The quantification of galaxy number, luminosity and mass distributions within dark matter halos is crucial to constrain galaxy formation and evolution models. In the current paradigm of galaxy formation theory, halos with masses comparable to that of the Milky Way (~1012h-1M☉) are the most efficient locations for star formation, exhibiting the highest stellar-to-halo mass ratio. In more massive halos, galaxy growth is further inhibited by feedback from active galactic nuclei, causing the stellar-to-halo mass ratio to decline as halo mass increases. Conversely, in low-mass halos, star formation efficiency is also markedly reduced by feedback 

mechanisms such as stellar winds and supernovae, resulting in a lower stellar-to-halo mass ratio as halo mass decreases. This trend is illustrated by the dashed lines in the small inset in Figure 1.

Professor Xiaohu Yang's research team at the Tsung-Dao Lee Institute and the School of Physics and Astronomy, Shanghai Jiao Tong University, has recently, for the first time, attained precise measurements of the conditional luminosity function and conditional stellar mass function of galaxies at the very faint/low-mass ends. This was accomplished using photometric and spectroscopic data from DESI LS DR9, SV3, and Y1. The research shows that at low redshift, the slope of the conditional luminosity (stellar mass) function of galaxies below 109 h-2L☉(h-2M☉) diverges from extrapolations of earlier work with significantly enhanced low mass end slope. This finding points to the existence of numerous low-mass satellite galaxies within dark halos, which were accreted into halos along with substructures.

Further analysis revealed that the slope of the conditional luminosity (stellar mass) function at the low-mass end is notably consistent with the slope of the subhalo mass function (SHMF) at the low-mass end, as indicated by the dashed lines in Figure 2. This finding suggests that the star formation efficiency in low-mass halos may be roughly constant, which significantly conflicts with the widely accepted theory that stellar winds and supernova feedback strongly suppress star formation.

It is important to highlight that the integral of the conditional luminosity function and the conditional stellar mass function of galaxies results in the total luminosity function and stellar mass function. Thus, the pronounced slope change mentioned earlier should have been detected in prior galaxy observations. Yet, so far, no research has indicated such a notable slope variation at the low-mass end within the galaxy luminosity and stellar mass functions.

To explore this, the research team performed an in-depth analysis of the spectroscopic completeness and magnitude limits of DESI Y1 and discovered two factors that could affect the overall measurement results: photometric redshift errors and the fact that we, as observers, are located in a nearby cosmic void region. After correcting for these two factors, the team observed that the overall luminosity function and stellar mass function of galaxies also undergo a significant slope change below 109 h-2L☉(h-2M☉), as denoted by the stars in Figure 3. Furthermore, the slopes of these functions align almost perfectly with the slope of the halo mass function at the low-mass end (as indicated by the dashed lines in Figure 3), thus providing a self-consistent validation of their measurement results.

Utilizing the galaxy stellar mass function measurements and the theoretical dark halo mass function, we can apply the abundance matching method to model the connection between a galaxy's stellar mass and its host halo mass to halo masses as low as 108 h-1M☉ (as depicted by the solid line in Figure 1). Our findings reveal that for halos with masses under 1010.5 h-1M☉, the stellar-to-halo mass ratio of galaxies exhibits a significant flattening trend. This trend reveals that efficient star formation continues in low-mass halos, which contrasts sharply with the strong suppression effects anticipated by the traditional stellar wind and supernova feedback theory.

This outcome could be linked to the recent discoveries made by the James Webb Space Telescope, which identified a large population of high-redshift galaxies, hinting at a comparable underlying process. These results offer a strong observational foundation for upcoming attempts to develop a more thorough and coherent theory of galaxy formation and evolution.

This work was published in The Astrophysical Journal. The first author is Yirong Wang, a Ph.D. student from the 2020 cohort at Shanghai Jiao Tong University. Professor Xiaohu Yang from the Tsung-Dao Lee Institute and the School of Physics and Astronomy at Shanghai Jiao Tong University is the corresponding author. The research was supported by the National Key R&D Program of China, the National Natural Science Foundation of China, the Shanghai Natural Science Foundation, and the China Manned Space Program.