Non-radial oscillations of the rapidly rotating Be star HD 163868

We study the pulsational stability of the rapidly rotating Be star HD 163868 using a newly developed 2D oscillation code which takes the Coriolis force fully into account and compare our results with observations (MOST) and recent other stability analyses of this ~ 6 Msun star. We find both prograde and retrograde overstable modes (although more prograde than retrograde modes) and confirm the existence of low degree odd r-modes destabilised by the kappa-mechanism. The ultra-low frequency modes that could not be explained in a previous analysis are interpreted as high degree, retrograde m=1 modes. A reasonably good fit to the observed oscillation spectrum is possible if we assume that only even modes are observed. This requires a nearly equator-on view of the observed star, consistent with the measured high v sin i value of 250 km/s.Comment: 7 pages, 7 figures; accepted by A&

Visibility of unstable oscillation modes in a rapidly rotating B star

Space missions like CoRoT and Kepler have provided numerous new observations of stellar oscillations in a multitude of stars by high precision photometry. This work compares the observed rich oscillation spectrum of the rapidly rotating B3 IV star HD 43317 with the first results obtained by a new method to calculate unstable oscillation modes in rapidly rotating stars in order to see whether some of the observed modes can be identified. The new numerical method consists of two parts. We first search for modes resonant with a prescribed forcing symmetry by moving through relevant regions of complex frequency space and monitoring any increase of the stellar response to the applied forcing and zooming in onto the resonance. These resonant non-adiabatic 2D-solutions are then fed into a 2D relaxation code with the same equations but without forcing terms. The complex oscillation frequency used in the forcing is now no longer prescribed, but added as an extra unknown. The corresponding free oscillation mode is usually obtained after a few ($<10$) iterations with only minor adjustment of the complex oscillation frequency. To compare with the observed light variations we calculate the `visibility' of the found unstable oscillation modes, taking into account the cancellation of the various parts of the radiating oscillating stellar surface as seen by the observer. The frequencies of unstable axisymmetric g-modes, which have the highest visibility, appear to nearly coincide with the observed largest amplitude photometric variations of HD 43317, making an identification of the latter oscillations as $m$=0 modes plausible. The identification of $m$=1 g-modes is less straightforward, while many of the unstable even $m$=2 g-modes may correspond to observed weaker photometric variations.Comment: 9 pages, 5 figures accepted by Astronomy & Astrophysic

Tidal interaction of a rotating 1 Msun star with a binary companion

We calculate the tidal torque on a uniformly rotating 1 Msun star at various stages of core hydrogen burning by an orbiting companion. We apply the `traditional approximation' and solve the radial part of the tidal perturbations by matrix inversion of the set of finite difference equations on a very fine grid. We have identified resonances with gravity- and quasi-toroidal modes with up to 1000 radial nodes in the more evolved stellar models. For low forcing frequencies we find significant tidal response due to viscous damping of inertial modes in the convective envelope of the solar-type star. We conclude that effects due to stellar rotation (including resonance locking) may considerably enhance the speed of tidal evolution in solar-type stars.Comment: accepted for publ. in A&A, 11 pages, 6 figure

Tidal evolution of eccentric orbits in massive binary systems; a study of resonance locking

We study the tidal evolution of a binary system consisting of a 1.4 Msun compact object in elliptic orbit about a 10 Msun uniformly rotating main sequence star for various values of the initial orbital parameters. We apply our previously published results of 2D non-adiabatic calculations of the non-radial g- and r-mode oscillations of the uniformly rotating MS star, and include the effects of resonant excitation of these modes in the tidal evolution calculations. A high orbital eccentricity enhances the effectiveness of the tidal interaction because of the large number of harmonic components of the tidal potential and the reduced orbital separation near periastron. By including the evolution of the MS star, especially of its rotation rate, many resonance crossings occur with enhanced tidal interaction. We analyse the phenomenon of resonance locking whereby a particular tidal harmonic is kept resonant with a stellar oscillation mode. Resonance locking of prograde g-modes appears an effective mechanism for orbital circularization of eccentric orbits. We consider the orbital evolution of the binary pulsar PSR J0045-7319 and conclude that resonance locking could explain the observed short orbital decay time of this system if the B-star spins in the direction counter to the orbital motion.Comment: 21 pages, 11 figures; some at reduced resolution, accepted for publication in A&

Formation of millisecond pulsars. I. Evolution of low-mass X-ray binaries with P > 2 days

