results for au:Porter_E in:gr-qc

- Mar 01 2018 gr-qc astro-ph.CO arXiv:1802.10194v2The detection of gravitational waves with Advanced LIGO and Advanced Virgo has enabled novel tests of general relativity, including direct study of the polarization of gravitational waves. While general relativity allows for only two tensor gravitational-wave polarizations, general metric theories can additionally predict two vector and two scalar polarizations. The polarization of gravitational waves is encoded in the spectral shape of the stochastic gravitational-wave background, formed by the superposition of cosmological and individually-unresolved astrophysical sources. Using data recorded by Advanced LIGO during its first observing run, we search for a stochastic background of generically-polarized gravitational waves. We find no evidence for a background of any polarization, and place the first direct bounds on the contributions of vector and scalar polarizations to the stochastic background. Under log-uniform priors for the energy in each polarization, we limit the energy-densities of tensor, vector, and scalar modes at 95% credibility to $\Omega^T_0 < 5.6 \times 10^{-8}$, $\Omega^V_0 < 6.4\times 10^{-8}$, and $\Omega^S_0 < 1.1\times 10^{-7}$ at a reference frequency $f_0 = 25$ Hz.
- Feb 15 2018 gr-qc arXiv:1802.05241v1We report on a new all-sky search for periodic gravitational waves in the frequency band 475-2000 Hz and with a frequency time derivative in the range of [-1.0e-8, +1e-9] Hz/s. Potential signals could be produced by a nearby spinning and slightly non-axisymmetric isolated neutron star in our galaxy. This search uses the data from Advanced LIGO's first observational run O1. No gravitational wave signals were observed, and upper limits were placed on their strengths. For completeness, results from the separately published low frequency search 20-475 Hz are included as well. Our lowest upper limit on worst-case (linearly polarized) strain amplitude h_0 is 4e-25 near 170 Hz, while at the high end of our frequency range we achieve a worst-case upper limit of 1.3e-24. For a circularly polarized source (most favorable orientation), the smallest upper limit obtained is ~1.5e-25.
- Dec 05 2017 gr-qc astro-ph.CO arXiv:1712.01168v2Cosmic strings are topological defects which can be formed in GUT-scale phase transitions in the early universe. They are also predicted to form in the context of string theory. The main mechanism for a network of Nambu-Goto cosmic strings to lose energy is through the production of loops and the subsequent emission of gravitational waves, thus offering an experimental signature for the existence of cosmic strings. Here we report on the analysis conducted to specifically search for gravitational-wave bursts from cosmic string loops in the data of Advanced LIGO 2015-2016 observing run (O1). No evidence of such signals was found in the data, and as a result we set upper limits on the cosmic string parameters for three recent loop distribution models. In this paper, we initially derive constraints on the string tension $G\mu$ and the intercommutation probability, using not only the burst analysis performed on the O1 data set, but also results from the previously published LIGO stochastic O1 analysis, pulsar timing arrays, cosmic microwave background and Big-Bang nucleosynthesis experiments. We show that these data sets are complementary in that they probe gravitational waves produced by cosmic string loops during very different epochs. Finally, we show that the data sets exclude large parts of the parameter space of the three loop distribution models we consider.
- Nov 16 2017 astro-ph.HE gr-qc arXiv:1711.05578v1On June 8, 2017 at 02:01:16.49 UTC, a gravitational-wave signal from the merger of two stellar-mass black holes was observed by the two Advanced LIGO detectors with a network signal-to-noise ratio of 13. This system is the lightest black hole binary so far observed, with component masses $12^{+7}_{-2}\,M_\odot$ and $7^{+2}_{-2}\,M_\odot$ (90% credible intervals). These lie in the range of measured black hole masses in low-mass X-ray binaries, thus allowing us to compare black holes detected through gravitational waves with electromagnetic observations. The source's luminosity distance is $340^{+140}_{-140}$ Mpc, corresponding to redshift $0.07^{+0.03}_{-0.03}$. We verify that the signal waveform is consistent with the predictions of general relativity.
- Oct 26 2017 astro-ph.HE gr-qc arXiv:1710.09320v1The first observation of a binary neutron star coalescence by the Advanced LIGO and Advanced Virgo gravitational-wave detectors offers an unprecedented opportunity to study matter under the most extreme conditions. After such a merger, a compact remnant is left over whose nature depends primarily on the masses of the inspiralling objects and on the equation of state of nuclear matter. This could be either a black hole or a neutron star (NS), with the latter being either long-lived or too massive for stability implying delayed collapse to a black hole. Here, we present a search for gravitational waves from the remnant of the binary neutron star merger GW170817 using data from Advanced LIGO and Advanced Virgo. We search for short ($\lesssim1$ s) and intermediate-duration ($\lesssim 500$ s) signals, which includes gravitational-wave emission from a hypermassive NS or supramassive NS, respectively. We find no signal from the post-merger remnant. Our derived strain upper limits are more than an order of magnitude larger than those predicted by most models. For short signals, our best upper limit on the root-sum-square of the gravitational-wave strain emitted from 1--4 kHz is $h_{\rm rss}^{50\%}=2.1\times 10^{-22}$ Hz$^{-1/2}$ at 50% detection efficiency. For intermediate-duration signals, our best upper limit at 50% detection efficiency is $h_{\rm rss}^{50\%}=8.4\times 10^{-22}$ Hz$^{-1/2}$ for a millisecond magnetar model, and $h_{\rm rss}^{50\%}=5.9\times 10^{-22}$ Hz$^{-1/2}$ for a bar-mode model. These results indicate that post-merger emission from a similar event may be detectable when advanced detectors reach design sensitivity or with next-generation detectors.
- Oct 17 2017 gr-qc arXiv:1710.05837v1The LIGO Scientific and Virgo Collaborations have announced the first detection of gravitational waves from the coalescence of two neutron stars. The merger rate of binary neutron stars estimated from this event suggests that distant, unresolvable binary neutron stars create a significant astrophysical stochastic gravitational-wave background. The binary neutron star background will add to the background from binary black holes, increasing the amplitude of the total astrophysical background relative to previous expectations. In the Advanced LIGO-Virgo frequency band most sensitive to stochastic backgrounds (near 25 Hz), we predict a total astrophysical background with amplitude $\Omega_{\rm GW} (f=25 \text{Hz}) = 1.8_{-1.3}^{+2.7} \times 10^{-9}$ with $90\%$ confidence, compared with $\Omega_{\rm GW} (f=25 \text{Hz}) = 1.1_{-0.7}^{+1.2} \times 10^{-9}$ from binary black holes alone. Assuming the most probable rate for compact binary mergers, we find that the total background may be detectable with a signal-to-noise-ratio of 3 after 40 months of total observation time, based on the expected timeline for Advanced LIGO and Virgo to reach their design sensitivity.
- Oct 09 2017 gr-qc astro-ph.HE arXiv:1710.02327v2Spinning neutron stars asymmetric with respect to their rotation axis are potential sources of continuous gravitational waves for ground-based interferometric detectors. In the case of known pulsars a fully coherent search, based on matched filtering, which uses the position and rotational parameters obtained from electromagnetic observations, can be carried out. Matched filtering maximizes the signal-to-noise (SNR) ratio, but a large sensitivity loss is expected in case of even a very small mismatch between the assumed and the true signal parameters. For this reason, \it narrow-band analyses methods have been developed, allowing a fully coherent search for gravitational waves from known pulsars over a fraction of a hertz and several spin-down values. In this paper we describe a narrow-band search of eleven pulsars using data from Advanced LIGO's first observing run. Although we have found several initial outliers, further studies show no significant evidence for the presence of a gravitational wave signal. Finally, we have placed upper limits on the signal strain amplitude lower than the spin-down limit for 5 of the 11 targets over the bands searched: in the case of J1813-1749 the spin-down limit has been beaten for the first time. For an additional 3 targets, the median upper limit across the search bands is below the spin-down limit. This is the most sensitive narrow-band search for continuous gravitational waves carried out so far.
- Sep 28 2017 gr-qc arXiv:1709.09203v1We present results from the first directed search for nontensorial gravitational waves. While general relativity allows for tensorial (plus and cross) modes only, a generic metric theory may, in principle, predict waves with up to six different polarizations. This analysis is sensitive to continuous signals of scalar, vector or tensor polarizations, and does not rely on any specific theory of gravity. After searching data from the first observation run of the advanced LIGO detectors for signals at twice the rotational frequency of 200 known pulsars, we find no evidence of gravitational waves of any polarization. We report the first upper limits for scalar and vector strains, finding values comparable in magnitude to previously-published limits for tensor strain. Our results may be translated into constraints on specific alternative theories of gravity.
