⚛️ phenomenology

Stochastic Tsunamis: Diffuse Scalar Background from Black Hole Formation

This paper proposes that the abrupt collapse of massive astrophysical objects into black holes releases accumulated static scalar fields as "scalar tsunamis," which accumulate over cosmic history to form a stochastic diffuse background in the 1–1000 Hz range, thereby extending experimental sensitivity to scalar masses up to $10^{-13}$ eV.

Original authors: Arturo de Giorgi, Joerg Jaeckel

Published 2026-07-15

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CC BY 4.0

Original authors: Arturo de Giorgi, Joerg Jaeckel

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, quiet ocean. For a long time, scientists have been looking for specific, loud splashes—like a single whale breaching the surface—to prove that invisible, ultra-light "scalar fields" (a type of dark matter candidate) exist. The problem? We might be unlucky. Maybe the nearest splash is too far away, or maybe the water is too calm right now.

But what if, instead of waiting for one big splash, we listened for the constant, gentle hum of millions of tiny ripples overlapping? That is the bold idea in this new paper by Arturo de Giorgi and Joerg Jaeckel. They suggest that the universe is actually filled with a "stochastic tsunami"—a diffuse, rolling background of scalar waves generated by the violent deaths of massive stars.

The Great Cosmic "Pop"

Here is how the tsunami starts. Imagine a massive star, like a giant balloon filled with a special, invisible gas (the scalar field). As long as the star exists, it holds this gas in place, creating a static, invisible cloud around it. But when the star runs out of fuel and collapses into a black hole, something dramatic happens. The black hole acts like a cosmic vacuum cleaner that swallows the star's core, but it also hides the "source" of that invisible gas behind its event horizon.

Suddenly, the gas has nowhere to go. It loses its anchor. The static cloud can't stay still anymore; it snaps free and rushes outward in a burst. The authors call this a "scalar tsunami."

The Accumulation Effect

In the past, researchers looked for these tsunamis from just one nearby star explosion (a supernova). But the paper argues that relying on a single event is like trying to hear a whisper in a hurricane; you need to be incredibly lucky to have a star explode close enough to Earth.

Instead, the authors suggest we look at the entire history of the universe. Think of it like a bucket. Every time a massive star collapses into a black hole across the cosmos, it drops a bucket of scalar waves into the cosmic ocean. Over billions of years, these billions of individual "tsunamis" have piled up. They haven't washed away; they have mixed together to form a permanent, rolling background noise that fills the universe today.

The Frequency of the Hum

The authors calculated what this background noise sounds like. They found that these waves are likely to be heard in a specific range of frequencies: between 1 and 1,000 Hz (1 to 10³ Hz). To put that in perspective, this is roughly the range of a low hum or a deep rumble, similar to the sound of a large engine or a distant thunderstorm, rather than a high-pitched squeak.

This background is special because it allows scientists to detect scalar fields that are much heavier than previously thought possible. While looking for single, nearby explosions could only detect very light fields (masses smaller than 10⁻²⁵ eV), this "diffuse background" method suggests we could detect fields up to 10⁻¹³ eV. That is ten orders of magnitude heavier! It's like being able to hear a heavy drum beat instead of just a tiny pin drop.

The Evidence and the "What Ifs"

The authors didn't just guess; they ran detailed simulations. They modeled two different types of "star clouds" before they collapsed:

Yukawa Profile: A cloud that fades out gradually, like a fog.
Compact Profile: A cloud that is tightly packed, like a solid ball.

They simulated the collapse of these clouds into black holes, accounting for the gravity of the new black hole and the fact that the universe is expanding (which stretches the waves). Their calculations show that even if only 10% of the star's mass is converted into this scalar energy, the resulting background would be strong enough to be detected by future experiments.

However, the paper is careful to note what it doesn't know. The exact strength of this signal depends on the "metallicity" of the stars (how heavy elements like iron are mixed in), which changes how much mass the star loses before it explodes. The authors show a range of possibilities based on different metal levels, meaning the signal could be slightly stronger or weaker, but it should still be there.

The Hunt is On

So, where do we listen? The paper points to a new generation of "listening devices" that are currently being built or planned. These include:

MAGIS-100 and MAGIS-km: Giant atom interferometers (using clouds of atoms to measure tiny changes).
AEDGE and AION-km: Similar atom-based detectors.
LIGO: The famous gravitational wave detector.

The authors suggest that these experiments, if they reach their planned sensitivity, could finally "hear" this cosmic hum. If they do, it would be a massive discovery, proving that the universe is filled with a relic background of scalar waves from black hole births.

The Bottom Line

This paper doesn't claim to have found the signal yet. It doesn't say, "We found it!" Instead, it says, "Here is a new, very promising way to look, and here is exactly where and how loud we expect to hear it." It suggests that by listening to the collective roar of the universe's history, rather than waiting for a single shout, we might finally catch a glimpse of the invisible dark matter that surrounds us. The authors are confident in their math and simulations, but the real proof will only come when the next generation of detectors turns on and starts listening to the cosmic ocean.

