Regular Oscillation Sub-spectrum of Rapidly Rotating Stars

We present an asymptotic theory that describes regular frequency spacings of pressure modes in rapidly rotating stars. We use an asymptotic method based on an approximate solution of the pressure wave equation constructed from a stable periodic solution of the ray limit. The approximate solution has a Gaussian envelope around the stable ray, and its quantization yields the frequency spectrum. We construct semi-analytical formulas for regular frequency spacings and mode spatial distributions of a subclass of pressure modes in rapidly rotating stars. The results of these formulas are in good agreement with numerical data for oscillations in polytropic stellar models. The regular frequency spacings depend explicitly on internal properties of the star, and their computation for different rotation rates gives new insights on the evolution of mode frequencies with rotation.Comment: 14 pages, 10 figure

Gravity modes in rapidly rotating stars. Limits of perturbative methods

CoRoT and Kepler missions are now providing high-quality asteroseismic data for a large number of stars. Among intermediate-mass and massive stars, fast rotators are common objects. Taking the rotation effects into account is needed to correctly understand, identify, and interpret the observed oscillation frequencies of these stars. A classical approach is to consider the rotation as a perturbation. In this paper, we focus on gravity modes, such as those occurring in gamma Doradus, slowly pulsating B (SPB), or Be stars. We aim to define the suitability of perturbative methods. With the two-dimensional oscillation program (TOP), we performed complete computations of gravity modes -including the Coriolis force, the centrifugal distortion, and compressible effects- in 2-D distorted polytropic models of stars. We started with the modes l=1, n=1-14, and l=2-3, n=1-5,16-20 of a nonrotating star, and followed these modes by increasing the rotation rate up to 70% of the break-up rotation rate. We then derived perturbative coefficients and determined the domains of validity of the perturbative methods. Second-order perturbative methods are suited to computing low-order, low-degree mode frequencies up to rotation speeds ~100 km/s for typical gamma Dor stars or ~150 km/s for B stars. The domains of validity can be extended by a few tens of km/s thanks to the third-order terms. For higher order modes, the domains of validity are noticeably reduced. Moreover, perturbative methods are inefficient for modes with frequencies lower than the Coriolis frequency 2Omega. We interpret this failure as a consequence of a modification in the shape of the resonant cavity that is not taken into account in the perturbative approach.Comment: 8 pages, 6 figures, Astronomy & Astrophysics (in press

On the Space Time of a Galaxy

We present an exact solution of the averaged Einstein's field equations in the presence of two real scalar fields and a component of dust with spherical symmetry. We suggest that the space-time found provides the characteristics required by a galactic model that could explain the supermassive central object and the dark matter halo at once, since one of the fields constitutes a central oscillaton surrounded by the dust and the other scalar field distributes far from the coordinate center and can be interpreted as a halo. We show the behavior of the rotation curves all along the background. Thus, the solution could be a first approximation of a ``long exposition photograph'' of a galaxy.Comment: 8 pages REVTeX, 11 eps figure

Analysis of the thermomechanical inconsistency of some extended hydrodynamic models at high Knudsen number

There are some hydrodynamic equations that, while their parent kinetic equation satisfies fundamental mechanical properties, appear themselves to violate mechanical or thermodynamic properties. This article aims to shed some light on the source of this problem. Starting with diffusive volume hydrodynamic models, the microscopic temporal and spatial scales are first separated at the kinetic level from the macroscopic scales at the hydrodynamic level. Then we consider Klimontovich’s spatial stochastic version of the Boltzmann kinetic equation, and show that, for small local Knudsen numbers, the stochastic term vanishes and the kinetic equation becomes the Boltzmann equation. The collision integral dominates in the small local Knudsen number regime, which is associated with the exact traditional continuum limit. We find a sub-domain of the continuum range which the conventional Knudsen number classification does not account for appropriately. In this sub-domain, it is possible to obtain a fully mechanically-consistent volume (or mass) diffusion model that satisfies the second law of thermodynamics on the grounds of extended non-local-equilibrium thermodynamics

A New Formation Channel for Double Neutron Stars Without Recycling: Implications for Gravitational Wave Detection

We report on a new evolutionary path leading to the formation of close double neutron stars (NS), with the unique characteristic that none of the two NS ever had the chance to be recycled by accretion. The existence of this channel stems from the evolution of helium-rich stars (cores of massive NS progenitors), which has been neglected in most previous studies of double compact object formation. We find that these non-recycled NS-NS binaries are formed from bare carbon-oxygen cores in tight orbits, with formation rates comparable to or maybe even higher than those of recycled NS-NS binaries. On the other hand, their detection probability as binary pulsars is greatly reduced (by about 1000) relative to recycled pulsars, because of their short lifetimes. We conclude that, in the context of gravitational-wave detection of NS-NS inspiral events, this new type of binaries calls for an increase of the rate estimates derived from the observed NS-NS with recycled pulsars, typically by factors of 1.5-3 or even higher.Comment: Accepted for publication in ApJ Letters; 5 pages, 1 figure, 2 tables. Two new paragraphs and one formula adde