- Sep 28 2017 gr-qc astro-ph.HE arXiv:1709.09660v3On August 14, 2017 at 10:30:43 UTC, the Advanced Virgo detector and the two Advanced LIGO detectors coherently observed a transient gravitational-wave signal produced by the coalescence of two stellar mass black holes, with a false-alarm-rate of $\lesssim$ 1 in 27000 years. The signal was observed with a three-detector network matched-filter signal-to-noise ratio of 18. The inferred masses of the initial black holes are $30.5_{-3.0}^{+5.7}$ Msun and $25.3_{-4.2}^{+2.8}$ Msun (at the 90% credible level). The luminosity distance of the source is $540_{-210}^{+130}~\mathrm{Mpc}$, corresponding to a redshift of $z=0.11_{-0.04}^{+0.03}$. A network of three detectors improves the sky localization of the source, reducing the area of the 90% credible region from 1160 deg$^2$ using only the two LIGO detectors to 60 deg$^2$ using all three detectors. For the first time, we can test the nature of gravitational wave polarizations from the antenna response of the LIGO-Virgo network, thus enabling a new class of phenomenological tests of gravity.
- Jul 11 2017 gr-qc astro-ph.IM arXiv:1707.02667v2We report on an all-sky search for periodic gravitational waves in the frequency band 20-475 Hz and with a frequency time derivative in the range of [-1.0, +0.1]e-8 Hz/s. Such a signal could be produced by a nearby spinning and slightly non-axisymmetric isolated neutron star in our galaxy. This search uses the data from Advanced LIGO's first observational run, O1. No periodic gravitational wave signals were observed, and upper limits were placed on their strengths. The lowest upper limits on worst-case (linearly polarized) strain amplitude h0 are 4e-25 near 170 Hz. For a circularly polarized source (most favorable orientation), the smallest upper limits obtained are 1.5e-25. These upper limits refer to all sky locations and the entire range of frequency derivative values. For a population-averaged ensemble of sky locations and stellar orientations, the lowest upper limits obtained for the strain amplitude are 2.5e-25.
- Jul 11 2017 gr-qc arXiv:1707.02669v2We report results of a deep all-sky search for periodic gravitational waves from isolated neutron stars in data from the first Advanced LIGO observing run. This search investigates the low frequency range of Advanced LIGO data, between 20 and 100 Hz, much of which was not explored in initial LIGO. The search was made possible by the computing power provided by the volunteers of the Einstein@Home project. We find no significant signal candidate and set the most stringent upper limits to date on the amplitude of gravitational wave signals from the target population, corresponding to a sensitivity depth of 48.7 [1/$\sqrt{{\textrm{Hz}}}$]. At the frequency of best strain sensitivity, near 100 Hz, we set 90% confidence upper limits of $1.8 \times 10^{-25}$. At the low end of our frequency range, 20 Hz, we achieve upper limits of $3.9 \times 10^{-24}$. At 55 Hz we can exclude sources with ellipticities greater than $10^{-5}$ within 100 pc of Earth with fiducial value of the principal moment of inertia of $10^{38} \textrm{kg m}^2$.
- Jun 13 2017 astro-ph.HE gr-qc arXiv:1706.03119v3We present the results of a semicoherent search for continuous gravitational waves from the low-mass X-ray binary Scorpius X-1, using data from the first Advanced LIGO observing run. The search method uses details of the modelled, parametrized continuous signal to combine coherently data separated by less than a specified coherence time, which can be adjusted to trade off sensitivity against computational cost. A search was conducted over the frequency range from 25 Hz to 2000 Hz, spanning the current observationally-constrained range of the binary orbital parameters. No significant detection candidates were found, and frequency-dependent upper limits were set using a combination of sensitivity estimates and simulated signal injections. The most stringent upper limit was set at 175 Hz, with comparable limits set across the most sensitive frequency range from 100 Hz to 200 Hz. At this frequency, the 95 pct upper limit on signal amplitude h0 is 2.3e-25 marginalized over the unknown inclination angle of the neutron star's spin, and 8.03e-26 assuming the best orientation (which results in circularly polarized gravitational waves). These limits are a factor of 3-4 stronger than those set by other analyses of the same data, and a factor of about 7 stronger than the best upper limits set using initial LIGO data. In the vicinity of 100 Hz, the limits are a factor of between 1.2 and 3.5 above the predictions of the torque balance model, depending on inclination angle, if the most likely inclination angle of 44 degrees is assumed, they are within a factor of 1.7.
- Jun 07 2017 gr-qc astro-ph.HE arXiv:1706.01812v1We describe the observation of GW170104, a gravitational-wave signal produced by the coalescence of a pair of stellar-mass black holes. The signal was measured on January 4, 2017 at 10:11:58.6 UTC by the twin advanced detectors of the Laser Interferometer Gravitational-Wave Observatory during their second observing run, with a network signal-to-noise ratio of 13 and a false alarm rate less than 1 in 70,000 years. The inferred component black hole masses are $31.2^{+8.4}_{-6.0}\,M_\odot$ and $19.4^{+5.3}_{-5.9}\,M_\odot$ (at the 90% credible level). The black hole spins are best constrained through measurement of the effective inspiral spin parameter, a mass-weighted combination of the spin components perpendicular to the orbital plane, $\chi_\mathrm{eff} = -0.12^{+0.21}_{-0.30}.$ This result implies that spin configurations with both component spins positively aligned with the orbital angular momentum are disfavored. The source luminosity distance is $880^{+450}_{-390}~\mathrm{Mpc}$ corresponding to a redshift of $z = 0.18^{+0.08}_{-0.07}$. We constrain the magnitude of modifications to the gravitational-wave dispersion relation and perform null tests of general relativity. Assuming that gravitons are dispersed in vacuum like massive particles, we bound the graviton mass to $m_g \le 7.7 \times 10^{-23}~\mathrm{eV}/c^2$. In all cases, we find that GW170104 is consistent with general relativity.
- Apr 18 2017 gr-qc arXiv:1704.04628v4During their first observational run, the two Advanced LIGO detectors attained an unprecedented sensitivity, resulting in the first direct detections of gravitational-wave signals and GW151226, produced by stellar-mass binary black hole systems. This paper reports on an all-sky search for gravitational waves (GWs) from merging intermediate mass black hole binaries (IMBHBs). The combined results from two independent search techniques were used in this study: the first employs a matched-filter algorithm that uses a bank of filters covering the GW signal parameter space, while the second is a generic search for GW transients (bursts). No GWs from IMBHBs were detected, therefore, we constrain the rate of several classes of IMBHB mergers. The most stringent limit is obtained for black holes of individual mass $100\,M_\odot$, with spins aligned with the binary orbital angular momentum. For such systems, the merger rate is constrained to be less than $0.93~\mathrm{Gpc^{-3}\,yr}^{-1}$ in comoving units at the $90\%$ confidence level, an improvement of nearly 2 orders of magnitude over previous upper limits.
- Apr 13 2017 gr-qc arXiv:1704.03719v3Results are presented from a semi-coherent search for continuous gravitational waves from the brightest low-mass X-ray binary, Scorpius X-1, using data collected during the first Advanced LIGO observing run (O1). The search combines a frequency domain matched filter (Bessel-weighted $\mathcal{F}$-statistic) with a hidden Markov model to track wandering of the neutron star spin frequency. No evidence of gravitational waves is found in the frequency range 60-650 Hz. Frequentist 95% confidence strain upper limits, $h_0^{95\%} = 4.0\times10^{-25}$, $8.3\times10^{-25}$, and $3.0\times10^{-25}$ for electromagnetically restricted source orientation, unknown polarization, and circular polarization, respectively, are reported at 106 Hz. They are $\leq 10$ times higher than the theoretical torque-balance limit at 106 Hz.
