SHAM-OT: Rapid Subhalo Abundance Matching with Optimal Transport
arXiv:2502.17553 · doi:10.1093/mnrasl/slaf062
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.
arXiv comment7 pages, 6 figures, accepted for publication in MNRAS Letters
References in corpus (35)
- SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
- The NumPy array: a structure for efficient numerical computation
- Constraints on the relationship between stellar mass and halo mass at low and high redshift
- A Comprehensive Analysis of Uncertainties Affecting the Stellar Mass - Halo Mass Relation for 0<z<4
- The Dark Side of the Halo Occupation Distribution
- The Connection between Galaxies and their Dark Matter Halos
- Modeling Luminosity-Dependent Galaxy Clustering Through Cosmic Time
- How do galaxies populate Dark Matter halos?
- Linking halo mass to galaxy luminosity
- The Connection between Galaxies and Dark Matter Structures in the Local Universe
- Galaxies in LCDM with Halo Abundance Matching: luminosity-velocity relation, baryonic mass-velocity relation, velocity function and clustering
- The halo mass function through the cosmic ages
- PINOCCHIO: pinpointing orbit-crossing collapsed hierarchical objects in a linear density field
- Galaxy Assembly Bias: A Significant Source of Systematic Error in the Galaxy-Halo Relationship
- The ALFALFA HI mass function: A dichotomy in the low-mass slope and a locally suppressed 'knee' mass
- Subhalo abundance matching and assembly bias in the EAGLE simulation
- Reconstruction of the early Universe as a convex optimization problem
- What determines satellite galaxy disruption?
- An accurate tool for the fast generation of dark matter halo catalogs
- The clustering of galaxies at z~0.5 in the SDSS-III Data Release 9 BOSS-CMASS sample: a test for the LCDM cosmology
- The stellar-to-halo mass relations of local galaxies segregates by color
- Predicting the number, spatial distribution and merging history of dark matter haloes
- Improving fast generation of halo catalogs with higher-order Lagrangian perturbation theory
- Testing Subhalo Abundance Matching in Cosmological Smoothed Particle Hydrodynamics Simulations
- PINOCCHIO and the hierarchical build-up of dark matter haloes
- Modeling color-dependent galaxy clustering in cosmological simulations
- Constraining Satellite Galaxy Stellar Mass Loss and Predicting Intrahalo Light I: Framework and Results at Low Redshift
- Does the Galaxy-Halo Connection Vary with Environment?
- Simulating cosmologies beyond CDM with PINOCCHIO
- Redshift requirements for cosmic shear with intrinsic alignment
- Rapid Simulations of Halo and Subhalo Clustering
- Testing subhalo abundance matching from redshift-space clustering
- Symbolic Implementation of Extensions of the Boltzmann Solver
- Fast Forward Modelling of Galaxy Spatial and Statistical Distributions
- Fast Simulation of Cosmological Neutral Hydrogen based on the Halo Model