168 research outputs found
Finite Mirror Effects in Advanced Interferometric Gravitational Wave Detectors
Thermal noise is expected to be the dominant source of noise in the most
sensitive frequency band of second generation ground based gravitational wave
detectors. Reshaping the beam to a flatter wider profile which probes more of
the mirror surface reduces this noise. The "Mesa" beam shape has been proposed
for this purpose and was subsequently generalized to a family of hyperboloidal
beams with two parameters: twist angle alpha and beam width D. Varying alpha
allows a continuous transition from the nearly-flat to the nearly-concentric
Mesa beam configurations. We analytically prove that in the limit of infinite D
hyperboloidal beams become Gaussians. The Advanced LIGO diffraction loss design
constraint is 1 ppm per bounce. In the past the diffraction loss has often been
calculated using the clipping approximation that, in general, underestimates
the diffraction loss. We develop a code using pseudo-spectral methods to
compute the diffraction loss directly from the propagator. We find that the
diffraction loss is not a strictly monotonic function of beam width, but has
local minima that occur due to finite mirror effects and leads to natural
choices of D. For the Mesa beam a local minimum occurs at D = 10.67 cm and
leads to a diffraction loss of 1.4 ppm. We find that if one requires a
diffraction loss of strictly 1 ppm, the alpha = 0.91 pi hyperboloidal beam is
optimal, leading to the coating thermal noise being lower by about 10% than for
a Mesa beam while other types of thermal noise decrease as well. We then
develop an iterative process that reconstructs the mirror to specifically
account for finite mirror effects. This allows us to increase the D parameter
and lower the coating noise by about 30% compared to the original Mesa
configuration.Comment: 13 pages, 12 figures, 4 tables. Referee input included and typos
fixed. Accepted by Phys. Rev.
Optimal Light Beams and Mirror Shapes for Future LIGO Interferometers
We report the results of a recent search for the lowest value of thermal
noise that can be achieved in LIGO by changing the shape of mirrors, while
fixing the mirror radius and maintaining a low diffractional loss. The result
of this minimization is a beam with thermal noise a factor of 2.32 (in power)
lower than previously considered Mesa Beams and a factor of 5.45 (in power)
lower than the Gaussian beams employed in the current baseline design. Mirrors
that confine these beams have been found to be roughly conical in shape, with
an average slope approximately equal to the mirror radius divided by arm
length, and with mild corrections varying at the Fresnel scale. Such a mirror
system, if built, would impact the sensitivity of LIGO, increasing the event
rate of observing gravitational waves in the frequency range of maximum
sensitivity roughly by a factor of three compared to an Advanced LIGO using
Mesa beams (assuming all other noises remain unchanged). We discuss the
resulting beam and mirror properties and study requirements on mirror tilt,
displacement and figure error, in order for this beam to be used in LIGO
detectors.Comment: 9 pages, 11 figure
Isometric embeddings of black hole horizons in three-dimensional flat space
The geometry of a two-dimensional surface in a curved space can be most easily visualized by using an isometric embedding in flat three-dimensional space. Here we present a new method for embedding surfaces with spherical topology in flat space when such a embedding exists. Our method is based on expanding the surface in spherical harmonics and minimizing for the differences between the metric on the original surface and the metric on the trial surface in the space of the expansion coefficients. We have applied this method to study the geometry of back hole horizons in the presence of strong, non-axisymmetric, gravitational waves (Brill waves). We have noticed that, in many cases, although the metric of the horizon seems to have large deviations from axisymmetry, the intrinsic geometry of the horizon is almost axisymmetric. The origin of the large apparent non-axisymmetry of the metric is the deformation of the coordinate system in which the metric was computed
Estimate of Tilt Instability of Mesa-Beam and Gaussian-Beam Modes for Advanced LIGO
Sidles and Sigg have shown that advanced LIGO interferometers will encounter
a serious tilt instability, in which symmetric tilts of the mirrors of an arm
cavity cause the cavity's light beam to slide sideways, so its radiation