- Jun 16 2016 gr-qc astro-ph.CO arXiv:1606.04856v3The first observational run of the Advanced LIGO detectors, from September 12, 2015 to January 19, 2016, saw the first detections of gravitational waves from binary black hole mergers. In this paper we present full results from a search for binary black hole merger signals with total masses up to $100 M_\odot$ and detailed implications from our observations of these systems. Our search, based on general-relativistic models of gravitational wave signals from binary black hole systems, unambiguously identified two signals, GW150914 and GW151226, with a significance of greater than $5\sigma$ over the observing period. It also identified a third possible signal, LVT151012, with substantially lower significance, and with an 87% probability of being of astrophysical origin. We provide detailed estimates of the parameters of the observed systems. Both GW150914 and GW151226 provide an unprecedented opportunity to study the two-body motion of a compact-object binary in the large velocity, highly nonlinear regime. We do not observe any deviations from general relativity, and place improved empirical bounds on several high-order post-Newtonian coefficients. From our observations we infer stellar-mass binary black hole merger rates lying in the range $9-240 \mathrm{Gpc}^{-3} \mathrm{yr}^{-1}$. These observations are beginning to inform astrophysical predictions of binary black hole formation rates, and indicate that future observing runs of the Advanced detector network will yield many more gravitational wave detections.
- Feb 12 2016 astro-ph.HE gr-qc arXiv:1602.03842v3A transient gravitational-wave signal, GW150914, was identified in the twin Advanced LIGO detectors on September 14, 2015 at 09:50:45 UTC. To assess the implications of this discovery, the detectors remained in operation with unchanged configurations over a period of 39 d around the time of the signal. At the detection statistic threshold corresponding to that observed for GW150914, our search of the 16 days of simultaneous two-detector observational data is estimated to have a false alarm rate (FAR) of $< 4.9 \times 10^{-6} \, \mathrm{yr}^{-1}$, yielding a $p$-value for GW150914 of $< 2 \times 10^{-7}$. Parameter estimation followup on this trigger identifies its source as a binary black hole (BBH) merger with component masses $(m_1, m_2) = \left(36^{+5}_{-4},29^{+4}_{-4}\right) \, M_\odot$ at redshift $z = 0.09^{+0.03}_{-0.04}$ (median and 90\% credible range). Here we report on the constraints these observations place on the rate of BBH coalescences. Considering only GW150914, assuming that all BBHs in the Universe have the same masses and spins as this event, imposing a search FAR threshold of 1 per 100 years, and assuming that the BBH merger rate is constant in the comoving frame, we infer a 90% credible range of merger rates between $2$--$53 \, \mathrm{Gpc}^{-3} \mathrm{yr}^{-1}$ (comoving frame). Incorporating all search triggers that pass a much lower threshold while accounting for the uncertainty in the astrophysical origin of each trigger, we estimate a higher rate, ranging from $13$--$600 \, \mathrm{Gpc}^{-3} \mathrm{yr}^{-1}$ depending on assumptions about the BBH mass distribution. All together, our various rate estimates fall in the conservative range $2$--$600 \, \mathrm{Gpc}^{-3} \mathrm{yr}^{-1}$.
- Sep 30 2015 gr-qc astro-ph.IM arXiv:1509.08867v2Compact binaries in our galaxy are expected to be one of the main sources of gravitational waves for the future eLISA mission. During the mission lifetime, many thousands of galactic binaries should be individually resolved. However, the identification of the sources, and the extraction of the signal parameters in a noisy environment are real challenges for data analysis. So far, stochastic searches have proven to be the most successful for this problem. In this work we present the first application of a swarm-based algorithm combining Particle Swarm Optimization and Differential Evolution. These algorithms have been shown to converge faster to global solutions on complicated likelihood surfaces than other stochastic methods. We first demonstrate the effectiveness of the algorithm for the case of a single binary in a 1 mHz search bandwidth. This interesting problem gave the algorithm plenty of opportunity to fail, as it can be easier to find a strong noise peak rather than the signal itself. After a successful detection of a fictitious low-frequency source, as well as the verification binary RXJ0806.3+1527, we then applied the algorithm to the detection of multiple binaries, over different search bandwidths, in the cases of low and mild source confusion. In all cases, we show that we can successfully identify the sources, and recover the true parameters within a 99\% credible interval.
- Jun 01 2015 gr-qc arXiv:1505.08058v1As the theme for the future L3 Cosmic Vision mission, ESA has recently chosen the `Gravitational Wave Universe'. Within this call, a mission concept called eLISA has been proposed. This observatory has a current initial configuration consisting of 4 laser links between the three satellites, which are separated by a distance of one million kilometers, constructing a single channel Michelson interferometer. However, the final configuration for the observatory will not be fixed until the end of this decade. With this in mind, we investigate the effect of different eLISA-like configurations on massive black hole detections. This work compares the results of a Bayesian inference study of 120 massive black hole binaries out to a redshift of $z\sim13$ for a $10^6$m arm-length eLISA with four and six links, as well as a $2\times10^6$m arm-length observatory with four links. We demonstrate that the original eLISA configuration should allow us to recover the luminosity distance of the source with an error of less than 10% out to a redshift of $z\sim4$, and a sky error box of $\leq10^2\,deg^2$ out to $z\sim0.1$. In contrast, both alternative configurations suggest that we should be able to conduct the same parameter recovery with errors of less than 10% in luminosity distance out to $z\sim12$ and $\leq10^2\,deg^2$ out to $z\sim0.4$. Using the information from these studies, we also infer that if we were able to construct a 2Gm, 6-link detector, the above values would shift to $z\sim20$ for luminosity distance and $z\sim0.9$ for sky error. While the final configuration will also be dependent on both technological and financial considerations, our study suggests that increasing the size of a two arm detector is a viable alternative to the inclusion of a third arm in a smaller detector. More importantly, this work further suggests no clear scientific loss between either choice.
- Feb 23 2015 gr-qc astro-ph.CO arXiv:1502.05735v1Massive black hole binaries are the primary source of gravitational waves (GW) for the future eLISA observatory. The detection and parameter estimation of these sources to high redshift would provide invaluable information on the formation mechanisms of seed black holes, and on the evolution of massive black holes and their host galaxies through cosmic time. The Fisher information matrix has been the standard tool for GW parameter estimation in the last two decades. However, recent studies have questioned the validity of using the Fisher matrix approach. For example, the Fisher matrix approach sometimes predicts errors of $\geq100\%$ in the estimation of parameters such as the luminosity distance and sky position. With advances in computing power, Bayesian inference is beginning to replace the Fisher matrix approximation in parameter estimation studies. In this work, we conduct a Bayesian inference analysis for 120 sources situated at redshifts of between $0.1\leq z\leq 13.2$, and compare the results with those from a Fisher matrix analysis. The Fisher matrix results suggest that for this particular selection of sources, eLISA would be unable to localize sources at redshifts of $z\lesssim6$. In contrast, Bayesian inference provides finite error estimations for all sources in the study, and shows that we can establish minimum closest distances for all sources. The study further predicts that we should be capable with eLISA, out to a redshift of at least $z\leq13$, of predicting a maximum error in the chirp mass of $\lesssim 1\%$, the reduced mass of $\lesssim20\%$, the time to coalescence of 2 hours, and to a redshift of $z\sim5$, the inclination of the source with a maximum error of $\sim60$ degrees.
- Jan 08 2015 gr-qc arXiv:1501.01529v1We investigate the dynamics of spinning binaries of compact objects at the next-to-leading order in the quadratic-in-spin effects, which corresponds to the third post-Newtonian order (3PN). Using a Dixon-type multipolar formalism for spinning point particles endowed with spin-induced quadrupoles and computing iteratively in harmonic coordinates the relevant pieces of the PN metric within the near zone, we derive the post-Newtonian equations of motion as well as the equations of spin precession. We find full equivalence with available results. We then focus on the far-zone field produced by those systems and obtain the previously unknown 3PN spin contributions to the gravitational-wave energy flux by means of the multipolar post-Minkowskian (MPM) wave generation formalism. Our results are presented in the center-of-mass frame for generic orbits, before being further specialized to the case of spin-aligned, circular orbits. We derive the orbital phase of the binary based on the energy balance equation and briefly discuss the relevance of the new terms.