Title: Stochastic Tsunamis: Diffuse Scalar Background from Black Hole Formation
Authors: Arturo de Giorgi and Joerg Jaeckel

Problem Statement

Ultralight scalar fields are well-motivated dark matter candidates, yet direct detection efforts relying on their local background abundance face significant caveats: the local density may be too low, the field may be clumped in distant structures, or the scalar may constitute only a subdominant fraction of dark matter. While transient signals from specific cosmic events (e.g., black hole formation) offer an alternative detection channel, they are limited by two factors:

Dispersion: For scalar masses $m_\phi \gtrsim 1/r$ (where $r$ is the distance to the source), the signal disperses too much to be detected as a coherent transient. This limits transient searches to extremely light masses ( $m_\phi \lesssim 10^{-25}$ eV for nearby sources).
Event Rarity: Successful detection requires a "lucky" nearby candidate to undergo a violent collapse, making the search rate-limited.

This paper addresses whether the accumulation of these transient signals over cosmological history can form a detectable stochastic, diffuse background, thereby circumventing the limitations of dispersion and event rarity.

Methodology

The authors propose a mechanism where massive astrophysical objects (stars) source large static configurations of a scalar field. When such an object collapses into a black hole (e.g., via core-collapse supernova), the scalar field loses its source abruptly. The previously static configuration becomes dynamical, propagating outward as a "scalar tsunami."

The methodology involves:

Signal Modeling: The authors model the energy spectrum of the emitted scalar radiation for two initial field profiles:
- Yukawa-type: Arising from linear coupling to fermion bilinears ( $\phi \bar{\psi}\psi$ ), characterized by a potential $\phi(r) \propto e^{-m_\phi r}/r$ .
- Compact source: A toy model for fields with attractive self-interactions, non-zero only within a finite radius $R$ .
  The spectrum calculation includes the gravitational effects of the resulting black hole remnant, utilizing results from Ref. [28].
Cosmological Integration: The stochastic background abundance $\Omega(f)$ is computed by integrating the emitted energy spectrum over the cosmological history from redshift $z_*$ to the present. This accounts for the expansion of the universe (Hubble rate $H(z)$ ), redshift of frequencies, and the event rate density $R(z)$ of the sources.
Source Characterization: The primary sources identified are core-collapse supernovae (CCSN), binary neutron star mergers (BNSM), and neutron star-black hole mergers (NSBH). The authors determine that CCSN events dominate the rate by orders of magnitude and focus the analysis on them. The CCSN rate is derived from the Star Formation Rate (SFR) and the Initial Mass Function (IMF), accounting for the fraction of progenitors that form black holes and the mapping from progenitor mass to remnant mass, which depends on metallicity.
Experimental Comparison: The predicted stochastic signal is compared against the projected sensitivities of future experiments, including atom interferometers (MAGIS-100, MAGIS-km, AION-km, AEDGE) and gravitational wave detectors (LIGO). The authors recast dark matter constraints for broadband signals, applying a statistical enhancement factor ( $\sqrt{Q_{DM}}$ ) to account for the integration over independent frequency bins.

Key Contributions

Novel Mechanism: The paper proposes and quantifies the "scalar tsunami" mechanism as a source of a stochastic diffuse scalar background, distinct from the standard dark matter background or transient bursts.
Extended Mass Reach: By shifting from transient to stochastic analysis, the authors demonstrate that the dispersion limit is removed. This allows the probing of scalar masses up to $m_\phi \lesssim 10^{-13}$ eV, which is ten orders of magnitude larger than the limit for individual transient events ( $m_\phi \lesssim 10^{-25}$ eV).
Systematic Uncertainty Analysis: The study explicitly incorporates uncertainties related to the progenitor-to-remnant mass mapping (dependent on metallicity) and the initial mass function, presenting results as systematic bands rather than single curves.
Recasting Constraints: The authors provide a method to recast narrow-band dark matter experimental limits (which assume a monochromatic signal) to the broadband stochastic signal regime, accounting for the quality factor $Q_{DM}$ and the statistical benefits of combining frequency bins.

Results

Spectrum Characteristics: The stochastic background spectrum is peaked around a characteristic frequency $f_c \simeq R^{-1}$ , where $R$ is the source size (typically a few times the Schwarzschild radius). The signal is approximately mass-independent for masses up to $m_\phi \lesssim 10^{-13}$ eV.
Experimental Sensitivity: Future experiments, particularly MAGIS-km and AEDGE, are projected to have sensitivity to the Yukawa case at low frequencies. The predicted signal strength, assuming 10% of the progenitor mass is stored in the field, falls within the reach of these detectors.
Parameter Space: The analysis shows that the stochastic background can populate a region of parameter space that would otherwise require an extremely rare, nearby transient event to detect. The signal is robust across different source radii ( $R = 2R_s$ and $20R_s$ ) and metallicity assumptions.

Significance and Claims

The authors claim that this work establishes a complementary detection channel for ultralight scalar fields. By relying on a persistent, stochastic signal rather than a transient one, the approach:

Removes the dispersion limitation, enabling the search for heavier scalar masses ( $m_\phi \lesssim 10^{-13}$ eV).
Removes the need for "luck" regarding nearby sources, as the signal is an irreducible contribution accumulated over the entire cosmological history.
Extends experimental reach significantly beyond what is possible with transient searches alone.

The paper concludes that while extending the analysis to larger scalar masses requires more detailed modeling of the black hole source structure, the current framework successfully identifies a viable target for upcoming experiments. Furthermore, for heavier scalars, the signal may eventually redshift into the non-relativistic regime, concentrating into a narrow spectral feature that could be targeted by direct detection experiments optimized for dark matter.