pressure exerts a torque that increases the tilt. Sidles and Sigg showed that
the strength T of this torque is 26.2 times greater for advanced LIGO's
baseline cavities -- nearly flat spherical mirrors which support Gaussian beams
(``FG'' cavities), than for nearly concentric spherical mirrors which support
Gaussian beams with the same diffraction losses as the baseline case -- ``CG''
cavities: T^{FG}/T^{CG} = 26.2. This has motivated a proposal to change the
baseline design to nearly concentric, spherical mirrors. In order to reduce
thermoelastic noise in advanced LIGO, O'Shaughnessy and Thorne have proposed
replacing the spherical mirrors and their Gaussian beams by ``Mexican-Hat''
(MH) shaped mirrors which support flat-topped, ``mesa'' shaped beams. In this
paper we compute the tilt-instability torque for advanced-LIGO cavities with
nearly flat MH mirrors and mesa beams (``FM'' cavities) and nearly concentric
MH mirrors and mesa beams (``CM'' cavities), with the same diffraction losses
as in the baseline FG case. We find that the relative sizes of the restoring
torques are T^{CM}/T^{CG} = 0.91, T^{FM}/T^{CG} = 96, T^{FM}/T^{FG} = 3.67.
Thus, the nearly concentric MH mirrors have a weaker tilt instability than any
other configuration. Their thermoelastic noise is the same as for nearly flat
MH mirrors, and is much lower than for spherical mirrors.Comment: 10 pages, 3 figures, 4 table
The dependence of test-mass thermal noises on beam shape in gravitational-wave interferometers
In second-generation, ground-based interferometric gravitational-wave
detectors such as Advanced LIGO, the dominant noise at frequencies
Hz to Hz is expected to be due to thermal fluctuations in the
mirrors' substrates and coatings which induce random fluctuations in the shape
of the mirror face. The laser-light beam averages over these fluctuations; the
larger the beam and the flatter its light-power distribution, the better the
averaging and the lower the resulting thermal noise. In semi-infinite mirrors,
scaling laws for the influence of beam shape on the four dominant types of
thermal noise (coating Brownian, coating thermoelastic, substrate Brownian, and
substrate thermoelastic) have been suggested by various researchers and derived
with varying degrees of rigour. Because these scaling laws are important tools
for current research on optimizing the beam shape, it is important to firm up
our understanding of them. This paper (1) gives a summary of the prior work and
of gaps in the prior analyses, (2) gives a unified and rigorous derivation of
all four scaling laws, and (3) explores, relying on work by J. Agresti,
deviations from the scaling laws due to finite mirror size.Comment: 25 pages, 10 figures, submitted to Class. Quantum Gra
Evolution of 3D Boson Stars with Waveform Extraction
Numerical results from a study of boson stars under nonspherical
perturbations using a fully general relativistic 3D code are presented together
with the analysis of emitted gravitational radiation. We have constructed a
simulation code suitable for the study of scalar fields in space-times of
general symmetry by bringing together components for addressing the initial
value problem, the full evolution system and the detection and analysis of
gravitational waves. Within a series of numerical simulations, we explicitly
extract the Zerilli and Newman-Penrose scalar gravitational waveforms
when the stars are subjected to different types of perturbations. Boson star
systems have rapidly decaying nonradial quasinormal modes and thus the complete
gravitational waveform could be extracted for all configurations studied. The
gravitational waves emitted from stable, critical, and unstable boson star
configurations are analyzed and the numerically observed quasinormal mode
frequencies are compared with known linear perturbation results. The
superposition of the high frequency nonspherical modes on the lower frequency
spherical modes was observed in the metric oscillations when perturbations with
radial and nonradial components were applied. The collapse of unstable boson
stars to black holes was simulated. The apparent horizons were observed to be
slightly nonspherical when initially detected and became spherical as the
system evolved. The application of nonradial perturbations proportional to
spherical harmonics is observed not to affect the collapse time. An unstable
star subjected to a large perturbation was observed to migrate to a stable
configuration.Comment: 26 pages, 12 figure
Three Dimensional Distorted Black Holes
We present three-dimensional, {\it non-axisymmetric} distorted black hole
