Notes on the integration of numerical relativity waveforms

A primary goal of numerical relativity is to provide estimates of the wave strain, $h$, from strong gravitational wave sources, to be used in detector templates. The simulations, however, typically measure waves in terms of the Weyl curvature component, $\psi_4$. Assuming Bondi gauge, transforming to the strain $h$ reduces to integration of $\psi_4$ twice in time. Integrations performed in either the time or frequency domain, however, lead to secular non-linear drifts in the resulting strain $h$. These non-linear drifts are not explained by the two unknown integration constants which can at most result in linear drifts. We identify a number of fundamental difficulties which can arise from integrating finite length, discretely sampled and noisy data streams. These issues are an artifact of post-processing data. They are independent of the characteristics of the original simulation, such as gauge or numerical method used. We suggest, however, a simple procedure for integrating numerical waveforms in the frequency domain, which is effective at strongly reducing spurious secular non-linear drifts in the resulting strain.Comment: 23 pages, 10 figures, matches final published versio

Connecting Numerical Relativity and Data Analysis of Gravitational Wave Detectors

Gravitational waves deliver information in exquisite detail about astrophysical phenomena, among them the collision of two black holes, a system completely invisible to the eyes of electromagnetic telescopes. Models that predict gravitational wave signals from likely sources are crucial for the success of this endeavor. Modeling binary black hole sources of gravitational radiation requires solving the Eintein equations of General Relativity using powerful computer hardware and sophisticated numerical algorithms. This proceeding presents where we are in understanding ground-based gravitational waves resulting from the merger of black holes and the implications of these sources for the advent of gravitational-wave astronomy.Comment: Appeared in the Proceedings of 2014 Sant Cugat Forum on Astrophysics. Astrophysics and Space Science Proceedings, ed. C.Sopuerta (Berlin: Springer-Verlag

Characteristic extraction in numerical relativity: binary black hole merger waveforms at null infinity

The accurate modeling of gravitational radiation is a key issue for gravitational wave astronomy. As simulation codes reach higher accuracy, systematic errors inherent in current numerical relativity wave-extraction methods become evident, and may lead to a wrong astrophysical interpretation of the data. In this paper, we give a detailed description of the Cauchy-characteristic extraction technique applied to binary black hole inspiral and merger evolutions to obtain gravitational waveforms that are defined unambiguously, that is, at future null infinity. By this method we remove finite-radius approximations and the need to extrapolate data from the near zone. Further, we demonstrate that the method is free of gauge effects and thus is affected only by numerical error. Various consistency checks reveal that energy and angular momentum are conserved to high precision and agree very well with extrapolated data. In addition, we revisit the computation of the gravitational recoil and find that finite radius extrapolation very well approximates the result at \scri. However, the (non-convergent) systematic differences to extrapolated data are of the same order of magnitude as the (convergent) discretisation error of the Cauchy evolution hence highlighting the need for correct wave-extraction.Comment: 41 pages, 8 figures, 2 tables, added references, fixed typos. Version matches published version

Development of a SERS strategy to overcome the nanoparticle stabilisation effect in serum-containing samples: Application to the quantification of dopamine in the culture medium of PC-12 cells

The analysis of serum samples by surface-enhanced Raman spectroscopy (SERS) has gained ground over the last years. However, the stabilisation of colloids by the proteins contained in these samples has restricted their use in common practice, unless antibodies or aptamers are used. Therefore, this work was dedicated to the development of a SERS methodology allowing the analysis of serum samples in a simple and easy-to-implement way. This approach was based on the pre-aggregation of the colloid with a salt solution. Gold nanoparticles (AuNPs) were used as the SERS substrate and, owing to its physiopathological importance, dopamine was chosen as a model to implement the SERS approach. The presence of this neurotransmitter could be determined in the concentration range 0.5 to 50 ppm (2.64 – 264 μM) in the culture medium of PC-12 cells, with a R2 of 0.9874, and even at lower concentrations (0.25 ppm, 1.32 μM) in another matrix containing fewer proteins. Moreover, the effect of calcium and potassium on the dopamine exocytosis from PC-12 cells was studied. Calcium was shown to have a predominant and dose-dependent effect. Finally, PC-12 cells were exposed to dexamethasone in order to increase their biosynthesis and release of dopamine. This increase was monitored with the developed SERS approach

The Current Status of Binary Black Hole Simulations in Numerical Relativity

Since the breakthroughs in 2005 which have led to long term stable solutions of the binary black hole problem in numerical relativity, much progress has been made. I present here a short summary of the state of the field, including the capabilities of numerical relativity codes, recent physical results obtained from simulations, and improvements to the methods used to evolve and analyse binary black hole spacetimes.Comment: 14 pages; minor changes and corrections in response to referee

