469 research outputs found
Features of the extreme events observed in the all-solid state laser with a saturable absorber
Extreme events (sometimes also called optical rogue waves), in the form of
pulses of extraordinary intensity, are easily observed in its chaotic regime if
the Fresnel number of the cavity is high. This result suggests that the
nonlinear interaction among transverse modes is an essential ingredient in the
formation of extreme events in this type of lasers, but there is no theoretical
description of the phenomenon yet. We report here a set of experimental results
on the regularities of these extreme events, to provide a basis for the
development of such a description. Among these results, we point out here: i)
the decay of the correlation across the transversal section of the laser beam,
and ii) the appearance of extreme events even if the time elapsed since the
previous pulse is relatively short (in terms of the average inter-pulse
separation), what indicates the existence of some unknown mechanism of energy
storage. We hypothesize that this mechanism is related with the imperfect
depletion of the gain by some of the transversal modes. We also present
evidence in support of this hypothesis.Comment: 9 pages, 9 figure
Jacobi-like bar mode instability of relativistic rotating bodies
We perform some numerical study of the secular triaxial instability of
rigidly rotating homogeneous fluid bodies in general relativity. In the
Newtonian limit, this instability arises at the bifurcation point between the
Maclaurin and Jacobi sequences. It can be driven in astrophysical systems by
viscous dissipation. We locate the onset of instability along several constant
baryon mass sequences of uniformly rotating axisymmetric bodies for compaction
parameter . We find that general relativity weakens the Jacobi
like bar mode instability, but the stabilizing effect is not very strong.
According to our analysis the critical value of the ratio of the kinetic energy
to the absolute value of the gravitational potential energy for compaction parameter as high as 0.275 is only 30% higher than the
Newtonian value. The critical value of the eccentricity depends very weakly on
the degree of relativity and for is only 2% larger than the
Newtonian value at the onset for the secular bar mode instability. We compare
our numerical results with recent analytical investigations based on the
post-Newtonian expansion.Comment: 15 pages, 8 figures, submitted to Phys. Rev.
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
Frequency spectrum of gravitational radiation from global hydromagnetic oscillations of a magnetically confined mountain on an accreting neutron star
Recent time-dependent, ideal-magnetohydrodynamic (ideal-MHD) simulations of
polar magnetic burial in accreting neutron stars have demonstrated that stable,
magnetically confined mountains form at the magnetic poles, emitting
gravitational waves at (stellar spin frequency) and . Global
MHD oscillations of the mountain, whether natural or stochastically driven, act
to modulate the gravitational wave signal, creating broad sidebands (full-width
half-maximum ) in the frequency spectrum around and . The oscillations can enhance the signal-to-noise ratio achieved by a
long-baseline interferometer with coherent matched filtering by up to 15 per
cent, depending on where lies relative to the noise curve minimum.
Coherent, multi-detector searches for continuous waves from nonaxisymmetric
pulsars should be tailored accordingly.Comment: 4 figures, accepted for publication in Ap
Binary black holes in circular orbits. II. Numerical methods and first results
We present the first results from a new method for computing spacetimes
representing corotating binary black holes in circular orbits. The method is
based on the assumption of exact equilibrium. It uses the standard 3+1
decomposition of Einstein equations and conformal flatness approximation for
the 3-metric. Contrary to previous numerical approaches to this problem, we do
not solve only the constraint equations but rather a set of five equations for
the lapse function, the conformal factor and the shift vector. The orbital
velocity is unambiguously determined by imposing that, at infinity, the metric
behaves like the Schwarzschild one, a requirement which is equivalent to the
virial theorem. The numerical scheme has been implemented using multi-domain
spectral methods and passed numerous tests. A sequence of corotating black
holes of equal mass is calculated. Defining the sequence by requiring that the
ADM mass decrease is equal to the angular momentum decrease multiplied by the
orbital angular velocity, it is found that the area of the apparent horizons is
constant along the sequence. We also find a turning point in the ADM mass and
angular momentum curves, which may be interpreted as an innermost stable
circular orbit (ISCO). The values of the global quantities at the ISCO,
especially the orbital velocity, are in much better agreement with those from
third post-Newtonian calculations than with those resulting from previous
numerical approaches.Comment: 27 pages, 20 PostScript figures, improved presentation of the
regularization procedure for the shift vector, new section devoted to the
check of the momentum constraint, references added + minor corrections,
accepted for publication in Phys. Rev.