initial data which generalizes the axisymmetric, distorted, non-rotating
[Bernstein93a] and rotating [Brandt94a] single black hole data developed by
Bernstein, Brandt, and Seidel. These initial data should be useful for studying
the dynamics of fully 3D, distorted black holes, such as those created by the
spiraling coalescence of two black holes. We describe the mathematical
construction of several families of such data sets, and show how to construct
numerical solutions. We survey quantities associated with the numerically
constructed solutions, such as ADM masses, apparent horizons, measurements of
the horizon distortion, and the maximum possible radiation loss ().Comment: 23 pages, 12 figures, accepted for publication in Classical and
Quantum Gravit
Gravitational waves from rapidly rotating neutron stars
Rapidly rotating neutron stars in Low Mass X-ray Binaries have been proposed
as an interesting source of gravitational waves. In this chapter we present
estimates of the gravitational wave emission for various scenarios, given the
(electromagnetically) observed characteristics of these systems. First of all
we focus on the r-mode instability and show that a 'minimal' neutron star model
(which does not incorporate exotica in the core, dynamically important magnetic
fields or superfluid degrees of freedom), is not consistent with observations.
We then present estimates of both thermally induced and magnetically sustained
mountains in the crust. In general magnetic mountains are likely to be
detectable only if the buried magnetic field of the star is of the order of
G. In the thermal mountain case we find that gravitational
wave emission from persistent systems may be detected by ground based
interferometers. Finally we re-asses the idea that gravitational wave emission
may be balancing the accretion torque in these systems, and show that in most
cases the disc/magnetosphere interaction can account for the observed spin
periods.Comment: To appear in 'Gravitational Waves Astrophysics: 3rd Session of the
Sant Cugat Forum on Astrophysics, 2014', Editor: Carlos F. Sopuert
Covariant coarse-graining of inhomogeneous dust flow in General Relativity
A new definition of coarse-grained quantities describing the dust flow in
General Relativity is proposed. It assigns the coarse--grained expansion, shear
and vorticity to finite-size comoving domains of fluid in a covariant,
coordinate-independent manner. The coarse--grained quantities are all
quasi-local functionals, depending only on the geometry of the boundary of the
considered domain. They can be thought of as relativistic generalizations of
simple volume averages of local quantities in a flat space. The procedure is
based on the isometric embedding theorem for S^2 surfaces and thus requires the
boundary of the domain in question to have spherical topology and positive
scalar curvature. We prove that in the limit of infinitesimally small volume
the proposed quantities reproduce the local expansion, shear and vorticity. In
case of irrotational flow we derive the time evolution for the coarse-grained
quantities and show that its structure is very similar to the evolution
equation for their local counterparts. Additional terms appearing in it may
serve as a measure of the backreacton of small-scale inhomogeneities of the
flow on the large-scale motion of the fluid inside the domain and therefore the
result may be interesting in the context of the cosmological backreaction
problem. We also consider the application of the proposed coarse-graining
procedure to a number of known exact solutions of Einstein equations with dust
and show that it yields reasonable results.Comment: 17 pages, 5 figures. Version accepted in Classical and Quantum
Gravity
Isometric embeddings of 2-spheres by embedding flow for applications in numerical relativity
We present a numerical method for solving Weyl's embedding problem which
consists of finding a global isometric embedding of a positively curved and
positive-definite spherical 2-metric into the Euclidean three space. The method
is based on a construction introduced by Weingarten and was used in Nirenberg's
proof of Weyl's conjecture. The target embedding results as the endpoint of an
embedding flow in R^3 beginning at the unit sphere's embedding. We employ
spectral methods to handle functions on the surface and to solve various
(non)-linear elliptic PDEs. Possible applications in 3+1 numerical relativity
range from quasi-local mass and momentum measures to coarse-graining in
inhomogeneous cosmological models.Comment: 18 pages, 14 figure
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