- Nov 04 2014 gr-qc arXiv:1411.0598v1With the advance in computational resources, Bayesian inference is increasingly becoming the standard tool of practise in GW astronomy. However, algorithms such as Markov Chain Monte Carlo (MCMC) require a large number of iterations to guarantee convergence to the target density. Each chain demands a large number of evaluations of the likelihood function, and in the case of a Hessian MCMC, calculations of the Fisher information matrix for use as a proposal distribution. As each iteration requires the generation of at least one gravitational waveform, we very quickly reach a point of exclusion for current Bayesian algorithms, especially for low mass systems where the length of the waveforms is large and the waveform generation time is on the order of seconds. This suddenly demands a timescale of many weeks for a single MCMC. As each likelihood and Fisher information matrix calculation requires the evaluation of noise-weighted scalar products, we demonstrate that by using the linearity of integration, and the fact that more than 90% of the generation time is spent at frequencies less that one third of the maximum, we can construct composite integrals that speed up the MCMCs for comparable mass binaries by a factor of between 3.5 and 5.5, depending on the waveform length. This method is both source and detector type independent, and can be applied to any waveform that displays significant frequency evolution, such as stellar mass binaries with Advanced LIGO/Virgo, as well as supermassive black holes with eLISA
- Motivated by the parameterized post-Einsteinian (ppE) scheme devised by Yunes and Pretorius, which introduces corrections to the post-Newtonian coefficients of the frequency domain gravitational waveform in order to emulate alternative theories of gravity, we compute analytical time domain waveforms that, after a numerical Fourier transform, aim to represent (phase corrected only) ppE waveforms. In this formalism, alternative theories manifest themselves via corrections to the phase and frequency, as predicted by General Relativity (GR), at different post-Newtonian (PN) orders. In order to present a generic test of alternative theories of gravity, we assume that the coupling constant of each alternative theory is manifestly positive, allowing corrections to the GR waveforms to be either positive or negative. By exploring the capabilities of massive black hole binary GR waveforms in the detection and parameter estimation of corrected time domain ppE signals, using the current eLISA configuration (as presented for the ESA Cosmic Vision L3 mission), we demonstrate that for corrections arising at higher than 1PN order in phase and frequency, GR waveforms are sufficient for both detecting and estimating the parameters of alternative theory signals. However, for theories introducing corrections at the 0 and 0.5 PN order, GR waveforms are not capable of covering the entire parameter space, requiring the use of non-GR waveforms for detection and parameter estimation.
- Oct 27 2014 gr-qc arXiv:1410.6687v1Gravitational-wave parameter estimation is only as good as the theory the waveform generation models are based upon. It is therefore crucial to test General Relativity (GR) once data becomes available. Many previous works, such as studies connected with the ppE framework by Yunes and Pretorius, rely on the stationary phase approximation (SPA) to model deviations from GR in the frequency domain. As Fast Fourier Transform algorithms have become considerably faster and in order to circumvent possible problems with the SPA, we test GR with corrected time domain waveforms instead of SPA waveforms. Since a considerable amount of work has been done already in the field using SPA waveforms, we establish a connection between leading-order-corrected waveforms in time and frequency domain, concentrating on phase-only corrected terms. In a Markov Chain Monte Carlo study, whose results are preliminary and will only be available later, we will assess the ability of the eLISA detector to measure deviations from GR for signals coming from supermassive black hole inspirals using these corrected waveforms.
- Jun 27 2014 gr-qc astro-ph.IM arXiv:1406.6891v1The Gravitational Wave (GW) universe contains a wealth of sources which, with the proper treatment, will open up the universe as never before. By observing massive black hole binaries to high redshifts, we should begin to explore the formation process of seed black holes and track galactic evolution to the present day. Observations of extreme mass ratio inspirals will allow us to explore galactic centers in the local universe, as well as providing tests of General Relativity and constraining the value of Hubble's constant. The detection of compact binaries in our own galaxy may allow us to model stellar evolution in the Milky Way. Finally, the detection of cosmic (super)strings and a stochastic background would help us to constrain cosmological models. However, all of this depends on our ability to not only resolve sources and carry out parameter estimation, but also on our ability to define an optimal data analysis strategy. In this presentation, I will examine the challenges that lie ahead in GW astronomy for the ESA L3 Cosmic Vision mission, eLISA.
- May 27 2013 astro-ph.CO gr-qc arXiv:1305.5720v1The last century has seen enormous progress in our understanding of the Universe. We know the life cycles of stars, the structure of galaxies, the remnants of the big bang, and have a general understanding of how the Universe evolved. We have come remarkably far using electromagnetic radiation as our tool for observing the Universe. However, gravity is the engine behind many of the processes in the Universe, and much of its action is dark. Opening a gravitational window on the Universe will let us go further than any alternative. Gravity has its own messenger: Gravitational waves, ripples in the fabric of spacetime. They travel essentially undisturbed and let us peer deep into the formation of the first seed black holes, exploring redshifts as large as z ~ 20, prior to the epoch of cosmic re-ionisation. Exquisite and unprecedented measurements of black hole masses and spins will make it possible to trace the history of black holes across all stages of galaxy evolution, and at the same time constrain any deviation from the Kerr metric of General Relativity. eLISA will be the first ever mission to study the entire Universe with gravitational waves. eLISA is an all-sky monitor and will offer a wide view of a dynamic cosmos using gravitational waves as new and unique messengers to unveil The Gravitational Universe. It provides the closest ever view of the early processes at TeV energies, has guaranteed sources in the form of verification binaries in the Milky Way, and can probe the entire Universe, from its smallest scales around singularities and black holes, all the way to cosmological dimensions.
- We present a parameter estimation procedure based on a Bayesian framework by applying a Markov Chain Monte Carlo algorithm to the calibration of the dynamical parameters of a space based gravitational wave detector. The method is based on the Metropolis-Hastings algorithm and a two-stage annealing treatment in order to ensure an effective exploration of the parameter space at the beginning of the chain. We compare two versions of the algorithm with an application to a LISA Pathfinder data analysis problem. The two algorithms share the same heating strategy but with one moving in coordinate directions using proposals from a multivariate Gaussian distribution, while the other uses the natural logarithm of some parameters and proposes jumps in the eigen-space of the Fisher Information matrix. The algorithm proposing jumps in the eigen-space of the Fisher Information matrix demonstrates a higher acceptance rate and a slightly better convergence towards the equilibrium parameter distributions in the application to LISA Pathfinder data . For this experiment, we return parameter values that are all within $\sim1\sigma$ of the injected values. When we analyse the accuracy of our parameter estimation in terms of the effect they have on the force-per-unit test mass noise estimate, we find that the induced errors are three orders of magnitude less than the expected experimental uncertainty in the power spectral density.
- Oct 31 2012 gr-qc arXiv:1210.8066v1The extreme-mass-ratio inspirals (EMRIs) of stellar mass compact objects into massive black holes in the centres of galaxies are an important source of low-frequency gravitational waves for space-based detectors. We discuss the prospects for detecting these sources with the evolved Laser Interferometer Space Antenna (eLISA), recently proposed as an ESA mission candidate under the name NGO. We show that NGO could observe a few tens of EMRIs over its two year mission lifetime at redshifts z < 0.5 and describe how the event rate changes under possible alternative specifications of the eLISA design.
- Jun 13 2012 gr-qc arXiv:1206.2509v1Extreme Mass Ratio Inspirals (EMRIs) are one of the main gravitational wave (GW) sources for a future space detector, such as eLISA/NGO, and third generation ground-based detectors, like the Einstein Telescope. These systems present an interest both in astrophysics and fundamental physics. In order to make a high precision determination of their physical parameters, we need very accurate theoretical waveform models or templates. In the case of a circular equatorial orbit, the key stumbling block to the creation of these templates is the flux function of the GW. This function can be modeled either via very expensive numerical simulations, which then make the templates unusable for GW astronomy, or via some analytic approximation method such as a post-Newtonian approximation. This approximation is known to be asymptotically divergent and is only known up to 5.5PN order for the Schwarzschild case and to 4PN order for the Kerr case. A way to improve the convergence of the flux is to use re-summation methods. In this work we extend previous results using the Padé and Chebyshev approximations, first by taking into account the absorption of the GWs by the central black hole which was neglected in previous studies, and secondly by using the information from the Schwarzschild and absorption terms to create a Kerr flux up to 5.5PN order. We found that these two additions both improve the convergence. We also demonstrate that the best re-summation method for improving the flux model is based on a flux function which we call the "inverted Chebyshev approximation".
- Jun 05 2012 gr-qc astro-ph.CO arXiv:1206.0331v1The advanced interferometer network will herald a new era in observational astronomy. There is a very strong science case to go beyond the advanced detector network and build detectors that operate in a frequency range from 1 Hz-10 kHz, with sensitivity a factor ten better in amplitude. Such detectors will be able to probe a range of topics in nuclear physics, astronomy, cosmology and fundamental physics, providing insights into many unsolved problems in these areas.
