Enhancing Constraints on Ultralight Axion Dark Matter from Gravitational Capture

Ultralight axions can be gravitationally captured by massive bodies such as the Sun, producing solar-bound gravitational atom states that amplify the local dark matter density through Bose-enhanced capture.

How it works

The mechanism relies on gravitational focusing where self-interacting bosonic particles in external gravitational potentials are trapped into bound states, leading to an exponential growth in the DM density. This process is governed by the parameter defined as:

pgiffin@princeton.edu

The evolution of the gravitational atom is governed by the parameter:

1. The parameter governing this evolution is defined as:

2. The growth of the bound DM mass is linear in time initially, but this growth saturates to a small constant overdensity on a timescale proportional to:

3. For the regime of interest where the gravitational focusing parameter ξfoc ≳ 1, the linear growth quickly turns exponential as a consequence of stimulated capture arising from Bose enhancement.

Key Physical Parameters and Models

The paper considers specific models for axion self-interactions and couplings to the Standard Model (SM):

1. The benchmark periodic potential for the axion a is given by:

2. The dimensionless coupling that characterizes the self-interactions of the axion field is denoted by λ, where:

3. The axion couples to the SM through the term:

Evolution of Dark Matter Density

The evolution of the dark matter density at Earth’s location is tracked using equations from Ref. [12], focusing only on the population of the ground state of the gravitational atom, neglecting contributions from higher excited states. The density at a radius r is given by:

1. The dark matter density at a radius r is given by:

2. The relaxation time τrel is defined as:

For the regime where gravitational focusing occurs (ξfoc ≳ 1), the growth proceeds in phases:

1. The growth is linear until a time tlin, which occurs at approximately tlin ≈ 0.3τrel.

2. For tlin < t < tcrit, the growth rate becomes exponential until it reaches a critical density at time tcrit.

Conditions for Large Overdensity

A large dark matter overdensity is expected under specific conditions related to the axion mass (ma) and decay constant (fa):

1. The region where gravitational focusing is relevant corresponds to a lower bound of ma ≳ 10−14 eV.

2. The enhancement is only exponential in the range fa ∼ 107 GeV ≲ fa ≲ 108 GeV.

3. For attractive potentials, a Bosenova explosion occurs when the critical density is reached at t ≈ tcrit, releasing a large fraction of captured DM as relativistic axions.

Impact on Experimental Constraints

The enhancement in the local dark matter density directly translates into stronger bounds on the axion-photon coupling (gaγγ):

1. An enhancement in the local density directly translates into stronger bounds on gaγγ by a factor of pρ/ρ0.

2. This effect is particularly relevant for experiments that rely on local measurements of oscillating electromagnetic fields induced by the axion, such as magnetometer-based searches and resonant cavity experiments.

The paper concludes that this gravitational capture in the Solar potential can play an important role in interpreting and improving searches for ultralight axion dark matter, potentially leading to an O(10) increase in sensitivity to gaγγ across a significant portion of the mass range 10−14 eV ≲ ma ≲ 10−13 eV.

Summary of Findings

The study demonstrates that solar gravitational capture can play an important role in interpreting and improving searches for ultralight axion dark matter, showing that experiments could have an O(10) increase in sensitivity to gaγγ in the mass range 10−14 ≲ ma ≲ 10−13 eV due to the local DM overdensity. This enhancement arises because many direct detection experiments probe the amplitude of the axion field, which scales as √ρ, so that an increase in the local density directly translates into stronger bounds on the axion-photon coupling. The presence of a solar axion halo can enhance the discovery potential of both current experiments and future proposals sensitive to the local dark matter density. A more detailed treatment of the nonlinear evolution of the halo, including the dynamics of excited states and a refined description of the Bosenova instability, is left for future work.

Figure 1 Interpretation

Figure 1 illustrates how the dark matter overdensity factor (pρ/ρ0) varies with axion mass (ma) and decay constant (fa) for both attractive and repulsive potentials.

Based on the provided scientific paper, here are the specific improvements that can be made to AI systems, categorized by application:

) 1. Enhanced Constraint Modeling for Ultralight Dark Matter Searches:

The paper provides a detailed framework for calculating how gravitational focusing (solar halo formation) increases local dark matter density and consequently tightens constraints on the axion-photon coupling constant, specifically in the mass range of 10−14 eV to 10−13 eV.

