A deep-learning algorithm to disentangle self-interacting dark matter and AGN feedback models

TL;DR

This work tackles the degeneracy between self-interacting dark matter (SIDM) and uncertain baryonic feedback in galaxy clusters by training a Convolutional Neural Network (CNN) on hydro-dynamical simulations (BAHAMAS-SIDM) to classify clusters into discrete SIDM cross-sections, using multi-channel inputs of total mass, stellar mass, and X-ray emissivity. The Inception-style CNN achieves about 80% accuracy in idealized data, with permutation-importance analyses showing central regions and total mass as dominant discriminants, and X-ray data proving crucial for disentangling AGN feedback, albeit sometimes increasing CDM–SIDM confusion. The study extends to observational realism by incorporating weak-lensing and X-ray noise, external metadata, and different seeds, demonstrating that ensemble analyses over hundreds to thousands of clusters from surveys like JWST and Euclid can constrain σ_DM/m to as tight as ≲0.01 cm^2/g, while noting residual biases from lensing noise that call for refined inference methods. Overall, the framework offers a scalable, data-driven path to probing dark matter physics with upcoming telescopes, while highlighting the need for robust handling of baryonic systematics and extending to broader DM models.

Abstract

Different models of dark matter can alter the distribution of mass in galaxy clusters in a variety of ways. However, so can uncertain astrophysical feedback mechanisms. Here we present a Machine Learning method that ''learns'' how the impact of dark matter self-interactions differs from that of astrophysical feedback in order to break this degeneracy and make inferences on dark matter. We train a Convolutional Neural Network on images of galaxy clusters from hydro-dynamic simulations. In the idealised case our algorithm is 80% accurate at identifying if a galaxy cluster harbours collisionless dark matter, dark matter with $σ_{\rm DM}/m = 0.1$cm$^2/$g or with $σ_{DM}/m = 1$cm$^2$/g. Whilst we find adding X-ray emissivity maps does not improve the performance in differentiating collisional dark matter, it does improve the ability to disentangle different models of astrophysical feedback. We include noise to resemble data expected from Euclid and Chandra and find our model has a statistical error of < 0.01cm$^2$/g and that our algorithm is insensitive to shape measurement bias and photometric redshift errors. This method represents a new way to analyse data from upcoming telescopes that is an order of magnitude more precise and many orders faster, enabling us to explore the dark matter parameter space like never before.

Figures (11)

• Figure 1: Left: Evolution of training for the base model (Inception plus all three input channels), classifying images of clusters in to three dark matter models ($\sigma_{\rm DM}/m=0,0.1,1.0$cm$^2$/g. The blue shows the training classification accuracy and the red the validation, showing how the model is not overfitting. Center Permutation importance (PI). We calculate the relative importance of each radial bin for each input channel. We show the mean importance (solid lines) and the mean density profile (dashed line). We normalise the importance to the most important radial and input channel bin, and the density to its respective input channel. We find that the importance of each mass component falls off exponentially from the centre of the halo, with a total matter increase in importance at radial bins $>200$kpc. Right We carry out the same PI for different mass bins normalise to the average important. We find no dependence of importance with mass.
• Figure 2: Dependence of the CNN to different models of baryonic feedback. Left: We train two models with two different inputs. The first model we train has one, fiducial CDM model (plus SIDM0.1 and SIDM1) with two inputs (red, total plus stellar matter) and three inputs (total, stellar and X-ray). We find in this case adding X-ray does not improve the performance. The second model has three CDM models, low, fiducial and high AGN CDM models (plus SIDM0.1 and SIDM1 at fiducial levels), again with two (green) and three (cyan) input channels. In this case, the performance is dramatically improved with the inclusion of X-rays. Right two matrices: Confusion matrices for the green model (left) and the cyan model (right). We see that the improvement is purely in the CDM sector where X-ray information greatly enables the CNN to differentiate between levels of AGN feedback.
• Figure 3: Combining estimates from individual clusters. We interpret the output weights of the CNN as probabilities and use them to make estimates of the cross-section for individual clusters. Left: SIDM0.3 Having trained our CNN on CDM, SIDM0.1 and SIDM1.0 we then test on the unseen SIDM0.3 and estimate the cross-section from the output weights. We run mock surveys of different sample sizes and shuffle the training sets multiple times to estimate uncertainty. We predict the estimated cross-section for the blind simulations for three sample sizes and find there is no bias. We estimate the precision as a function of the sample size in the lower plot. Center: vdSIDM We test our model that is trained on a velocity independent cross-section on a simulation of velocity dependent SIDM. We split the test set in to mass bins and measure the cross-section. The dashed line shows the expected theoretical cross-section and the points show the model predictions. Right: Baryonic Uncertainty. We train on CDM-low AGN, CDM fiducial AGN and two SIDM models and test on the unseen CDM-hi AGN. We find on individual clusters we can be biased up to $\sigma_{\rm DM}/m=0.1$cm$^2$/g, however this is reduced with larger samples sizes, with an expected bias of $\sigma_{\rm DM}/m<0.02$cm$^2$/g.
• Figure 4: Observationally matched data products that are use to test the performance of the network. From top to bottom, each row represents low, middle and high signal to noise, the left column are weak lensing maps of the same cluster and the right hand column is the X-ray emission. The top, middle and bottom row have increasing galaxy density in the weak lensing (50, 100 and 200 galaxies per square arc minute) and the right column has increasing exposure time (1ks, 10ks and 100ks exposure time (ET)).
• Figure 5: The impact of noise on the accuracy of the neural network. We find adding weak lensing (left panel) noise significantly degrades the accuracy on a single cluster. The model is comparably insensitive to X-ray noise (right).