- We review the expected science performance of the New Gravitational-Wave Observatory (NGO, a.k.a. eLISA), a mission under study by the European Space Agency for launch in the early 2020s. eLISA will survey the low-frequency gravitational-wave sky (from 0.1 mHz to 1 Hz), detecting and characterizing a broad variety of systems and events throughout the Universe, including the coalescences of massive black holes brought together by galaxy mergers; the inspirals of stellar-mass black holes and compact stars into central galactic black holes; several millions of ultracompact binaries, both detached and mass transferring, in the Galaxy; and possibly unforeseen sources such as the relic gravitational-wave radiation from the early Universe. eLISA's high signal-to-noise measurements will provide new insight into the structure and history of the Universe, and they will test general relativity in its strong-field dynamical regime.
- This document introduces the exciting and fundamentally new science and astronomy that the European New Gravitational Wave Observatory (NGO) mission (derived from the previous LISA proposal) will deliver. The mission (which we will refer to by its informal name "eLISA") will survey for the first time the low-frequency gravitational wave band (about 0.1 mHz to 1 Hz), with sufficient sensitivity to detect interesting individual astrophysical sources out to z = 15. The eLISA mission will discover and study a variety of cosmic events and systems with high sensitivity: coalescences of massive black holes binaries, brought together by galaxy mergers; mergers of earlier, less-massive black holes during the epoch of hierarchical galaxy and black-hole growth; stellar-mass black holes and compact stars in orbits just skimming the horizons of massive black holes in galactic nuclei of the present era; extremely compact white dwarf binaries in our Galaxy, a rich source of information about binary evolution and about future Type Ia supernovae; and possibly most interesting of all, the uncertain and unpredicted sources, for example relics of inflation and of the symmetry-breaking epoch directly after the Big Bang. eLISA's measurements will allow detailed studies of these signals with high signal-to-noise ratio, addressing most of the key scientific questions raised by ESA's Cosmic Vision programme in the areas of astrophysics and cosmology. They will also provide stringent tests of general relativity in the strong-field dynamical regime, which cannot be probed in any other way. This document not only describes the science but also gives an overview on the mission design and orbits.
- Dec 15 2011 gr-qc arXiv:1112.3222v1The inspiral of two compact objects in gravitational wave astronomy is described by a post-Newtonian expansion in powers of $(v/c)$. In most cases, it is believed that the post-Newtonian expansion is asymptotically divergent. A standard technique for accelerating the convergence of a power series is to re-sum the series by means of a rational polynomial called a Padé approximation. If we liken this approximation to a matrix, the best convergence is achieved by staying close to a diagonal Padé approximation. This broadly presents two subsets of the approximation : a super-diagonal approximation $P^M_N$ and a sub-diagonal approximation $P_M^N$, where $M = N+\epsilon$, and $\epsilon$ takes the values of 0 or 1. Left as rational polynomials, the coefficients in both the numerator and denominator need to be re-calculated as the order of the initial power series approximation is increased. However, the sub-diagonal Padé approximant is computationally advantageous as it can be expressed in terms of a Gauss-like continued fraction. Once in this form, each coefficient in the continued fraction is uniquely determined at each order. This means that as we increase the order of approximation of the original power series, we now have only one new additional coefficient to calculate in the continued fraction. While it is possible to provide explicit expressions for the continued fraction coefficients, they rapidly become unwieldy at high orders of approximation. It is also possible to numerically calculate the coefficients by means of ratios of Hankel determinants. However, these determinants can be ill-conditioned and lead to numerical instabilities. In this article, we present a method for calculating the continued fraction coefficients at arbitrary orders of approximation.
- Oct 11 2010 gr-qc arXiv:1010.1641v1In the last few years there has been an enormous effort in parameter estimation studies for different sources with the space based gravitational wave detector, LISA. While these studies have investigated sources of differing complexity, the one thing they all have in common is they assume continuous data streams. In reality, the LISA data stream will contain gaps from such possible events such as repointing of the satellite antennae, to discharging static charge build up on the satellites, to disruptions due to micro-meteor strikes. In this work we conduct a large scale Monte Carlo parameter estimation simulation for galactic binaries assuming data streams containing gaps. As the expected duration and frequency of the gaps are currently unknown, we have decided to focus on gaps of approximately one hour, occurring either once per day or once per week. We also study the case where, as well as the expected periodic gaps, we have a data drop-out of one continuous week. Our results show that for for galactic binaries, a gap of once per week introduces a bias of between 0.5% and 1% in the estimation of parameters, for the most important parameters such as the sky position, amplitude and frequency. This number rises to between 3% and 7% for the case of one gap a day, and to between 4% and 9% when we have one gap a day and a spurious gap of a week. A future study will investigate the effect of data gaps on supermassive black hole binaries and extreme mass ratio inspirals.
- May 31 2010 gr-qc arXiv:1005.5296v1One of the major assumptions in the search for gravitational wave signatures from massive and supermassive black hole binaries with LISA, is that these systems will have circularized before entering the LISA bandwidth. Current astrophysical simulations now suggest that systems could have a non-negligible eccentricity in the LISA band, and an important level of eccentricity in the Pulsar Timing regime. In this work, we use a set of source catalogues from astrophysically motivated models of massive black hole binary formation and assume a one year LISA mission lifetime. Depending on the model in question, the initial eccentricities in the final year of the inspiral can be as high as 0.6 for high mass seeds and 0.8 for low mass seeds. We show that restricted post-Newtonian circular templates are extremely inefficient in recovering eccentric binaries, with median optimal signal to noise ratio recoveries of approximately 10% for all models considered. This coupled with extremely large errors in parameter recovery from individual Markov chain Monte Carlo's demonstrate quite clearly that even to search for binaries with initial eccentricities as low as $10^{-4}$, we will require eccentric templates for LISA data analysis.
- Dec 04 2009 gr-qc arXiv:0912.0548v2The Mock LISA Data Challenges are a program to demonstrate LISA data-analysis capabilities and to encourage their development. Each round of challenges consists of one or more datasets containing simulated instrument noise and gravitational waves from sources of undisclosed parameters. Participants analyze the datasets and report best-fit solutions for the source parameters. Here we present the results of the third challenge, issued in Apr 2008, which demonstrated the positive recovery of signals from chirping Galactic binaries, from spinning supermassive--black-hole binaries (with optimal SNRs between ~ 10 and 2000), from simultaneous extreme-mass-ratio inspirals (SNRs of 10-50), from cosmic-string-cusp bursts (SNRs of 10-100), and from a relatively loud isotropic background with Omega_gw(f) ~ 10^-11, slightly below the LISA instrument noise.
- Oct 05 2009 gr-qc arXiv:0910.0373v1The development of search algorithms for gravitational wave sources in the LISA data stream is currently a very active area of research. It has become clear that not only does difficulty lie in searching for the individual sources, but in the case of galactic binaries, evaluating the fidelity of resolved sources also turns out to be a major challenge in itself. In this article we review the current status of developed algorithms for galactic binary, non-spinning supermassive black hole binary and extreme mass ratio inspiral sources. While covering the vast majority of algorithms, we will highlight those that represent the state of the art in terms of speed and accuracy.
- Oct 05 2009 gr-qc arXiv:0910.0380v1The Einstein Telescope is a proposed third generation gravitational wave detector that will operate in the region of 1 Hz to a few kHz. As well as the inspiral of compact binaries composed of neutron stars or black holes, the lower frequency cut-off of the detector will open the window to a number of new sources. These will include the end stage of inspirals, plus merger and ringdown of intermediate mass black holes, where the masses of the component bodies are on the order of a few hundred solar masses. There is also the possibility of observing intermediate mass ratio inspirals, where a stellar mass compact object inspirals into a black hole which is a few hundred to a few thousand times more massive. In this article, we investigate some of the data analysis challenges for the Einstein Telescope such as the effects of increased source number, the need for more accurate waveform models and the some of the computational issues that a data analysis strategy might face.