Triangulation of gravitational wave sources with a network of detectors

There is significant benefit to be gained by pursuing multi-messenger astronomy with gravitational wave and electromagnetic observations. In order to undertake electromagnetic follow-ups of gravitational wave signals, it will be necessary to accurately localize them in the sky. Since gravitational wave detectors are not inherently pointing instruments, localization will occur primarily through triangulation with a network of detectors. We investigate the expected timing accuracy for observed signals and the consequences for localization. In addition, we discuss the effect of systematic uncertainties in the waveform and calibration of the instruments on the localization of sources. We provide illustrative results of timing and localization accuracy as well as systematic effects for coalescing binary waveforms.Comment: 20 pages, 5 figure

Status of NINJA: the Numerical INJection Analysis project

The 2008 NRDA conference introduced the Numerical INJection Analysis project (NINJA), a new collaborative effort between the numerical relativity community and the data analysis community. NINJA focuses on modeling and searching for gravitational wave signatures from the coalescence of binary system of compact objects. We review the scope of this collaboration and the components of the first NINJA project, where numerical relativity groups shared waveforms and data analysis teams applied various techniques to detect them when embedded in colored Gaussian noise

Implications for the origin of GRB 051103 from LIGO observations

We present the results of a LIGO search for gravitational waves (GWs) associated with GRB 051103, a short-duration hard-spectrum gamma-ray burst (GRB) whose electromagnetically determined sky position is coincident with the spiral galaxy M81, which is 3.6Mpc from Earth. Possible progenitors for short-hard GRBs include compact object mergers and soft gamma repeater (SGR) giant flares. A merger progenitor would produce a characteristic GW signal that should be detectable at a distance of M81, while GW emission from an SGR is not expected to be detectable at that distance. We found no evidence of a GW signal associated with GRB 051103. Assuming weakly beamed γ-ray emission with a jet semi-angle of 30°, we exclude a binary neutron star merger in M81 as the progenitor with a confidence of 98%. Neutron star-black hole mergers are excluded with \u3e99% confidence. If the event occurred in M81, then our findings support the hypothesis that GRB 051103 was due to an SGR giant flare, making it one of the most distant extragalactic magnetars observed to date. © 2012 The American Astronomical Society. All rights reserved

All-sky search for gravitational-wave bursts in the second joint LIGO-Virgo run

We present results from a search for gravitational-wave bursts in the data collected by the LIGO and Virgo detectors between July 7, 2009 and October 20, 2010: data are analyzed when at least two of the three LIGO-Virgo detectors are in coincident operation, with a total observation time of 207 days. The analysis searches for transients of duration -1s over the frequency band 64-5000 Hz, without other assumptions on the signal waveform, polarization, direction or occurrence time. All identified events are consistent with the expected accidental background. We set frequentist upper limits on the rate of gravitational-wave bursts by combining this search with the previous LIGO-Virgo search on the data collected between November 2005 and October 2007. The upper limit on the rate of strong gravitational-wave bursts at the Earth is 1.3 events per year at 90% confidence. We also present upper limits on source rate density per year and Mpc3 for sample populations of standard-candle sources. As in the previous joint run, typical sensitivities of the search in terms of the root-sum-squared strain amplitude for these waveforms lie in the range ∼5×10-22Hz-1/2 to ∼1×10-20Hz-1/2. The combination of the two joint runs entails the most sensitive all-sky search for generic gravitational-wave bursts and synthesizes the results achieved by the initial generation of interferometric detectors. © 2012 American Physical Society

Beating the spin-down limit on gravitational wave emission from the Vela pulsar

We present direct upper limits on continuous gravitational wave emission from the Vela pulsar using data from the Virgo detector\u27s second science run. These upper limits have been obtained using three independent methods that assume the gravitational wave emission follows the radio timing. Two of the methods produce frequentist upper limits for an assumed known orientation of the star\u27s spin axis and value of the wave polarization angle of, respectively, 1.9 × 10-24 and 2.2 × 10-24, with 95% confidence. The third method, under the same hypothesis, produces a Bayesian upper limit of 2.1 × 10-24, with 95% degree of belief. These limits are below the indirect spin-down limit of 3.3 × 10-24 for the Vela pulsar, defined by the energy loss rate inferred from observed decrease in Vela\u27s spin frequency, and correspond to a limit on the star ellipticity of ∼10-3. Slightly less stringent results, but still well below the spin-down limit, are obtained assuming the star\u27s spin axis inclination and the wave polarization angles are unknown. © 2011. The American Astronomical Society. All rights reserved