Three evolutionary paths for magnetar oscillations

Quasi-periodic oscillations have been seen in the light curves following several magnetar giant flares. These oscillations are of great interest as they probably provide our first ever view of the normal modes of oscillation of neutron stars. The state-of-the-art lies in the study of the oscillations of elastic-magnetic stellar models, mainly with a view to relating the observed frequencies to the structure and composition of the star itself. We advance this programme by considering several new physical mechanisms that are likely to be important for magnetar oscillations. These relate to the superfluid/superconducting nature of the stellar interior, and the damping of the modes, both through internal dissipation mechanisms and the launching of waves into the magnetosphere. We make simple order-of-magnitude estimates to show that both the frequencies and the damping time of magnetar oscillations can evolve in time, identifying three distinct `pathways' that can be followed, depending upon the initial magnitude of the mode excitation. These results are interesting as they show that the information buried in magnetar QPOs may be even richer than previously thought, and motivate more careful examination of magnetar light curves, to search for signatures of the different types of evolution that we have identified.Comment: To appear in MNRAS. This version reflects changes made in response to referee's comments, mainly extra discussion in Section 2.

Magnetic neutron star equilibria with stratification and type-II superconductivity

We construct two-fluid equilibrium configurations for neutron stars with magnetic fields, using a self-consistent and nonlinear numerical approach. The two-fluid approach - likely to be valid for large regions of all but the youngest NSs - provides us with a straightforward way to introduce stratification and allows for more realistic models than the ubiquitous barotropic assumption. In all our models the neutrons are modelled as a superfluid, whilst for the protons we consider two cases: one where they are a normal fluid and another where they form a type-II superconductor. We consider a variety of field configurations in the normal-proton case and purely toroidal fields in the superconducting case. We find that stratification allows for a stronger toroidal component in mixed-field configurations, though the poloidal component remains the largest in all our models. We provide quantitative results for magnetic ellipticities of NSs, both in the normal- and superconducting-proton cases.Comment: 21 pages, 14 figures; some minor changes to match published versio

Superfluid instability of r-modes in "differentially rotating" neutron stars

Superfluid hydrodynamics affects the spin-evolution of mature neutron stars, and may be key to explaining timing irregularities such as pulsar glitches. However, most models for this phenomenon exclude the global instability required to trigger the event. In this paper we discuss a mechanism that may fill this gap. We establish that small scale inertial r-modes become unstable in a superfluid neutron star that exhibits a rotational lag, expected to build up due to vortex pinning as the star spins down. Somewhat counterintuitively, this instability arises due to the (under normal circumstances dissipative) vortex-mediated mutual friction. We explore the nature of the superfluid instability for a simple incompressible model, allowing for entrainment coupling between the two fluid components. Our results recover a previously discussed dynamical instability in systems where the two components are strongly coupled. In addition, we demonstrate for the first time that the system is secularly unstable (with a growth time that scales with the mutual friction) throughout much of parameter space. Interestingly, large scale r-modes are also affected by this new aspect of the instability. We analyse the damping effect of shear viscosity, which should be particularly efficient at small scales, arguing that it will not be sufficient to completely suppress the instability in astrophysical systems.Comment: RevTex, 11 figure

Eikonal quasinormal modes of black holes beyond general relativity III: scalar Gauss-Bonnet gravity

In a recent series of papers we have shown how the eikonal/geometrical optics approximation can be used to calculate analytically the fundamental quasinormal mode frequencies associated with coupled systems of wave equations, which arise, for instance, in the study of perturbations of black holes in gravity theories beyond General Relativity. As a continuation to this series, we here focus on the quasinormal modes of nonrotating black holes in scalar Gauss-Bonnet gravity assuming a small-coupling expansion. We show that the axial perturbations are purely tensorial and are described by a modified Regge-Wheeler equation, while the polar perturbations are of mixed scalar-tensor character and are described by a system of two coupled wave equations. When applied to these equations, the eikonal machinery leads to axial modes that deviate from the general relativistic results at quadratic order in the Gauss-Bonnet coupling constant. We show that this result is in agreement with an analysis of unstable circular null orbits around blackholes in this theory, allowing us to establish the geometrical optics-null geodesic correspondence for the axial modes. For the polar modes the small-coupling approximation forces us to consider the ordering between eikonal and small-coupling perturbative parameters; one of which we show, by explicit comparison against numerical data, yields the correct identification of the quasinormal modes of the scalar-tensor coupled system of wave equations. These corrections lift the general relativistic degeneracy between scalar and tensorial eikonal quasinormal modes at quadratic order in Gauss-Bonnet coupling in a way reminiscent of the Zeeman effect. In general, our analytic, eikonal quasinormal mode frequencies (normalized to the General Relativity ones) agree with numerical results with an error of $\sim 10\%$ in the regime of small coupling constant. (abridged