- The dynamical evolution of binaries of intermediate-massive black holes (IMBHs, massive black holes with a mass ranging between $10^2$ and $10^4 M_{\odot}$) in stellar clusters has recently received an increasing amount of attention. This is at least partially due to the fact that if the binary is hard enough to evolve to the phase at which it will start emitting gravitational waves (GWs) efficiently, there is a good probability that it will be detectable by future space-borne detectors like LISA. We study this evolution in the presence of rotation in the cluster. The eccentricity is strongly connected to the initial IMBHs velocities, and values of $\sim 0.7$ up to 0.9 are reached for low initial velocities, while almost circular orbits result if the initial velocities are increased. A Monte Carlo study indicates that these sources will be detectable by a detector such as LISA with median signal to noise ratios of between 10 and 20 over a three year period, although some events had signal to noise ratios of 300 or greater. Furthermore, one should also be able to estimate the chirp-mass with median fractional errors of $10^{-4}$, reduced mass on the order of $10^{-3}$ and luminosity distance on the order of $10^{-1}$. Finally, these sources will have a median angular resolution in the LISA detector of about 3 square degrees, putting events firmly in the field of view of future electromagnetic detectors such as LSST.
- Apr 10 2009 gr-qc astro-ph.IM arXiv:0904.1544v2We describe an application of the MultiNest algorithm to gravitational wave data analysis. MultiNest is a multimodal nested sampling algorithm designed to efficiently evaluate the Bayesian evidence and return posterior probability densities for likelihood surfaces containing multiple secondary modes. The algorithm employs a set of live points which are updated by partitioning the set into multiple overlapping ellipsoids and sampling uniformly from within them. This set of live points climbs up the likelihood surface through nested iso-likelihood contours and the evidence and posterior distributions can be recovered from the point set evolution. The algorithm is model-independent in the sense that the specific problem being tackled enters only through the likelihood computation, and does not change how the live point set is updated. In this paper, we consider the use of the algorithm for gravitational wave data analysis by searching a simulated LISA data set containing two non-spinning supermassive black hole binary signals. The algorithm is able to rapidly identify all the modes of the solution and recover the true parameters of the sources to high precision.
- Mar 24 2009 gr-qc arXiv:0903.3733v1We describe a hybrid evolutionary algorithm that can simultaneously search for multiple supermassive black hole binary (SMBHB) inspirals in LISA data. The algorithm mixes evolutionary computation, Metropolis-Hastings methods and Nested Sampling. The inspiral of SMBHBs presents an interesting problem for gravitational wave data analysis since, due to the LISA response function, the sources have a bi-modal sky solution. We show here that it is possible not only to detect multiple SMBHBs in the data stream, but also to investigate simultaneously all the various modes of the global solution. In all cases, the algorithm returns parameter determinations within $5\sigma$ (as estimated from the Fisher Matrix) of the true answer, for both the actual and antipodal sky solutions.
- Feb 25 2009 gr-qc astro-ph.CO arXiv:0902.4133v1The gravitational wave signal from a compact object spiralling toward a massive black hole (MBH) is thought to be one of the most difficult sources to detect in the LISA data stream. Due to the large parameter space of possible signals and many orbital cycles spent in the sensitivity band of LISA, it has been estimated previously that of the order of 10^35 templates would be required for a fully coherent search with a template grid, which is computationally impossible. Here we describe an algorithm based on a constrained Metropolis-Hastings stochastic search which allows us to find and accurately estimate parameters of isolated EMRI signals buried in Gaussian instrumental noise. We illustrate the effectiveness of the algorithm with results from searches of the Mock LISA Data Challenge round 1B data sets.
- The LISA Parameter Estimation (LISAPE) Taskforce was formed in September 2007 to provide the LISA Project with vetted codes, source distribution models, and results related to parameter estimation. The Taskforce's goal is to be able to quickly calculate the impact of any mission design changes on LISA's science capabilities, based on reasonable estimates of the distribution of astrophysical sources in the universe. This paper describes our Taskforce's work on massive black-hole binaries (MBHBs). Given present uncertainties in the formation history of MBHBs, we adopt four different population models, based on (i) whether the initial black-hole seeds are small or large, and (ii) whether accretion is efficient or inefficient at spinning up the holes. We compare four largely independent codes for calculating LISA's parameter-estimation capabilities. All codes are based on the Fisher-matrix approximation, but in the past they used somewhat different signal models, source parametrizations and noise curves. We show that once these differences are removed, the four codes give results in extremely close agreement with each other. Using a code that includes both spin precession and higher harmonics in the gravitational-wave signal, we carry out Monte Carlo simulations and determine the number of events that can be detected and accurately localized in our four population models.
- Sep 19 2008 gr-qc arXiv:0809.3218v1GGR News: - Remembering Wheeler, by Jim Isenberg; Research Briefs: - A Brief Summary of the WMAP5 Results, by Lyman Page; - Science with LIGO, by Maria Alessandra Papa; Conference Reports: - 7th LISA Symposium, by Edward K. Porter; - The Fourth Gulf Coast Gravity Conference, by Lior Burko
- Jun 13 2008 gr-qc arXiv:0806.2110v2The Mock LISA Data Challenges are a programme to demonstrate and encourage the development of LISA data-analysis capabilities, tools and techniques. At the time of this workshop, three rounds of challenges had been completed, and the next was about to start. In this article we provide a critical analysis of entries to the latest completed round, Challenge 1B. The entries confirm the consolidation of a range of data-analysis techniques for Galactic and massive--black-hole binaries, and they include the first convincing examples of detection and parameter estimation of extreme--mass-ratio inspiral sources. In this article we also introduce the next round, Challenge 3. Its data sets feature more realistic waveform models (e.g., Galactic binaries may now chirp, and massive--black-hole binaries may precess due to spin interactions), as well as new source classes (bursts from cosmic strings, isotropic stochastic backgrounds) and more complicated nonsymmetric instrument noise.
- Apr 22 2008 gr-qc arXiv:0804.3322v2We describe a search for the extreme-mass-ratio inspiral sources in the Round 1B Mock LISA Data Challenge data sets. The search algorithm is a Monte-Carlo search based on the Metropolis-Hastings algorithm, but also incorporates simulated, thermostated and time annealing, plus a harmonic identification stage designed to reduce the chance of the chain locking onto secondary maxima. In this paper, we focus on describing the algorithm that we have been developing. We give the results of the search of the Round 1B data, although parameter recovery has improved since that deadline. Finally, we describe several modifications to the search pipeline that we are currently investigating for incorporation in future searches.
- Apr 03 2008 gr-qc arXiv:0804.0332v1Massive black hole binaries are key targets for the space based gravitational wave interferometer LISA. Several studies have investigated how LISA observations could be used to constrain the parameters of these systems. Until recently, most of these studies have ignored the higher harmonic corrections to the waveforms. Here we analyze the effects of the higher harmonics in more detail by performing extensive Monte Carlo simulations. We pay particular attention to how the higher harmonics impact parameter correlations, and show that the additional harmonics help mitigate the impact of having two laser links fail, by allowing for an instantaneous measurement of the gravitational wave polarization with a single interferometer channel. By looking at parameter correlations we are able to explain why certain mass ratios provide dramatic improvements in certain parameter estimations, and illustrate how the improved polarization measurement improves the prospects for single interferometer operation.
- Nov 19 2007 gr-qc arXiv:0711.2667v1The Mock LISA Data Challenges are a program to demonstrate LISA data-analysis capabilities and to encourage their development. Each round of challenges consists of several data sets containing simulated instrument noise and gravitational-wave sources of undisclosed parameters. Participants are asked to analyze the data sets and report the maximum information about source parameters. The challenges are being released in rounds of increasing complexity and realism: in this proceeding we present the results of Challenge 2, issued in January 2007, which successfully demonstrated the recovery of signals from supermassive black-hole binaries, from ~20,000 overlapping Galactic white-dwarf binaries, and from the extreme-mass-ratio inspirals of compact objects into central galactic black holes.
- Jun 04 2007 gr-qc arXiv:0706.0114v3In order to improve the phasing of the comparable-mass waveform as we approach the last stable orbit for a system, various re-summation methods have been used to improve the standard post-Newtonian waveforms. In this work we present a new family of templates for the detection of gravitational waves from the inspiral of two comparable-mass black hole binaries. These new adiabatic templates are based on re-expressing the derivative of the binding energy and the gravitational wave flux functions in terms of shifted Chebyshev polynomials. The Chebyshev polynomials are a useful tool in numerical methods as they display the fastest convergence of any of the orthogonal polynomials. In this case they are also particularly useful as they eliminate one of the features that plagues the post-Newtonian expansion. The Chebyshev binding energy now has information at all post-Newtonian orders, compared to the post-Newtonian templates which only have information at full integer orders. In this work, we compare both the post-Newtonian and Chebyshev templates against a fiducially exact waveform. This waveform is constructed from a hybrid method of using the test-mass results combined with the mass dependent parts of the post-Newtonian expansions for the binding energy and flux functions. Our results show that the Chebyshev templates achieve extremely high fitting factors at all PN orders and provide excellent parameter extraction. We also show that this new template family has a faster Cauchy convergence, gives a better prediction of the position of the Last Stable Orbit and in general recovers higher Signal-to-Noise ratios than the post-Newtonian templates.
