J. V. is supported by the Spanish Ministry of Universities Grant No. FPU22/02211. M. R.-S. is supported by the Spanish Ministry of Universities Grant No. FPU21/05009. R. T. is supported by European Research Council (ERC) Starting Grant No. 945155–GWmining, Cariplo Foundation Grant No. 2021-0555, Ministero dell’Università e della Ricerca (MUR) Progetti di Ricerca di Interesse Nazionale (PRIN) Grant No. 2022-Z9X4XS, MUR Grant “Progetto Dipartimenti di Eccellenza 2023-2027” (BiCoQ), and the ICSC National Research Centre funded by NextGenerationEU. This work was supported by the Universitat de les Illes Balears (UIB); the Spanish Agencia Estatal de Investigación Grants No. PID2022-138626NB-I00, No. RED2022-134204-E, and No. RED2022-134411-T, funded by Ministerio de Ciencia, Innovación y Universidades (MICIU)/Agencia Estatal de Investigación (AEI)/10.13039/501100011033, by the European Social Fund Plus (ESF+) and European Regional Development Fund (ERDF)/EU; the MICIU with funding from the European Union NextGenerationEU/Plan de Recuperación, Transformación y Resiliencia (PRTR) (PRTR-C17.I1); the Comunitat Autònoma de les Illes Balears through the Direcció General de Recerca, Innovació I Transformació Digital with funds from the Tourist Stay Tax Law (PDR2020/11-ITS2017-006), the Conselleria d’Economia, Hisenda i Innovació Grants No. SINCO2022/18146 and No. SINCO2022/6719, cofinanced by the European Union and Fondo Europeo de Desarrollo Regional (FEDER) Operational Program 2021–2027 of the Balearic Islands. This paper has been assigned document number LIGO-P2400263.

Gravitational-wave memory is characterized by a signal component that persists after a transient signal has decayed. Treating such signals in the frequency domain is nontrivial, since discrete Fourier transforms assume periodic signals on finite time intervals. In order to reduce artifacts in the Fourier transform, it is common to use recipes that involve windowing and padding with constant values. Here, we discuss how to regularize the Fourier transform in a straightforward way by splitting the signal into a given sigmoid function that can be Fourier transformed in closed form and a residual which does depend on the details of the gravitational-wave signal and has to be Fourier transformed numerically but does not contain a persistent component. We provide a detailed discussion of how to map between continuous and discrete Fourier transforms of signals that contain a persistent component. We apply this approach to discuss the frequency-domain phenomenology of the (ℓ =2,𝑚 =0) spherical harmonic mode, which contains both a memory and an oscillatory ringdown component.

Published in PRD under the title "Frequency-domain analysis of gravitational-wave memory waveforms"

Peer reviewed