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.Comment: Submitted to Ap

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.Comment: 10 pages, 4 figures, emulate ApJ forma

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.Comment: 31 pages, double spacing, minor typos fixe

The dynamics of dissipative multi-fluid neutron star cores

We present a Newtonian multi-fluid formalism for superfluid neutron star cores, focussing on the additional dissipative terms that arise when one takes into account the individual dynamical degrees of freedom associated with the coupled "fluids". The problem is of direct astrophysical interest as the nature of the dissipative terms can have significant impact on the damping of the various oscillation modes of the star and the associated gravitational-wave signatures. A particularly interesting application concerns the gravitational-wave driven instability of f- and r-modes. We apply the developed formalism to two specific three-fluid systems: (i) a hyperon core in which both Lambda and Sigma^- hyperons are present, and (ii) a core of deconfined quarks in the colour-flavour-locked phase in which a population of neutral K^0 kaons is present. The formalism is, however, general and can be applied to other problems in neutron-star dynamics (such as the effect of thermal excitations close to the superfluid transition temperature) as well as laboratory multi-fluid systems.Comment: RevTex, no figure

Gravitational waves from rapidly rotating neutron stars

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. Sopuert

A new misfit function for multimodal inversion of surface waves

Higher-mode contribution is important in surface-wave inversion because it allows more information to be exploited, increases investigation depth, and improves model resolution. A new misfit function for multimodal inversion of surface waves, based on the Haskell-Thomson matrix method, allows higher modes to be taken into account without the need to associate experimental data points to a specific mode, thus avoiding mode-misidentification errors in the retrieved velocity profiles. Computing cost is reduced by avoiding the need for calculating synthetic apparent or modal dispersion curves. Based on several synthetic and real examples with inversion results from the classical and the proposed methods, we find that correct velocity models can be retrieved through the multimodal inversion when higher modes are superimposed in the apparent dispersion-curve or when it is not trivial to determine a priori to which mode each data point of the experimental dispersion curve belongs. The main drawback of the method is related to the presence of several local minima in the misfit function. This feature makes the choice of a consistent initial model very importan

R-mode oscillations and rocket effect in rotating superfluid neutron stars. I. Formalism

We derive the hydrodynamical equations of r-mode oscillations in neutron stars in presence of a novel damping mechanism related to particle number changing processes. The change in the number densities of the various species leads to new dissipative terms in the equations which are responsible of the {\it rocket effect}. We employ a two-fluid model, with one fluid consisting of the charged components, while the second fluid consists of superfluid neutrons. We consider two different kind of r-mode oscillations, one associated with comoving displacements, and the second one associated with countermoving, out of phase, displacements.Comment: 10 page

Lagrangian perturbation theory for a superfluid immersed in an elastic neutron star crust

The inner crust of mature neutron stars, where an elastic lattice of neutron-rich nuclei coexists with a neutron superfluid, impacts on a range of astrophysical phenomena. The presence of the superfluid is key to our understanding of pulsar glitches, and is expected to affect the thermal conductivity and hence the evolution of the surface temperature. The coupling between crust and superfluid must also be accounted for in studies of neutron star dynamics, discussions of global oscillations and associated instabilities. In this paper we develop Lagrangian perturbation theory for this problem, paying attention to key issues like superfluid entrainment, potential vortex pinning, dissipative mutual friction and the star's magnetic field. We also discuss the nature of the core-crust interface. The results provide a theoretical foundation for a range of interesting astrophysical applications.Comment: 13 pages, no figures, to appear in MNRA

Optimal Time Advance In Terminal Area Arrivals: Throughput vs. Fuel Savings

The current operational practice in scheduling air traffic arriving at an airport is to adjust flight schedules by delay, i.e. a postponement of an aircrafts arrival at a scheduled location, to manage safely the FAA-mandated separation constraints between aircraft. To meet the observed and forecast growth in traffic demand, however, the practice of time advance (speeding up an aircraft toward a scheduled location) is envisioned for future operations as a practice additional to delay. Time advance has two potential advantages. The first is the capability to minimize, or at least reduce, the excess separation (the distances between pairs of aircraft immediately in-trail) and thereby to increase the throughput of the arriving traffic. The second is to reduce the total traffic delay when the traffic sample is below saturation density. A cost associated with time advance is the fuel expenditure required by an aircraft to speed up. We present an optimal control model of air traffic arriving in a terminal area and solve it using the Pontryagin Maximum Principle. The admissible controls allow time advance, as well as delay, some of the way. The cost function reflects the trade-off between minimizing two competing objectives: excess separation (negatively correlated with throughput) and fuel burn. A number of instances are solved using three different methods, to demonstrate consistency of solutions