Gravitational Wave Effects on Radio Spectral Lines of Atomic Hydrogen: Hyperfine Splitting and Broadening Mechanisms

arXiv:2503.13118v2 Announce Type: replace-cross Abstract: We explore the effects of gravitational waves (GWs) on hydrogen's radio spectral lines, focusing on the ground-state hyperfine transition and radiative transitions in highly excited Rydberg states. To analyze GW impacts on hyperfine structure, we derive Maxwell's equations in a gravitational-wave background using linearized gravity and the $3+1$ formalism. Our findings reveal that GWs induce energy shifts in hyperfine magnetic substates, modifying the 21 cm line. However, these energy shifts fall well below the detection limits of current radio astronomical instruments. For transitions in highly excited states, which produce radio recombination lines (RRL), the influence of GW manifests itself as spectral broadening, with the fractional linewidth for $\mathrm{H}n\alpha$ scaling as $\Delta\nu/\nu_0 \sim n^7\omega^2_{\mathrm{gw}}h(t)$. This suggests that RRLs could serve as probes for ultra-high-frequency GWs, particularly given that Rydberg atoms in the interstellar medium can reach quantum numbers above $n=100$. As an example of possibly detectable high frequency GW source, We investigate GWs emitted during the inspiral of planetary-mass primordial black hole binaries, where GW-induced broadening in RRLs could exceed natural broadening effects. Additionally, we examine the influence of the recently detected stochastic gravitational-wave background on hydrogen spectral lines.

Abstract:We explore the effects of gravitational waves (GWs) on hydrogen's radio spectral lines, focusing on the ground-state hyperfine transition and radiative transitions in highly excited Rydberg states. To analyze GW impacts on hyperfine structure, we derive Maxwell's equations in a gravitational-wave background using linearized gravity and the $3+1$ formalism. Our findings reveal that GWs induce energy shifts in hyperfine magnetic substates, modifying the 21 cm line. However, these energy shifts fall well below the detection limits of current radio astronomical instruments. For transitions in highly excited states, which produce radio recombination lines (RRL), the influence of GW manifests itself as spectral broadening, with the fractional linewidth for $\mathrm{H}n\alpha$ scaling as $\Delta\nu/\nu_0 \sim n^7\omega^2_{\mathrm{gw}}h(t)$. This suggests that RRLs could serve as probes for ultra-high-frequency GWs, particularly given that Rydberg atoms in the interstellar medium can reach quantum numbers above $n=100$. As an example of possibly detectable high frequency GW source, We investigate GWs emitted during the inspiral of planetary-mass primordial black hole binaries, where GW-induced broadening in RRLs could exceed natural broadening effects. Additionally, we examine the influence of the recently detected stochastic gravitational-wave background on hydrogen spectral lines.

General Relativity and Quantum Cosmology (gr-qc); High Energy Astrophysical Phenomena (astro-ph.HE); Quantum Physics (quant-ph)

arXiv:2503.13118 [gr-qc]

(or arXiv:2503.13118v2 [gr-qc] for this version)

https://doi.org/10.48550/arXiv.2503.13118 Focus to learn more arXiv-issued DOI via DataCite

Phys. Rev. D 112, 044061, 2025

https://doi.org/10.1103/9qjr-tfgp Focus to learn more DOI(s) linking to related resources

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Gravitational Wave Effects on Radio Spectral Lines of Atomic Hydrogen: Hyperfine Splitting and Broadening Mechanisms

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