![]() In a companion work, we apply this technique to search for exotic objects beyond the standard model known as Proca stars which, if real, may account for part of what we know as dark matter. Moreover, as the number of gravitational wave detections quickly increases, we can now reliably compare them to any simulations that supercomputers can deliver. While this may seem a trivial change, this allows us to use numerical simulations as is, making them free from unavoidable integration errors. We flip things around: Rather than taking integrals on our simulations, we propose taking derivatives on the detector data. Here, we present a simple way to avoid these errors, allowing for studies of a wider range of astrophysical phenomena. While this sounds easy enough, this operation is subject to well-known errors that we have under control for only a handful of systems we simulate. Therefore, obtaining the strain requires us to take two integrals. However, most simulations do not provide us with the strain directly but a related parameter, known as the Newman-Penrose scalar, which tracks the “acceleration” of spacetime. Researchers then deduce the origin of the waves by comparing these measurements to predictions for the strain produced by possible sources, much like the popular Shazam app tells you which song is being played. These detectors measure the subtle stretching and squeezing of spacetime, known as strain. to the LIGO and Virgo detectors, researchers now regularly observe ripples in spacetime known as gravitational waves, which are caused by catastrophic cosmic events such as black-hole mergers, star explosions, or the big bang itself.8Department of Electrical Engineering (ESAT), KU Leuven, Kasteelpark Arenberg 10, B-3001 Leuven, Belgium.7Institute for Theoretical Physics, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium.6Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai, Maharashtra 400076, India.5Observatori Astronòmic, Universitat de València, C/ Catedrático José Beltrán 2, 46980 Paterna (València), Spain.4Departamento de Matemática da Universidade de Aveiro and Centre for Research and Development in Mathematics and Applications (CIDMA), Campus de Santiago, 3810-183 Aveiro, Portugal.Moliner 50, 46100 Burjassot (València), Spain 3Departamento de Astronomía y Astrofísica, Universitat de València, Dr.2Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong.1Instituto Galego de Física de Altas Enerxías, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Galicia, Spain.Font 3,5, Carlos Herdeiro 4, Eugen Radu 4, and Tjonnie G. F. Leong 2, Alejandro Torres-Forné 3,5, Koustav Chandra 6, José A. Wong 2,†, Nicolas Sanchis-Gual 3,4, Samson H. W. Juan Calderón Bustillo 1,2,*, Isaac C. F. We remove the need to obtain strain waveforms from numerical relativity simulations, avoiding the associated systematic errors. Finally, we show that our framework fixes significant biases in the interpretation of the high-mass gravitational-wave trigger S200114f arising from the usage of strain templates. We find, however, that integration errors would strongly impact our analysis if GW190521 was 4 times louder. Next, we reanalyze the event GW190521 under the hypothesis of a Proca-star merger, obtaining results equivalent to those previously published, where we used the classical strain framework. We first demonstrate this formalism, and the impact of integration artifacts in strain templates, through the recovery of numerically simulated signals from head-on collisions of Proca stars injected in Advanced LIGO noise. ![]() By taking second-order finite differences on the detector data and inferring the corresponding background noise distribution, we develop a framework to perform gravitational-wave data analysis directly using ψ 4 ( t ) templates. ![]() Therefore, obtaining strain templates involves an integration process that introduces artifacts that need to be treated in a rather manual way. These, however, commonly output a quantity known as the Newman-Penrose scalar ψ 4 ( t ) which, under the Bondi gauge, is related to the gravitational-wave strain by ψ 4 ( t ) = d 2 h ( t ) / d t 2. Detection and parameter inference of gravitational-wave signals from compact mergers rely on the comparison of the incoming detector strain data d ( t ) to waveform templates for the gravitational-wave strain h ( t ) that ultimately rely on the resolution of Einstein’s equations via numerical relativity simulations.
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