30 research outputs found
Eccentricities of Planets in Binary Systems
The most puzzling property of the extrasolar planets discovered by recent
radial velocity surveys is their high orbital eccentricities, which are very
difficult to explain within our current theoretical paradigm for planet
formation. Current data reveal that at least 25% of these planets, including
some with particularly high eccentricities, are orbiting a component of a
binary star system. The presence of a distant companion can cause significant
secular perturbations in the orbit of a planet. At high relative inclinations,
large-amplitude, periodic eccentricity perturbations can occur. These are known
as "Kozai cycles" and their amplitude is purely dependent on the relative
orbital inclination. Assuming that every planet host star also has a (possibly
unseen, e.g., substellar) distant companion, with reasonable distributions of
orbital parameters and masses, we determine the resulting eccentricity
distribution of planets and compare it to observations? We find that
perturbations from a binary companion always appear to produce an excess of
planets with both very high (e>0.6) and very low (e<0.1) eccentricities. The
paucity of near-circular orbits in the observed sample implies that at least
one additional mechanism must be increasing eccentricities. On the other hand,
the overproduction of very high eccentricities observed in our models could be
combined with plausible circularization mechanisms (e.g., friction from
residual gas) to create more planets with intermediate eccentricities
(e=0.1-0.6).Comment: 8 pages, to appear in "Close Binaries in the 21st Century: New
Opportunities and Challenges", ed. A. Gimenez et al. (Springer
Post-Newtonian SPH calculations of binary neutron star coalescence. II. Binary mass ratio, equation of state, and spin dependence
Using our new Post-Newtonian SPH (smoothed particle hydrodynamics) code, we
study the final coalescence and merging of neutron star (NS) binaries. We vary
the stiffness of the equation of state (EOS) as well as the initial binary mass
ratio and stellar spins. Results are compared to those of Newtonian
calculations, with and without the inclusion of the gravitational radiation
reaction. We find a much steeper decrease in the gravity wave peak strain and
luminosity with decreasing mass ratio than would be predicted by simple
point-mass formulae. For NS with softer EOS (which we model as simple
polytropes) we find a stronger gravity wave emission, with a
different morphology than for stiffer EOS (modeled as polytropes as
in our previous work). We also calculate the coalescence of NS binaries with an
irrotational initial condition, and find that the gravity wave signal is
relatively suppressed compared to the synchronized case, but shows a very
significant second peak of emission. Mass shedding is also greatly reduced, and
occurs via a different mechanism than in the synchronized case. We discuss the
implications of our results for gravity wave astronomy with laser
interferometers such as LIGO, and for theoretical models of gamma-ray bursts
(GRBs) based on NS mergers.Comment: RevTeX, 38 pages, 24 figures, Minor Corrections, to appear in Phys.
Rev.
Post-Newtonian SPH calculations of binary neutron star coalescence. I. Method and first results
We present the first results from our Post-Newtonian (PN) Smoothed Particle
Hydrodynamics (SPH) code, which has been used to study the coalescence of
binary neutron star (NS) systems. The Lagrangian particle-based code
incorporates consistently all lowest-order (1PN) relativistic effects, as well
as gravitational radiation reaction, the lowest-order dissipative term in
general relativity. We test our code on sequences of single NS models of
varying compactness, and we discuss ways to make PN simulations more relevant
to realistic NS models. We also present a PN SPH relaxation procedure for
constructing equilibrium models of synchronized binaries, and we use these
equilibrium models as initial conditions for our dynamical calculations of
binary coalescence. Though unphysical, since tidal synchronization is not
expected in NS binaries, these initial conditions allow us to compare our PN
work with previous Newtonian results.
