50 research outputs found
Thermodynamics of magnetized binary compact objects
Binary systems of compact objects with electromagnetic field are modeled by
helically symmetric Einstein-Maxwell spacetimes with charged and magnetized
perfect fluids. Previously derived thermodynamic laws for helically-symmetric
perfect-fluid spacetimes are extended to include the electromagnetic fields,
and electric currents and charges; the first law is written as a relation
between the change in the asymptotic Noether charge \dl Q and the changes in
the area and electric charge of black holes, and in the vorticity, baryon rest
mass, entropy, charge and magnetic flux of the magnetized fluid. Using the
conservation laws of the circulation of magnetized flow found by Bekenstein and
Oron for the ideal magnetohydrodynamic (MHD) fluid, and also for the flow with
zero conducting current, we show that, for nearby equilibria that conserve the
quantities mentioned above, the relation \dl Q=0 is satisfied. We also
discuss a formulation for computing numerical solutions of magnetized binary
compact objects in equilibrium with emphasis on a first integral of the ideal
MHD-Euler equation.Comment: 21 pages, to appear in PR
Discontinuous collocation and symmetric integration methods for distributionally-sourced hyperboloidal partial differential equations
This work outlines a time-domain numerical integration technique for linear
hyperbolic partial differential equations sourced by distributions (Dirac
-functions and their derivatives). Such problems arise when studying
binary black hole systems in the extreme mass ratio limit. We demonstrate that
such source terms may be converted to effective domain-wide sources when
discretized, and we introduce a class of time-steppers that directly account
for these discontinuities in time integration. Moreover, our time-steppers are
constructed to respect time reversal symmetry, a property that has been
connected to conservation of physical quantities like energy and momentum in
numerical simulations. To illustrate the utility of our method, we numerically
study a distributionally-sourced wave equation that shares many features with
the equations governing linear perturbations to black holes sourced by a point
mass.Comment: 29 pages, 4 figures
Discontinuous collocation methods and gravitational self-force applications
Numerical simulations of extereme mass ratio inspirals, the mostimportant
sources for the LISA detector, face several computational challenges. We
present a new approach to evolving partial differential equations occurring in
black hole perturbation theory and calculations of the self-force acting on
point particles orbiting supermassive black holes. Such equations are
distributionally sourced, and standard numerical methods, such as
finite-difference or spectral methods, face difficulties associated with
approximating discontinuous functions. However, in the self-force problem we
typically have access to full a-priori information about the local structure of
the discontinuity at the particle. Using this information, we show that
high-order accuracy can be recovered by adding to the Lagrange interpolation
formula a linear combination of certain jump amplitudes. We construct
discontinuous spatial and temporal discretizations by operating on the
corrected Lagrange formula. In a method-of-lines framework, this provides a
simple and efficient method of solving time-dependent partial differential
equations, without loss of accuracy near moving singularities or
discontinuities. This method is well-suited for the problem of time-domain
reconstruction of the metric perturbation via the Teukolsky or
Regge-Wheeler-Zerilli formalisms. Parallel implementations on modern CPU and
GPU architectures are discussed.Comment: 29 pages, 5 figure
Iteration Stability for Simple Newtonian Stellar Systems
For an equation of state in which pressure is a function only of density, the
analysis of Newtonian stellar structure is simple in principle if the system is
axisymmetric, or consists of a corotating binary. It is then required only to
solve two equations: one stating that the "injection energy", , a
potential, is constant throughout the stellar fluid, and the other being the
integral over the stellar fluid to give the gravitational potential. An
iterative solution of these equations generally diverges if is held
fixed, but converges with other choices. We investigate the mathematical reason
for this convergence/divergence by starting the iteration from an approximation
that is perturbatively different from the actual solution. A cycle of iteration
is then treated as a linear "updating" operator, and the properties of the
linear operator, especially its spectrum, determine the convergence properties.
For simplicity, we confine ourselves to spherically symmetric models in which
we analyze updating operators both in the finite dimensional space
corresponding to a finite difference representation of the problem, and in the
continuum, and we find that the fixed- operator is self-adjoint and
generally has an eigenvalue greater than unity; in the particularly important
case of a polytropic equation of state with index greater than unity, we prove
that there must be such an eigenvalue. For fixed central density, on the other
hand, we find that the updating operator has only a single eigenvector, with
zero eigenvalue, and is nilpotent in finite dimension, thereby giving a
convergent solution.Comment: 16 pages, 3 figure
Inferring the neutron star equation of state from binary inspiral waveforms
The properties of neutron star matter above nuclear density are not precisely
known. Gravitational waves emitted from binary neutron stars during their late
stages of inspiral and merger contain imprints of the neutron-star equation of
state. Measuring departures from the point-particle limit of the late inspiral
waveform allows one to measure properties of the equation of state via
gravitational wave observations. This and a companion talk by J. S. Read
reports a comparison of numerical waveforms from simulations of inspiraling
neutron-star binaries, computed for equations of state with varying stiffness.
