DALI sensitivity to streaming axion dark matter

This paper demonstrates that the DALI experiment, a next-generation wavy dark matter interferometer, possesses the sensitivity to detect fine-grained streaming axion dark matter substructures entering the Solar System across a two-decade mass bandwidth, effectively covering the photon coupling range of representative axion models.

The Gist

The Big Picture: Hunting for "Invisible" Ghosts

Imagine the universe is filled with a vast, invisible ocean of "dark matter." We know it's there because it holds galaxies together, but we can't see it, touch it, or smell it. For decades, scientists have been trying to catch a specific type of dark matter particle called the axion. Think of the axion as a tiny, ghostly whisper that moves through everything.

The paper discusses a new experiment called DALI (Dark-photons & Axion-Like particles Interferometer). While DALI was originally built to listen for the "background hum" of dark matter that fills our entire galaxy, this paper asks a different question: What if we catch a specific, fast-moving "stream" of these axions instead?

The Two Types of Axion "Weather"

To understand the paper's idea, imagine the dark matter in our galaxy isn't just a smooth, calm fog. Instead, it's like a river system with two very different types of water flow:

1. The Smooth Lake (Standard Halo): This is the usual view. Dark matter is spread out evenly, moving at a steady, moderate speed. Most experiments are designed to listen for this steady hum.
2. The Fast-Flowing Streams (Fine-Grained Streams): The paper suggests that, like tributaries feeding a river, there are billions of distinct, narrow "streams" of axions zooming through the galaxy. These streams are incredibly "cold" (meaning the particles aren't jiggling around much) and move in very specific directions.

The Two Ways DALI Can Catch Them

The authors propose two ways DALI could detect these streams, depending on where the experiment is standing relative to the Earth.

Scenario A: Catching the Stream Before It Hits Earth (Direct Detection)

Imagine a high-speed train (the axion stream) barreling toward a station (Earth).

• The Setup: DALI acts like a sensor placed right on the tracks just before the train arrives.
• The Advantage: Because the train is moving in a straight line and the passengers (axions) are all moving in perfect sync, the signal is very sharp and clear.
• The Challenge: These streams are thin. It's like trying to hear a whisper from a specific person in a crowded stadium. You have to be lucky enough to be standing in the exact right spot where the stream passes.

Scenario B: Catching the Stream After It Hits Earth (Gravitational Focusing)

Now, imagine that same train hits a giant, invisible funnel made by Earth's gravity.

• The Setup: As the axion stream passes Earth, our planet's gravity acts like a magnifying glass or a funnel, squeezing the stream together.
• The Result: Behind Earth, the axions get packed incredibly tightly. The density of these particles could increase by a factor of 100 million (10⁸).
• The Catch: To catch this super-dense "bunch" of axions, DALI has to be in the exact right place at the exact right time. It's like trying to catch a specific raindrop that has been focused by a magnifying glass; the rain is much heavier there, but the focused spot is very small and moves quickly.

How DALI Works (The "Radio" Analogy)

DALI is essentially a super-sensitive radio tuned to a very specific frequency.

• The Magic Trick: When an axion passes through a strong magnetic field inside DALI, it can magically transform into a tiny photon (a particle of light/radio wave).
• The Amplifier: DALI uses a special mirror system (a Fabry-Pérot interferometer) to bounce these radio waves back and forth, making the signal louder, much like an echo in a canyon.
• The Tuning: The experiment scans through different frequencies (like tuning a radio dial) to see if it can catch the axion "whisper."

What the Paper Actually Found

The authors ran the numbers to see if DALI is sensitive enough to catch these streams. Their conclusion is optimistic:

1. It's Possible: DALI is sensitive enough to detect these streams if they exist.
2. The Sweet Spot: The experiment can scan a wide range of axion masses (a "window" of possibilities) that covers the most popular theories about what axions are.
3. The Trade-off:
   • If you look for the direct streams (Scenario A), you have a better chance of finding some axions, but the signal is weaker.
   • If you look for the focused streams (Scenario B), the signal is massive (100 million times stronger), but the chance of the stream actually passing over your detector in a single day is very low (like winning a lottery).

The Bottom Line

The paper argues that while DALI was built to listen to the "ocean" of dark matter, it is also perfectly tuned to catch the "waves" (streams) if they crash into our solar system. Even though catching a focused stream is a rare event, the signal would be so loud that if it happens, DALI would definitely hear it. This opens up a new way to hunt for dark matter: not just looking for the background noise, but listening for the specific, high-pitched whistles of axion streams zooming past us.

Technical Summary

1. Problem Statement

• Dark Matter Substructures: While the standard halo model assumes a smooth, isotropic distribution of dark matter (DM) with a Maxwellian velocity dispersion (~300 km/s), cosmological simulations suggest the existence of "fine-grained streams" of DM. These streams possess extremely small primordial velocity dispersions (approx. $10^{-17}c$ for axions) and could number up to $10^{14}$ in the Galaxy.
• Gravitational Focusing (GF): These low-velocity streams are subject to significant gravitational focusing by solar system bodies, particularly Earth. This effect can amplify the local DM flux by factors up to $10^8$ in specific downstream regions, creating high-density "caustics."
• Detection Gap: Current axion haloscopes (like ADMX) are primarily optimized for the standard halo model. They often struggle to detect transient, coherent, high-density streams because their integration times and frequency resolutions are tuned for broad, isotropic signals. There is a need to evaluate the sensitivity of next-generation detectors to these specific, transient substructures.
• The DALI Experiment: The Dark-photons & Axion-Like particles Interferometer (DALI) is a proposed next-generation wavy DM interferometer. While its primary goal is searching for virialized DM, this paper investigates its potential to detect streaming axions, both directly and after gravitational focusing.

