Axion Dark Matter: Fine-Grained Substructure

• Fine-grained axion dark matter substructure is the intricate phase-space layout characterized by numerous cold, narrow streams and caustic rings.
• Models extend beyond the standard halo model by incorporating ensembles of streams with unique velocity dispersions and density profiles.
• High-resolution haloscope analyses can resolve narrow spectral signatures from these streams, enhancing sensitivity and informing early-Universe cosmology.

Fine-grained axion dark matter substructure refers to the ultra-detailed phase-space structure of axion dark matter at galactic and sub-galactic scales, characterized by a plethora of coherent flows or “streams,” dense tidal remnants of early subhalos, and sharp features such as caustic rings. Unlike cold dark matter modeled with a smooth Maxwellian velocity distribution, axion dark matter’s phase-space is highly structured, reflecting the non-linear folding of the early Universe’s nearly smooth phase-space sheet. This fine-grained substructure can, under certain conditions, have direct impact on the detectability of axion dark matter in laboratory experiments—most notably in haloscope searches—due to the unique spectral signatures these features imprint on the axion field.

1. Phase-space Structure and the Origin of Streams

Galactic dark matter halos are formed by the infall and virialization of dark matter particles whose six-dimensional phase-space sheet undergoes repeated stretching and folding under gravity. Each fold corresponds to a stream: a set of particles with nearly identical velocities and small intrinsic velocity dispersion. On solar-system scales, a cold collisionless dark matter model predicts an extremely large number of such streams (∼10¹⁴ at the solar radius for generic cold relics), each overlapping in physical space but separated in velocity.

For axion dark matter, especially produced in a post-inflationary scenario, an even richer phenomenology is found: early microhalos or “miniclusters” can form and are later tidally stripped as Galactic structure assembles. The debris from these disrupted miniclusters populates phase-space with hundreds to thousands of cold, high-density streams with low velocity dispersions (as small as σ_str ∼ 10⁻² km/s), with a typical stream density at the percent-level or lower compared to the local median (O'Hare et al., 18 Sep 2025).

2. Phenomenological Models of Fine-grained Substructure

To capture the observable consequences of this fine substructure, models move beyond the standard halo model (SHM), which assumes an isotropic, single-component Maxwellian velocity distribution:

$$f(\mathbf{v};\mathbf{v}_c, \sigma_v) = \frac{1}{(2\pi \sigma_v^2)^{3/2}} \exp\left(-\frac{|\mathbf{v} - \mathbf{v}_c|^2}{2 \sigma_v^2}\right)$$

and consider ensembles of streams:

• Monostream models: A single stream with small dispersion replaces the SHM.
• Multistream models: Sums over many streams, each with its own mean velocity $\mathbf{v}_{\text{str}}$ and small $\sigma_{\text{str}}$; densities may be equal or drawn from a distribution to reflect astrophysical expectations (such as the mass function of minicluster debris).
• Physical models: Post-inflationary axion production naturally yields a few hundred to a thousand discrete tidal streams with typical velocity dispersions $\sigma_{\text{str}} \sim 0.01$–$0.05$ km/s; only the densest streams (by mass fraction) need be modeled explicitly, as the rest blend into a quasi-smooth background (O'Hare et al., 18 Sep 2025).

3. Spectral Signatures in Axion Haloscope Experiments

The unique property of axion haloscope experiments is that the local axion field, being a classical oscillating field, directly inherits its frequency content from the kinetic energy distribution, with frequency

$\omega = m_a\left(1 + \frac{v^2}{2}\right)$

where $m_a$ is the axion mass and $v$ is the local dark matter speed. In typical haloscope experiments, the observed power spectrum (“lineshape”) from an axion signal is

$\langle S(\omega) \rangle = \frac{\mathcal{A} T}{2} \int_0^\infty dv\, f(v)\,\sinc^2 \left[\frac{T}{2}(\omega_v - \omega)\right]$

where $T$ is the integration time and $\mathcal{A}$ captures all experimental parameters.

The sinc² term arises from Fourier-transforming a finite time trace of the field. For large $T$ (high frequency resolution), this function approaches a $\delta$-function, accurately resolving the underlying velocity structure. Therefore, if $T$ is chosen such that the frequency resolution $\Delta\omega = 2\pi/T$ is smaller than or comparable to the intrinsic frequency spread of a stream, the power in that stream is concentrated in a small number of frequency bins; this increases the experimental signal-to-noise ratio in those bins (O'Hare et al., 18 Sep 2025).

