arXiv subjects

N. Andersson

Publications and source records attributed to N. Andersson.

At least 37 records · Page 2Linked to original sources

arXiv2020

Relativistic fluid dynamics: physics for many different scales

The relativistic fluid is a highly successful model used to describe the dynamics of many-particle systems moving at high velocities and/or in strong gravity. It takes as input physics from microscopic scales and yields as output predictions of bulk, macroscopic motion. By inverting the process-e.g., drawing on astrophysical observations-an understanding of relativistic features can lead to insight into physics on the microscopic scale. Relativistic fluids have been used to model systems as "small" as colliding heavy ions in laboratory experiments, and as large as the Universe itself, with "intermediate" sized objects like neutron stars being considered along the way. The purpose of this review is to discuss the mathematical and theoretical physics underpinnings of the relativistic (multi-) fluid model. We focus on the variational principle approach championed by Brandon Carter and collaborators, in which a crucial element is to distinguish the momenta that are conjugate to the particle number density currents. This approach differs from the "standard" text-book derivation of the equations of motion from the divergence of the stress-energy tensor in that one explicitly obtains the relativistic Euler equation as an "integrability" condition on the relativistic vorticity. We discuss the conservation laws and the equations of motion in detail, and provide a number of (in our opinion) interesting and relevant applications of the general theory. The formalism provides a foundation for complex models, e.g., including electromagnetism, superfluidity and elasticity-all of which are relevant for state of the art neutron-star modelling.

gr-qc↗

arXiv2019

A variational approach to relativistic superfluid vortex elasticity

It is well known that a superfluid rotates by forming an array of quantized vortices. A relativistic formulation for superfluid vortex dynamics is required for a range of problems in astrophysics and cosmology, from neutron star interiors and radio pulsar glitches to possible dark matter condensates on galactic scales. This paper develops a formalism for such systems, extending the well-established variational approach to relativistic fluids to account for the presence of a collection of quantized vortices. The model is firmly anchored in the geometry of the problem (drawing on aspects from basic string dynamics) and accounts for elastic aspects associated with a vortex array, providing a precise foundation for applications which have so far been based on somewhat ad hoc phenomenology.

gr-qc↗

arXiv2019

The sum of Love: Exploring the effective tidal deformability of neutron stars

Finite size effects come into play during the late stages of neutron star binary inspiral, with the tidal deformability of the supranuclear density matter leaving an imprint on the gravitational-wave signal. As demonstrated in the case of GW170817, this leads to a constraint on the neutron star radius (and hence the equation of state). A deeper understanding of the tidal response requires an analysis of both the state and composition of matter. While these aspects may not have dramatic impact, they could lead to systematic effects that need to be kept in mind as the observational data become more precise. As a step in this direction we explore the role of the composition of matter, which is likely to remain "frozen" during the late stages of binary inspiral. We provide the first in-depth analysis of the problem, including estimates of how composition impacts on the effective tidal deformability. The results provide improved insight into how aspects of physics that tend to be "ignored" impact on binary neutron star gravitational-wave signals.

astro-ph.HE↗

arXiv2019

Exploring universality in neutron star mergers

We explore the correlation between the pre-merger tidal deformability and the post-merger remnant oscillations seen in numerical simulation of neutron star binaries, with the aim of understanding to what extent the physics support the existence of such a relation. We consider the impact of thermal and rotational effects and argue that the proposed relation does, indeed, make sense and provide simple arguments that help explain the result.

gr-qc↗

arXiv2019

The g-mode spectrum of reactive neutron star cores

We discuss the impact of nuclear reactions on the spectrum of gravity g-modes of a mature neutron star, demonstrating the anticipated disappearance of these modes when the timescale associated with the oscillations is longer than that of nuclear reactions. This is the expected result, but different aspects of the demonstration may be relevant for related problems in neutron star astrophysics. In particular, we develop the framework required for an explicit implementation of finite-time nuclear reactions in neutron star oscillation problems and demonstrate how this formulation connects with the usual bulk viscosity prescription. We also discuss implications of the absence of very high order g-modes for problems of astrophysical relevance.

