R-modes in accreting and young neutron stars

Recent work has raised the exciting possibility that r-mode pulsations (Rossby waves) in rotating neutron star cores may be strong gravitational wave sources. Rapidly rotating young neutron stars born in supernovae enter the r-mode instability region within the first minutes of their lives and may spin down by substantial amounts due to gravitational radiation from r-modes. Accreting neutron stars in low-mass X-ray binaries (LMXBs) are spun up by accretion to such short rotation periods that they may be unstable to r-mode pulsations as well. Gravitational waves from these neutron stars are strong enough to be detectable by second-generation, "enhanced" gravitational wave interferometers. I review the recent progress in understanding the r-mode instability in young and accreting neutron stars, with the focus on the issues of the coupling of the pulsations to the crust and nonlinear saturation amplitudes

Time-Variable Emission from Transiently Accreting Neutron Stars In Quiescence due to Deep Crustal Heating

Transiently accreting neutron stars in quiescence (Lx<10^34 erg/s) have been observed to vary in intensity by factors of few, over timescales of days to years. If the quiescent luminosity is powered by a hot NS core, the core cooling timescale is much longer than the recurrence time, and cannot explain the observed, more rapid variability. However, the non-equilibrium reactions which occur in the crust during outbursts deposit energy in iso-density shells, from which the thermal diffusion timescale to the photosphere is days to years. The predicted magnitude of variability is too low to explain the observed variability unless - as is widely believed - the neutrons beyond the neutron-drip density are superfluid. Even then, variability due to this mechanism in models with standard core neutrino cooling processes is less than 50 per cent - still too low to explain the reported variability. However, models with rapid core neutrino cooling can produce variability by a factor as great as 20, on timescales of days to years following an outburst. Thus, the factors of few intensity variability observed from transiently accreting neutron stars can be accounted for by this mechanism only if rapid core cooling processes are active.Comment: 12 pages, 5 figures, submitted to MNRA

Gravitational Waves from Low-Mass X-ray Binaries: a Status Report

We summarize the observations of the spin periods of rapidly accreting neutron stars. If gravitational radiation is responsible for balancing the accretion torque at the observed spin frequencies of ~300 Hz, then the brightest of these systems make excellent gravitational wave sources for LIGO-II and beyond. We review the recent theoretical progress on two mechanisms for gravitational wave emission: mass quadrupole radiation from deformed neutron star crusts and current quadrupole radiation from r-mode pulsations in neutron star cores.Comment: 10 pages, 5 figures, 3rd Edoardo Amaldi Conference on Gravitational Wave

Viscous Boundary Layer Damping of R-Modes in Neutron Stars

Recent work has raised the exciting possibility that r-modes (Rossby waves) in rotating neutron star cores might be strong gravitational wave sources. We estimate the effect of a solid crust on their viscous damping rate and show that the dissipation rate in the viscous boundary layer between the oscillating fluid and the nearly static crust is >10^5 times higher than that from the shear throughout the interior. This increases the minimum frequency for the onset of the gravitational r-mode instability to at least 500 Hz when the core temperature is less than 10^10 K. It eliminates the conflict of the r-mode instability with the accretion-driven spin-up scenario for millisecond radio pulsars and makes it unlikely that the r-mode instability is active in accreting neutron stars. For newborn neutron stars, the formation of a solid crust shortly after birth affects their gravitational wave spin-down and hence detectability by ground-based interferometric gravitational wave detectors

The Crustal Rigidity of a Neutron Star, and Implications for PSR 1828-11 and other Precession Candidates

We calculate the crustal rigidity parameter, b, of a neutron star (NS), and show that b is a factor 40 smaller than the standard estimate due to Baym & Pines (1971). For a NS with a relaxed crust, the NS's free-precession frequency is directly proportional to b. We apply our result for b to PSR 1828-11, a 2.5 Hz pulsar that appears to be precessing with period 511 d. Assuming this 511-d period is set by crustal rigidity, we show that this NS's crust is not relaxed, and that its reference spin (roughly, the spin for which the crust is most relaxed) is 40 Hz, and that the average spindown strain in the crust is 5 \times 10^{-5}. We also briefly describe the implications of our b calculation for other well-known precession candidates.Comment: 44 pages, 10 figures, submitted to Ap

