Narrowing Down Sources of High-Frequency Gravitational Waves

TL;DR

This work addresses the challenge of identifying detectable high-frequency gravitational-wave (HFGW) sources by adopting a model-independent, energy-conservation framework that emphasizes locality. By relating GW energy flux to measurable mass-loss rates in the Milky Way, Solar System, and Earth, the authors derive robust bounds that tightly constrain the admissible $(M,L,f,d)$ parameter space for HF sources and show that detectable signals above ~1 MHz must originate within the Solar System, or nearby Galactic environments for lower HF. They introduce a simple source parametrization and map out the detectable region, highlighting centers of mass such as the Earth or Sun as optimal sites and analyzing accompanying effects like sound waves and gravitational memory. A concrete plausibility scenario—spinning non-axisymmetric dark composites (“spinning footballs”)—is discussed as a flexible template capable of spanning the relevant parameter space, with production, trapping, and energy-dissipation considerations. Overall, the paper provides a principled guide for narrowing the theory space and guiding experimental strategies in the quest for HFGWs.

Abstract

Detecting gravitational waves above 100 kHz would constitute a major discovery, as any observable signal would have to arise from new physics within the late universe. Although many technologies have been identified to explore this high-frequency regime, the known landscape of promising sources remains extremely sparse. In this work, we aim to rectify this issue by providing model-independent arguments that highlight the most interesting parts of theory space, while remaining agnostic of the specific signal mechanism. For example, energy-conservation implies that gravitational waves detectable by future experiments well above a MHz would most likely have to originate from within the Solar System. Based on these arguments, we also constrain the physical properties of such sources.

Figures (3)

• Figure 1: Viable parameter space and experimental sensitivity to the strain amplitude $h_0$ (left panel) or root-sum-squared amplitude $h_\text{rss}$ (right panel) for a continuous (left panel) or burst-like (right panel) signal of frequency $f$. The colored shaded regions indicate parameters consistent with the mass-loss constraints of Eq. \ref{['eq:MdotUB']}, for sources localized within the Earth (blue), a Sun-Earth distance (orange), or within the Milky Way (purple). For burst-like signals in the right panel, we also demand that there is on-average at least one event per observation time $t_\text{obs} = 1 \ \text{yr}$. For comparison, we overlay limits from the Holometer experiment Holometer:2016qoh (shaded black) as well as projected sensitivities of various proposed detectors Domcke:2024mfuSchnabel:2024hemDomcke:2024etiDomcke:2023batDeMiguel:2023nmzRingwald:2020ist (collectively shown as the dashed gray line).
• Figure 2: Allowed values of the source mass $M$ and distance to the source $d$ for a gravitational wave signal frequency of $f = 1 \ \text{MHz}$ (left panel) or $f = 1 \ \text{GHz}$ (right panel). For each choice of $M$ and $d$, the size $L$ of the source is allowed to float in the range consistent with the restrictions of Eq. \ref{['eq:Lrange']}. In the green region, sources satisfying the self-consistency and energy-loss constraints of Sec. \ref{['sec:MLFd']} are detectable by an experiment with an observation time of $t_\text{obs} = 1 \ \text{yr}$ and strain-equivalent noise spectral density $S_n = 10^{-40} \ \text{Hz}^{-1}$. In the shaded gray regions, we show a collection of bounds on the static effect of exotic dark masses bound to the Solar System that extend outside of the Sun or Earth. These include limits from planets, asteroids, spacecraft, Voyager ranging to Uranus, as well as Moon and Earth-bound artificial satellites. The blue, orange, and purple regions show the allowed range of masses for a source bound to the center of the Earth, Sun, and Milky Way, respectively.
• Figure 3: Allowed characteristic size $L$ and mass $M$ of detectable HFGW sources at the center of the Earth (shaded blue) or Sun (shaded orange), with frequency $f=1\ \text{MHz}$ (left panel) or $f=1\ \text{GHz}$ (right panel). The steeper/flatter SNR=1 lower boundaries correspond to sound-wave/GW dissipation, respectively. The source mass is limited to be $M\lesssim 10^{-1} \ M_\oplus$ inside the Earth and $M\lesssim 10^{-2} \ M_\odot$ inside the Sun. The largest possible $M$ for a given $L$ is further limited by $r_s=2GM\lesssim L$. The upper limits on $L$ are set by superluminality avoidance ($Lf\lesssim 1$), and limits on the average GW luminosity from Eq. \ref{['eq:LGWbarlimits']} (see also Eq. \ref{['eq:LGWlimitonSNR']}). For $f=1\ \text{GHz}$, there is no viable parameter space for a detectable source located at the center of the Sun.