9 research outputs found
Self-gravitating Newtonian disks revisited
Recent analytic results concerning stationary, self-gravitating fluids in
Newtonian theory are discussed. We give a theorem that forbids infinitely
extended fluids, depending on the assumed equation of state and the rotation
law. This part extends previous results that have been obtained for static
configurations. The second part discusses a Sobolev bound on the mass of the
fluid and a rigorous Jeans-type inequality that is valid in the stationary
case.Comment: A talk given at the Spanish Relativity Meeting in Portugal 2012. To
appear in Progress in Mathematical Relativity, Gravitation and Cosmology,
Proceedings of the Spanish Relativity Meeting ERE2012, University of Minho,
Guimaraes, Portugal, 3-7 September 2012, Springer Proceedings in Mathematics
& Statistics, Vol. 6
Nonlinear Dynamical Stability of Newtonian Rotating White Dwarfs and Supermassive Stars
We prove general nonlinear stability and existence theorems for rotating star
solutions which are axi-symmetric steady-state solutions of the compressible
isentropic Euler-Poisson equations in 3 spatial dimensions. We apply our
results to rotating and non-rotating white dwarf, and rotating high density
supermassive (extreme relativistic) stars, stars which are in convective
equilibrium and have uniform chemical composition. This paper is a continuation
of our earlier work ([28])
Existence and Nonlinear Stability of Rotating Star Solutions of the Compressible Euler-Poisson Equations
We prove existence of rotating star solutions which are steady-state
solutions of the compressible isentropic Euler-Poisson (EP) equations in 3
spatial dimensions, with prescribed angular momentum and total mass. This
problem can be formulated as a variational problem of finding a minimizer of an
energy functional in a broader class of functions having less symmetry than
those functions considered in the classical Auchmuty-Beals paper. We prove the
nonlinear dynamical stability of these solutions with perturbations having the
same total mass and symmetry as the rotating star solution. We also prove local
in time stability of W^{1, \infty}(\RR^3) solutions where the perturbations
are entropy-weak solutions of the EP equations. Finally, we give a uniform (in
time) a-priori estimate for entropy-weak solutions of the EP equations
Asteroseismology of Eclipsing Binary Stars in the Kepler Era
Eclipsing binary stars have long served as benchmark systems to measure
fundamental stellar properties. In the past few decades, asteroseismology - the
study of stellar pulsations - has emerged as a new powerful tool to study the
structure and evolution of stars across the HR diagram. Pulsating stars in
eclipsing binary systems are particularly valuable since fundamental properties
(such as radii and masses) can determined using two independent techniques.
Furthermore, independently measured properties from binary orbits can be used
to improve asteroseismic modeling for pulsating stars in which mode
identifications are not straightforward. This contribution provides a review of
asteroseismic detections in eclipsing binary stars, with a focus on space-based
missions such as CoRoT and Kepler, and empirical tests of asteroseismic scaling
relations for stochastic ("solar-like") oscillations.Comment: 28 pages, 12 figures, 2 tables; Proceedings of the AAS topical
conference "Giants of Eclipse" (AASTCS-3), July 28 - August 2 2013, Monterey,
C