: 4 pages, 4 figures; proceedings of Nuclei in the Cosmos 2016 in Niigata, Japan, S. Kubono (ed.)

Carter and Lichnerowicz have established that barotropic fluid flows are conformally geodesic and obey Hamilton's principle. This variational approach can accommodate neutral, or charged and poorly conducting, fluids. We show that, unlike what has been previously thought, this approach can also accommodate perfectly conducting magnetofluids, via the Bekenstein-Oron description of ideal magnetohydrodynamics. When Noether symmetries associated with Killing vectors or tensors are present in geodesic flows, they lead to constants of motion polynomial in the momenta. We generalize these concepts to hydrodynamic flows. Moreover, the Hamiltonian descriptions of ideal magnetohydrodynamics allow one to cast the evolution equations into a hyperbolic form useful for evolving rotating or binary compact objects with magnetic fields in numerical general relativity. Conserved circulation laws, such as those of Kelvin, Alfv\'en and Bekenstein-Oron, emerge simply as special cases of the Poincar\'e-Cartan integral invariant of Hamiltonian systems. We use this approach to obtain an extension of Kelvin's theorem to baroclinic (non-isentropic) fluids, based on a temperature-dependent time parameter. We further extend this result to perfectly or poorly conducting baroclinic magnetoflows. Finally, in the barotropic case, such magnetoflows are shown to also be geodesic, albeit in a Finsler (rather than Riemann) space., Comment: 23 pages

Neutron stars are astrophysical laboratories of many extremes of physics. Their rich phenomenology provides insights into the state and composition of matter at densities which cannot be reached in terrestrial experiments. Since the core of a mature neutron star is expected to be dominated by superfluid and superconducting components, observations also probe the dynamics of large-scale quantum condensates. The testing and understanding of the relevant theory tends to focus on the interface between the astrophysics phenomenology and nuclear physics. The connections with low-temperature experiments tend to be ignored. However, there has been dramatic progress in understanding laboratory condensates (from the different phases of superfluid helium to the entire range of superconductors and cold atom condensates). In this review, we provide an overview of these developments, compare and contrast the mathematical descriptions of laboratory condensates and neutron stars and summarise the current experimental state-of-the-art. This discussion suggests novel ways that we may make progress in understanding neutron star physics using low-temperature laboratory experiments., Comment: accepted for publication in International Journal of Modern Physics D

The X-ray source 1E 161348-5055 in the supernova remnant RCW 103 recently exhibited X-ray activity typical of magnetars, i.e. neutron stars with magnetic fields > 10^14-10^15 G. However, 1E 161348-5055 has an observed period of 6.67 hr, in contrast to magnetars which have a spin period of seconds. Here we describe a simple model which can explain the spin evolution of 1E 161348-5055, as well as other magnetars, from an initial period of milliseconds that would be required for dynamo generation of magnetar-strength magnetic fields. We propose that the key difference between 1E 161348-5055 and other magnetars is the persistence of a remnant disk of small total mass. This disk caused 1E 161348-5055 to undergo ejector and propeller phases in its life, during which strong torques caused a rapid increase of its spin period. By matching its observed spin period and ~1-3 kyr age, we find that 1E 161348-5055 has the (slightly) highest magnetic field of all known magnetars, with B~5x10^15 G, and that its disk had a mass of ~10^24 g, comparable to that of the asteroid Ceres., Comment: 5 pages, 3 figures; accepted for publication in MNRAS Letters; v2, minor edits and references added