We have performed detailed numerical calculations of the non-conservative evolution of close binary systems with low-mass (1.0-2.0 M_sun) donor stars and a 1.3 M_sun accreting neutron star. Rather than using analytical expressions for simple polytropes, we calculated the thermal response of the donor star to mass loss, in order to determine the stability and follow the evolution of the mass transfer. Tidal spin-orbit interactions and Reimers wind mass-loss were also taken into account. We have re-calculated the correlation between orbital period and white dwarf mass in wide binary radio pulsar systems. Furthermore, we find an anti-correlation between orbital period and neutron star mass under the assumption of the "isotropic re-emission" model and compare this result with observations. We conclude that the accretion efficiency of neutron stars is rather low and that they eject a substantial fraction of the transferred material even when accreting at a sub-Eddington level. The mass-transfer rate is a strongly increasing function of initial orbital period and donor star mass. For relatively close systems with light donors (P < 10 days and M_2 < 1.3 M_sun) the mass-transfer rate is sub-Eddington, whereas it can be highly super-Eddington by a factor of 10^4 for wide systems with relatively heavy donor stars (1.6 - 2.0 M_sun) as a result of their deep convective envelopes. We briefly discuss the evolution of X-ray binaries with donor stars in excess of 2 M_sun. Based on our calculations we present evidence that PSR J1603-7202 evolved through a phase with unstable mass transfer from a relatively heavy donor star and therefore is likely to host a CO white dwarf companion.Comment: Accepted for publication in A&A. 18 pages, 6 figures, 2 table

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

Dynamical Tide in Solar-Type Binaries

Circularization of late-type main-sequence binaries is usually attributed to turbulent convection, while that of early-type binaries is explained by resonant excitation of g modes. We show that the latter mechanism operates in solar-type stars also and is at least as effective as convection, despite inefficient damping of g modes in the radiative core. The maximum period at which this mechanism can circularize a binary composed of solar-type stars in 10 Gyr is as low as 3 days, if the modes are damped by radiative diffusion only and g-mode resonances are fixed; or as high as 6 days, if one allows for evolution of the resonances and for nonlinear damping near inner turning points. Even the larger theoretical period falls short of the observed transition period by a factor two.Comment: 17 pages, 2 postscript figures, uses aaspp4.sty. Submitted to Ap

Nonadiabatic resonant dynamic tides and orbital evolution in close binaries

This investigation is devoted to the effects of nonadiabatic resonant dynamic tides generated in a uniformly rotating stellar component of a close binary. The companion is considered to move in a fixed Keplerian orbit, and the effects of the centrifugal force and the Coriolis force are neglected. Semi-analytical solutions for the linear, nonadiabatic resonant dynamic tides are derived by means of a two-time variable expansion procedure. The solution at the lowest order of approximation consists of the resonantly excited oscillation mode and displays a phase shift with respect to the tide-generating potential. Expressions are established for the secular variations of the semi-major axis, the orbital eccentricity, and the star's angular velocity of rotation caused by the phase shift. The orders of magnitude of these secular variations are considerably larger than those derived earlier by Zahn (1977) for the limiting case of dynamic tides with small frequencies. For a 5 solar mass ZAMS star, an orbital eccentricity e = 0.5, and orbital periods in the range from 2 to 5 days, numerous resonances of dynamic tides with second-degree lower-order gravity modes are seen to induce secular variations of the semi-major axis, the orbital eccentricity, and the star's angular velocity of rotation with time scales shorter than the star's nuclear life time.Comment: accepted for publication in A&A, 13 page

Three-dimensional waves generated at Lindblad resonances in thermally stratified disks

We analyze the linear, 3D response to tidal forcing of a disk that is thin and thermally stratified in the direction normal to the disk plane. We model the vertical disk structure locally as a polytrope which represents a disk of high optical depth. We solve the 3D gas-dynamic equations semi-analytically in the neighborhood of a Lindblad resonance. These solutions match asymptotically on to those valid away from resonances and provide solutions valid at all radii. We obtain the following results. 1) A variety of waves are launched at resonance. However, the f mode carries more than 95% of the torque exerted at the resonance. 2) These 3D waves collectively transport exactly the amount of angular momentum predicted by the 2D torque formula. 3) Near resonance, the f mode occupies the full vertical extent of the disk. Away from resonance, the f mode becomes confined near the surface of the disk, and, in the absence of other dissipation mechanisms, damps via shocks. The radial length scale for this process is roughly r_L/m (for resonant radius r_L and azimuthal wavenumber m), independent of the disk thickness H. This wave channeling process is due to the variations of physical quantities in r and is not due to wave refraction. 4) However, the inwardly propagating f mode launched from an m=2 inner Lindblad resonance experiences relatively minor channeling. We conclude that for binary stars, tidally generated waves in highly optically thick circumbinary disks are subject to strong nonlinear damping by the channeling mechanism, while those in circumstellar accretion disks are subject to weaker nonlinear effects. We also apply our results to waves excited by young planets for which m is approximately r/H and conclude that the waves are damped on the scale of a few H.Comment: 15 pages, 3 figures, 2 colour plates, to be published in the Astrophysical Journa