- Jan 31 2007 gr-qc arXiv:gr-qc/0701170v4The Mock Data Challenges (MLDCs) have the dual purpose of fostering the development of LISA data-analysis tools and capabilities and of demonstrating the technical readiness already achieved by the gravitational-wave community in distilling a rich science payoff from the LISA data. The first round of MLDCs has just been completed and the second-round data sets are being released shortly after this workshop. The second-round data sets contain radiation from an entire Galactic population of stellar-mass binary systems, from massive--black-hole binaries, and from extreme--mass-ratio inspirals. These data sets are designed to capture much of the complexity that is expected in the actual LISA data, and should provide a fairly realistic setting to test advanced data-analysis techniques, and in particular the global aspect of the analysis. Here we describe the second round of MLDCs and provide details about its implementation.
- Jan 31 2007 gr-qc arXiv:gr-qc/0701167v1The Mock LISA Data Challenge is a worldwide effort to solve the LISA data analysis problem. We present here our results for the Massive Black Hole Binary (BBH) section of Round 1. Our results cover Challenge 1.2.1, where the coalescence of the binary is seen, and Challenge 1.2.2, where the coalescence occurs after the simulated observational period. The data stream is composed of Gaussian instrumental noise plus an unknown BBH waveform. Our search algorithm is based on a variant of the Markov Chain Monte Carlo method that uses Metropolis-Hastings sampling and thermostated frequency annealing. We present results from the training data sets and the blind data sets. We demonstrate that our algorithm is able to rapidly locate the sources, accurately recover the source parameters, and provide error estimates for the recovered parameters.
- Jan 26 2007 gr-qc arXiv:gr-qc/0701139v3The Mock LISA Data Challenges (MLDCs) have the dual purpose of fostering the development of LISA data analysis tools and capabilities, and demonstrating the technical readiness already achieved by the gravitational-wave community in distilling a rich science payoff from the LISA data output. The first round of MLDCs has just been completed: nine data sets containing simulated gravitational wave signals produced either by galactic binaries or massive black hole binaries embedded in simulated LISA instrumental noise were released in June 2006 with deadline for submission of results at the beginning of December 2006. Ten groups have participated in this first round of challenges. Here we describe the challenges, summarise the results, and provide a first critical assessment of the entries.
- Dec 15 2006 gr-qc arXiv:gr-qc/0612091v3In this work we focus on the search and detection of Massive black hole binary (MBHB) systems, including systems at high redshift. As well as expanding on previous works where we used a variant of Markov Chain Monte Carlo (MCMC), called Metropolis-Hastings Monte Carlo, with simulated annealing, we introduce a new search method based on frequency annealing which leads to a more rapid and robust detection. We compare the two search methods on systems where we do and do not see the merger of the black holes. In the non-merger case, we also examine the posterior distribution exploration using a 7-D MCMC algorithm. We demonstrate that this method is effective in dealing with the high correlations between parameters, has a higher acceptance rate than previously proposed methods and produces posterior distribution functions that are close to the prediction from the Fisher Information matrix. Finally, after carrying out searches where there is only one binary in the data stream, we examine the case where two black hole binaries are present in the same data stream. We demonstrate that our search algorithm can accurately recover both binaries, and more importantly showing that we can safely extract the MBHB sources without contaminating the rest of the data stream.
- Sep 06 2006 gr-qc arXiv:gr-qc/0609015v1We introduce a new method for modelling the gravitational wave flux function of a test-mass particle inspiralling into an intermediate mass Schwarzschild black hole which is based on Chebyshev polynomials of the first kind. It is believed that these Intermediate Mass Ratio Inspiral events (IMRI) are expected to be seen in both the ground and space based detectors. Starting with the post-Newtonian expansion from Black Hole Perturbation Theory, we introduce a new Chebyshev approximation to the flux function, which due to a process called Chebyshev economization gives a model with faster convergence than either post-Newtonian or Padé based methods. As well as having excellent convergence properties, these polynomials are also very closely related to the elusive minimax polynomial. We find that at the last stable orbit, the error between the Chebyshev approximation and a numerically calculated flux is reduced, $< 1.8%$, at all orders of approximation. We also find that the templates constructed using the Chebyshev approximation give better fitting factors, in general $> 0.99$, and smaller errors, $< 1/10%$, in the estimation of the Chirp mass when compared to a fiducial exact waveform, constructed using the numerical flux and the exact expression for the orbital energy function, again at all orders of approximation. We also show that in the intermediate test-mass case, the new Chebyshev template is superior to both PN and Padé approximant templates, especially at lower orders of approximation.
- The gravitational wave signals from coalescing Supermassive Black Hole Binaries are prime targets for the Laser Interferometer Space Antenna (LISA). With optimal data processing techniques, the LISA observatory should be able to detect black hole mergers anywhere in the Universe. The challenge is to find ways to dig the signals out of a combination of instrument noise and the large foreground from stellar mass binaries in our own galaxy. The standard procedure of matched filtering against a grid of templates can be computationally prohibitive, especially when the black holes are spinning or the mass ratio is large. Here we develop an alternative approach based on Metropolis-Hastings sampling and simulated annealing that is orders of magnitude cheaper than a grid search. We demonstrate our approach on simulated LISA data streams that contain the signals from binary systems of Schwarzschild Black Holes, embedded in instrument noise and a foreground containing 26 million galactic binaries. The search algorithm is able to accurately recover the 9 parameters that describe the black hole binary without first having to remove any of the bright foreground sources, even when the black hole system has low signal-to-noise.
- May 16 2006 gr-qc arXiv:gr-qc/0605085v2The Laser Interferometer Space Antenna will be able to detect the inspiral and merger of Super Massive Black Hole Binaries (SMBHBs) anywhere in the Universe. Standard matched filtering techniques can be used to detect and characterize these systems. Markov Chain Monte Carlo (MCMC) methods are ideally suited to this and other LISA data analysis problems as they are able to efficiently handle models with large dimensions. Here we compare the posterior parameter distributions derived by an MCMC algorithm with the distributions predicted by the Fisher information matrix. We find excellent agreement for the extrinsic parameters, while the Fisher matrix slightly overestimates errors in the intrinsic parameters.
- Oct 31 2005 gr-qc arXiv:gr-qc/0510121v1We introduce a new template for the detection of gravitational waves from compact binary systems which is based on Chebyshev polynomials of the first kind. As well as having excellent convergence properties, these polynomials are also very closely related to the elusive minimax polynomial. In this study we have limited ourselves to the test-mass regime, where we model a test particle in a circular equatorial orbit around a Schwarzschild black hole. Our objective is to model the numerical gravitational wave flux function, starting with the post-Newtonian expansion from Black Hole Perturbation Theory. We introduce a new Chebyshev approximation to the flux function, which due to a process called Chebyshev economization gives a better model than either post-Newtonian or Pade based methods. A graphical examination of the new flux function shows that it gives an excellent fit to the numerical flux, but more importantly we find that at the last stable orbit the error is reduced, < 1.8%, at all orders of approximation. We also find that the templates constructed using the Chebyshev approximation give better fitting factors, in general > 0.99, and smaller errors, < 1/10%, in the estimation of the Chirp mass when compared to a fiducial exact waveform, constructed using the numerical flux and the exact expression for the orbital energy function, again at all orders of approximation. We also show that in the test-mass case, the new Chebyshev template is superior to both PN and Pade approximant templates, especially at lower orders of approximation.
- Aug 10 2005 gr-qc arXiv:gr-qc/0508032v1In this study we apply post-Newtonian (T-approximants) and resummed post-Newtonian (P-approximants) to the case of a test-particle in equatorial orbit around a Kerr black hole. We compare the two approximants by measuring their effectualness (i.e. larger overlaps with the exact signal), and faithfulness (i.e. smaller biases while measuring the parameters of the signal) with the exact (numerical) waveforms. We find that in the case of prograde orbits, T-approximant templates obtain an effectualness of ~0.99 for spins q < 0.75. For 0.75 < q < 0.95, the effectualness drops to about 0.82. The P-approximants achieve effectualness of > 0.99 for all spins up to q = 0.95. The bias in the estimation of parameters is much lower in the case of P-approximants than T-approximants. We find that P-approximants are both effectual and faithful and should be more effective than T-approximants as a detection template family when q > 0. For q < 0 both T- and P-approximants perform equally well so that either of them could be used as a detection template family. However, for parameter estimation, the P-approximant templates still outperforms the T-approximants.