gr-qc↗

arXiv2018

The dynamics of neutron star crusts: Lagrangian perturbation theory for a relativistic superfluid-elastic system

The inner crust of a mature neutron star is composed of an elastic lattice of neutron-rich nuclei penetrated by free neutrons. These neutrons can flow relative to the crust once the star cools below the superfluid transition temperature. In order to model the dynamics of this system, which is relevant for a range of problems from pulsar glitches to magnetar seismology and continuous gravitational-wave emission from rotating deformed neutron stars, we need to understand general relativistic Lagrangian perturbation theory for elastic matter coupled to a superfluid component. This paper develops the relevant formalism to the level required for astrophysical applications.

gr-qc↗

arXiv2018

Heat conduction in rotating relativistic stars

In the standard form of the relativistic heat equation used in astrophysics, information propagates instantaneously, rather than being limited by the speed of light as demanded by relativity. We show how this equation nonetheless follows from a more general, causal theory of heat propagation in which the entropy plays the role of a fluid. In deriving this result, however, we see that it is necessary to make some assumptions which are not universally valid: the dynamical timescales of the process must be long compared with the explicitly causal physics of the theory, the heat flow must be sufficiently steady, and the spacetime static. Generalising the heat equation (e.g. restoring causality) would thus entail retaining some of the terms we neglected. As a first extension, we derive the heat equation for the spacetime associated with a slowly-rotating star or black hole, showing that it only differs from the static result by an additional advection term due to the rotation, and as a consequence demonstrate that a hotspot on a neutron star will be seen to be modulated at the rotation frequency by a distant observer.

astro-ph.HE↗

arXiv2017

The enigmatic spin evolution of PSR J0537-6910: r-modes, gravitational waves and the case for continued timing

We discuss the unique spin evolution of the young X-ray pulsar PSR J0537-6910, a system in which the regular spin down is interrupted by glitches every few months. Drawing on the complete timing data from the Rossi X-ray Timing Explorer (RXTE, from 1999-2011), we argue that a trend in the inter-glitch behaviour points to an effective braking index close to $n=7$, much larger than expected. This value is interesting because it would accord with the neutron star spinning down due to gravitational waves from an unstable r-mode. We discuss to what extent this, admittedly speculative, scenario may be consistent and if the associated gravitational-wave signal would be within reach of ground based detectors. Our estimates suggest that one may, indeed, be able to use future observations to test the idea. Further precision timing would help enhance the achievable sensitivity and we advocate a joint observing campaign between the Neutron Star Interior Composition ExploreR (NICER) and the LIGO-Virgo network.

astro-ph.HE↗

arXiv2017

Using gravitational-wave data to constrain dynamical tides in neutron star binaries

We discuss the role of dynamical tidal effects for inspiralling neutron star binaries, focussing on features that may be considered "unmodelled" in gravitational-wave searches. In order to cover the range of possibilities, we consider i) individual oscillation modes becoming resonant with the tide, ii) the elliptical instability, where a pair of inertial modes exhibit a nonlinear resonance with the tide, and iii) the non-resonant p-g instability which may arise as high order p- and g-modes in the star couple nonlinearly to the tide. In each case, we estimate the amount of additional energy loss that needs to be associated with the dynamical tide in order for the effect to impact on an observed gravitational-wave signal. We explore to what extent the involved neutron star physics may be considered known and how one may be able to use observational data to constrain theory.

astro-ph.HE↗

arXiv2017

Whispers from the edge of physics

Neutron stars involve extreme physics which is difficult (perhaps impossible) to explore in laboratory experiments. We have to turn to astrophysical observations, and try to extract information from the entire range of the electromagnetic spectrum. In addition, neutron stars may radiate gravitational waves through a range of scenarios. In this brief summary I outline some of the main ideas, focussing on what we do and do not know, and describe the challenges involved in trying to catch these faint whispers from the very edge of physics.

