918 research outputs found
Homoclinic and heteroclinic solutions for a class of second-order non-autonomous ordinary differential equations: Multiplicity results for stepwise potentials
We prove some multiplicity results for a class of one-dimensional nonlinear Schr\uf6dinger-type equations of the form x\u2033 + 2kx - 2g(t)x3 = 0, where k gt; 0 and the weight g(t) is a positive stepwise function. Instead of the cubic term, more general nonlinearities can be considered as well. \ua9 2013 Ellero and Zanolin
Gravitational waves from three-dimensional core-collapse supernova models: The impact of moderate progenitor rotation
We present predictions for the gravitational-wave (GW) emission of
three-dimensional supernova (SN) simulations performed for a 15 solar-mass
progenitor with the Prometheus-Vertex code using energy-dependent, three-flavor
neutrino transport. The progenitor adopted from stellar evolution calculations
including magnetic fields had a fairly low specific angular momentum (j_Fe <~
10^{15} cm^2/s) in the iron core (central angular velocity ~0.2 rad/s), which
we compared to simulations without rotation and with artificially enhanced
rotation (j_Fe <~ 2*10^{16} cm^2/s; central angular velocity ~0.5 rad/s). Our
results confirm that the time-domain GW signals of SNe are stochastic, but
possess deterministic components with characteristic patterns at low
frequencies (<~200 Hz), caused by mass motions due to the standing accretion
shock instability (SASI), and at high frequencies, associated with gravity-mode
oscillations in the surface layer of the proto-neutron star (PNS). Non-radial
mass motions in the post-shock layer as well as PNS convection are important
triggers of GW emission, whose amplitude scales with the power of the
hydrodynamic flows. There is no monotonic increase of the GW amplitude with
rotation, but a clear correlation with the strength of SASI activity. Our
slowly rotating model is a fainter GW emitter than the non-rotating model
because of weaker SASI activity and damped convection in the post-shock layer
and PNS. In contrast, the faster rotating model exhibits a powerful SASI spiral
mode during its transition to explosion, producing the highest GW amplitudes
with a distinctive drift of the low-frequency emission peak from ~80-100 Hz to
~40-50 Hz. This migration signifies shock expansion, whereas non-exploding
models are discriminated by the opposite trend.Comment: Added new figure, figure 9. Updated figure 9, now figure 10. Modified
the discussion of the proto-neutron star convection. Added a figure showing
the average rotation rate as a function of radius. Added a section discussing
where the low-frequency gravitational waves are generated, this information
is visualized in figure 9. We also made some minor changes to the text and
selected plot
Gravitational Wave Burst Source Direction Estimation using Time and Amplitude Information
In this article we study two problems that arise when using timing and
amplitude estimates from a network of interferometers (IFOs) to evaluate the
direction of an incident gravitational wave burst (GWB). First, we discuss an
angular bias in the least squares timing-based approach that becomes
increasingly relevant for moderate to low signal-to-noise ratios. We show how
estimates of the arrival time uncertainties in each detector can be used to
correct this bias. We also introduce a stand alone parameter estimation
algorithm that can improve the arrival time estimation and provide
root-sum-squared strain amplitude (hrss) values for each site. In the second
part of the paper we discuss how to resolve the directional ambiguity that
arises from observations in three non co-located interferometers between the
true source location and its mirror image across the plane containing the
detectors. We introduce a new, exact relationship among the hrss values at the
three sites that, for sufficiently large signal amplitudes, determines the true
source direction regardless of whether or not the signal is linearly polarized.
