Nonlinear r-modes in a spherical shell: issues of principle

We use a simple physical model to study the nonlinear behaviour of the r-mode instability. We assume that r-modes (Rossby waves) are excited in a thin spherical shell of rotating incompressible fluid. For this case, exact Rossby wave solutions of arbitrary amplitude are known. We find that: (a) These nonlinear Rossby waves carry ZERO physical angular momentum and positive physical energy, which is contrary to the folklore belief that the r-mode angular momentum and energy are negative. (b) Within our model, we confirm the differential drift reported by Rezzolla, Lamb and Shapiro (1999). Radiation reaction is introduced into the model by assuming that the fluid is electrically charged; r-modes are coupled to electromagnetic radiation through current (magnetic) multipole moments. We find that: (c) To linear order in the mode amplitude, r-modes are subject to the CFS instability, as expected. (d) Radiation reaction decreases the angular velocity of the shell and causes differential rotation (which is distinct from but similar in magnitude to the differential drift reported by Rezzolla et al.) prior to saturation of the r-mode growth. This is contrary to the phenomenological treatments to date, which assume that the loss of stellar angular momentum is accounted for by the r-mode growth. We demonstrate, for the first time, that r-mode radiation reaction leads to differential rotation. (e) We show that for l=2 r-mode electromagnetic radiation reaction is equivalent to gravitational radiation reaction in the lowest post-Newtonian order.Comment: 8 pages, no figures, uses MNRAS style, abstract abridged to fit into 24 line

Effect of a neutron-star crust on the r-mode instability

The presence of a viscous boundary layer under the solid crust of a neutron star dramatically increases the viscous damping rate of the fluid r-modes. We improve previous estimates of this damping rate by including the effect of the Coriolis force on the boundary-layer eigenfunction and by using more realistic neutron-star models. If the crust is assumed to be perfectly rigid, the gravitational radiation driven instability in the r-modes is completely suppressed in neutron stars colder than about 1.5 x 10^8 K. Energy generation in the boundary layer will heat the star, and will even melt the crust if the amplitude of the r-mode is large enough. We solve the heat equation explicitly (including the effects of thermal conduction and neutrino emission) and find that the r-mode amplitude needed to melt the crust is approximately a_c = 5 x 10^{-3} for maximally rotating neutron stars. If the r-mode saturates at an amplitude larger than a_c, the heat generated is sufficient to maintain the outer layers of the star in a mixed fluid-solid state analogous to the pack ice on the fringes of the Arctic Ocean. We argue that in young, rapidly rotating neutron stars this effect considerably delays the formation of the crust. By considering the dissipation in the ice flow, we show that the final spin frequency of stars with r-mode amplitude of order unity is close to the value estimated for fluid stars without a crust

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

Thermal states of coldest and hottest neutron stars in soft X-ray transients

We calculate the thermal structure and quiescent thermal luminosity of accreting neutron stars (warmed by deep crustal heating in accreted matter) in soft X-ray transients (SXTs). We consider neutron stars with nucleon and hyperon cores and with accreted envelopes. It is assumed that an envelope has an outer helium layer (of variable depth) and deeper layers of heavier elements, either with iron or with much heavier nuclei (of atomic weight A > 100) on the top (Haensel & Zdunik 1990, 2003, astro-ph/0305220). The relation between the internal and surface stellar temperatures is obtained and fitted. The quiescent luminosity of the hottest (low-mass) and coldest (high-mass) neutron stars is calculated, together with the ranges of its possible variations due to variable thickness of the helium layer. The results are compared with observations of SXTs, particularly, containing the coldest (SAX J1808.4-3658) and the hottest (Aql X-1) neutron stars. The observations of SAX J1808.4-3658 in a quiescent state on March 24, 2001 (Campana et al. 2002, astro-ph/0206376) can be explained only if this SXT contains a massive neutron star with a nucleon/hyperon core; a hyperon core with a not too low fraction of electrons is preferable. Future observations may discriminate between the various models of hyperon/nucleon dense matter. The thermal emission of SAX J1808.4-3658 is also sensitive to the models of plasma ionization in the outermost surface layers and can serve for testing such models.Comment: 12 pages, 5 figures, 4 tables, LaTeX2e with aa.cls v.5.3 (included). Accepted by A&

