Sensitivity toward dark matter annihilation imprints on 21-cm signal with SKA-Low: A convolutional neural network approach

Technical Summary: Sensitivity toward Dark Matter Annihilation Imprints on 21-cm Signal with SKA-Low: A Convolutional Neural Network Approach

Problem Statement
The fundamental nature of dark matter remains one of the most significant unsolved problems in cosmology. While the Lambda Cold Dark Matter ($\Lambda$CDM) model successfully describes large-scale structure, it does not elucidate the particle physics of dark matter. A potential probe is the annihilation of dark matter particles, which injects energy into the intergalactic medium (IGM) during the pre-reionization era, altering the thermal and ionization history of neutral hydrogen. This energy injection modifies the 21-cm differential brightness temperature signal.

Current analyses of the 21-cm signal often rely on summary statistics, such as the power spectrum, which may fail to capture the full information encoded in three-dimensional brightness temperature fields. Furthermore, distinguishing between different dark matter models is complicated by degeneracies among astrophysical parameters. A critical distinction exists between homogeneous energy injection (assuming uniform deposition across space) and inhomogeneous injection (where energy deposition scales with local dark matter density contrasts and gas properties). Previous studies have focused on distinguishing dark matter annihilation from the standard $\Lambda$CDM model; this paper addresses the more subtle challenge of distinguishing inhomogeneous dark matter annihilation models from homogeneous ones using the upcoming Square Kilometre Array Low-frequency (SKA-Low) telescope.

Methodology
The authors employ a machine learning approach, specifically Convolutional Neural Networks (CNNs), to classify 3D 21-cm differential brightness temperature maps.

1. Simulation Framework:

   • Codes: The study utilizes the DM21cm code, which integrates 21cmFAST (a semi-numerical cosmological simulation code) and DarkHistory (for thermal and ionization evolution).
   • Physics: The simulations model dark matter annihilation into two primary channels: electron-positron pairs ($e^+e^-$) and photon pairs ($\gamma\gamma$). The energy injection rate is calculated based on the local dark matter density contrast, $\delta(x,z)$, allowing for spatially inhomogeneous deposition.
   • Parameters: The study explores dark matter masses ($m_{DM}$) ranging from 1 MeV to 100 MeV and various annihilation cross-sections ($\langle\sigma v\rangle$). The simulations cover a box size of 48 Mpc with a resolution of $64^3$ grids (voxel size 0.75 Mpc).
   • Noise Modeling: To reflect realistic observational conditions, Gaussian thermal noise corresponding to the SKA-Low specifications (512 stations, 74 km max baseline, $10^4$ hours integration time) is added to the simulated maps. The noise level is parameterized by a fraction $f_{Noise}$ ranging from 0 to 1.

2. Machine Learning Architecture:

   • Model: A standard CNN architecture is used, consisting of four convolutional layers (3$\times$3 kernels), Leaky ReLU activations, 2$\times$2 max pooling, and batch normalization.
   • Input: The network processes 3D voxels (16$\times$16$\times$16 sub-regions of the simulation box).
   • Preprocessing: To address the limitation that standard normalization (mean subtraction and standard deviation scaling) might suppress global amplitude differences between homogeneous and inhomogeneous models, the authors explicitly extract the mean and standard deviation of the input images and concatenate these statistics with the latent feature vector before the fully connected layers.
   • Training: The model is trained on 128,000 images (half homogeneous, half inhomogeneous) generated from 1,000 distinct cosmological realizations. The dataset is split into training (80%), validation (20%), and test (20%) sets.

Key Results

1. Electron-Positron Channel ($e^+e^-$):

   • Discrimination Capability: The CNN successfully distinguishes between inhomogeneous and homogeneous annihilation scenarios for the $e^+e^-$ channel.
   • Performance Metrics: For a dark matter mass of $m_{DM} = 1$ MeV, the model achieves an Area Under the Curve (AUC) of $\geq 0.72$ (indicating discrimination better than random guessing) for annihilation cross-sections $\langle\sigma v\rangle \geq 5 \times 10^{-30}$ cm$^3$/s, even with moderate noise ($f_{Noise} \leq 0.1$).
   • Optimal Cross-Section: The discrimination performance is non-monotonic with respect to the cross-section. It peaks at intermediate values (e.g., $\langle\sigma v\rangle \approx 5 \times 10^{-29}$ cm$^3$/s for $m_{DM}=1$ MeV).
     • Low Cross-Section: Energy injection is too weak to create distinct signatures.
     • Intermediate Cross-Section: Energy injection is localized enough to create "bubbles" of heating/ionization distinct from the background, maximizing the contrast between models.
     • High Cross-Section: The mean free path of secondary photons increases, causing energy to smear out over larger volumes, making the inhomogeneous scenario resemble the homogeneous one and reducing AUC.
   • Mass Dependence: For $m_{DM} = 100$ MeV, the required cross-section for effective discrimination increases to $\langle\sigma v\rangle \geq 5 \times 10^{-29}$ cm$^3$/s due to the longer mean free path of higher-energy secondary photons.

2. Photon-Photon Channel ($\gamma\gamma$):

   • Failure to Discriminate: The CNN fails to distinguish between inhomogeneous and homogeneous models for the $\gamma\gamma$ channel across all tested mass and cross-section ranges (AUC $\lesssim 0.7$).
   • Physical Reason: The mean free path of photons emitted by dark matter annihilation is significantly larger than the simulation cell size (and often the Hubble radius) at the relevant redshifts. Consequently, photons travel freely and deposit energy homogeneously, erasing the spatial inhomogeneities of the source distribution. The "on-the-spot" approximation is invalid for this channel.

3. Power Spectrum Analysis:

   • The inhomogeneous scenario exhibits a lower 21-cm power spectrum compared to the homogeneous scenario. This is because localized heating creates "bubbles" where the 21-cm absorption amplitude is suppressed, while the rest of the volume remains closer to the global mean. This statistical homogenization reduces the variance of the signal fluctuations.

Significance and Claims
The paper claims that machine learning techniques, specifically CNNs, offer a novel and effective approach to extracting subtle spatial features from complex 21-cm data that traditional summary statistics (like the power spectrum) might miss.

• Feasibility: The study demonstrates that the SKA-Low telescope, even with thermal noise, possesses the sensitivity to detect the imprints of inhomogeneous dark matter annihilation for specific parameter ranges ($m_{DM} \sim 1$ MeV, $\langle\sigma v\rangle \geq 5 \times 10^{-30}$ cm$^3$/s).
• Methodological Advance: The work highlights the importance of incorporating global statistical features (mean and standard deviation) into the neural network input to prevent the suppression of critical distinguishing features during normalization.
• Physical Insight: The research clarifies that the detectability of inhomogeneous annihilation is highly dependent on the annihilation channel and the mean free path of the resulting particles. While electron-positron channels offer a viable probe for spatial inhomogeneities, photon channels effectively wash out these spatial signatures due to large mean free paths.

The authors conclude that future 21-cm observations, combined with advanced machine learning analysis, provide a robust pathway to probe exotic energy injection sources and constrain the microscopic properties of dark matter, particularly distinguishing between spatially varying and uniform energy deposition mechanisms.