2. Methodology

The authors analyze the sensitivity of a DALI-like apparatus to axion streams using the following theoretical and experimental framework:

• Signal Model:

  • Axions are modeled as coherent waves: $a(t, x) = a_0 e^{i(p \cdot x - \omega t)}$.
  • The conversion of axions to photons occurs via the inverse Primakoff effect in a magnetic field ($B_0$), generating an electric field amplitude $E_0 \propto g_{a\gamma\gamma} B_0 a_0$.
  • The power spectral density is derived, incorporating the axion-photon coupling constant ($g_{a\gamma\gamma}$), magnetic field strength, and the DM distribution function ($f_{DM}$).

• Sensitivity Calculation:

  • The authors derive a sensitivity equation (Eq. 4) based on the Dicke radiometer equation: $SNR = P / (k_B T) \sqrt{t/\delta\nu}$.
  • Key parameters include the integration time ($t$), system temperature ($T_{sys}$), quality factor ($Q$), and bandwidth ($\delta\nu$).
  • Two Scenarios Analyzed:
    1. Direct Streams: DALI intercepts a stream before it passes Earth. These have low density ($\rho \sim 10^{-2}\rho_0$) but extremely narrow linewidths ($\sigma \sim 10^{-17}c$).
    2. Gravitationally Focused (GsF) Streams: DALI intercepts a stream after Earth's gravity has focused it. These have high density ($\rho \sim 10^6\rho_0$) but broader linewidths due to deflection ($\sigma \sim 10^{-10}c$).

• Instrumental Constraints:

  • The analysis accounts for the specific limitations of DALI, including its Fabry-Pérot interferometer design, dual-resonance capability, and electronic noise floors (specifically $1/f$ noise and gain fluctuations).
  • The minimum frequency bin width is determined by the data integration time ($\delta\nu_b \sim 1/t$).

3. Key Contributions

• Re-evaluation of DALI Capabilities: The paper demonstrates that DALI is not limited to standard halo searches but is uniquely suited to detect transient axion streams due to its high sensitivity and ability to handle narrow spectral features.
• Quantification of GF Effects: The authors compile a comprehensive table (Table I) estimating the probability of Earth-based experiments encountering GsF regions for various stream densities. They show that while high-density GsF regions are rare, lower-density streams are frequent enough to be statistically accessible.
• Resolution vs. Sensitivity Trade-off: The paper addresses the "spectral dilution" problem. For direct streams, the intrinsic linewidth is so narrow that the detector's resolution (limited by integration time) dominates. The authors show that for short-duration events ($t \sim 10$ s), the resolution is limited by the event duration rather than the velocity dispersion, allowing for effective detection.
• Dual-Mode Strategy: The study proposes a search strategy where the same DALI data can be processed via different pipelines: one optimized for the standard halo (broad bandwidth) and another optimized for transient streams (high resolution, short integration).

4. Results

• Sensitivity Projections:

  • Using benchmark parameters ($B_0 \approx 11.7$ T, $N=50$ layers, $T_{sys} \approx 1$ K, $SNR=5$), the authors project DALI's sensitivity over a stacked bandwidth of two decades in mass.
  • Figure 2 illustrates that DALI can probe the coupling strength ($g_{a\gamma\gamma}$) of representative QCD axion models (KSVZ and DFSZ) for both direct and focused streams.
  • The sensitivity fully spans the window defined by the coupling strength to photons for representative axion models.

• Event Probability:

  • For a stream with density $\rho \sim 0.01\rho_0$, the probability of a direct encounter is high, making it a prime candidate for direct probing.
  • For GsF regions with density $\rho \sim 10\rho_0$, the daily encounter probability is $\sim 6 \times 10^{-3}$. While lower, the massive flux amplification ($10^6$ to $10^8$) makes these events detectable if the stream velocity aligns with the detector ($\sim 20$ km/s).

• Noise Performance:

  • The study confirms that for integration times up to $10^{18}$ seconds (far exceeding the age of the universe), the radiometer remains stabilized against $1/f$ noise, validating the use of long integration times for these specific transient events.

5. Significance

• New Discovery Channel: This work establishes a "new potential discovery channel" for axion dark matter. It shifts the focus from static, isotropic halos to dynamic, coherent substructures (streams and clusters).
• Complementarity: The DALI experiment, by utilizing the same hardware but different data analysis pipelines, can simultaneously search for the standard halo and transient streams. This maximizes the scientific return of the instrument.
• Theoretical Validation: The results support the cosmological scenario where axion angular fields acquire propagating degrees of freedom in a post-inflationary universe, leading to the formation of these substructures.
• Feasibility: The paper proves that current and near-future technology (specifically the DALI prototype) is sensitive enough to detect these elusive, fine-grained streams, potentially solving the "missing" axion detection problem by looking in the right transient windows.

In conclusion, the paper argues that the DALI experiment is a powerful tool for detecting streaming axion dark matter, offering sensitivity that covers the full parameter space of representative axion models, specifically targeting the unique signatures of gravitationally focused and direct fine-grained streams.