Crust-core coupling and r-mode damping in neutron stars: a toy model

R-modes in neutron stars with crusts are damped by viscous friction at the crust-core boundary. The magnitude of this damping, evaluated by Bildsten and Ushomirsky (BU) under the assumption of a perfectly rigid crust, sets the maximum spin frequency for a neutron star spun up by accretion in a Low-Mass X-ray binary (LMXB). In this paper we explore the mechanical coupling between the core r-modes and the elastic crust, using a toy model of a constant density neutron star with a constant shear modulus crust. We find that, at spin frequencies in excess of ~50 Hz, the r-modes strongly penetrate the crust. This reduces the relative motion (slippage) between the crust and the core compared to the rigid crust limit. We therefore revise down, by as much as a factor of 10^2-10^3, the damping rate computed by BU, significantly reducing the maximal possible spin frequency of neutron star with a solid crust. The dependence of the crust-core slippage on the spin frequency is complicated, and is very sensitive to the physical thickness of the crust. If the crust is sufficiently thick, the curve of the critical spin frequency for the onset of the r-mode instability becomes multi-valued for some temperatures; this is related to the avoided crossings between the r-mode and the higher-order torsional modes in the crust. The critical frequencies are comparable to the observed spins of neutron stars in LMXBs and millisecond pulsars.Comment: 6 pages, 2 figures, submitted to MNRA

Propagation of thermonuclear flames on rapidly rotating neutron stars: extreme weather during type I X-ray bursts

We analyze the global hydrodynamic flow in the ocean of an accreting, rapidly rotating, non-magnetic neutron star in an LMXB during a type I X-ray burst. Our analysis takes into account the rapid rotation of the star and the lift-up of the burning ocean during the burst. We find a new regime for spreading of a nuclear burning front, where the flame is carried along a coherent shear flow across the front. If turbulent viscosity is weak, the speed of flame propagation is ~20 km/s, while, if turbulent viscosity is dynamically important, the flame speed increases, and reaches the maximum value, ~300 km/s, when the eddy overturn frequency is comparable to the Coriolis parameter. We show that, due to rotationally reduced gravity, the thermonuclear runaway is likely to begin on the equator. The equatorial belt is ignited first, and the flame then propagates from the equator to the poles. Inhomogeneous cooling (equator first, poles second) drives strong zonal currents which may be unstable to formation of Jupiter-type vortices; we conjecture that these vortices are responsible for modulation of X-ray flux in the tails of some bursts. We consider the effect of strong zonal currents on the frequency of modulation of the X-ray flux and show that the large values of the frequency drifts observed in some bursts can be accounted for within our model combined with the model of homogeneous radial expansion. Also, if inhomogeneities are trapped in the forward zonal flows around the propagating burning front, chirps with large frequency ranges (~25-500 Hz) may be detectable during the burst rise. We argue that an MHD dynamo within the burning front can generate a small-scale magnetic field, which may enforce vertically rigid flow in the front's wake and can explain the coherence of oscillations in the burst tail.Comment: Submitted to ApJ, 23 pages (including 8 figures), abstract abridge

Lithium Depletion in Fully Convective Pre-Main Sequence Stars

We present an analytic calculation of the thermonuclear depletion of lithium in contracting, fully convective, pre-main sequence stars of mass M < 0.5 M_sun. Previous numerical work relies on still-uncertain physics (atmospheric opacities and convection, in particular) to calculate the effective temperature as a unique function of stellar mass. We assume that the star's effective temperature, T_eff, is fixed during Hayashi contraction and allow its actual value to be a free parameter constrained by observation. Using this approximation, we compute lithium burning analytically and explore the dependence of lithium depletion on T_eff, M, and composition. Our calculations yield the radius, age, and luminosity of a pre-main sequence star as a function of lithium depletion. This allows for more direct comparisons to observations of lithium depleted stars. Our results agree with those numerical calculations that explicitly determine stellar structure during Hayashi contraction. In agreement with Basri, Marcy, and Graham (1996), we show that the absence of lithium in the Pleiades star HHJ 3 implies that it is older than 100 Myr. We also suggest a generalized method for dating galactic clusters younger than 100 Myr (i.e., those with contracting stars of M > 0.08 M_sun) and for constraining the masses of lithium depleted stars.Comment: 13 pages, LaTex with 2 postscript figures, uses aaspp4.sty and epsfig.sty, to appear in the Astrophysical Journa