91,676 research outputs found
On the stability and deformability of top stars
Topological stars, or top stars for brevity, are smooth horizonless static
solutions of Einstein-Maxwell theory in 5-d that reduce to spherically
symmetric solutions of Einstein-Maxwell-Dilaton theory in 4-d. We study linear
scalar perturbations of top stars and argue for their stability and
deformability. We tackle the problem with different techniques including WKB
approximation, numerical analysis, Breit-Wigner resonance method and quantum
Seiberg-Witten curves. We identify three classes of quasi-normal modes
corresponding to prompt-ring down modes, long-lived meta-stable modes and what
we dub `blind' modes. All mode frequencies we find have negative imaginary
parts, thus suggesting linear stability of top stars. Moreover we determine the
tidal Love and dissipation numbers encoding the response to tidal deformations
and, similarly to black holes, we find zero value in the static limit but,
contrary to black holes, we find non-trivial dynamical Love numbers and
vanishing dissipative effects at linear order. For the sake of illustration in
a simpler context, we also consider a toy model with a piece-wise constant
potential and a centrifugal barrier that captures most of the above features in
a qualitative fashion
Dynamics of magnetic flux tubes in close binary stars I. Equilibrium and stability properties
Surface reconstructions of active close binary stars based on photometric and
spectroscopic observations reveal non-uniform starspot distributions, which
indicate the existence of preferred spot longitudes (with respect to the
companion star). We consider the equilibrium and linear stability of toroidal
magnetic flux tubes in close binaries to examine whether tidal effects are
capable to initiate the formation of rising flux loops at preferred longitudes
near the bottom of the stellar convection zone. The tidal force and the
deviation of the stellar structure from spherical symmetry are treated in
lowest-order perturbation theory assuming synchronised close binaries with
orbital periods of a few days. The frequency, growth time, and spatial
structure of linear eigenmodes are determined by a stability analysis. We find
that, despite their small magnitude, tidal effects can lead to a considerable
longitudinal asymmetry in the formation probability of flux loops, since the
breaking of the axial symmetry due to the presence of the companion star is
reinforced by the sensitive dependence of the stability properties on the
stellar stratification and by resonance effects. The orientation of preferred
longitudes of loop formation depends on the equilibrium configuration and the
wave number of the dominating eigenmode. The change of the growth times of
unstable modes with respect to the case of a single star is very small.Comment: 11 pages, 11 figures, accepted for publication in A&
Interaction Between Convection and Pulsation
This article reviews our current understanding of modelling convection
dynamics in stars. Several semi-analytical time-dependent convection models
have been proposed for pulsating one-dimensional stellar structures with
different formulations for how the convective turbulent velocity field couples
with the global stellar oscillations. In this review we put emphasis on two,
widely used, time-dependent convection formulations for estimating pulsation
properties in one-dimensional stellar models. Applications to pulsating stars
are presented with results for oscillation properties, such as the effects of
convection dynamics on the oscillation frequencies, or the stability of
pulsation modes, in classical pulsators and in stars supporting solar-type
oscillations.Comment: Invited review article for Living Reviews in Solar Physics. 88 pages,
14 figure
Relativistic stars with a linear equation of state: analogy with classical isothermal spheres and black holes
We complete our previous investigation concerning the structure and the
stability of "isothermal" spheres in general relativity. This concerns objects
that are described by a linear equation of state so that the
pressure is proportional to the energy density. In the Newtonian limit , this returns the classical isothermal equation of state. We consider
specifically a self-gravitating radiation (q=1/3), the core of neutron stars
(q=1/3) and a gas of baryons interacting through a vector meson field (q=1). We
study how the thermodynamical parameters scale with the size of the object and
find unusual behaviours due to the non-extensivity of the system. We compare
these scaling laws with the area scaling of the black hole entropy. We also
determine the domain of validity of these scaling laws by calculating the
critical radius above which relativistic stars described by a linear equation
of state become dynamically unstable. For photon stars, we show that the
criteria of dynamical and thermodynamical stability coincide. Considering
finite spheres, we find that the mass and entropy as a function of the central
density present damped oscillations. We give the critical value of the central
density, corresponding to the first mass peak, above which the series of
equilibria becomes unstable. Finally, we extend our results to d-dimensional
spheres. We show that the oscillations of mass versus central density disappear
above a critical dimension d_{crit}(q). For Newtonian isothermal stars (q=0) we
recover the critical dimension d_{crit}=10. For the stiffest stars (q=1) we
find d_{crit}=9 and for a self-gravitating radiation (q=1/d) we find
d_{crit}=9.96404372... very close to 10. Finally, we give analytical solutions
of relativistic isothermal spheres in 2D gravity.Comment: A minor mistake in calculation has been corrected in the second
version (v2
Dynamical Boson Stars
The idea of stable, localized bundles of energy has strong appeal as a model
for particles. In the 1950s John Wheeler envisioned such bundles as smooth
configurations of electromagnetic energy that he called {\em geons}, but none
were found. Instead, particle-like solutions were found in the late 1960s with
the addition of a scalar field, and these were given the name {\em boson
stars}. Since then, boson stars find use in a wide variety of models as sources
of dark matter, as black hole mimickers, in simple models of binary systems,
and as a tool in finding black holes in higher dimensions with only a single
killing vector. We discuss important varieties of boson stars, their dynamic
properties, and some of their uses, concentrating on recent efforts.Comment: 79 pages, 25 figures, invited review for Living Reviews in
Relativity; major revision in 201
Secular Instabilities of Keplerian Stellar Discs
We present idealized models of a razor-thin, axisymmetric, Keplerian stellar
disc around a massive black hole, and study non-axisymmetric secular
instabilities in the absence of either counter-rotation or loss cones. These
discs are prograde mono-energetic waterbags, whose phase space distribution
functions are constant for orbits within a range of eccentricities (e) and zero
outside this range. The linear normal modes of waterbags are composed of
sinusoidal disturbances of the edges of distribution function in phase space.
Waterbags which include circular orbits (polarcaps) have one stable linear
normal mode for each azimuthal wavenumber m. The m = 1 mode always has positive
pattern speed and, for polarcaps consisting of orbits with e < 0.9428, only the
m = 1 mode has positive pattern speed. Waterbags excluding circular orbits
(bands) have two linear normal modes for each m, which can be stable or
unstable. We derive analytical expressions for the instability condition,
pattern speeds, growth rates and normal mode structure. Narrow bands are
unstable to modes with a wide range in m. Numerical simulations confirm linear
theory and follow the non-linear evolution of instabilities. Long-time
integration suggests that instabilities of different m grow, interact
non-linearly and relax collisionlessly to a coarse-grained equilibrium with a
wide range of eccentricities.Comment: Manuscript accepted for publication in MNRA
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