Diffuse Dark Flux Hypothesis Overview

• The Diffuse Dark Flux Hypothesis is a framework that defines non-luminous dark sector particle fluxes from both astrophysical events and dark matter interactions, deviating from the standard cold halo model.
• It integrates diverse mechanisms such as dark disc formation, particle decay or annihilation, and burst-driven relativistic events to explain observed discrepancies in direct and indirect detection.
• Detection strategies combine direct nuclear/electron recoil measurements with astrophysical surveys and indirect neutrino/gamma-ray observations to constrain and validate the diverse dark flux scenarios.

The Diffuse Dark Flux Hypothesis encapsulates a broad class of scenarios in which the non-luminous flux of dark sector particles—originating from both astrophysical and non-astrophysical (dark sector) sources—enters the observable universe as a persistent or modulated background, distinct from the canonical cold halo dark matter distribution. This hypothesis unifies diverse models where the dark sector injects relativistic or semi-relativistic particles (or otherwise modifies the phase-space structure of nonrelativistic dark matter), with observable consequences for direct/indirect detection and astrophysical surveys.

1. Conceptual Foundations

The Diffuse Dark Flux Hypothesis (DDFH) posits that signatures of dark matter (DM), or more generally non-Standard-Model "dark sector" physics, may arise not only through gravitational effects associated with a virialized cold dark halo, but also via diffuse backgrounds of energetic or structurally distinct particles produced in a variety of processes. DDFH is motivated by the realization that the standard halo model (SHM)—in which dark matter is smoothly and isotropically distributed with a Maxwellian velocity distribution—is an idealization, and that both astrophysical processes (e.g., mergers, baryonic interactions, transient events) and particle-physics effects (e.g., decay, annihilation, interaction with Standard Model or dark radiation) can give rise to additional, sometimes dominant, observable dark sector flux components.

This paradigm explicitly includes dark matter subcomponents or products with non-negligible velocities, diffuse origin (not localized or point-like), and/or temporal/spatial modulations, as distinct from both compact dark matter objects and rare, highly anisotropic events. In addition, many implementations of DDFH overlap with or generalize the "boosted dark matter" or "dark radiation" scenarios, further broadening its relevance.

2. Theoretical Realizations

2.1. Galactic Structural Contributions

A canonical realization is the formation of a thick, rotating dark matter disc ("dark disc") in the Milky Way and similar galaxies, as demonstrated by hydrodynamic simulations that incorporate baryonic physics (0901.2938). The dark disc arises as merging satellites are preferentially disrupted in the plane of the baryonic disc at $z\sim1$, depositing both stars and dark matter debris into a co-rotating, equilibrium structure.

Key quantitative result:

$$\rho_{\mathrm{DDISC}} \sim (0.25-1)\times \rho_{\mathrm{HALO}}$$

at the solar neighborhood, with a velocity lag of $v_{\mathrm{lag}} \sim 50$–150 km/s relative to the local circular speed.

2.2. Cosmological Backgrounds from Annihilation and Decay

The DDFH also encompasses diffuse fluxes generated by annihilation or decay of cosmological DM throughout structure formation history. For annihilating DM, the cosmological diffuse neutrino (and gamma-ray) flux can be calculated by integrating over halos at all redshifts (Moline et al., 2014):

$$\frac{d\phi_{\nu}}{dE_0} = \frac{\langle \sigma v \rangle}{2} \frac{\rho_{m,0}^2}{m_{\mathrm{DM}}^2} \int \frac{dz}{H(z)} \, \xi^2(z) \sum_i \text{Br}_i \frac{dN_{\nu,i}}{dE}$$

where $\xi^2(z)$ incorporates the uncertain halo mass and concentration functions.

For decaying DM—and especially for scenarios where a subcomponent decays after recombination with non-negligible branching to visible particles—the resulting diffuse photon and neutrino backgrounds are tightly constrained by observations (Kalashev et al., 2019).

Key bounds include $f_\mathrm{DM} \lesssim 10^{-5}$ for the fraction of DM decaying after recombination to Standard Model particles, across a broad mass range.