Transition from inspiral to plunge for eccentric equatorial Kerr orbits

Ori and Thorne have discussed the duration and observability (with LISA) of the transition from circular, equatorial inspiral to plunge for stellar-mass objects into supermassive ($10^{5}-10^{8}M_{\odot}$) Kerr black holes. We extend their computation to eccentric Kerr equatorial orbits. Even with orbital parameters near-exactly determined, we find that there is no universal length for the transition; rather, the length of the transition depends sensitively -- essentially randomly -- on initial conditions. Still, Ori and Thorne's zero-eccentricity results are essentially an upper bound on the length of eccentric transitions involving similar bodies (e.g., $a$ fixed). Hence the implications for observations are no better: if the massive body is $M=10^{6}M_{\odot}$, the captured body has mass $m$, and the process occurs at distance $d$ from LISA, then $S/N \lesssim (m/10 M_{\odot})(1\text{Gpc}/d)\times O(1)$, with the precise constant depending on the black hole spin. For low-mass bodies ($m \lesssim 7 M_\odot$) for which the event rate is at least vaguely understood, we expect little chance (probably [much] less than 10%, depending strongly on the astrophysical assumptions) of LISA detecting a transition event with $S/N>5$ during its run; however, even a small infusion of higher-mass bodies or a slight improvement in LISA's noise curve could potentially produce $S/N>5$ transition events during LISA's lifetime.Comment: Submitted to PR

Perturbative Approach to an orbital evolution around a Supermassive black hole

A charge-free, point particle of infinitesimal mass orbiting a Kerr black hole is known to move along a geodesic. When the particle has a finite mass or charge, it emits radiation which carries away orbital energy and angular momentum, and the orbit deviates from a geodesic. In this paper we assume that the deviation is small and show that the half-advanced minus half-retarded field surprisingly provides the correct radiation reaction force, in a time-averaged sense, and determines the orbit of the particle.Comment: accepted for publication in the Physical Revie

Rotating black hole orbit functionals in the frequency domain

In many astrophysical problems, it is important to understand the behavior of functions that come from rotating (Kerr) black hole orbits. It can be particularly useful to work with the frequency domain representation of those functions, in order to bring out their harmonic dependence upon the fundamental orbital frequencies of Kerr black holes. Although, as has recently been shown by W. Schmidt, such a frequency domain representation must exist, the coupled nature of a black hole orbit's $r$ and $\theta$ motions makes it difficult to construct such a representation in practice. Combining Schmidt's description with a clever choice of timelike coordinate suggested by Y. Mino, we have developed a simple procedure that sidesteps this difficulty. One first Fourier expands all quantities using Mino's time coordinate $\lambda$. In particular, the observer's time $t$ is decomposed with $\lambda$. The frequency domain description is then built from the $\lambda$-Fourier expansion and the expansion of $t$. We have found this procedure to be quite simple to implement, and to be applicable to a wide class of functionals. We test the procedure using a simple test function, and then apply it in a particularly interesting case, the Weyl curvature scalar $\psi_4$ used in black hole perturbation theory.Comment: 16 pages, 2 figures. Submitted to Phys Rev D. New version gives a vastly improved algorithm due to Drasco for computing the Fourier transforms. Drasco has been added as an author. Also fixed some references and exterminated a small herd of typos; final published versio

Gravitational waveforms from a point particle orbiting a Schwarzschild black hole

We numerically solve the inhomogeneous Zerilli-Moncrief and Regge-Wheeler equations in the time domain. We obtain the gravitational waveforms produced by a point-particle of mass $\mu$ traveling around a Schwarzschild black hole of mass M on arbitrary bound and unbound orbits. Fluxes of energy and angular momentum at infinity and the event horizon are also calculated. Results for circular orbits, selected cases of eccentric orbits, and parabolic orbits are presented. The numerical results from the time-domain code indicate that, for all three types of orbital motion, black hole absorption contributes less than 1% of the total flux, so long as the orbital radius r_p(t) satisfies r_p(t)> 5M at all times.Comment: revtex4, 24 pages, 23 figures, 3 tables, submitted to PR