In contrast, for short integration times (low resolution), the narrow stream features are smeared out, recovering a spectrum similar to the SHM. The “halo integral”

$$\eta = \left[ \int dv\, \frac{(f(v))^2}{v} \right]^{1/4}$$

quantifies the possible boost in sensitivity: fine-grained substructure, when resolved, can increase $\eta$ compared to the SHM value, leading to potentially greater experimental reach.

4. Statistical Detection Methods and Sensitivity Enhancement

Analyses in the fine-grained case use two approaches:

• Profile Likelihood Ratio (PLR): The signal plus background hypothesis is compared to background only, using models for $f(v)$ composed of sums of streams. In the $T \to \infty$ limit and with $N$ frequency bins, the test statistic (TS) scales as

$${\rm TS} \propto \frac{\mathcal{A}^2 T_{\text{tot}}}{m_a \mathcal{B}^2} \int dv\, \frac{(f(v))^2}{v}$$

with $\mathcal{B}$ the typical spectral noise level.

• Extreme Value Statistics (EVS): The maximum observed power in a frequency window is compared against the noise distribution. This approach is sensitive to rare, narrow stream peaks, allowing detection of “outlier” bins with significant excess even if the total signal amplitude is below that required for standard detection in the SHM (O'Hare et al., 18 Sep 2025).

If the local dark matter field includes streams with densities $0.1$–$1\%$ of the local average, and if experimenters analyze their data at high enough resolution to resolve the expected frequency width, then a substantial excess in a single frequency bin can surpass the detection threshold. This can make the axion discoverable at lower axion-photon coupling $g_{a\gamma}$ than predicted from a purely SHM-based analysis.

5. Theoretical and Observational Implications

The implications are twofold:

1. Experimental Strategy: Haloscope experiments such as ADMX and similar searches should systematically incorporate high-resolution frequency analysis to maximize sensitivity to narrow features from fine-grained streams. Complementary low-resolution analyses remain relevant for broad, SHM-like features.
2. Astrophysical Model Testing: The presence, density, and velocity width of fine-grained streams provide information on the cosmological origin of the axion field (pre- versus post-inflation, minicluster formation, tidal disruption history). The detection of discrete frequency peaks in haloscope spectra would inform models of early-Universe structure formation for axion dark matter and quantitate the survival and phase-space distribution of disrupted miniclusters (O'Hare et al., 18 Sep 2025).

Under some plausible scenarios, the dominant axion signal in an experiment could be attributable to a small number of easily-resolved streams, rather than the broad background predicted by the SHM.

6. Comparison with Other Probes of Fine-grained Substructure

In most direct-detection experiments for WIMPs or other particle dark matter, the ultra-fine folding of phase-space is irrelevant: the interaction rate is averaged over all velocity components, and the experiment is only sensitive to coarse-grained distributions. However, axion haloscopes are exceptional in that the conversion power at a given frequency is directly related to the amplitude of the oscillating axion field at that frequency, permitting unprecedented sensitivity to fine velocity features.

By contrast, astrophysical probes such as gravitational lensing or caustic ring searches are sensitive to much larger-scale features (∼parsec or greater) but do not directly resolve the velocity-space substructure on laboratory scales. Theoretical models—including those with caustic rings for axions as a Bose-Einstein condensate (Sikivie, 2010)—predict unique phase-space structures that could motivate dedicated searches for narrow frequency spikes in laboratory data.

7. Motivation for High-resolution Haloscope Analyses

The experimental and theoretical insights outlined motivate a paradigm shift for haloscope collaborations: by supplementing broadband (SHM) searches with high--frequency resolution analysis tailored to the potential existence of fine-grained structure, experiments can target models and parameter space that would otherwise remain out of reach. Such an approach is particularly promising for:

• Post-inflationary axion scenarios with disrupted minicluster tidal streams,
• Generic cold dark matter models with immense numbers of fine-phase-space folds,
• Scenarios with enhanced substructure arising from early-Universe processes (e.g., early matter domination, isocurvature fluctuations).

In conclusion, fine-grained axion dark matter substructure materially affects both the theoretical modeling of dark matter in galactic halos and the practical strategies adopted in axion search experiments. Its inclusion in data analysis pipelines is empirically justified and may be essential for discovery in a substantial class of viable axion dark matter models (O'Hare et al., 18 Sep 2025).