2.3. Relativistic Axion and Dark Sector Backgrounds

The Diffuse Axion Background (D$a$B) exemplifies an explicitly burst-driven, cosmologically accumulated dark flux scenario, sourced by historic transient events such as axion star bosenovae, supernovae, or primordial black hole evaporation (Eby et al., 31 Jan 2024). The cumulative axion flux at Earth is given by

$$\frac{d\phi}{d\omega} = \int_0^\infty dz\,(1+z)\frac{dN_a(\omega(1+z))}{d\omega} R_{\text{burst}}(z)\left|\frac{dt}{dz}\right|$$

with deep constraints arising from non-observation of excess axion-induced photons in the X-ray and gamma-ray backgrounds.

2.4. Non-Thermal and Astrophysically-Triggered Dark Fluxes

Astrophysical mechanisms—including accretion onto black holes (Cai et al., 2020), particle upscattering by cosmic rays or the diffuse supernova neutrino background (Ghosh et al., 18 Nov 2024), and energetic interactions near blazars (Marchi et al., 6 Jun 2025)—can generate non-virialized, diffuse dark fluxes with energies extending from sub-keV to PeV.

For instance, cosmic-ray upscattering of sub-GeV DM to detectable energies produces a flux:

$$\frac{d\Phi_\chi}{dT_\chi} = D_{\text{eff}} \frac{\rho_\chi}{M_\chi} \int_{T_i^{\text{min}}(T_\chi)}^{\infty} \frac{d\Phi_i^{\text{LIS}}}{dT_i} \frac{d\sigma_{\chi i}}{dT_\chi} dT_i$$

where $D_{\text{eff}}$ is an effective path length traversed by the CR in the DM halo.

3. Methodologies for Detection and Differentiation

A multi-pronged experimental approach is central to probing the DDFH:

• Direct Detection: Nuclear or electron recoil rates are sensitive to the altered velocity distribution and the presence of boosted or relativistic components; specific spectral and temporal recoil features can signal non-standard dark flux origins (0901.2938, Ghosh et al., 18 Nov 2024).
• Indirect Detection via Neutrinos and Gamma Rays: Cosmological and Galactic backgrounds from DM annihilation/decay or from D$a$B conversion/decay are bounded by diffuse $\gamma$-ray and neutrino measurements (e.g., Fermi-LAT, IceCube, COMPTEL/XMM/INTEGRAL) (Moline et al., 2014, Kalashev et al., 2019, Eby et al., 31 Jan 2024, Jeong, 23 Jul 2024).
• Astrophysical Surveys: Kinematic signatures in stellar populations, e.g., the velocity distribution of accreted thick disc stars, can indirectly reveal the presence and properties of a dark disc (0901.2938).

Many DDFH scenarios require disentangling the diffuse dark flux from dominant astrophysical backgrounds (cosmic-ray induced $\gamma$-ray floors (Bérat et al., 2022), atmospheric or galactic neutrino backgrounds).

4. Observational Constraints and Phenomenological Outcomes

Comprehensive analyses leveraging diffuse photon and neutrino flux measurements yield strong, often order-of-magnitude, constraints on the parameter space of DDFH scenarios:

• For decaying dark matter after recombination, the fraction decaying with visible signatures is limited to $f_\mathrm{DM}\lesssim 10^{-5}$ by the Fermi and IceCube diffuse backgrounds, with tighter constraints at high DM mass from neutrino non-observation (Kalashev et al., 2019).
• For annihilating dark matter in the cosmic background, next-generation neutrino telescopes probe $\langle\sigma v\rangle$ near or above the thermal relic target for $$100\,\mathrm{GeV}\lesssim m_{\mathrm{DM}}\lesssim 10\,\mathrm{TeV}$$, limited by halo model uncertainties (Moline et al., 2014).
• For dark disc scenarios, the local density and velocity structure at the solar circle receive robust prediction from baryon-inclusive hydrodynamics; consequences include dramatic boosts in expected direct/indirect detection rates (especially for low-velocity-sensitive channels), but also model-dependent uncertainty due to merger history (0901.2938, 0902.4001).
• For axionic or other relativistic background fluxes, photon non-detections from axion-photon coupling dominate bounds for $m_a\lesssim10^{-3}\,\mathrm{eV}$ and $\omega\gtrsim \mathrm{MeV}$ (Eby et al., 31 Jan 2024).

