Revealing Hidden Cosmic Flows through the Zone of Avoidance with Deep Learning

TL;DR

This work presents a 3D V-Net-based framework to reconstruct the dark matter density $\rho$, gravitational potential $\phi$, and peculiar velocity $\vec{v}$ from radial peculiar velocities in the Zone of Avoidance, trained on the A-SIM simulation and validated with CF4-like mocks. By training separate networks for $\rho$ and $\phi$ on $128^3$ voxels within $160\ \mathrm{Mpc}/h$ boxes and using bias-corrected velocities from an HMC CF4 reconstruction, the authors recover key large-scale structures and produce consistent bulk-flow statistics. Application to 1,000 corrected CF4 realizations yields mean reconstructions that align with known nearby clusters and identify a Great Attractor candidate with a 64.4% probability at Galactic coordinates $(l,b)=(308.4^{\circ},29.0^{\circ})$ and $cz=4960\pm404\ \mathrm{km}\ \mathrm{s}^{-1}$. The method demonstrates strong potential for data-sparse regions, offering high-resolution, nonlinear insights beyond traditional velocity-field reconstructions, and sets the stage for future surveys and constrained simulations. Acknowledging current uncertainties in CF4 and the HMC correction, the study proposes incorporating bias models directly into the learning framework and expanding grid coverage to enhance applicability to upcoming datasets.

Abstract

We present a refined deep-learning-based method to reconstruct the three-dimensional dark matter density, gravitational potential, and peculiar velocity fields in the Zone of Avoidance (ZOA), a region near the galactic plane with limited observational data. Using a convolutional neural network (V-Net) trained on A-SIM simulation data, our approach reconstructs density or potential fields from galaxy positions and radial peculiar velocities. The full 3D peculiar velocity field is then derived from the reconstructed potential. We validate the method with mocks that mimic the spatial distribution of the Cosmicflows-4 (CF4) catalog and apply it to actual data. Given CF4's significant observational uncertainties and since our model does not yet account for them, we use peculiar velocities corrected via an existing Hamiltonian Monte Carlo reconstruction, rather than raw catalog distances. Our results demonstrate that the reconstructed density field recovers known galaxy clusters detected in an H \textsc{i} survey of the ZOA, despite this dataset not being used in the reconstruction. This agreement underscores the potential of our method to reveal structures in data-sparse regions. Most notably, streamline convergence and watershed analysis identify a mass concentration consistent with the Great Attractor, at $(l, b) = (308.4^\circ \pm 2.4^\circ, 29.0^\circ \pm 1.9^\circ)$ and $cz = 4960.1 \pm 404.4,{\rm km/s}$, for 64\% of realizations. Our method is particularly valuable as it does not rely on data point density, enabling accurate reconstruction in data-sparse regions and offering strong potential for future surveys with more extensive galaxy datasets.

Figures (15)

• Figure 1: Comparison between the CF4 observational data (within the 160 Mpc/$h$ box) and a CF4-like mock sample. From left to right: SGX-SGY slice of width $-15<\mathrm{SGZ}<15$ Mpc/$h$, distributions of galactic longitude $l$, galactic latitude $b$, and redshift $cz$. In each panel, black points and dashed lines represent the CF4 observational data, while blue squares and solid lines correspond to the mock sample.
• Figure 2: Input and output quantities for the Deep Learning algorithm. Each panel corresponds to the same SGX-SGY slice of width $-7.5<\mathrm{SGZ}<7.5$ Mpc/$h$ and of various quantities. From left to right: (a) mock from which the input and output quantities have been generated, (b) galaxy number density $N_\mathrm{gal}$, (c) mean radial peculiar velocity $V_\mathrm{pec}$, (d) true dark matter density field, (e) true gravitational potential field.
• Figure 3: Distribution of radial peculiar velocities. The blue dashed lines represent the A-SIM validation samples, with thin lines showing individual samples and the thicker line indicating the mean distribution. The red solid lines correspond to the CF4 dataset after correction using HMC reconstruction, with thin lines representing individual samples and the thicker line showing the mean. The black dotted line depicts the CF4 distribution before correction.
• Figure 4: Architecture of the 3D V-Net used in this work. The input has two channels: galaxy number density $N_{\mathrm{gal}}$ and mean radial peculiar velocity $V_{\mathrm{pec}}$. Spatial features are encoded via convolutional layers (convX), followed by a bottleneck layer and a symmetric decoder path (upconvX) with skip connections. The output is a single channel representing either the dark matter density field $\rho$ or the gravitational potential field $\phi$, trained separately using the same input and architecture. The width and height of each block indicate the number of channels (below) and spatial dimensions (left), respectively. The detailed sub-operations within each encoding and decoding block are summarized on the right.
• Figure 5: Learning rate range test showing the evolution of the loss $\mathcal{L}_\mathrm{MSE}$ as a function of the learning rate $\alpha$. Top: test training on the dark matter density field. Bottom: test training on the gravitational potential field. The adequate range for the triangular cyclic learning rate used for the final training is shown as a thicker solid line on each panel.