We compare calculations with and without 1PN effects, for NS with stiff
equations of state, modeled as polytropes with . We find that 1PN
effects can play a major role in the coalescence, accelerating the final
inspiral and causing a significant misalignment in the binary just prior to
final merging. In addition, the character of the gravitational wave signal is
altered dramatically, showing strong modulation of the exponentially decaying
waveform near the end of the merger. We also discuss briefly the implications
of our results for models of gamma-ray bursts at cosmological distances.Comment: RevTeX, 37 pages, 17 figures, to appear in Phys. Rev. D, minor
corrections onl
Scattering of particles by neutron stars: Time-evolutions for axial perturbations
The excitation of the axial quasi-normal modes of a relativistic star by
scattered particles is studied by evolving the time dependent perturbation
equations. This work is the first step towards the understanding of more
complicated perturbative processes, like the capture or the scattering of
particles by rotating stars. In addition, it may serve as a test for the
results of the full nonlinear evolution of binary systems.Comment: 7 pages, 5 figures, Phys. Rev. D in pres
Irrotational binary neutron stars in quasiequilibrium
We report on numerical results from an independent formalism to describe the
quasi-equilibrium structure of nonsynchronous binary neutron stars in general
relativity. This is an important independent test of controversial numerical
hydrodynamic simulations which suggested that nonsynchronous neutron stars in a
close binary can experience compression prior to the last stable circular
orbit. We show that, for compact enough stars the interior density increases
slightly as irrotational binary neutron stars approach their last orbits. The
magnitude of the effect, however, is much smaller than that reported in
previous hydrodynamic simulations.Comment: 4 pages, 2 figures, revtex, accepted for publication in Phys. Rev.
Relativistic Hydrodynamic Evolutions with Black Hole Excision
We present a numerical code designed to study astrophysical phenomena
involving dynamical spacetimes containing black holes in the presence of
relativistic hydrodynamic matter. We present evolutions of the collapse of a
fluid star from the onset of collapse to the settling of the resulting black
hole to a final stationary state. In order to evolve stably after the black
hole forms, we excise a region inside the hole before a singularity is
encountered. This excision region is introduced after the appearance of an
apparent horizon, but while a significant amount of matter remains outside the
hole. We test our code by evolving accurately a vacuum Schwarzschild black
hole, a relativistic Bondi accretion flow onto a black hole, Oppenheimer-Snyder
dust collapse, and the collapse of nonrotating and rotating stars. These
systems are tracked reliably for hundreds of M following excision, where M is
the mass of the black hole. We perform these tests both in axisymmetry and in
full 3+1 dimensions. We then apply our code to study the effect of the stellar
spin parameter J/M^2 on the final outcome of gravitational collapse of rapidly
rotating n = 1 polytropes. We find that a black hole forms only if J/M^2<1, in
agreement with previous simulations. When J/M^2>1, the collapsing star forms a
torus which fragments into nonaxisymmetric clumps, capable of generating
appreciable ``splash'' gravitational radiation.Comment: 17 pages, 14 figures, submitted to PR
Close encounters of a rotating star with planets in parabolic orbits of varying inclination and the formation of Hot Jupiters
(abbreviated) We extend the theory of close encounters of a planet on a
parabolic orbit with a star to include the effects of tides induced on the
central rotating star. Orbits with arbitrary inclination to the stellar
rotation axis are considered. We obtain results both from an analytic treatment
and numerical one that are in satisfactory agreement. These results are applied
to the initial phase of the tidal circularisation problem. We find that both
tides induced in the star and planet can lead to a significant decrease of the
orbital semi-major axis for orbits having periastron distances smaller than 5-6
stellar radii (corresponding to periods days after the
circularisation has been completed) with tides in the star being much stronger
for retrograde orbits compared to prograde orbits. We use the simple Skumanich
law for the stellar rotation with its rotational period equal to one month at
the age of 5Gyr. The strength of tidal interactions is characterised by
circularisation time scale, defined as a time scale of evolution of
the planet's semi-major axis due to tides considered as a function of orbital
period after the process of tidal circularisation has been completed.
