Galaxy formation in the first billion years

Abstract

These notes present material from lectures given at the 54th Saas-Fee Advanced Course of the Swiss Society of Astrophysics and Astronomy in January 2025, entitled "Galaxies and Black Holes in the First Billion Years as seen by the JWST", and are intended for early career researchers or those new to the sub-field. My lectures covered the theory of galaxy formation with a focus on the first billion years of cosmic evolution. In these notes, I discuss cosmological structure formation, properties of dark matter halos at $z\gtrsim 6$, and whether any of the JWST observations to date present a serious and fundamental challenge for the $Λ$ Cold Dark Matter Paradigm. I then give an overview of physical processes and modeling techniques, including translating simulation-based quantities to observables, and discuss recent progress and future directions in galaxy formation modeling. The closing section presents a summary of some of the theoretical puzzles and challenges raised by the first three years of high redshift observations with JWST, and how our models of galaxy formation may need to be revised to accommodate them.

Figures (25)

• Figure 1: Halo mass functions (HMF) from the GUREFT N-body simulation suite shown at $z=0$, 2, 6, 10, 15, 20, 25, and 30, compared with commonly used halo mass functions from analytic models and extrapolations of fitting functions based on lower resolution simulations that were not analyzed at ultra-high redshift (see Yung2024a and Yung2025 for details). The bottom panels show the fractional difference of the number density of halos from these HMFs relative to the GUREFT outputs. Halo mass functions that are commonly used in the literature can deviate from these robust N-body based results by up to an order of magnitude at ultra-high redshift. Based on Yung2024a, Fig. 5 and Yung2025, Fig. A1.
• Figure 2: UV luminosity functions at $z=12$, 14, 17, and 25, showing a compilation of recent observational estimates (see Yung2025 for details). The blue lines show the predicted UVLF from the simple empirical model described in the text, with a maximal baryon conversion efficiency $\epsilon_*=1$. The purple shaded regions show the predicted UVLF for the fitted functional form of $\epsilon_*(M_h,z)$ (Eqn. \ref{['eqn:estaremp']}). The fact that the blue lines are everywhere higher than the observations implies that there is no fundamental tension between $\Lambda$CDM and these observations. Reproduced from Yung2025, Fig. 4.
• Figure 3: The median (solid lines) and 16th and 84th percentiles (shaded regions) baryon conversion efficiency $\epsilon_*(M_h,z)$ obtained from fitting the empirical model described in the text to the observed UVLF. Darker lines and shaded regions show the approximate range of halo mass where there are current observational constraints. The required efficiencies of up to $\sim 20$--50 % are high, but perhaps not unphysically so. Reproduced from Yung2025, Fig. 5.
• Figure 4: Ratio of galaxy UV continuum radius to host dark matter halo radius, $r_e/r_{\rm vir}$, as a function of redshift. The black diamonds and downward triangles indicate the results from pre-JWST studies of $z \sim 4$--8 star-forming galaxies. The red open circles and red filled circles represent the results of individual measurements of relatively luminous galaxies, and results from stacked images of fainter galaxies, respectively, at $z\sim 10$--16 from the analysis of Ono:2025. The blue circles indicate spectroscopically confirmed galaxies. It is striking that the ratio of galaxy radius to DM halo virial radius at $z\sim 10$--16 is so similar to that at much lower redshifts. Reproduced from Ono:2025, Fig. 20.
• Figure 5: Fraction of baryonic mass within halos as a function of total halo mass at three redshifts, for simulations that include a spatially uniform, time-varying meta-galactic UV background. Hydrogen reionization is assumed to start at $z = 9$. The top row shows all halos, and the bottom row shows isolated halos. After reionization, cooling and accretion is dramatically suppressed in halos below a critical mass, due to photo-ionization "squelching". Reproduced from Okamoto:2008, Fig. 2.