Slowly Rotating Two-Fluid Neutron Star Model

We study stationary axisymmetric configurations of a star model consisting of two barotropic fluids, which are uniformly rotating at two different rotation rates. Analytic approximate solutions in the limit of slow rotation are obtained with the classical method of Chandrasekhar, which consists of an expansion of the solution in terms of the rotation rate, and which is generalized to the case of two fluids in order to apply it to the present problem. This work has a direct application to neutron star models, in which the neutron superfluid can rotate at a different speed than the fluid of charged components. Two cases are considered, the case of two non-interacting fluids, and the case of an interaction of a special type, corresponding to the vortices of the neutron superfluid being completely pinned to the second fluid. The special case of the equation of state P~rho^2 is solved explicitly as an illustration of the foregoing results.Comment: 9 pages, uses aa.sty and amssymb.sty; submitted to Astron.Astrophy

Search for Continuous Gravitational Waves: simple criterion for optimal detector networks

We derive a simple algebraic criterion to select the optimal detector network for a coherent wide parameter-space (all-sky) search for continuous gravitational waves. Optimality in this context is defined as providing the highest (average) sensitivity per computing cost. This criterion is a direct consequence of the properties of the multi-detector F-statistic metric, which has been derived recently. Interestingly, the choice of the optimal network only depends on the noise-levels and duty-cycles of the respective detectors, and not on the available computing power.Comment: 3 pages, 2 figures; Proceedings of the 11th Marcel-Grossmann Meeting (MG11

Variational description of multi-fluid hydrodynamics: Coupling to gauge fields

In this work we extend our previously developed formalism of Newtonian multi-fluid hydrodynamics to allow for coupling between the fluids and the electromagnetic and gravitational field. This is achieved within the convective variational principle by using a standard minimal coupling prescription. In addition to the conservation of total energy and momentum, we derive the conservation of canonical vorticity and helicity, which generalize the corresponding conserved quantities of uncharged fluids. We discuss the application of this formalism to electrically conducting systems, magnetohydrodynamics and superconductivity. The equations of electric conductors derived here are more general than those found in the standard description of such systems, in which the effect of entrainment is overlooked, despite the fact that it will generally be present in any conducting multi-constituent system.Comment: 16 pages; to appear in Phys.Rev.

Fully coherent follow-up of continuous gravitational-wave candidates

The search for continuous gravitational waves from unknown isolated sources is computationally limited due to the enormous parameter space that needs to be covered and the weakness of the expected signals. Therefore semi-coherent search strategies have been developed and applied in distributed computing environments such as Einstein@Home, in order to narrow down the parameter space and identify interesting candidates. However, in order to optimally confirm or dismiss a candidate as a possible gravitational-wave signal, a fully-coherent follow-up using all the available data is required. We present a general method and implementation of a direct (2-stage) transition to a fully-coherent follow-up on semi-coherent candidates. This method is based on a grid-less Mesh Adaptive Direct Search (MADS) algorithm using the F-statistic. We demonstrate the detection power and computing cost of this follow-up procedure using extensive Monte-Carlo simulations on (simulated) semi-coherent candidates from a directed as well as from an all-sky search setup.Comment: 12 pages, 5 figure

Line-robust statistics for continuous gravitational waves: safety in the case of unequal detector sensitivities

The multi-detector F-statistic is close to optimal for detecting continuous gravitational waves (CWs) in Gaussian noise. However, it is susceptible to false alarms from instrumental artefacts, for example quasi-monochromatic disturbances ('lines'), which resemble a CW signal more than Gaussian noise. In a recent paper [Keitel et al 2014, PRD 89 064023], a Bayesian model selection approach was used to derive line-robust detection statistics for CW signals, generalising both the F-statistic and the F-statistic consistency veto technique and yielding improved performance in line-affected data. Here we investigate a generalisation of the assumptions made in that paper: if a CW analysis uses data from two or more detectors with very different sensitivities, the line-robust statistics could be less effective. We investigate the boundaries within which they are still safe to use, in comparison with the F-statistic. Tests using synthetic draws show that the optimally-tuned version of the original line-robust statistic remains safe in most cases of practical interest. We also explore a simple idea on further improving the detection power and safety of these statistics, which we however find to be of limited practical use.Comment: 21 pages, 11 figures, updated to match published versio

The search for continuous gravitational waves: metric of the multi-detector F-statistic

We develop a general formalism for the parameter-space metric of the multi-detector F-statistic, which is a matched-filtering detection statistic for continuous gravitational waves. We find that there exists a whole family of F-statistic metrics, parametrized by the (unknown) amplitude parameters of the gravitational wave. The multi-detector metric is shown to be expressible in terms of noise-weighted averages of single-detector contributions, which implies that the number of templates required to cover the parameter space does not scale with the number of detectors. Contrary to using a longer observation time, combining detectors of similar sensitivity is therefore the computationally cheapest way to improve the sensitivity of coherent wide-parameter searches for continuous gravitational waves. We explicitly compute the F-statistic metric family for signals from isolated spinning neutron stars, and we numerically evaluate the quality of different metric approximations in a Monte-Carlo study. The metric predictions are tested against the measured mismatches and we identify regimes in which the local metric is no longer a good description of the parameter-space structure.Comment: 20 pages, 15 figures, revtex4; v2: some edits of style and notation, fixed minor typo

