arXiv : Gravitational waves from decaying sources in strong phase transitions

Caprini, Chiara; Jinno, Ryusuke; Stomberg, Isak; Roper Pol, Alberto; Rubira, Henrique; Konstandin, Thomas

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Preprint
Report number	arXiv:2409.03651
Title	Gravitational waves from decaying sources in strong phase transitions
Author(s)	Caprini, Chiara (Geneva U. ; CERN) ; Jinno, Ryusuke (Kobe U.) ; Konstandin, Thomas (DESY) ; Roper Pol, Alberto (Geneva U.) ; Rubira, Henrique (Munich, Tech. U.) ; Stomberg, Isak (DESY)
Document contact	Contact: arXiv
Imprint	2024-09-05
Number of pages	55
Note	55 pages, 15 figures
Subject category	astro-ph.CO ; Astrophysics and Astronomy ; gr-qc ; General Relativity and Cosmology
Abstract	We study the generation of gravitational waves (GWs) during a first-order cosmological phase transition (PT) using the recently introduced Higgsless approach to numerically evaluate the fluid motion induced by the PT. We present for the first time spectra from strong first-order PTs ($\alpha = 0.5$), alongside weak ($\alpha = 0.0046$) and intermediate ($\alpha = 0.05$) transitions previously considered in the literature. We test the regime of applicability of the stationary source assumption, characteristic of the sound-shell model, and show that it agrees with our numerical results when the kinetic energy, sourcing GWs, does not decay with time. However, we find in general that for intermediate and strong PTs, the kinetic energy in our simulations decays following a power law in time, and provide a theoretical framework that extends the stationary assumption to one that allows to include the time evolution of the source. This decay of the kinetic energy, potentially determined by non-linear dynamics and hence, related to the production of vorticity, modifies the usually assumed linear growth with the source duration to an integral over time of the kinetic energy fraction, effectively reducing the growth rate. We validate the novel theoretical model with the results of our simulations covering a broad range of wall velocities. We provide templates for the GW amplitude and spectral shape for a broad range of PT parameters.
Other source	Inspire
Copyright/License	preprint: (License: CC BY 4.0)

$Velocity (upper panel), enthalpy fluctuations (middle panel), and vorticity (lower panel) in an $xy$-plane slice of the simulation volume at $z = 0$ and at different times $\tilde t$, for a strong PT with $\alpha = 0.5$ and wall velocity $\vw = 0.36$, which corresponds to a deflagration (see \Fig{fig:1d_profiles}).$ $Plots showing the kinetic energy fraction $K$ and the integrated GW spectrum ${\cal I}_{\rm sim}^{\rm int}$ as a function of grid spacing $\delta{\tilde{x}}/\vw = (\tilde L/\vw)/N$ for runs with $\tilde L/\vw = 20$. Upper and middle panels respectively show $K$ at the time when all the simulation domain is in the broken phase around $\tilde t_0 \simeq 10$, $K_0$, and its rms value, $K_{\rm rms}\, \equiv K_{\rm int}/\tilde T_{\rm GW}^{1/2}$, both normalized by the single-bubble kinetic energy fraction $K_\xi$ [see \Eq{Kxi}]. Lower panel shows ${\cal I}_{\rm sim}^{\rm int}$ normalized by a reference value $\tilde \Omega_{\rm GW} \sim 10^{-2}$ \cite{Hindmarsh:2013xza,Hindmarsh:2015qta,Hindmarsh:2017gnf}, and by $\tilde T_{\rm GW} K_\xi^2 R_\ast \beta$, based on the expected scaling of \Eq{OmGW_general}. Both $K_{\rm rms}$ and ${\cal I}_{\rm sim}^{\rm int}$ are computed for $\tilde t_{\rm init} = 16$ and $\tilde t_{\rm end} = 32$, with $\tilde T_{\rm GW} = 16$. Left, middle, and right columns are weak, intermediate, and strong PTs respectively. Solid lines show the least-squares fits of the extrapolation scheme given in \Eq{eq:E_kin_convergence} when the fit is valid, while dotted lines indicate the numerical trend when the fit is not valid (see footnote \ref{trend_N}). Stars indicate the extrapolated values at $\delta{\tilde{x}} \to 0$.$ $Plots showing the kinetic energy fraction $K$ and the integrated GW spectrum ${\cal I}_{\rm sim}^{\rm int}$ as a function of grid spacing $\delta{\tilde{x}}/\vw = (\tilde L/\vw)/N$ for runs with $\tilde L/\vw = 20$. Upper and middle panels respectively show $K$ at the time when all the simulation domain is in the broken phase around $\tilde t_0 \simeq 10$, $K_0$, and its rms value, $K_{\rm rms}\, \equiv K_{\rm int}/\tilde T_{\rm GW}^{1/2}$, both normalized by the single-bubble kinetic energy fraction $K_\xi$ [see \Eq{Kxi}]. Lower panel shows ${\cal I}_{\rm sim}^{\rm int}$ normalized by a reference value $\tilde \Omega_{\rm GW} \sim 10^{-2}$ \cite{Hindmarsh:2013xza,Hindmarsh:2015qta,Hindmarsh:2017gnf}, and by $\tilde T_{\rm GW} K_\xi^2 R_\ast \beta$, based on the expected scaling of \Eq{OmGW_general}. Both $K_{\rm rms}$ and ${\cal I}_{\rm sim}^{\rm int}$ are computed for $\tilde t_{\rm init} = 16$ and $\tilde t_{\rm end} = 32$, with $\tilde T_{\rm GW} = 16$. Left, middle, and right columns are weak, intermediate, and strong PTs respectively. Solid lines show the least-squares fits of the extrapolation scheme given in \Eq{eq:E_kin_convergence} when the fit is valid, while dotted lines indicate the numerical trend when the fit is not valid (see footnote \ref{trend_N}). Stars indicate the extrapolated values at $\delta{\tilde{x}} \to 0$.$ Show more plots

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Record created 2024-10-09, last modified 2024-10-11

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