Both the algorithm estimating arrival times, arrival time uncertainties, and
hrss values and the directional follow-up can be applied to any set of
gravitational wave candidates observed in a network of three non co-located
interferometers. As a case study we test the methods on simulated waveforms
embedded in simulations of the noise of the LIGO and Virgo detectors at design
sensitivity.Comment: 10 pages, 14 figures, submitted to PR
Observing gravitational waves from core-collapse supernovae in the advanced detector era
The next galactic core-collapse supernova (CCSN) has already exploded, and its electromagnetic (EM) waves, neutrinos, and gravitational waves (GWs) may arrive at any moment. We present an extensive study on the potential sensitivity of prospective detection scenarios for GWs from CCSNe within 5 Mpc, using realistic noise at the predicted sensitivity of the Advanced LIGO and Advanced Virgo detectors for 2015, 2017, and 2019. We quantify the detectability of GWs from CCSNe within the Milky Way and Large Magellanic Cloud, for which there will be an observed neutrino burst. We also consider extreme GW emission scenarios for more distant CCSNe with an associated EM signature. We find that a three-detector network at design sensitivity will be able to detect neutrino-driven CCSN explosions out to ∼5.5  kpc, while rapidly rotating core collapse will be detectable out to the Large Magellanic Cloud at 50 kpc. Of the phenomenological models for extreme GW emission scenarios considered in this study, such as long-lived bar-mode instabilities and disk fragmentation instabilities, all models considered will be detectable out to M31 at 0.77 Mpc, while the most extreme models will be detectable out to M82 at 3.52 Mpc and beyond
Application of asymptotic expansions of maximum likelihood estimators errors to gravitational waves from binary mergers: the single interferometer case
In this paper we describe a new methodology to calculate analytically the
error for a maximum likelihood estimate (MLE) for physical parameters from
Gravitational wave signals. All the existing litterature focuses on the usage
of the Cramer Rao Lower bounds (CRLB) as a mean to approximate the errors for
large signal to noise ratios. We show here how the variance and the bias of a
MLE estimate can be expressed instead in inverse powers of the signal to noise
ratios where the first order in the variance expansion is the CRLB. As an
application we compute the second order of the variance and bias for MLE of
physical parameters from the inspiral phase of binary mergers and for noises of
gravitational wave interferometers . We also compare the improved error
estimate with existing numerical estimates. The value of the second order of
the variance expansions allows to get error predictions closer to what is
observed in numerical simulations. It also predicts correctly the necessary SNR
to approximate the error with the CRLB and provides new insight on the
relationship between waveform properties SNR and estimation errors. For example
the timing match filtering becomes optimal only if the SNR is larger than the
kurtosis of the gravitational wave spectrum
Search for Gravitational Waves Associated with Gamma-Ray Bursts During the First Advanced LIGO Observing Run and Implications for the Origin of GRB 150906B
We present the results of the search for gravitational waves (GWs) associated with γ-ray bursts detected during the first observing run of the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO). We find no evidence of a GW signal for any of the 41 γ-ray bursts for which LIGO data are available with sufficient duration. For all γ-ray bursts, we place lower bounds on the distance to the source using the optimistic assumption that GWs with an energy of were emitted within the – Hz band, and we find a median 90% confidence limit of 71 Mpc at 150 Hz. For the subset of 19 short/hard γ-ray bursts, we place lower bounds on distance with a median 90% confidence limit of 90 Mpc for binary neutron star (BNS) coalescences, and 150 and 139 Mpc for neutron star–black hole coalescences with spins aligned to the orbital angular momentum and in a generic configuration, respectively. These are the highest distance limits ever achieved by GW searches. We also discuss in detail the results of the search for GWs associated with GRB 150906B, an event that was localized by the InterPlanetary Network near the local galaxy NGC 3313, which is at a luminosity distance of Mpc (z = 0.0124). Assuming the γ-ray emission is beamed with a jet half-opening angle , we exclude a BNS and a neutron star–black hole in NGC 3313 as the progenitor of this event with confidence \u3e99%. Further, we exclude such progenitors up to a distance of 102 Mpc and 170 Mpc, respectively
All-Sky Search for Long-Duration Gravitational Wave Transients in the First Advanced LIGO Observing Run
We present the results of a search for long-duration gravitational wave transients in the data of the LIGO Hanford and LIGO Livingston second generation detectors between and , with a total observational time of . The search targets gravitational wave transients of 10–500 s duration in a frequency band of 24–2048 Hz, with minimal assumptions about the signal waveform, polarization, source direction, or time of occurrence. No significant events were observed. As a result we set 90% confidence upper limits on the rate of long-duration gravitational wave transients for different types of gravitational wave signals. We also show that the search is sensitive to sources in the Galaxy emitting at least  ~10−8 in gravitational waves
A First Comparison Between LIGO and Virgo Inspiral Search Pipelines
This article reports on a project that is the first step the LIGO Scientific
Collaboration and the Virgo Collaboration have taken to prepare for the mutual
search for inspiral signals. The project involved comparing the analysis
pipelines of the two collaborations on data sets prepared by both sides,
containing simulated noise and injected events. The ability of the pipelines to
detect the injected events was checked, and a first comparison of how the
parameters of the events were recovered has been completed.Comment: GWDAW-9 proceeding
LOOC UP: Locating and observing optical counterparts to gravitational wave bursts
Gravitational wave (GW) bursts (short duration signals) are expected to be
associated with highly energetic astrophysical processes. With such high
energies present, it is likely these astrophysical events will have signatures
in the EM spectrum as well as in gravitational radiation. We have initiated a
program, "Locating and Observing Optical Counterparts to Unmodeled Pulses in
Gravitational Waves" (LOOC UP) to promptly search for counterparts to GW burst
candidates. The proposed method analyzes near real-time data from the
LIGO-Virgo network, and then uses a telescope network to seek optical-transient
counterparts to candidate GW signals. We carried out a pilot study using
S5/VSR1 data from the LIGO-Virgo network to develop methods and software tools
for such a search. We will present the method, with an emphasis on the
potential for such a search to be carried out during the next science run of
LIGO and Virgo, expected to begin in 2009.Comment: 11 pages, 2 figures; v2) added acknowledgments, additional
references, and minor text changes v3) added 1 figure, additional references,
and minor text changes. v4) Updated references and acknowledgments. To be
published in the GWDAW 12 Conf. Proc. by Classical and Quantum Gravit
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