DiffstarPop: A generative physical model of galaxy star formation history

TL;DR

This work introduces DiffstarPop, a differentiable forward model that links dark matter halo mass assembly histories to galaxy star formation histories through Diffmah and Diffstar, formalized as the population PDF $P(\theta_{\rm SFH}|\theta_{\rm MAH})$. Built in JAX, it enables gradient-based optimization and rapid generation of SFHs for large galaxy populations, and it is stress-tested against three representative simulations—UniverseMachine, IllustrisTNG, and Galacticus—demonstrating faithful reproduction of key PDFs such as $P(M_{\star}|M_{\rm h},z)$ and $P({\rm sSFR}|M_{\star},z)$ with typical KL divergences around $0.01$–$0.03$. The model combines a parametric MAH (Diffmah) with a parametric SFH (Diffstar) and represents the galaxy population with a two-component Gaussian mixture (quenched and main sequence), totaling 79 parameters whose means and covariances scale with halo mass and formation time. DiffstarPop achieves fast SFH generation (up to $10^{6}$ galaxies in 1.1 CPU-s or 0.03 GPU-s) and provides a physics-based, differentiable framework suitable for forward modeling, Bayesian inference, and generating synthetic catalogs for upcoming surveys; the authors have released the public code and outline future extensions to include ex-situ SFH, dust, and SED modeling within the Diffsky framework.

Abstract

We present DiffstarPop, a differentiable forward model of cosmological populations of galaxy star formation histories (SFH). In the model, individual galaxy SFH is parametrized by Diffstar, which has parameters $θ_{\rm SFH}$ that have a direct interpretation in terms of galaxy formation physics, such as star formation efficiency and quenching. DiffstarPop is a model for the statistical connection between $θ_{\rm SFH}$ and the mass assembly history (MAH) of dark matter halos. We have formulated DiffstarPop to have the minimal flexibility needed to accurately reproduce the statistical distributions of galaxy SFH predicted by a diverse range of simulations, including the IllustrisTNG hydrodynamical simulation, the Galacticus semi-analytic model, and the UniverseMachine semi-empirical model. Our publicly available code written in JAX includes Monte Carlo generators that supply statistical samples of galaxy assembly histories that mimic the populations seen in each simulation, and can generate SFHs for $10^6$ galaxies in 1.1 CPU-seconds, or 0.03 GPU-seconds. We conclude the paper with a discussion of applications of DiffstarPop, which we are using to generate catalogs of synthetic galaxies populating the merger trees in cosmological N-body simulations.

Figures (24)

• Figure 1: Diffmah model of individual halo growth. The solid blue curve shows the mass assembly history (MAH) of an individual dark matter halo in the SMDPL simulation. The dashed black curve shows the Diffmah approximation of the simulated halo MAH. The dotted vertical line shows $t_{\rm p},$ the Diffmah parameter encoding the time at which halo growth is arrested.
• Figure 2: Diffstar model of individual galaxy SFH. The solid blue curve shows the SFH of an individual UniverseMachine galaxy. The dashed black curve shows the Diffstar approximation.
• Figure 3: Average critical main sequence efficiency vs. halo mass. The solid curves show the average value of $\log\epsilon_{\rm crit}$ as a function of present-day halo mass $m_{\rm p,0}$ for UniverseMachine, IllustrisTNG and Galacticus galaxies, obtained by fitting Diffstar to individual galaxies. The dashed curves shows the DiffstarPop approximation of this scaling relation, which are later used as the initial guess for our gradient descent optimizations. DiffstarPop contains ingredients capturing scaling relations such as this one for each of the eight parameters in $\theta_{\rm SFH}$, for both the mean and standard deviation.
• Figure 4: Quenched fraction vs. halo mass. The solid curves show the average value of the fraction of galaxies that experience a quenching event (i.e. $t_{\rm q}<t_0$) as a function of present-day halo mass $m_{\rm p,0}$ for UniverseMachine, IllustrisTNG and Galacticus galaxies (using only in-situ SFH). The dashed curves show the DiffstarPop approximation of this scaling relation, which are later used as the initial guess for our gradient descent optimizations. Central galaxies are shown on the top panel, and satellites on the bottom panel.
• Figure 5: UniverseMachine stellar-to-halo-mass relation across redshift. Each panel compares $P(M_{\star}\vert M_{\rm h}, z_{\rm obs})$ in UniverseMachine to its best-fitting DiffstarPop counterpart. Different colored histograms show comparisons for different halo masses, as indicated in the legend. Shaded histograms show the stellar-to-halo-mass PDF in UniverseMachine, and dashed lines show the best-fitting DiffstarPop model.