Gravitational Waves from Neutron Stars with Large Toroidal B-fields

We show that NS's with large toroidal B-fields tend naturally to evolve into potent gravitational-wave (gw) emitters. The toroidal field B_t tends to distort the NS into a prolate shape, and this magnetic distortion can easily dominate over the oblateness ``frozen into'' the NS crust. An elastic NS with frozen-in B-field of this magnitude is clearly secularly unstable: the wobble angle between the NS's angular momentum J^i and the star's magnetic axis n_B^i grow on a dissipation timescale until J^i and n_B^i are orthogonal. This final orientation is clearly the optimal one for gravitational-wave (gw) emission. The basic cause of the instability is quite general, so we conjecture that the same final state is reached for a realistic NS. Assuming this, we show that for LMXB's with B_t of order 10^{13}G, the spindown from gw's is sufficient to balance the accretion torque--supporting a suggestion by Bildsten. The spindown rates of most millisecond pulsars can also be attributed to gw emission sourced by toroidal B-fields, and both these sources could be observed by LIGO II. While the first-year spindown of a newborn NS is most likely dominated by em processes, reasonable values of B_t and the (external) dipolar field B_d can lead to detectable levels of gw emission, for a newborn NS in our own galaxy.Comment: 7 pages; submitted to PRD; only minor revision

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

Unstable quasi g-modes in rotating main-sequence stars

This paper studies the oscillatory stability of uniformly rotating main-sequence stars of mass 3-8 M_sun by solving the linearized non-adiabatic, non-radial oscillation equations with a forcing term and searching for resonant response to a complex forcing frequency. By using the traditional approximation the solution of the forced oscillation equations becomes separable, whereby the energy equation is made separable by approximation. It is found that the kappa-mechanism in rotating B-stars can destabilize not only gravity- or pressure modes, but also a branch of low frequency retrograde (in corotating frame) oscillations in between the retrograde g-modes and toroidal r-modes. These unstable quasi g-modes (or `q-modes') hardly exhibit rotational confinement to the equatorial regions of the star, while the oscillations are always prograde in the observer's frame, all in contrast to g-modes. The unstable q-modes occur in a few narrow period bands (defined by their azimuthal index m), and seem to fit the oscillation spectra observed in SPB stars rather well. The unstable q-mode oscillation spectrum of a very rapidly rotating 8 M_sun star appears similar to that of the well studied Be-star mu Cen. The unstable q-modes thus seem far better in explaining the observed oscillation spectra in SPB-stars and Be-stars than normal g-modes.Comment: 15 pages, 16 figures, to appear in Astronomy & Astrophysic

The faint neutron star soft X-ray transient SAX J1810.8-2609 in quiescence

We present the analysis of a 35 ksec long Chandra observation of the neutron star soft X-ray transient (SXT) SAX J1810.8-2609. We detect three sources in the field of view. The position of one of them is consistent with the location of the ROSAT error circle of SAX J1810.8-2609. The accurate Chandra position of that source coincides with the position of the proposed optical counterpart, strengthening the identification as the counterpart. We detected the neutron star SXT system in quiescence at an unabsorbed luminosity of ~1x10^32 erg s^-1 (assuming a distance of 4.9 kpc). This luminosity is at the low-end of quiescent luminosities found in other neutron star SXTs. This renders support to the existence of a group of faint soft X-ray transients of which the accreting millisecond X-ray pulsar SAX J1808.4-3658 is the most prominent member. The quiescent spectrum of SAX J1810.8-2609 is well-fit with an absorbed power law with photon index of 3.3+-0.5. With a value of 3.3x10^21 cm^-2 the Galactic absorption is consistent with the value derived in outburst. Since the spectra of quiescent neutron star SXTs are often fit with an absorbed blackbody or neutron star atmosphere plus power-law model we also fitted the spectrum using those fit functions. Both models provide a good fit to the data. If cooling of the neutron star core and/or crust is responsible for the soft part of the spectrum the time averaged mass accretion rate must have been very low (~5.7x10^-13 Msun yr^-1; assuming standard core cooling only) or the neutron star must be massive. We also discuss the possibility that the thermal spectral component in neutron stars in quiescence is produced by residual accretion.Comment: 5 pages, 1 figure, accepted for publication by MNRA