One of the primary science goals of the next generation of hard X-ray timing instruments is to determine the equation of state of the matter at supranuclear densities inside neutron stars, by measuring the radius of neutron stars with different masses to accuracies of a few percent. Three main techniques can be used to achieve this goal. The first involves waveform modelling. The flux we observe from a hotspot on the neutron star surface offset from the rotational pole will be modulated by the star's rotation, giving rise to a pulsation. Information about mass and radius is encoded into the pulse profile via relativistic effects, and tight constraints on mass and radius can be obtained. The second technique involves characterising the spin distribution of accreting neutron stars. The most rapidly rotating stars provide a very clean constraint, since the mass-shedding limit is a function of mass and radius. However the overall spin distribution also provides a guide to the torque mechanisms in operation and the moment of inertia, both of which can depend sensitively on dense matter physics. The third technique is to search for quasi-periodic oscillations in X-ray flux associated with global seismic vibrations of magnetars (the most highly magnetized neutron stars), triggered by magnetic explosions. The vibrational frequencies depend on stellar parameters including the dense matter equation of state. We illustrate how these complementary X-ray timing techniques can be used to constrain the dense matter equation of state, and discuss the results that might be expected from a 10m$^2$ instrument. We also discuss how the results from such a facility would compare to other astronomical investigations of neutron star properties. [Modified for arXiv], Comment: To appear in Reviews of Modern Physics as a Colloquium, 23 pages, 9 figures

Pulsars are known for their superb timing precision, although glitches can interrupt the regular timing behavior when the stars are young. These glitches are thought to be caused by interactions between normal and superfluid matter in the crust of the star. However, glitching pulsars such as Vela have been shown to require a superfluid reservoir that greatly exceeds that available in the crust. We examine a model in which glitches tap the superfluid in the core. We test a variety of theoretical superfluid models against the most recent glitch data and find that only one model can successfully explain up to 45 years of observational data. We develop a new technique for combining radio and X-ray data to measure pulsar masses, thereby demonstrating how current and future telescopes can probe fundamental physics such as superfluidity near nuclear saturation., Comment: 5 pages, 3 figures; published in Science Advances on 2 Oct 2015

The presence of superconducting and superfluid components in the core of mature neutron stars calls for the rethinking of a number of key magnetohydrodynamical notions like resistivity, the induction equation, magnetic energy and flux-freezing. Using a multi-fluid magnetohydrodynamics formalism, we investigate how the magnetic field evolution is modified when neutron star matter is composed of superfluid neutrons, type-II superconducting protons and relativistic electrons. As an application of this framework, we derive an induction equation where the resistive coupling originates from the mutual friction between the electrons and the vortex/fluxtube arrays of the neutron and proton condensates. The resulting induction equation allows the identification of two timescales that are significantly different from those of standard magnetohydrodynamics. The astrophysical implications of these results are briefly discussed.

With an average density higher than the nuclear density, neutron stars (NS) provide a unique test-ground for nuclear physics, quantum chromodynamics (QCD), and nuclear superfluidity. Determination of the fundamental interactions that govern matter under such extreme conditions is one of the major unsolved problems of modern physics, and -- since it is impossible to replicate these conditions on Earth -- a major scientific motivation for SKA. The most stringent observational constraints come from measurements of NS bulk properties: each model for the microscopic behaviour of matter predicts a specific density-pressure relation (its `Equation of state', EOS). This generates a unique mass-radius relation which predicts a characteristic radius for a large range of masses and a maximum mass above which NS collapse to black holes. It also uniquely predicts other bulk quantities, like maximum spin frequency and moment of inertia. The SKA, in Phase 1 and particularly in Phase 2 will, thanks to the exquisite timing precision enabled by its raw sensitivity, and surveys that dramatically increase the number of sources: 1) Provide many more precise NS mass measurements (high mass NS measurements are particularly important for ruling out EOS models); 2) Allow the measurement of the NS moment of inertia in highly relativistic binaries such as the Double Pulsar; 3) Greatly increase the number of fast-spinning NS, with the potential discovery of spin frequencies above those allowed by some EOS models; 4) Improve our knowledge of new classes of binary pulsars such as black widows and redbacks (which may be massive as a class) through sensitive broad-band radio observations; and 5) Improve our understanding of dense matter superfluidity and the state of matter in the interior through the study of rotational glitches, provided that an ad-hoc campaign is developed., Comment: 22 pages, 8 figures, to be published in: "Advancing Astrophysics with the Square Kilometre Array", Proceedings of Science, PoS(AASKA14)043

