472 research outputs found
Inertial modes in slowly rotating stars : an evolutionary description
We present a new hydro code based on spectral methods using spherical
coordinates. The first version of this code aims at studying time evolution of
inertial modes in slowly rotating neutron stars. In this article, we introduce
the anelastic approximation, developed in atmospheric physics, using the mass
conservation equation to discard acoustic waves. We describe our algorithms and
some tests of the linear version of the code, and also some preliminary linear
results. We show, in the Newtonian framework with differentially rotating
background, as in the relativistic case with the strong Cowling approximation,
that the main part of the velocity quickly concentrates near the equator of the
star. Thus, our time evolution approach gives results analogous to those
obtained by Karino {\it et al.} \cite{karino01} within a calculation of
eigenvectors. Furthermore, in agreement with the work of Lockitch {\it et al.}
\cite{lockandf01}, we found that the velocity seems to always get a
non-vanishing polar part.Comment: 36 pages, 27 figures, accepted for publication in Phys. Rev. D
(discussion added in the introduction
MHD of rotating compact stars with spectral methods: description of the algorithm and tests
A flexible spectral code for the study of general relativistic
magnetohydrodynamics is presented. Aiming at investigating the physics of
slowly rotating magnetized compact stars, this new code makes use of various
physically motivated approximations. Among them, the relativistic anelastic
approximation is a key ingredient of the current version of the code. In this
article, we mainly outline the method, putting emphasis on algorithmic
techniques that enable to benefit as much as possible of the non-dissipative
character of spectral methods, showing also a potential astrophysical
application and providing a few illustrative tests.Comment: 15 pages, 4 figures (new figure added, misprints corrected) Article
accepted for publication in a special issue of Classical and Quantum Gravity
"New Frontiers in Numerical Relativity
Inertial modes in stratified rotating neutron stars : An evolutionary description
With (non-barotropic) equations of state valid even when the neutron, proton
and electron content of neutron star cores is not in beta equilibrium, we study
inertial and composition gravity modes of relativistic rotating neutron stars.
We solve the relativistic Euler equations in the time domain with a three
dimensional numerical code based on spectral methods, in the slow rotation,
relativistic Cowling and anelastic approximations. Principally, after a short
description of the gravity modes due to smooth composition gradients, we focus
our analysis on the question of how the inertial modes are affected by
non-barotropicity of the nuclear matter. In our study, the deviation with
respect to barotropicity results from the frozen composition of non-superfluid
matter composed of neutrons, protons and electrons, when beta equilibrium is
broken by millisecond oscillations. We show that already for moderatly fast
rotating stars the increasing coupling between polar and axial modes makes
those two cases less different than for very slowly rotating stars. In
addition, as we directly solve the Euler equations, without coupling only a few
number of spherical harmonics, we always found, for the models that we use, a
discrete spectrum for the inertial mode. Finally, we find that, for
non-barotropic stars, the frequency of this mode, which is our main focus,
decreases in a non-negligible way, whereas the time dependence of the energy
transfer between polar and axial modes is substantially different due to the
existence of low-frequencies gravity modes.Comment: 34 pages, 24 figures, published versio
Relativistic models of magnetars: structure and deformations
We find numerical solutions of the coupled system of Einstein-Maxwell's
equations with a linear approach, in which the magnetic field acts as a
perturbation of a spherical neutron star. In our study, magnetic fields having
both poloidal and toroidal components are considered, and higher order
multipoles are also included. We evaluate the deformations induced by different
field configurations, paying special attention to those for which the star has
a prolate shape. We also explore the dependence of the stellar deformation on
the particular choice of the equation of state and on the mass of the star. Our
results show that, for neutron stars with mass M = 1.4 Msun and surface
magnetic fields of the order of 10^15 G, a quadrupole ellipticity of the order
of 10^(-6) - 10^(-5) should be expected. Low mass neutron stars are in
principle subject to larger deformations (quadrupole ellipticities up to
10^(-3) in the most extreme case). The effect of quadrupolar magnetic fields is
comparable to that of dipolar components. A magnetic field permeating the whole
star is normally needed to obtain negative quadrupole ellipticities, while
fields confined to the crust typically produce positive quadrupole
ellipticities.Comment: 25 pages, 9 figures, submitted to MNRA
Jeans criterion in a turbulent medium