We find that the ratio of the initial circularisation time scales corresponding
to prograde and retrograde orbits is of order 1.5-2 for a planet of one Jupiter
mass and four days. It grows with the mass of the planet, being
of order five for a five Jupiter mass planet with the same . Thus, the
effect of stellar rotation may provide a bias in the formation of planetary
systems having planets on close orbits around their host stars, as a
consequence of planet-planet scattering, favouring systems with retrograde
orbits. The results may also be applied to the problem of tidal capture of
stars in young stellar clusters.Comment: to be published in Celestial Mechanics and Dynamical Astronom
Magnetic Braking in Differentially Rotating, Relativistic Stars
We study the magnetic braking and viscous damping of differential rotation in
incompressible, uniform density stars in general relativity. Differentially
rotating stars can support significantly more mass in equilibrium than
nonrotating or uniformly rotating stars. The remnant of a binary neutron star
merger or supernova core collapse may produce such a "hypermassive" neutron
star. Although a hypermassive neutron star may be stable on a dynamical
timescale, magnetic braking and viscous damping of differential rotation will
ultimately alter the equilibrium structure, possibly leading to delayed
catastrophic collapse. Here we consider the slow-rotation, weak-magnetic field
limit in which E_rot << E_mag << W, where E_rot is the rotational kinetic
energy, E_mag is the magnetic energy, and W is the gravitational binding energy
of the star. We assume the system to be axisymmetric and solve the MHD
equations in both Newtonian gravitation and general relativity. Toroidal
magnetic fields are generated whenever the angular velocity varies along the
initial poloidal field lines. We find that the toroidal fields and angular
velocities oscillate independently along each poloidal field line, which
enables us to transform the original 2+1 equations into 1+1 form and solve them
along each field line independently. The incoherent oscillations on different
field lines stir up turbulent-like motion in tens of Alfven timescales ("phase
mixing"). In the presence of viscosity, the stars eventually are driven to
uniform rotation, with the energy contained in the initial differential
rotation going into heat. Our evolution calculations serve as qualitative
guides and benchmarks for future, more realistic MHD simulations in full 3+1
general relativity.Comment: 26 pages, 27 graphs, 1 table, accepted for publication by Phys. Rev.
Towards a Realistic Neutron Star Binary Inspiral: Initial Data and Multiple Orbit Evolution in Full General Relativity
This paper reports on our effort in modeling realistic astrophysical neutron
star binaries in general relativity. We analyze under what conditions the
conformally flat quasiequilibrium (CFQE) approach can generate
``astrophysically relevant'' initial data, by developing an analysis that
determines the violation of the CFQE approximation in the evolution of the
binary described by the full Einstein theory. We show that the CFQE assumptions
significantly violate the Einstein field equations for corotating neutron stars
at orbital separations nearly double that of the innermost stable circular
orbit (ISCO) separation, thus calling into question the astrophysical relevance
of the ISCO determined in the CFQE approach. With the need to start numerical
simulations at large orbital separation in mind, we push for stable and long
term integrations of the full Einstein equations for the binary neutron star
system. We demonstrate the stability of our numerical treatment and analyze the
stringent requirements on resolution and size of the computational domain for
an accurate simulation of the system.Comment: 22 pages, 18 figures, accepted to Phys. Rev.
Dynamics of spherically symmetric spacetimes: hydrodynamics and radiation
Using the 3+1 formalism of general relativity we obtain the equations
governing the dynamics of spherically symmetric spacetimes with arbitrary
sources. We then specialize for the case of perfect fluids accompanied by a
flow of interacting massless or massive particles (e.g. neutrinos) which are
described in terms of relativistic transport theory. We focus in three types of
coordinates: 1) isotropic gauge and maximal slicing, 2) radial gauge and polar
slicing, and 3) isotropic gauge and polar slicing.Comment: submitted to Phys. Rev. D, 46 pages, RevTex file, no figure