We study the low T/W instability associated with the f-mode of differentially rotating stars. Our stellar models are described by a polytropic equation of state and the rotation profile is given by the standard j-constant law. The properties of the relevant oscillation modes, including the instability growth time, are determined from time evolutions of the linearised dynamical equations in Newtonian gravity. In order to analyse the instability we monitor also the canonical energy and angular momentum. Our results demonstrate that the l=m=2 f-mode becomes unstable as soon as a co-rotation point develops inside the star (i.e. whenever there is a point where the mode's pattern speed matches the bulk angular velocity). Considering various degrees of differential rotation, we show that the instability grows faster deep inside the co-rotation region and deduce an empirical relation that correlates the mode frequency and the star's parameters, which captures the main features of the l=m=2 f-mode growth time. This function is proportional to the product of the kinetic to gravitational energy ratio and the gradient of the star's spin, strengthening further the relationship between the co-rotation point and the low T/W instability. We briefly consider also the l=m=2 r-mode and demonstrate that it never moves far inside the co-rotation region even for significant differential rotation., Comment: 12 pages, 8 figures, 2 tables. Submitted to MNRAS

Rapidly rotating neutron stars in Low Mass X-ray Binaries have been proposed as an interesting source of gravitational waves. In this chapter we present estimates of the gravitational wave emission for various scenarios, given the (electromagnetically) observed characteristics of these systems. First of all we focus on the r-mode instability and show that a 'minimal' neutron star model (which does not incorporate exotica in the core, dynamically important magnetic fields or superfluid degrees of freedom), is not consistent with observations. We then present estimates of both thermally induced and magnetically sustained mountains in the crust. In general magnetic mountains are likely to be detectable only if the buried magnetic field of the star is of the order of $B\approx 10^{12}$ G. In the thermal mountain case we find that gravitational wave emission from persistent systems may be detected by ground based interferometers. Finally we re-asses the idea that gravitational wave emission may be balancing the accretion torque in these systems, and show that in most cases the disc/magnetosphere interaction can account for the observed spin periods., Comment: To appear in 'Gravitational Waves Astrophysics: 3rd Session of the Sant Cugat Forum on Astrophysics, 2014', Editor: Carlos F. Sopuerta

Many pulsars are formed with a binary companion from which they can accrete matter. Torque exerted by accreting matter can cause the pulsar spin to increase or decrease, and over long times, an equilibrium spin rate is achieved. Application of accretion theory to these systems provides a probe of the pulsar magnetic field. We compare the large number of recent torque measurements of accreting pulsars with a high-mass companion to the standard model for how accretion affects the pulsar spin period. We find that many long spin period (P > 100 s) pulsars must possess either extremely weak (B < 10^10 G) or extremely strong (B > 10^14 G) magnetic fields. We argue that the strong-field solution is more compelling, in which case these pulsars are near spin equilibrium. Our results provide evidence for a fundamental link between pulsars with the slowest spin periods and strong magnetic fields around high-mass companions and pulsars with the fastest spin periods and weak fields around low-mass companions. The strong magnetic fields also connect our pulsars to magnetars and strong-field isolated radio/X-ray pulsars. The strong field and old age of our sources suggests their magnetic field penetrates into the superconducting core of the neutron star., Comment: 6 pages, 4 figures; to appear in MNRAS

We consider a new mechanism for damping the oscillations of a mature neutron star. The new dissipation channel arises if superfluid vortices are forced to cut through superconducting fluxtubes. This mechanism is interesting because the oscillation modes need to exceed a critical amplitude in order for it to operate. Once it acts the effect is very strong (and nonlinear) leading to efficient damping. The upshot of this is that modes are unlikely to ever evolve far beyond the critical amplitude. We consider the effect of this new dissipation channel on the r-modes, that may be driven unstable by the emission of gravitational waves. Our estimates show that the fluxtube cutting leads to a saturation threshold for the instability that can be smaller than that of other proposed mechanisms. This suggests that the idea may be of direct astrophysical relevance.