58 research outputs found
Strategies for observing extreme mass ratio inspirals
I review the status of research, conducted by a variety of independent
groups, aimed at the eventual observation of Extreme Mass Ratio Inspirals
(EMRIs) with gravitational wave detectors. EMRIs are binary systems in which
one of the objects is much more massive than the other, and which are in a
state of dynamical evolution that is dominated by the effects of gravitational
radiation. Although these systems are highly relativistic, with the smaller
object moving relative to the larger at nearly light-speed, they are well
described by perturbative calculations which exploit the mass ratio as a
natural small parameter. I review the use of such approximations to generate
waveforms needed by data analysis algorithms for observation. I also briefly
review the status of developing the data analysis algorithms themselves.
Although this article is almost entirely a review of previous work, it includes
(as an appendix) a new analytical estimate for the time over which the
influence of radiation on the binary itself is observationally negligible.Comment: 17 pages, to appear in Classical and Quantum Gravity, minor edits to
first version along with a revamped appendix and figure 3. Final published
versio
Forced motion near black holes
We present two methods for integrating forced geodesic equations in the Kerr spacetime. The methods can accommodate arbitrary forces. As a test case, we compute inspirals caused by a simple drag force, mimicking motion in the presence of gas.We verify that both methods give the same results for this simple force. We find that drag generally causes eccentricity to increase throughout the inspiral. This is a relativistic effect qualitatively opposite to what is seen in gravitational-radiation-driven inspirals, and similar to what others have observed in hydrodynamic simulations of gaseous binaries. We provide an
analytic explanation by deriving the leading order relativistic correction to the Newtonian dynamics. If
observed, an increasing eccentricity would thus provide clear evidence that the inspiral was occurring in a
nonvacuum environment. Our two methods are especially useful for evolving orbits in the adiabatic regime. Both use the method of osculating orbits, in which each point on the orbit is characterized by the parameters of the geodesic with the same instantaneous position and velocity. Both methods describe the orbit in terms of the geodesic energy, axial angular momentum, Carter constant, azimuthal phase, and two angular variables that increase monotonically and are relativistic generalizations of the eccentric anomaly. The two methods differ in their treatment of the orbital phases and the representation of the force. In the first method, the geodesic phase and phase constant are evolved together as a single orbital phase parameter, and the force is expressed in terms of its components on the Kinnersley orthonormal tetrad. In
the second method, the phase constants of the geodesic motion are evolved separately and the force is
expressed in terms of its Boyer-Lindquist components. This second approach is a direct generalization of earlier work by Pound and Poisson [A. Pound and E. Poisson, Phys. Rev. D 77, 044013 (2008).] for planar forces in a Schwarzschild background
Verifying black hole orbits with gravitational spectroscopy
Gravitational waves from test masses bound to geodesic orbits of rotating
black holes are simulated, using Teukolsky's black hole perturbation formalism,
for about ten thousand generic orbital configurations. Each binary radiates
power exclusively in modes with frequencies that are
integer-linear-combinations of the orbit's three fundamental frequencies. The
following general spectral properties are found with a survey of orbits: (i)
99% of the radiated power is typically carried by a few hundred modes, and at
most by about a thousand modes, (ii) the dominant frequencies can be grouped
into a small number of families defined by fixing two of the three integer
frequency multipliers, and (iii) the specifics of these trends can be
qualitatively inferred from the geometry of the orbit under consideration.
Detections using triperiodic analytic templates modeled on these general
properties would constitute a verification of radiation from an adiabatic
sequence of black hole orbits and would recover the evolution of the
fundamental orbital frequencies. In an analogy with ordinary spectroscopy, this
would compare to observing the Bohr model's atomic hydrogen spectrum without
being able to rule out alternative atomic theories or nuclei. The suitability
of such a detection technique is demonstrated using snapshots computed at
12-hour intervals throughout the last three years before merger of a kludged
inspiral. Because of circularization, the number of excited modes decreases as
the binary evolves. A hypothetical detection algorithm that tracks mode
families dominating the first 12 hours of the inspiral would capture 98% of the
total power over the remaining three years.Comment: 18 pages, expanded section on detection algorithms and made minor
edits. Final published versio
Towards adiabatic waveforms for inspiral into Kerr black holes: II. Dynamical sources and generic orbits
This is the second in a series of papers whose aim is to generate
``adiabatic'' gravitational waveforms from the inspiral of stellar-mass compact
objects into massive black holes. In earlier work, we presented an accurate
(2+1)D finite-difference time-domain code to solve the Teukolsky equation,
which evolves curvature perturbations near rotating (Kerr) black holes. The key
new ingredient there was a simple but accurate model of the singular source
term based on a discrete representation of the Dirac-delta function and its
derivatives. Our earlier work was intended as a proof of concept, using simple
circular, equatorial geodesic orbits as a testbed. Such a source is effectively
static, in that the smaller body remains at the same coordinate radius and
orbital inclination over an orbit. (It of course moves through axial angle, but
we separate that degree of freedom from the problem. Our numerical grid has
only radial, polar, and time coordinates.) We now extend the time-domain code
so that it can accommodate dynamic sources that move on a variety of physically
interesting world lines. We validate the code with extensive comparison to
frequency-domain waveforms for cases in which the source moves along generic
(inclined and eccentric) bound geodesic orbits. We also demonstrate the ability
of the time-domain code to accommodate sources moving on interesting
non-geodesic worldlines. We do this by computing the waveform produced by a
test mass following a ``kludged'' inspiral trajectory, made of bound geodesic
segments driven toward merger by an approximate radiation loss formula.Comment: 14 pages, 5 figures. Accepted by Phys. Rev.
