Learning the Universe: Cosmological and Astrophysical Parameter Inference with Galaxy Luminosity Functions and Colours

TL;DR

We introduce a simulation-based inference framework to jointly constrain cosmological parameters $Ω_m$ and $σ_8$ and astrophysical feedback from forward-modelled galaxy luminosity functions and colours using the CAMELS hydrodynamic simulations. The forward model (Synthesizer) computes rest-frame UV–NIR emission with two SPS models and a simple dust attenuation scheme, enabling rest-frame photometry across multiple bands and redshifts; a neural posterior estimation (LtU-ILI SBI) then infers the desired parameters from LF and colour distributions. We find that $Ω_m$ is tightly constrained by colours, while $σ_8$ benefits most from combining LFs and colours and from higher redshift information (notably $z=2$). Generalization across galaxy formation models is limited due to divergent subgrid physics and a simplistic forward model, underscoring the need for more flexible emission modelling and larger, higher-fidelity simulations. The generated photometric catalogs are public, illustrating a promising direction for cosmology- with-baryons analyses that complement traditional clustering probes.

Abstract

We perform the first direct cosmological and astrophysical parameter inference from the combination of galaxy luminosity functions and colours using a simulation based inference approach. Using the Synthesizer code we simulate the dust attenuated ultraviolet-near infrared stellar emission from galaxies in thousands of cosmological hydrodynamic simulations from the CAMELS suite, including the Swift-EAGLE, IllustrisTNG, Simba & Astrid galaxy formation models. For each galaxy we calculate the rest-frame luminosity in a number of photometric bands, including the SDSS $\textit{ugriz}$ and GALEX FUV & NUV filters; this dataset represents the largest catalogue of synthetic photometry based on hydrodynamic galaxy formation simulations produced to date, totalling >200 million sources. From these we compile luminosity functions and colour distributions, and find clear dependencies on both cosmology and feedback. We then perform simulation based (likelihood-free) inference using these distributions to constrain $Ω_m$, $σ_8$, and four parameters controlling the strength of stellar and AGN feedback. Both colour distributions and luminosity functions provide complementary information on certain parameters when performing inference. We achieve constraints on the stellar feedback parameters, as well as $Ω_m$ and $σ_8$. The latter is attributable to the fact that the photometry encodes the star formation-metal enrichment history of each galaxy; galaxies in a universe with a higher $σ_8$ tend to form earlier and have higher metallicities, which leads to redder colours. We find that a model trained on one galaxy formation simulation generalises poorly when applied to another, and attribute this to differences in the subgrid prescriptions, and lack of flexibility in our emission modelling. The photometric catalogues are publicly available at: https://camels.readthedocs.io/

Figures (21)

• Figure 1: Spectral energy distribution of an example galaxy from the IllustrisTNG CV set at $z = 0.1$. Shown is the intrinsic emission from young and old stars, the combined intrinsic emission, as well as the total attenuated emission. Filter transmission curves for some of the key rest-frame filters used in this work are also shown.
• Figure 2: CV set Luminosity functions (LFs; in AB magnitudes) at $z = 0.1$ for the IllustrisTNG, Simba, Astrid and Swift-EAGLE simulation suites in the GALEX FUV, SDSS $g$ and $i$, and UKIRT K bands. Each LF is built using galaxies from all CV simulations combined. Each panel shows the LFs obtained from the attenuated (solid lines) and intrinsic (dashed lines) emission. For Swift-EAGLE in the UKIRT K band we additionally show each individual CV simulation as thin red line, to illustrate the impact of cosmic variance.
• Figure 3: The same as Figure \ref{['fig:CV_sims_lfs']}, but showing normalised colour distributions. An additional magnitude cut for galaxies above $M_r < -20$ has been applied to remove faint galaxies. Left to right: GALEX $\mathrm{FUV}-\mathrm{NUV}$, SDSS $g-r$, $r-i$, $i-z$.
• Figure 4: Luminosity functions (LFs; in AB magnitudes) in the GALEX FUV, SDSS $g$ and $i$, and UKIRT K bands, over a range of redshifts ($z \in [0, 6]$). Each LF is built using galaxies from all CV simulations combined, normalised by the total volume ($27 \times (25 \, h^{-1})^3 \; \mathrm{Mpc^3}$). We show the relations for the IllustrisTNG, Simba, Astrid and Swift-EAGLE simulation suites. Each panel shows the LFs for both attenuated (solid lines) and intrinsic (faded dashed lines) emission.
• Figure 5: 1P set variations of the dust-attenuated photometry at $z = 0.1$ for IllustrisTNG, Simba, Astrid and Swift-EAGLE (columns left to right, respectively), when changing $\Omega_{\mathrm{m}}$. Top row: GALEX FUV luminosity function, with observations from GALEX in the FUV budavari_ultraviolet_2005. Second row: SDSS $r$-band luminosity function, with observations from the GAMA survey loveday_galaxy_2012. Third row: GALEX FUV-NUV colour distribution, with observational constraints from GAMA. Fourth row: SDSS $g-r$ colour distribution, with observational constraints from GAMA. Fifth row: GALEX FUV subhalo mass-to-light ratio against halo mass (individual objects are plotted where there are fewer than 10 sources in a halo mass bin). Sixth row: binned SDSS $r$-band subhalo mass-to-light ratio against halo mass. See Section \ref{['sec:difficulties']} for caveats on the observational constraints.