SHAM-OT: Rapid Subhalo Abundance Matching with Optimal Transport

TL;DR

SHAM-OT introduces an optimal transport-based approach to galaxy-halo matching that is more efficient and flexible than traditional methods, enabling rapid and accurate abundance matching in cosmological simulations.

Contribution

It formulates subhalo abundance matching as an optimal transport problem, eliminating sampling and sorting, and allowing natural incorporation of scatter and multiple distributions.

Findings

Efficiently solves abundance matching using optimal transport algorithms.

Validates method with analytical tests and simulated catalogues.

Facilitates Bayesian inference by marginalizing over uncertainties.

Abstract

Subhalo abundance matching (SHAM) is widely used for connecting galaxies to dark matter haloes. In SHAM, galaxies and (sub-)haloes are sorted according to their mass (or mass proxy) and matched by their rank order. In this work, we show that SHAM is the solution of the optimal transport (OT) problem on empirical distributions (samples or catalogues) for any metric transport cost function. In the limit of large number of samples, it converges to the solution of the OT problem between continuous distributions. We propose SHAM-OT: a formulation of abundance matching where the halo-galaxy relation is obtained as the optimal transport plan between galaxy and halo mass functions. By working directly on these (discretized) functions, SHAM-OT eliminates the need for sampling or sorting and is solved using efficient OT algorithms at negligible compute and memory cost. Scatter in the galaxy-halo relation can be naturally incorporated through regularization of the transport plan. SHAM-OT can easily be generalized to multiple marginal distributions. We validate our method using analytical tests with varying cosmology and luminosity function parameters, and on simulated halo catalogues. The efficiency of SHAM-OT makes it particularly advantageous for Bayesian inference that requires marginalization over stellar mass or luminosity function uncertainties.