Stochastic Tsunamis: Diffuse Scalar Background from Black Hole Formation ✛ ✦

The death of a massive star is not just the flash of a supernova, but also the birth of a black hole. There’s a hidden act in this cosmic drama: an ultralight scalar field — a hypothetical candidate for dark matter, first suspected after observations by Vera Rubin — envelops the star in a static configuration, like an invisible ripple on the ocean surface. While the star remains intact, the field is locked in a strained equilibrium, but the moment the core collapses into a singularity, its support vanishes, and the field races outward as a spherical wave — a true tsunami that has lost its seabed.

A single burst is a rare event. But the real intrigue is that collapses happen all the time: every second, between 10⁴ and 10⁵ massive stars perish in the universe. The event rate tracks the star formation rate in the past, and models of stellar evolution — accounting for the metallicity of progenitors — let us calculate the total contribution. Each collapse leaves behind a scalar echo, and over billions of years these waves overlap, giving rise to a stochastic diffuse background — a kind of orchestra of billions of percussion instruments.

Thanks to the expansion of the universe, discovered by Edwin Hubble, waves from distant sources are stretched — their frequency shifted toward the low end of the spectrum. The final background spectrum is described by an integral linking the source rate, spectral energy density, and redshift. Remarkably, the signal peak lies in the acoustic range of 1–1000 Hz. If our ears could pick up scalar perturbations, we would hear a constant hum — the noise of thousands of distant tsunamis sounding at once.

This mechanism strikingly resembles the stochastic backgrounds of gravitational waves and neutrinos, yet opens a completely new window into ultralight scalar physics. Even if scalars do not dominate dark matter, the background turns out to be almost independent of the field mass up to $10^{-13}$ eV — ten orders of magnitude higher than what is accessible in searches for single transients. Future atom interferometers (MAGIS-km, AEDGE) and gravitational-wave observatories could pick up this hum, turning the entire universe into a giant detector for the scalar shadow.

The prospect is thrilling: we need full relativistic modeling that accounts for dispersion and black hole horizon suppression, as well as strategies for processing the broadband signal. If, at redshift, the scalars slow down to nonrelativistic speeds, the background could concentrate into a narrow peak near the rest frequency — and then direct dark matter search experiments would gain a new target. Particle physics and astrophysics are converging ever closer, and scalar tsunamis could become the echo that finally reveals the nature of the invisible mass.