We calculate the signal strength of the difference between waveforms for
various commissioned and proposed interferometric gravitational wave detectors
and show that observations at frequencies around 1 kHz will be able to measure
a compactness parameter and constrain the possible neutron-star equations of
state.Comment: Talk given at the 12th Marcel Grossman Meeting, Paris, France, 12-18
Jul 200
Binary Neutron Stars with Generic Spin, Eccentricity, Mass ratio, and Compactness - Quasi-equilibrium Sequences and First Evolutions
Information about the last stages of a binary neutron star inspiral and the
final merger can be extracted from quasi-equilibrium configurations and
dynamical evolutions. In this article, we construct quasi-equilibrium
configurations for different spins, eccentricities, mass ratios, compactnesses,
and equations of state. For this purpose we employ the SGRID code, which allows
us to construct such data in previously inaccessible regions of the parameter
space. In particular, we consider spinning neutron stars in isolation and in
binary systems; we incorporate new methods to produce highly eccentric and
eccentricity reduced data; we present the possibility of computing data for
significantly unequal-mass binaries; and we create equal-mass binaries with
individual compactness up to 0.23. As a proof of principle, we explore the
dynamical evolution of three new configurations. First, we simulate a
mass ratio which is the highest mass ratio for a binary neutron star evolved in
numerical relativity to date. We find that mass transfer from the companion
star sets in a few revolutions before merger and a rest mass of
is transferred between the two stars. This configuration
also ejects a large amount of material during merger, imparting a substantial
kick to the remnant. Second, we simulate the first merger of a precessing
binary neutron star. We present the dominant modes of the gravitational waves
for the precessing simulation, where a clear imprint of the precession is
visible in the (2,1) mode. Finally, we quantify the effect of an eccentricity
reduction procedure on the gravitational waveform. The procedure improves the
waveform quality and should be employed in future precision studies, but also
other errors, notably truncation errors, need to be reduced in order for the
improvement due to eccentricity reduction to be effective. [abridged]Comment: (37pages, 26 figures
Equilibriums of extremely magnetized compact stars with force-free magnetotunnels
We present numerical solutions for stationary and axisymmetric equilibriums
of compact stars associated with extremely strong magnetic fields. The interior
of the compact stars is assumed to satisfy ideal magnetohydrodynamic (MHD)
conditions, while in the region of negligible mass density the force-free
conditions or electromagnetic vacuum are assumed. Solving all components of
Einstein's equations, Maxwell's equations, ideal MHD equations, and force-free
conditions, equilibriums of rotating compact stars associated with mixed
poloidal and toroidal magnetic fields are obtained. It is found that in the
extreme cases the strong mixed magnetic fields concentrating in a toroidal
region near the equatorial surface expel the matter and form a force-free
toroidal magnetotunnel. We also introduce a new differential rotation law for
computing solutions associated with force-free magnetosphere, and present other
extreme models without the magnetotunnel.Comment: 13 pages, 4 figure
Measuring the neutron star equation of state with gravitational wave observations
We report the results of a first study that uses numerical simulations to
estimate the accuracy with which one can use gravitational wave observations of
double neutron star inspiral to measure parameters of the neutron-star equation
of state. The simulations use the evolution and initial-data codes of Shibata
and Uryu to compute the last several orbits and the merger of neutron stars,
with matter described by a parametrized equation of state. Previous work
suggested the use of an effective cutoff frequency to place constraints on the
equation of state. We find, however, that greater accuracy is obtained by
measuring departures from the point-particle limit of the gravitational
waveform produced during the late inspiral.
As the stars approach their final plunge and merger, the gravitational wave
phase accumulates more rapidly for smaller values of the neutron star
compactness (the ratio of the mass of the neutron star to its radius). We
estimate that realistic equations of state will lead to gravitational waveforms
that are distinguishable from point particle inspirals at an effective distance
(the distance to an optimally oriented and located system that would produce an
equivalent waveform amplitude) of 100 Mpc or less. As Lattimer and Prakash
observed, neutron-star radius is closely tied to the pressure at density not
far above nuclear. Our results suggest that broadband gravitational wave
observations at frequencies between 500 and 1000 Hz will constrain this
pressure, and we estimate the accuracy with which it can be measured. Related
first estimates of radius measurability show that the radius can be determined
to an accuracy of ~1 km at 100 Mpc.Comment: 12 pages, 5 figures, to be submitted to Phys. Rev.
Neutron star equation of state via gravitational wave observations
Gravitational wave observations can potentially measure properties of neutron
star equations of state by measuring departures from the point-particle limit
of the gravitational waveform produced in the late inspiral of a neutron star
binary. Numerical simulations of inspiraling neutron star binaries computed for
equations of state with varying stiffness are compared. As the stars approach
their final plunge and merger, the gravitational wave phase accumulates more
rapidly if the neutron stars are more compact. This suggests that gravitational
wave observations at frequencies around 1 kHz will be able to measure a
compactness parameter and place stringent bounds on possible neutron star
equations of state. Advanced laser interferometric gravitational wave
observatories will be able to tune their frequency band to optimize sensitivity
in the required frequency range to make sensitive measures of the late-inspiral
phase of the coalescence.Comment: Talk given at the 13th Conference on Recent Developments in Gravity
(NEB XIII), Thessaloniki, Greece, 4-6 Jun 200