A critical empirical feature is the "background floor" effect: e.g., the irreducible diffuse $\gamma$-ray flux from cosmic-ray interactions over the Galactic disk forms a floor below which no signal from DM decay can be detected, capping sensitivity to SHDM lifetime at fixed mass (Bérat et al., 2022, Collaboration et al., 4 Feb 2025).

5. Astrophysical and Dark Sector Source Diversity

DDFH is realized across both standard and exotic scenarios:

• Astrophysical Sources: Supernovae, neutron star mergers, axion star bosenovae, evaporating primordial black holes, cosmic ray upscattering, and baryonic-affected halo structures (Eby et al., 31 Jan 2024, 0901.2938, Bérat et al., 2022).
• Dark Sector Sources: Non-thermal processes exclusive to the dark sector, e.g., dark photon or axion emission from novel early-universe phenomena, black hole superradiance (Eby et al., 31 Jan 2024, Cai et al., 2020).

Astrophysical origin typically yields more robust and less model-dependent connection to observed cosmic histories and is susceptible to tracer constraints. Dark sector-driven backgrounds allow broader parameter ranges but can evade some traditional astrophysical bounds.

6. Outstanding Challenges and Prospects

Despite substantial theoretical motivation and advances in detection capability, the DDFH is subject to robust, cross-channel observational constraints:

• No direct evidence for a significant DDFH contribution to present neutrino or photon backgrounds has been established. Astrophysical sources remain the leading explanation for the observed diffuse high-energy neutrino flux (Jeong, 23 Jul 2024).
• Future observatories such as LHAASO, AMEGO/e-ASTROGAM, and expanded neutrino detectors (DUNE, Hyper-Kamiokande) are expected to test deeper into DDFH parameter space, with potential to distinguish DM-induced signals from guaranteed cosmic-ray and astrophysical backgrounds (Neronov et al., 2020, Eby et al., 31 Jan 2024).
• Disentangling DDFH signals from astrophysical backgrounds remains a principal challenge, requiring improved modeling of Galactic gas distributions, cosmic ray propagation, and precise multi-messenger correlation studies (Bérat et al., 2022, Tavakoli et al., 2013).

7. Synthesis and Outlook

The Diffuse Dark Flux Hypothesis encapsulates the broad class of models where the observable dark sector is richer than a purely cold, collisionless halo, encompassing rotationally supported discs, cosmological relic backgrounds, event-driven relativistic fluxes, and non-thermal emission from complex astrophysical environments. Indirect and direct detection methodologies place strong global constraints, but DDFH remains a critical framework for interpreting next-generation signals—especially for multi-messenger, time- and direction-resolved observations, and for scenarios not encompassed by WIMP or cold axion cosmologies.

A table summarizing key DDFH source classes, observables, and constraints:

Source Class	Main Observable	Principal Constraint
Galactic dark disc	Local DM velocity/density	Enhanced direct/indirect rates; kinematics of thick disc stars (0901.2938, 0902.4001)
Annihilating/decaying DM (cosmic)	Diffuse $\nu$, $\gamma$	Non-observation in IceCube, Fermi: $f_\mathrm{DM} \ll 0.01$ (Kalashev et al., 2019, Moline et al., 2014, Jeong, 23 Jul 2024)
Relativistic axion background	$\gamma$-ray, $X$-ray, radio	$g_{a\gamma}$ constraints from non-observation (Eby et al., 31 Jan 2024)
Boosted DM (CR/DSNB)	Nuclear/electron recoils	Direct detection event rates (Ghosh et al., 18 Nov 2024)
Black hole/dark star	Direct detection; keV flux	Far below detection threshold in conventional models (Cai et al., 2020)