) Improved AI System Capabilities:

A specialized simulation and analysis AI could be developed to perform real-time Constraint Projection Modeling.

) Specific Improvements:

a. Real-Time Sensitivity Mapping: The AI can ingest parameters for axion mass and self-interaction coupling (ma, fa), calculate the expected dark matter overdensity factor (pρ/ρ0) using the derived equations (Equations 7, 8, 9), and immediately project the corresponding improvement in constraints on the axion-photon coupling constant (gaγγ).

b. Scenario Testing: The system can simulate different physical scenarios—such as attractive vs. repulsive self-interactions (Bosenova explosion vs. saturation)—to determine which physical regime yields the most significant constraint tightening for a given experimental setup (e.g., Suzaku, CAST, ADBC).

c. Exclusion Boundary Identification: The AI can precisely identify the boundaries in the (ma, fa) parameter space that correspond to specific physical events (e.g., where a Bosenova occurs within 5 Gyr), allowing researchers to quickly navigate regions where current results might be unreliable (red box in Figure 1).

) What the Improved AI System Can Do:

This system would transform constraint analysis from static lookup tables into a dynamic, predictive tool. It allows experimentalists and theorists to rapidly assess how solar halo enhancement will affect their limits on axion-photon coupling, enabling faster prioritization of future experimental runs or theoretical model selection.

) 2. Advanced Dark Matter Halo Characterization:

The paper discusses the evolution of the gravitational atom and the resulting density profile around a massive body like the Sun, focusing on ground states versus excited states.

) Improved AI System Capabilities:

A Gravitational Atom Evolution Simulator AI could be built to model non-linear dynamics of self-interacting bosonic dark matter (DM).

) Specific Improvements:

a. Non-Linear Dynamics Prediction: The system could move beyond the simplified treatment of only the ground state (Equation 5) by incorporating higher excited states and their subsequent decay/amplification effects, providing a more conservative and physically complete density evolution model.

b. Time-Dependent Density Profiling: The AI can simulate the time evolution of the dark matter density, distinguishing between linear growth phases, exponential growth phases (stimulated capture), and saturation/Bosenova events based on the input parameters (ma, fa).

) What the Improved AI System Can Do:

This system would enable researchers to create more accurate physical models of solar axion halos. It could predict not just the final overdensity but also how this density profile evolves over cosmic time, which is crucial for accurately modeling interactions with terrestrial detectors or astrophysical environments.

) 3. Automated Model Parameter Space Exploration:

The paper explores the relationship between axion mass (ma), decay constant (fa), and coupling constants (gaγγ) across a multi-dimensional parameter space, constrained by various experimental data.

) Improved AI System Capabilities:

A Bayesian Inference and Constraint Explorer AI could be implemented to perform rapid global searches for axion parameters.

) Specific Improvements:

a. Degeneracy Resolution: The system can explicitly map the degeneracy between the local dark matter density and the axion-photon coupling, as highlighted in Section IV, by calculating the factor of improvement (pρ/ρ0).

b. Automated Constraint Mapping: By integrating data from various experiments (Suzaku, CAST, ADBC) into a Bayesian framework, the AI can automatically generate updated exclusion contours in the (ma vs. gaγγ) plane that explicitly include the enhancement factor derived from gravitational focusing.

) What the Improved AI System Can Do:

This system would drastically reduce the time required for global parameter estimation in axion dark matter searches. It allows researchers to efficiently search for new physics by automatically incorporating complex astrophysical effects like gravitational focusing into their likelihood functions, thereby maximizing discovery potential from existing and future datasets.

Ultralight axions can be gravitationally captured by massive bodies such as the Sun, producing solar-bound gravitational atom states that amplify the local dark matter density through Bose-enhanced capture. For axion masses in the range 10-14 eV m a 10-13 eV, this mechanism becomes exponentially efficient. We show that, for a representative decay constant f a about 3.5 times10 7 GeV, the local axion dark matter density at Earth can grow to more than ten times the standard Galactic value of ρ 0 = 0.4 GeV/cm cubed. Incorporating this overdensity, we derive updated limits on the axion-photon coupling from existing satellite and terrestrial measurements and present improved projections for upcoming experiments.