Flat parameter-space metric for all-sky searches for gravitational-wave pulsars

All-sky, broadband, coherent searches for gravitational-wave pulsars are computationally limited. It is therefore important to make efficient use of available computational resources, notably by minimizing the number of templates used to cover the signal parameter space of sky position and frequency evolution. For searches over the sky, however, the required template density (determined by the parameter-space metric) is different at each sky position, which makes it difficult in practice to achieve an efficient covering. Previous work on this problem has found various choices of sky and frequency coordinates that render the parameter-space metric approximately constant, but which are limited to coherent integration times of either less than a few days, or greater than several months. These limitations restrict the sensitivity achievable by hierarchical all-sky searches, and hinder the development of follow-up pipelines for interesting gravitational-wave pulsar candidates. We present a new flat parameter-space metric approximation, and associated sky and frequency coordinates, that do not suffer from these limitations. Furthermore, the new metric is numerically well-conditioned, which facilitates its practical use.Comment: 19 pages, 20 figure

Directed searches for continuous gravitational waves from binary systems: parameter-space metrics and optimal Scorpius X-1 sensitivity

We derive simple analytic expressions for the (coherent and semi-coherent) phase metrics of continuous-wave sources in low-eccentricity binary systems, both for the long-segment and short- segment regimes (compared to the orbital period). The resulting expressions correct and extend previous results found in the literature. We present results of extensive Monte-Carlo studies comparing metric mismatch predictions against the measured loss of detection statistic for binary parameter offsets. The agreement is generally found to be within ~ 10%-30%. As an application of the metric template expressions, we estimate the optimal achievable sensitivity of an Einstein@Home directed search for Scorpius X-1, under the assumption of sufficiently small spin wandering. We find that such a search, using data from the upcoming advanced detectors, would be able to beat the torque- balance level [1,2] up to a frequency of ~ 500 - 600 Hz, if orbital eccentricity is well-constrained, and up to a frequency of ~ 160 - 200 Hz for more conservative assumptions about the uncertainty on orbital eccentricity.Comment: 25 pages, 8 figure

Ambipolar diffusion in superfluid neutron stars

In this paper we reconsider the problem of magnetic field diffusion in neutron star cores. We model the star as consisting of a mixture of neutrons, protons and electrons, and allow for particle reactions and binary collisions between species. Our analysis is in much the same spirit as that of Goldreich & Reisenegger (1992), and we content ourselves with rough estimates of magnetic diffusion timescales, rather than solving accurately for some particular field geometry. However, our work improves upon previous treatments in one crucial respect: we allow for superfluidity in the neutron star matter. We find that the consequent mutual friction force, coupling the neutrons and charged particles, together with the suppression of particles collisions and reactions, drastically affect the ambipolar magnetic field diffusion timescale. In particular, the addition of superfluidity means that it is unlikely that there is ambipolar diffusion in magnetar cores on the timescale of the lifetimes of these objects, contradicting an assumption often made in the modelling of the flaring activity commonly observed in magnetars. Our work suggests that if a decaying magnetic field is indeed the cause of magnetar activity, the field evolution is likely to take place outside of the core, and might represent Hall/Ohmic diffusion in the stellar crust, or else that a mechanism other than standard ambipolar diffusion is active, e.g. flux expulsion due to the interaction between neutron vortices and magnetic fluxtubes.Comment: Paper changed to incorporate comments from referee. To appear in MNRA

Inertial modes of neutron stars with the superfluid core

We investigate the modal properties of inertial modes of rotating neutron stars with the core filled with neutron and proton superfluids, taking account of entrainment effects between the superfluids. In this paper, the entrainment effects are modeled by introducing a parameter $\eta$ so that no entrainment state is realized at $\eta=0$. We find that inertial modes of rotating neutron stars with the superfluid core are split into two families, which we call ordinary fluid inertial modes ($i^o$-mode) and superfluid inertial modes ($i^s$-mode). The two superfluids in the core counter-move for the $i^s$-modes. For the $i^o$-modes, $\kappa_0=\lim_{\Omega\to 0}\omega/\Omega$ is only weakly dependent on the entrainment parameter $\eta$, where $\Omega$ and $\omega$ are the angular frequency of rotation and the oscillation frequency observed in the corotating frame of the star, respectively. For the $i^s$-modes, on the other hand, $|\kappa_0|$ almost linearly increases as $\eta$ increases. Avoided crossings as functions of $\eta$ are therefore quite common between $i^o$- and $i^s$-modes. We find that some of the $i^s$-modes that are unstable against the gravitational radiation reaction at $\eta=0$ become stable when $\eta$ is larger than $\eta_{crit}$, the value of which depends on the mode. Since the radiation driven instability associated with the current multipole radiation is quite weak for the inertial modes and the mutual friction damping in the superfluid core is strong, the instability caused by the inertial modes will be easily suppressed unless the entrainment parameter $\eta$ is extremely small and the mutual friction damping is sufficiently weak.Comment: 19 pages, 20 figures. To appear in MNRA