337 research outputs found
Location of the innermost stable circular orbit of binary neutron stars in the post Newtonian approximations of general relativity
In this paper, we present results obtained from our recent studies on the
location of the innermost stable circular orbit (ISCO) for binary neutron stars
(BNSs) in several levels of post Newtonian (PN) approximations. We reach the
following conclusion at present: (1) even in the Newtonian case, there exists
the ISCO for binary of sufficiently stiff equation of state (EOS). If the mass
and the radius of each star are fixed, the angular velocity at the ISCO
is larger for softer EOS: (2) when we include the first PN
correction, there appear roughly two kinds of effects. One is the effect to the
self-gravity of each star of binary and the other is to the gravity acting
between two stars. Due to the former one, each star of binary becomes compact
and the tidal effect is less effective. As a result, tends to
be increased. On the other hand, the latter one has the property to destabilize
the binary orbit, and tends to be decreased. If we take into
account both effects, however, the former effect is stronger than the latter
one, and becomes large with increase of the 1PN correction: (3)
the feature mentioned above is more remarkable for softer EOS if the mass and
radius are fixed. This is because for softer EOS, each star has the larger
central density and is susceptible to the GR correction: (4) there has been no
self consistent calculation including all the 2PN effects and only exist
studies in which one merely includes the effect of the 2PN gravity acting
between two stars. In this case, the effect has the property to destabilize the
binary orbit, so that is always smaller than that for the
Newtonian case. If we include the PN effect of the self-gravity to each star,
will increase.Comment: 33 pages ptptex file, 29 figures, to appear in Progress of
Theoretical Physics Supplement No.128 (1997) `Perturbative and Numerical
Approaches to Gravitational Radiation
Irrotational and Incompressible Ellipsoids in the First Post-Newtonian Approximation of General Relativity
First post-Newtonian (1PN) hydrostatic equations for an irrotational fluid
which have been recently derived are solved for an incompressible star. The 1PN
configurations are expressed as a deformation of the Newtonian irrotational
Riemann ellipsoid using Lagrangian displacement vectors introduced by
Chandrasekhar. For the 1PN solutions, we also calculate the luminosity of
gravitational waves in the 1PN approximation using the Blanchet-Damour
formalism. It is found that the solutions of the 1PN equations exhibit
singularities at points where the axial ratios of semi-axes are 1:0.5244:0.6579
and 1:0.2374:0.2963, and the singularities seem to show that at the points, the
irrotational Riemann ellipsoid is unstable to the deformation induced by the
effect of general relativity. For stable cases (a_2/a_1 > 0.5244, where a_1 and
a_2 are the semi-major and minor axes, respectively) we find that when
increasing the 1PN correction, the angular velocity and total angular momentum
increase, while the total energy and luminosity of gravitational waves
decrease. These 1PN solutions will be useful when examining the accuracy of
numerical code for obtaining relativistic irrotational stars.
We also investigate the validity of an ellipsoidal approximation, in which a
1PN solution is obtained assuming an ellipsoidal figure and neglecting the
deformation. It is found that for , the ellipsoidal
approximation gives a fairly accurate result for the energy, angular momentum,
and angular velocity, although in the approximation we cannot find the
singularities.Comment: 33 pages with 3 figures, ptptex, corrected some typos, tables and
figure
Quasiequilibrium sequences of binary neutron stars undergoing dynamical scalarization
We calculate quasiequilibrium sequences of equal-mass, irrotational binary
neutron stars (BNSs) in a scalar-tensor (ST) theory of gravity that admits
dynamical scalarization. We model neutron stars with realistic equations of
state (notably through piecewise polytropic equations of state). Using these
quasiequilibrium sequences we compute the binary's scalar charge and binding
energy versus orbital angular frequency. We find that the absolute value of the
binding energy is smaller than in general relativity (GR), differing at most by
~14% at high frequencies for the cases considered. We use the newly computed
binding energy and the balance equation to estimate the number of
gravitational-wave (GW) cycles during the adiabatic, quasicircular inspiral
stage up to the end of the sequence, which is the last stable orbit or the
mass-shedding point, depending on which comes first. We find that, depending on
the ST parameters, the number of GW cycles can be substantially smaller than in
GR. In particular, we obtain that when dynamical scalarization sets in around a
GW frequency of ~130 Hz, the sole inclusion of the ST binding energy causes a
reduction of GW cycles from ~120 Hz up to the end of the sequence (~1200 Hz) of
~11% with respect to the GR case. We estimate that when the ST energy flux is
also included the reduction in GW cycles becomes of ~24%. Quite interestingly,
dynamical scalarization can produce a difference in the number of GW cycles
with respect to the GR point-particle case that is much larger than the effect
due to tidal interactions, which is on the order of only a few GW cycles. These
results further clarify and confirm recent studies that have evolved BNSs
either in full numerical relativity or in post-Newtonian theory, and point out
the importance of developing accurate ST-theory waveforms for systems composed
of strongly self-gravitating objects, such as BNSs.Comment: 16 pages, 14 figures, 2 tables, updated to match the published
versio
Coalescence of binary neutron stars in a scalar-tensor theory of gravity
We carry out numerical-relativity simulations of coalescing binary neutron
stars in a scalar-tensor theory that admits spontaneous scalarization. We model
neutron stars with realistic equations of state. We choose the free parameters
of the theory taking into account the constraints imposed by the latest
observations of neutron-star-- white-dwarf binaries with pulsar timing. We show
that even within those severe constraints, scalarization can still affect the
evolution of the binary neutron stars not only during the late inspiral, but
also during the merger stage. We also confirm that even when both neutron stars
have quite small scalar charge at large separations, they can be strongly
scalarized dynamically during the final stages of the inspiral. In particular,
we identify the binary parameters for which scalarization occurs either during
the late inspiral or only after the onset of the merger when a remnant,
supramassive or hypermassive neutron star is formed. We also discuss how those
results can impact the extraction of physical information on gravitational
waves once they are detected.Comment: 17 pages, 12 figure
The Relation between Seismic Activities and Earth Tides in the Case of the Matsushiro Earthquake Swarm
The temporal variations of dilatational strains by solid earth tides were calculated and compared with the variation of seismic activities in the case of the Matsushiro earthquake swarm. It has been found that in the beginning of each stage of the swarm, major earthquake activity has important relation with the expansive peaks of dilatational strains caused by earth tides. The swarm started on August 3, 1965 with a few events a day. Each group of small felt shocks in the first week began around some of the peaks of dilatational strains. There were four periods in which major earthquake activity occurred around the peak of dilatational strains. These correspond to the beginning of new kinds of seismic activities. The first period was the beginning of the Matsushiro earthquake swarm. The second was that of a larger earthquake series. The third was the period in which the epicentral area extended into a wider area. The fourth was the beginning of the expansion of the seismic area, again. In these four periods, the type of the seismic activity which occurred was predominantly a large main shock with aftershocks. It suggests that fracturing was beginning in a new area. Such phenomena show that dilatation causes a decrease in the strength of rocks under the condition of the critical stress level and thus becomes a trigger for the occurrence of earthquakes. Such a synchronization of small events with the dilatational change may be related to the stress level and its changes in the crust
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