Geometrical locus of massive test particle orbits in the space of physical parameters in Kerr space-time
Gravitational radiation of binary systems can be studied by using the
adiabatic approximation in General Relativity. In this approach a small
astrophysical object follows a trajectory consisting of a chained series of
bounded geodesics (orbits) in the outer region of a Kerr Black Hole,
representing the space time created by a bigger object. In our paper we study
the entire class of orbits, both of constant radius (spherical orbits), as well
as non-null eccentricity orbits, showing a number of properties on the physical
parameters and trajectories. The main result is the determination of the
geometrical locus of all the orbits in the space of physical parameters in Kerr
space-time. This becomes a powerful tool to know if different orbits can be
connected by a continuous change of their physical parameters. A discussion on
the influence of different values of the angular momentum of the hole is given.
Main results have been obtained by analytical methods.Comment: 26 pages, 12 figure
Forced motion near black holes
We present two methods for integrating forced geodesic equations in the Kerr
spacetime, which can accommodate arbitrary forces. As a test case, we compute
inspirals under a simple drag force, mimicking the presence of gas. We verify
that both methods give the same results for this simple force. We find that
drag generally causes eccentricity to increase throughout the inspiral. This is
a relativistic effect qualitatively opposite to what is seen in
gravitational-radiation-driven inspirals, and similar to what is observed in
hydrodynamic simulations of gaseous binaries. We provide an analytic
explanation by deriving the leading order relativistic correction to the
Newtonian dynamics. If observed, an increasing eccentricity would provide clear
evidence that the inspiral was occurring in a non-vacuum environment. Our two
methods are especially useful for evolving orbits in the adiabatic regime. Both
use the method of osculating orbits, in which each point on the orbit is
characterized by the parameters of the geodesic with the same instantaneous
position and velocity. Both methods describe the orbit in terms of the geodesic
energy, axial angular momentum, Carter constant, azimuthal phase, and two
angular variables that increase monotonically and are relativistic
generalizations of the eccentric anomaly. The two methods differ in their
treatment of the orbital phases and the representation of the force. In one
method the geodesic phase and phase constant are evolved together as a single
orbital phase parameter, and the force is expressed in terms of its components
on the Kinnersley orthonormal tetrad. In the second method, the phase constants
of the geodesic motion are evolved separately and the force is expressed in
terms of its Boyer-Lindquist components. This second approach is a
generalization of earlier work by Pound and Poisson for planar forces in a
Schwarzschild background.Comment: 28 pages, 2 figures, submitted to Phys. Rev. D; v2 has minor changes
for consistency with published version, plus a new section discussing the
relative advantages of the two approache
Gravitational radiation reaction and inspiral waveforms in the adiabatic limit
We describe progress evolving an important limit of binary orbits in general
relativity, that of a stellar mass compact object gradually spiraling into a
much larger, massive black hole. These systems are of great interest for
gravitational wave observations. We have developed tools to compute for the
first time the radiated fluxes of energy and angular momentum, as well as
instantaneous snapshot waveforms, for generic geodesic orbits. For special
classes of orbits, we compute the orbital evolution and waveforms for the
complete inspiral by imposing global conservation of energy and angular
momentum. For fully generic orbits, inspirals and waveforms can be obtained by
augmenting our approach with a prescription for the self force in the adiabatic
limit derived by Mino. The resulting waveforms should be sufficiently accurate
to be used in future gravitational-wave searches.Comment: Accepted for publication in Phys. Rev. Let
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