astro-ph.HE↗

arXiv2017

Pulsar spin-down: the glitch-dominated rotation of PSR J0537-6910

The young, fast-spinning, X-ray pulsar J0537-6910 displays an extreme glitch activity, with large spin-ups interrupting its decelerating rotation every ~100 days. We present nearly 13 years of timing data from this pulsar, obtained with the {\it Rossi X-ray Timing Explorer}. We discovered 22 new glitches and performed a consistent analysis of all 45 glitches detected in the complete data span. Our results corroborate the previously reported strong correlation between glitch spin-up size and the time to the next glitch, a relation that has not been observed so far in any other pulsar. The spin evolution is dominated by the glitches, which occur at a rate ~3.5 per year, and the post-glitch recoveries, which prevail the entire inter-glitch intervals. This distinctive behaviour provides invaluable insights into the physics of glitches. The observations can be explained with a multi-component model which accounts for the dynamics of the neutron superfluid present in the crust and core of neutron stars. We place limits on the moment of inertia of the component responsible for the spin-up and, ignoring differential rotation, the velocity difference it can sustain with the crust. Contrary to its rapid decrease between glitches, the spin-down rate increased over the 13 years, and we find the long-term braking index $n_{\rm l}=-1.22(4)$, the only negative braking index seen in a young pulsar. We briefly discuss the plausible interpretations of this result, which is in stark contrast to the predictions of standard models of pulsar spin-down.

astro-ph.HE↗

arXiv2017

The Spin Distribution of Fast Spinning Neutron Stars in Low Mass X-Ray Binaries: Evidence for Two Sub-Populations

We study the current sample of rapidly rotating neutron stars in both accreting and non-accreting binaries in order to determine whether the spin distribution of accreting neutron stars in low-mass X-ray binaries can be reconciled with current accretion torque models. We perform a statistical analysis of the spin distributions and show that there is evidence for two sub-populations among low-mass X-ray binaries, one at relatively low spin frequency, with an average of ~300 Hz and a broad spread, and a peaked population at higher frequency with average spin frequency of ~575 Hz. We show that the two sub-populations are separated by a cut-point at a frequency of ~540 Hz. We also show that the spin frequency of radio millisecond pulsars does not follow a log-normal distribution and shows no evidence for the existence of distinct sub-populations. We discuss the uncertainties of different accretion models and speculate that either the accreting neutron star cut-point marks the onset of gravitational waves as an efficient mechanism to remove angular momentum or some of the neutron stars in the fast sub-population do not evolve into radio millisecond pulsars.

astro-ph.HE↗

arXiv2016

A variational approach to resistive relativistic plasmas

We develop an action principle to construct the field equations for a multi-fluid system containing charge-neutral fluids, plasmas, and dissipation (via resistive interactions), by combining the standard, Maxwell action and minimal coupling of the electromagnetic field with a recently developed action for relativistic dissipative fluids. We use a pull-back formalism from spacetime to abstract matter spaces to build unconstrained variations for both the charge-neutral fluids and currents making up the plasmas. Using basic linear algebra techniques, we show that a general "relabeling" invariance exists for the abstract matter spaces. With the field equations in place, a phenomenological model for the resistivity is developed, using as constraints charge conservation and the Second Law of Thermodynamics. A minimal model for a system of electrons, protons, and heat is developed using the Onsager procedure for incorporating dissipation.

gr-qc↗

arXiv2016

Beyond ideal magnetohydrodynamics: From fibration to 3+1 foliation

We consider a resistive multi-fluid framework from the 3+1 space-time foliation point-of-view, paying particular attention to issues relating to the use of multi-parameter equations of state and the associated inversion from evolved to primitive variables. We highlight relevant numerical issues that arise for general systems with relative flows. As an application of the new formulation, we consider a three-component system relevant for hot neutron stars. In this case we let the baryons (neutrons and protons) move together, but allow heat and electrons to exhibit relative flow. This reduces the problem to three momentum equations; overall energy-momentum conservation, a generalised Ohm's law and a heat equation. Our results provide a hierarchy of increasingly complex models and prepare the ground for new state-of-the-art simulations of relevant scenarios in relativistic astrophysics.