- Apr 05 2005 gr-qc arXiv:gr-qc/0504012v2One of the main sources of gravitational waves for the LISA space-borne interferometer are galactic binary systems. The waveforms for these sources are represented by eight parameters, of which four are extrinsic, and four are intrinsic to the system. Geometrically, these signals exist in an 8-d parameter space. By calculating the metric tensor on this space, we calculate the number of templates needed to search for such sources. We show in this study that below a particular monochromatic frequency, we can ignore one of the intrinsic parameters and search over a 7-d space. Beyond this frequency, we have a sudden change in dimensionality of the parameter space from 7 to 8 dimensions, which results in a change in the scaling of the growth of template number as a function of monochromatic frequency.
- Feb 28 2005 gr-qc arXiv:gr-qc/0502114v2In this work we examine the Cauchy convergence of both post-Newtonian (T-approximant) and re-summed post-Newtonian (P-approximant) templates for the case of a test-mass orbiting a Kerr black hole along a circular equatorial orbit. The Cauchy criterion demands that the inner product between the $n$ and $n+1$ order approximation approaches unity, as we increase the order of approximation. In previous works, it has been shown that we achieve greater fitting factors and better parameter estimation using the P-approximant templates for both Schwarzschild and Kerr black holes. In this work, we show that the P-approximant templates also display a faster Cauchy convergence making them a superior template to the standard post-Newtonian templates.
- Jun 11 2004 gr-qc arXiv:gr-qc/0406038v1The standard post-Newtonian approximation to gravitational waveforms, called T-approximants, from non-spinning black hole binaries are known not to be sufficiently accurate close to the last stable orbit of the system. A new approximation, called P-approximants, is believed to improve the accuracy of the waveforms rendering them applicable up to the last stable orbit. In this study we apply P-approximants to the case of a test-particle in equatorial orbit around a Kerr black hole parameterized by a spin parameter q that takes values between -1 and 1. In order to assess the performance of the two approximants we measure their effectualness (i.e. larger overlaps with the exact signal), and faithfulness (i.e. smaller biases while measuring the parameters of the signal) with the exact (numerical) waveforms. We find that in the case of prograde orbits, that is orbits whose angular momentum is in the same sense as the spin angular momentum of the black hole, T-approximant templates obtain an effectualness of ~ 0.99 for spins q < 0.75. For 0.75 < q < 0.95, the effectualness drops to about 0.82. The P-approximants achieve effectualness of > 0.99 for all spins up to q = 0.95. The bias in the estimation of parameters is much lower in the case of P-approximants than T-approximants. We find that P-approximants are both effectual and faithful and should be more effective than T-approximants as a detection template family when q>0. For q<0 both T- and P-approximants perform equally well so that either of them could be used as a detection template family.
- Jul 24 2003 gr-qc arXiv:gr-qc/0307101v3Trying to detect the gravitational wave (GW) signal emitted by a type II supernova is a main challenge for the GW community. Indeed, the corresponding waveform is not accurately modeled as the supernova physics is very complex; in addition, all the existing numerical simulations agree on the weakness of the GW emission, thus restraining the number of sources potentially detectable. Consequently, triggering the GW signal with a confidence level high enough to conclude directly to a detection is very difficult, even with the use of a network of interferometric detectors. On the other hand, one can hope to take benefit from the neutrino and optical emissions associated to the supernova explosion, in order to discover and study GW radiation in an event already detected independently. This article aims at presenting some realistic scenarios for the search of the supernova GW bursts, based on the present knowledge of the emitted signals and on the results of network data analysis simulations. Both the direct search and the confirmation of the supernova event are considered. In addition, some physical studies following the discovery of a supernova GW emission are also mentioned: from the absolute neutrino mass to the supernova physics or the black hole signature, the potential spectrum of discoveries is wide.
- Jul 24 2003 gr-qc arXiv:gr-qc/0307100v3Network data analysis methods are the only way to properly separate real gravitational wave (GW) transient events from detector noise. They can be divided into two generic classes: the coincidence method and the coherent analysis. The former uses lists of selected events provided by each interferometer belonging to the network and tries to correlate them in time to identify a physical signal. Instead of this binary treatment of detector outputs (signal present or absent), the latter method involves first the merging of the interferometer data and looks for a common pattern, consistent with an assumed GW waveform and a given source location in the sky. The thresholds are only applied later, to validate or not the hypothesis made. As coherent algorithms use a more complete information than coincidence methods, they are expected to provide better detection performances, but at a higher computational cost. An efficient filter must yield a good compromise between a low false alarm rate (hence triggering on data at a manageable rate) and a high detection efficiency. Therefore, the comparison of the two approaches is achieved using so-called Receiving Operating Characteristics (ROC), giving the relationship between the false alarm rate and the detection efficiency for a given method. This paper investigates this question via Monte-Carlo simulations, using the network model developed in a previous article.
- Nov 19 2002 gr-qc arXiv:gr-qc/0211064v2Searching for a signal depending on unknown parameters in a noisy background with matched filtering techniques always requires an analysis of the data with several templates in parallel in order to ensure a proper match between the filter and the real waveform. The key feature of such an implementation is the design of the filter bank which must be small to limit the computational cost while keeping the detection efficiency as high as possible. This paper presents a geometrical method which allows one to cover the corresponding physical parameter space by a set of ellipses, each of them being associated to a given template. After the description of the main characteristics of the algorithm, the method is applied in the field of gravitational wave (GW) data analysis, for the search of damped sine signals. Such waveforms are expected to be produced during the de-excitation phase of black holes -- the so-called 'ringdown' signals -- and are also encountered in some numerically computed supernova signals.
- Oct 30 2002 gr-qc arXiv:gr-qc/0210098v2Filters developed in order to detect short bursts of gravitational waves in interferometric detector outputs are compared according to three main points. Conventional Receiver Operating Characteristics (ROC) are first built for all the considered filters and for three typical burst signals. Optimized ROC are shown for a simple pulse signal in order to estimate the best detection efficiency of the filters in the ideal case, while realistic ones obtained with filters working with several ``templates'' show how detection efficiencies can be degraded in a practical implementation. Secondly, estimations of biases and statistical errors on the reconstruction of the time of arrival of pulse-like signals are then given for each filter. Such results are crucial for future coincidence studies between Gravitational Wave detectors but also with neutrino or optical detectors. As most of the filters require a pre-whitening of the detector noise, the sensitivity to a non perfect noise whitening procedure is finally analysed. For this purpose lines of various frequencies and amplitudes are added to a Gaussian white noise and the outputs of the filters are studied in order to monitor the excess of false alarms induced by the lines. The comparison of the performances of the different filters finally show that they are complementary rather than competitive.
- Mar 07 2002 gr-qc arXiv:gr-qc/0203020v1The prior knowledge of the gravitational waveform from compact binary systems makes matched filtering an attractive detection strategy. This detection method involves the filtering of the detector output with a set of theoretical waveforms or templates. One of the most important factors in this strategy is knowing how many templates are needed in order to reduce the loss of possible signals. In this study we calculate the number of templates and computational power needed for a one-step search for gravitational waves from inspiralling binary systems. We build on previous works by firstly expanding the post-Newtonian waveforms to 2.5-PN order and secondly, for the first time, calculating the number of templates needed when using P-approximant waveforms. The analysis is carried out for the four main first-generation interferometers, LIGO, GEO600, VIRGO and TAMA. As well as template number, we also calculate the computational cost of generating banks of templates for filtering GW data. We carry out the calculations for two initial conditions. In the first case we assume a minimum individual mass of $1 M_{\odot}$ and in the second, we assume a minimum individual mass of $5 M_{\odot}$. We find that, in general, we need more P-approximant templates to carry out a search than if we use standard PN templates. This increase varies according to the order of PN-approximation, but can be as high as a factor of 3 and is explained by the smaller span of the P-approximant templates as we go to higher masses. The promising outcome is that for 2-PN templates the increase is small and is outweighed by the known robustness of the 2-PN P-approximant templates.