# Accelerated calibration of semi-analytic galaxy formation models

## TL;DR

This paper introduces a fast calibration framework for semi-analytic galaxy formation models, enabling efficient fitting to multiple datasets and revealing model limitations in reproducing galaxy properties across redshifts.

## Contribution

The authors develop a rapid likelihood-based calibration method that reduces computational cost and allows extensive parameter space exploration for galaxy formation models.

## Key findings

- The calibration reproduces the low-redshift stellar mass function.
- The model overpredicts low-mass and underpredicts high-mass galaxies at higher redshifts.
- Size evolution is approximately correct, but the mass-size relation is too flat.

## Abstract

We present an accelerated calibration framework for semi-analytic galaxy formation models, demonstrated with Galacticus. Rather than fitting directly to properties such as the low-redshift stellar mass function (SMF) - which requires evolving thousands of halos per likelihood evaluation - we construct a fast likelihood from the stellar-to-halo mass relation (SHMR; mean and scatter) evaluated at a small set of target halo masses, reducing each evaluation to simulating only tens of galaxies. We sample the posterior over Galacticus parameters with Markov Chain Monte Carlo and show that the resulting calibration reproduces the low-redshift SMF. We then extend the method to additional datasets, using a higher-redshift SHMR and the low-redshift stellar mass-size relation as examples, and assess performance for large scale structure survey-relevant properties: stellar masses, sizes, and emission-line strengths. The SMF matches data well at low redshift, but toward higher redshift the model yields too few massive galaxies and too many low-mass galaxies. Size evolution with redshift is approximately correct, but the mass-size relation is too flat, producing massive galaxies that are too small. The H$\alpha$ luminosity function is well reproduced at z~2, but by z~0.4 the model overproduces highly star-forming, H$\alpha$-bright systems. These discrepancies suggest the model lacks sufficient flexibility (e.g. in gas cooling/recycling or feedback) to reconcile all datasets simultaneously. Our strategy complements emulator-based methods for calibrating semi-analytic models by enabling rapid, low-cost scans of model choices and parameterisations - a capability we envision leveraging to supply calibrated starting points for more detailed follow-up inference.