syren-baryon: Analytic emulators for the impact of baryons on the matter power spectrum

¹ Heuristic and Evolutionary Algorithms Laboratory, University of Applied Sciences Upper Austria, Hagenberg, Austria
² CNRS & Sorbonne Université, Institut d’Astrophysique de Paris (IAP), UMR 7095, 98 bis bd Arago, F-75014 Paris, France
³ Astrophysics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, UK
⁴ Institute of Cosmology & Gravitation, University of Portsmouth, Dennis Sciama Building, Portsmouth PO1 3FX, UK

^⋆ Corresponding authors: Lukas.Kammerer@fh-hagenberg.at; deaglan.bartlett@physics.ox.ac.uk

Received: 10 June 2025
Accepted: 5 August 2025

Abstract

Context. Baryonic physics has a considerable impact on the distribution of matter in our Universe on scales probed by current and future cosmological surveys, acting as a key systematic in such analyses.

Aims. We seek simple symbolic parametrisations for the impact of baryonic physics on the matter power spectrum for a range of physically motivated models, as a function of wavenumber, redshift, cosmology, and parameters controlling the baryonic feedback.

Methods. We used symbolic regression to construct analytic approximations for the ratio of the matter power spectrum in the presence of baryons to that without such effects. We obtained separate functions of each of four distinct sub-grid prescriptions of baryonic physics from the CAMELS suite of hydrodynamical simulations (Astrid, IllustrisTNG, SIMBA, and Swift-EAGLE) as well as for a baryonification algorithm. We also provide functions that describe the uncertainty on these predictions, due to both the stochastic nature of baryonic physics and the errors on our fits.

Results. The error on our approximations to the hydrodynamical simulations is comparable to the sample variance estimated through varying initial conditions, and our baryonification expression has a root mean squared error of better than one percent, although this increases on small scales. These errors are comparable to those of previous numerical emulators for these models. Our expressions are enforced to have the physically correct behaviour on large scales and at high redshift. Due to their analytic form, we are able to directly interpret the impact of varying cosmology and feedback parameters, and we can identify parameters that have little to no effect.

Conlcusions. Each function is based on a different implementation of baryonic physics, and can therefore be used to discriminate between these models when applied to real data. We provide a publicly available code for all symbolic approximations found.