Relativistic stars in differential rotation: bounds on the dragging rate and on the rotational energy
For general relativistic equilibrium stellar models (stationary axisymmetric
asymptotically flat and convection-free) with differential rotation, it is
shown that for a wide class of rotation laws the distribution of angular
velocity of the fluid has a sign, say "positive", and then both the dragging
rate and the angular momentum density are positive. In addition, the "mean
value" (with respect to an intrinsic density) of the dragging rate is shown to
be less than the mean value of the fluid angular velocity (in full general,
without having to restrict the rotation law, nor the uniformity in sign of the
fluid angular velocity); this inequality yields the positivity and an upper
bound of the total rotational energy.Comment: 23 pages, no figures, LaTeX. Submitted to J. Math. Phy
Equilibrium sequences of irrotational binary polytropic stars : The case of double polytropic stars
Solutions to equilibrium sequences of irrotational binary polytropic stars in
Newtonian gravity are expanded in a power of , where R and
are the orbital separation of the binary system and the radius of each
star for . For each order of , we should solve ordinary
differential equations for arbitrary polytropic indices n. We show solutions
for polytropic indices n= 0.5, 1, 1.5 and 2 up to orders. Our
semi-analytic solutions can be used to check the validity of numerical
solutions.Comment: 59 pages including 15 tables and 13 figures, revtex, accepted to
Phys. Rev.
Relativistic stars with purely toroidal magnetic fields
We investigate the effects of the purely toroidal magnetic field on the
equilibrium structures of the relativistic stars. The master equations for
obtaining equilibrium solutions of relativistic rotating stars containing
purely toroidal magnetic fields are derived for the first time. To solve these
master equations numerically, we extend the Cook-Shapiro-Teukolsky scheme for
calculating relativistic rotating stars containing no magnetic field to
incorporate the effects of the purely toroidal magnetic fields. By using the
numerical scheme, we then calculate a large number of the equilibrium
configurations for a particular distribution of the magnetic field in order to
explore the equilibrium properties. We also construct the equilibrium sequences
of the constant baryon mass and/or the constant magnetic flux, which model the
evolution of an isolated neutron star as it loses angular momentum via the
gravitational waves. Important properties of the equilibrium configurations of
the magnetized stars obtained in this study are summarized as follows ; (1) For
the non-rotating stars, the matter distribution of the stars is prolately
distorted due to the toroidal magnetic fields. (2) For the rapidly rotating
stars, the shape of the stellar surface becomes oblate because of the
centrifugal force. But, the matter distribution deep inside the star is
sufficiently prolate for the mean matter distribution of the star to be
prolate. (3) The stronger toroidal magnetic fields lead to the mass-shedding of
the stars at the lower angular velocity. (4) For some equilibrium sequences of
the constant baryon mass and magnetic flux, the stars can spin up as they lose
angular momentum.Comment: 13 figures, 7 tables, submitted to PR
Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity. I. Method and tests
We present a numerical method to compute quasiequilibrium configurations of
close binary neutron stars in the pre-coalescing stage. A hydrodynamical
treatment is performed under the assumption that the flow is either rigidly
rotating or irrotational. The latter state is technically more complicated to
treat than the former one (synchronized binary), but is expected to represent
fairly well the late evolutionary stages of a binary neutron star system. As
regards the gravitational field, an approximation of general relativity is
used, which amounts to solving five of the ten Einstein equations (conformally
flat spatial metric). The obtained system of partial differential equations is
solved by means of a multi-domain spectral method. Two spherical coordinate
systems are introduced, one centered on each star; this results in a precise
description of the stellar interiors. Thanks to the multi-domain approach, this
high precision is extended to the strong field regions. The computational
domain covers the whole space so that exact boundary conditions are set to
infinity. Extensive tests of the numerical code are performed, including
comparisons with recent analytical solutions. Finally a constant baryon number
sequence (evolutionary sequence) is presented in details for a polytropic
equation of state with gamma=2.Comment: Minor corrections, references updated, 42 pages, 25 PostScript
figures, accepted for publication in Phys. Rev.
Relativistic kinetic equation for Compton scattering of polarized radiation in strong magnetic field
We derive the relativistic kinetic equation for Compton scattering of
polarized radiation in strong magnetic field using the Bogolyubov method. The
induced scattering and the Pauli exclusion principle are taken into account.
The electron polarization is also considered in the general form of the kinetic
equation. The special forms of the equation for the cases of the non-polarized
electrons, the rarefied electron gas and the two polarization mode description
of radiation are found. The derived equations are valid for any photon and
electron energies and the magnetic field strength below about 10^{16} G. These
equations provide the basis for formulation of the equation for polarized
radiation transport in atmospheres and magnetospheres of strongly magnetized
neutron stars.Comment: 23 pages, accepted for publication in Phys. Rev.
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