Discovering the building blocks of dark matter halo density profiles with neural networks
This work addresses the problem of accurately modeling dark matter halo structures for astrophysicists, offering a novel method that improves upon empirical fits by discovering key features like the splashback boundary, though it is incremental in applying neural networks to this domain.
The researchers tackled modeling dark matter halo density profiles by training a neural network to map raw density fields to profiles, recovering the NFW profile up to the virial radius and capturing variability in outer profiles. They found that a two-dimensional latent representation suffices for modeling up to the virial radius, while a three-dimensional one is needed for outer profiles, revealing the splashback boundary without prior dynamical knowledge.
The density profiles of dark matter halos are typically modeled using empirical formulae fitted to the density profiles of relaxed halo populations. We present a neural network model that is trained to learn the mapping from the raw density field containing each halo to the dark matter density profile. We show that the model recovers the widely-used Navarro-Frenk-White (NFW) profile out to the virial radius, and can additionally describe the variability in the outer profile of the halos. The neural network architecture consists of a supervised encoder-decoder framework, which first compresses the density inputs into a low-dimensional latent representation, and then outputs $ρ(r)$ for any desired value of radius $r$. The latent representation contains all the information used by the model to predict the density profiles. This allows us to interpret the latent representation by quantifying the mutual information between the representation and the halos' ground-truth density profiles. A two-dimensional representation is sufficient to accurately model the density profiles up to the virial radius; however, a three-dimensional representation is required to describe the outer profiles beyond the virial radius. The additional dimension in the representation contains information about the infalling material in the outer profiles of dark matter halos, thus discovering the splashback boundary of halos without prior knowledge of the halos' dynamical history.