gr-qc↗

arXiv2016

Beyond ideal magnetohydrodynamics: Resistive, reactive and relativistic plasmas

We develop a new framework for the modelling of charged fluid dynamics in general relativity. The model, which builds on a recently developed variational multi-fluid model for dissipative fluids, accounts for relevant effects like the inertia of both charge currents and heat and, for mature systems, the decoupling of superfluid components. We discuss how the model compares to standard relativistic magnetohydronamics and consider the connection between the fluid dynamics, the microphysics and the underlying equation of state. As illustrations of the formalism, we consider three distinct two-fluid models describing i) an Ohm's law for resistive charged flows, ii) a relativistic heat equation, and iii) an equation representing the momentum of a decoupled superfluid component. As a more complex example, we also formulate a three-fluid model which demonstrates the thermo-electric effect. This framework allows us to model neutron stars (and related systems) at a hierarchy of increasingly complex levels, and should enable us to make progress on a range of exciting problems in astrophysics and cosmology.

gr-qc↗

arXiv2016

Quantised vortices and mutual friction in relativistic superfluids

We consider the detailed dynamics of an array of quantised superfluid vortices in the framework of general relativity, as required for quantitative modelling of realistic neutron star cores. Our model builds on the variational approach to relativistic (multi-) fluid dynamics, where the vorticity plays a central role. The description provides a natural extension of, and as it happens a better insight into, existing Newtonian models. In particular, we account for the mutual friction associated with scattering of a second "normal" component in the mixture off of the superfluid vortices.

gr-qc↗

arXiv2015

A covariant action principle for dissipative fluid dynamics: From formalism to fundamental physics

We present a new variational framework for dissipative general relativistic fluid dynamics. The model extends the convective variational principle for multi-fluid systems to account for a range of dissipation channels. The key ingredients in the construction are i) the use of a lower dimensional matter space for each fluid component, and ii) an extended functional dependence for the associated volume forms. In an effort to make the concepts clear, the formalism is developed in steps with the model example of matter coupled to heat considered at each level. Thus we discuss a model for heat flow, derive the relativistic Navier-Stokes equations and discuss why the individual dissipative stress tensors need not be spacetime symmetric. We argue that the new formalism, which notably does not involve an expansion away from an assumed equilibrium state, provides a conceptual breakthrough in this area of research and provide an ambitious list of directions in which one may want to extend it in the future. This involves an exciting set of problems, relating to both applications and foundational issues.

gr-qc↗

arXiv2015

Buoyancy and g-modes in young superfluid neutron stars

We consider the local dynamics of a realistic neutron star core, including composition gradients, superfluidity and thermal effects. The main focus is on the gravity g-modes, which are supported by composition stratification and thermal gradients. We derive the equations that govern this problem in full detail, paying particular attention to the input that needs to be provided through the equation of state and distinguishing between normal and superfluid regions. The analysis highlights a number of key issues that should be kept in mind whenever equation of state data is compiled from nuclear physics for use in neutron star calculations. We provide explicit results for a particular stellar model and a specific nucleonic equation of state, making use of cooling simulations to show how the local wave spectrum evolves as the star ages. Our results show that the composition gradient is effectively dominated by the muons whenever they are present. When the star cools below the superfluid transition, the support for g-modes at lower densities (where there are no muons) is entirely thermal. We confirm the recent suggestion that the g-modes in this region may be unstable, but our results indicate that this instability will be weak and would only be present for a brief period of the star's life. Our analysis accounts for the presence of thermal excitations encoded in entrainment between the entropy and the superfluid component. Finally, we discuss the complete spectrum, including the normal sound waves and, in superfluid regions, the second sound.

astro-ph.SR↗