According to the classical Jeans analysis, all the molecular clouds of mass larger than a few 100 M(solar), size larger than about 1pc and kinetic temperature Tk less than 30K are gravitationally unstable. We have shown that in clouds supported by internal supersonic motions, local gravitational instabilities may appear within molecular clouds which are globally stable. The argument is threefold: (1) when the turbulent kinetic energy is included into the internal energy term, the virial equilibrium condition shows that molecular clouds such as those observed, which are gravitationally unstable according to the Jeans criterion, are indeed globally stable if supported by a turbulent velocity field of power spectrum steeper than 3; (2) 2D compressible hydrodynamical simulations show that a supersonic turbulent velocity field generates a turbulent pressure within clouds, the gradients of which stabilize the unstable scales (i.e., the largest scales and the cloud itself) against gravitational collapse; (3) an analysis similar to the Jeans approach but including the turbulent pressure gradient term, gives basically the same results as those given in (1). Clouds of mean density lower than a critical value are found to be stable even though more massive than their Jeans mass. In clouds of mean density larger than that critical value, the gravitational instability appears only over a range of scales smaller than the cloud size, the largest scales being stable. In practice, the observed mean densities are lower than this critical value: the observation of a small number of cores and stars of a few solar masses embedded in clouds of several hundred solar masses can only be understood in terms of small scale density fluctuations of large amplitude generated by the supersonic turbulence which would occasionally overtake the limit of gravitational stability
Keplerian frequency of uniformly rotating neutron stars and quark stars
We calculate Keplerian (mass shedding) configurations of rigidly rotating
neutron stars and quark stars with crusts. We check the validity of empirical
formula for Keplerian frequency, f_K, proposed by Lattimer & Prakash, f_K(M)=C
(M/M_sun)^1/2 (R/10km)^-3/2, where M is the (gravitational) mass of Keplerian
configuration, R is the (circumferential) radius of the non-rotating
configuration of the same gravitational mass, and C = 1.04 kHz. Numerical
calculations are performed using precise 2-D codes based on the multi-domain
spectral methods. We use a representative set of equations of state (EOSs) of
neutron stars and quark stars. We show that the empirical formula for f_K(M)
holds within a few percent for neutron stars with realistic EOSs, provided 0.5
M_sun < M < 0.9 M_max,stat, where M_max,stat is the maximum allowable mass of
non-rotating neutron stars for an EOS, and C=C_NS=1.08 kHz. Similar precision
is obtained for quark stars with 0.5 M_sun < M < 0.9 M_max,stat. For maximal
crust masses we obtain C_QS = 1.15 kHz, and the value of C_QS is not very
sensitive to the crust mass. All our C's are significantly larger than the
analytic value from the relativistic Roche model, C_Roche = 1.00 kHz. For 0.5
M_sun < M < 0.9 M_max,stat, the equatorial radius of Keplerian configuration of
mass M, R_K(M), is, to a very good approximation, proportional to the radius of
the non-rotating star of the same mass, R_K(M) = aR(M), with a_NS \approx a_QS
\approx 1.44. The value of a_QS is very weakly dependent on the mass of the
crust of the quark star. Both a's are smaller than the analytic value a_Roche =
1.5 from the relativistic Roche model.Comment: 6 pages, 6 color figures, submitted to A&
The bar-mode instability in differentially rotating neutron stars: Simulations in full general relativity
We study the dynamical stability against bar-mode deformation of rapidly
spinning neutron stars with differential rotation. We perform fully
relativistic 3D simulations of compact stars with , where is
the total gravitational mass and the equatorial circumferential radius. We
adopt an adiabatic equation of state with adiabatic index . As in
Newtonian theory, we find that stars above a critical value of (where is the rotational kinetic energy and the gravitational
binding energy) are dynamically unstable to bar formation. For our adopted
choices of stellar compaction and rotation profile, the critical value of
is , only slightly smaller than the
well-known Newtonian value for incompressible Maclaurin spheroids.
The critical value depends only very weakly on the degree of differential
rotation for the moderate range we surveyed. All unstable stars form bars on a
dynamical timescale. Models with sufficiently large subsequently form
spiral arms and eject mass, driving the remnant to a dynamically stable state.
Models with moderately large do not develop spiral
arms or eject mass but adjust to form dynamically stable ellipsoidal-like
configurations. If the bar-mode instability is triggered in supernovae collapse
or binary neutron star mergers, it could be a strong and observable source of
gravitational waves. We determine characteristic wave amplitudes and
frequencies.Comment: 17 pages, accepted for publication in AP
Numerical models of irrotational binary neutron stars in general relativity
We report on general relativistic calculations of quasiequilibrium
configurations of binary neutron stars in circular orbits with zero vorticity.
These configurations are expected to represent realistic situations as opposed
to corotating configurations. The Einstein equations are solved under the
assumption of a conformally flat spatial 3-metric (Wilson-Mathews
approximation). The velocity field inside the stars is computed by solving an
elliptical equation for the velocity scalar potential. Results are presented
for sequences of constant baryon number (evolutionary sequences). Although the
central density decreases much less with the binary separation than in the
corotating case, it still decreases. Thus, no tendency is found for the stars
to individually collapse to black hole prior to merger.Comment: Minor corrections, improved figure, 5 pages, REVTeX, Phys. Rev. Lett.
in pres
Relativistic models of magnetars: Nonperturbative analytical approach
In the present paper we focus on building simple nonperturbative analytical
relativistic models of magnetars. With this purpose in mind we first develop a
method for generating exact interior solutions to the static and axisymmetric
Einstein-Maxwell-hydrodynamic equations with anisotropic perfect fluid and with
pure poloidal magnetic field. Then using an explicit exact solution we present
a simple magnetar model and calculate some physically interesting quantities as
the surface elipticity and the total energy of the magnetized star.Comment: 10 pages, LaTe
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