The stellar-to-halo mass relation of central galaxies across three orders of halo mass

The stellar content of galaxies is tightly connected to the mass and growth of their host dark matter halos. Observational constraints on this relation remain limited, particularly for low-mass groups, leaving uncertainties in how galaxies assemble their stars across halo mass scales. Accurately measuring the brightest central galaxy (BCG) stellar-to-halo mass relation (SHMR) over a wide mass range is therefore crucial for understanding galaxy formation and the role of feedback processes. Here we present the SHMR spanning $M_{\rm halo} \sim 10^{12}$-$10^{15},M_\odot$, using halo masses derived from eROSITA eRASS1 X-ray data and BCG stellar masses based on SDSS photometry. By stacking X-ray spectra of optically selected groups, we recover robust average halo gas temperatures for each bin, which are then converted to halo masses via the $M$-$T_X$ relation. We find that the SHMR peaks near $M_{\rm halo} \sim 10^{12},M_\odot$, with a declining stellar fraction at higher masses. This trend reflects a combination of processes that reduce the efficiency of stellar mass growth in massive halos, such as AGN feedback, reduced cooling efficiency, and the increasing dominance of ex-situ assembly, while halos continue to grow through mergers and accretion. Our measurements are consistent over the full mass range with previous observational studies, including weak lensing, X-ray analyses of individual clusters, and kinematical and dynamical methods. Comparisons with hydrodynamical simulations show good agreement at low masses but reveal significant discrepancies in the normalization at cluster scales, highlighting the sensitivity of BCG stellar growth to feedback prescriptions and halo assembly history. These results provide the first X-ray-based observational SHMR covering three orders of magnitude in halo mass, establish a robust benchmark for testing galaxy formation models.

💡 Research Summary

This paper presents a comprehensive measurement of the stellar‑to‑halo mass relation (SHMR) for brightest central galaxies (BCGs) across three orders of magnitude in halo mass, from Milky Way‑scale groups (Mhalo≈10¹² M⊙) up to massive clusters (Mhalo≈10¹⁵ M⊙). The authors combine optical group catalogs (Yang et al. 2007) with the first all‑sky X‑ray survey from eROSITA (eRASS1). Because individual low‑mass groups are too faint in X‑rays, they stack the X‑ray spectra of optically selected systems in bins of either BCG stellar mass or an optical halo‑mass proxy, thereby obtaining high‑signal‑to‑noise average spectra for each mass bin.

Spectral fitting is performed with the Sherpa package using a multi‑temperature plasma model (gadem, built from several mekal components) to represent the intracluster medium, a power‑law component for unresolved AGN, and Galactic absorption. Metallicity is fixed at 0.3 Z⊙. The mean temperature is left free while the width of the temperature distribution is fixed to avoid degeneracies. The resulting temperatures are converted to halo masses via a calibrated mass‑temperature (M–Tₓ) relation from Topun et al. (2025). BCG stellar masses are derived from SDSS photometry and the GSWLC‑X2 catalog assuming a Chabrier IMF.

The resulting SHMR shows a clear peak at Mhalo≈10¹² M⊙ where the stellar‑to‑halo mass fraction reaches ≈2–3 %. Above this mass the fraction declines steadily, confirming the classic “bell‑shaped” SHMR predicted by abundance‑matching and semi‑empirical models. The authors interpret the low‑mass rise as being limited by supernova‑driven winds, the peak as the regime where stellar and AGN feedback are comparable, and the high‑mass decline as a consequence of strong AGN heating, long cooling times, and an increasing contribution of ex‑situ (merger‑driven) stellar mass growth.

Comparisons with previous observational techniques—weak gravitational lensing, individual X‑ray analyses, and dynamical methods—show good agreement across the full mass range. However, when juxtaposed with state‑of‑the‑art hydrodynamical simulations (e.g., Magneticum, IllustrisTNG), the authors find that simulations match the observed SHMR at low masses but diverge at group and cluster scales, typically over‑predicting the stellar mass of BCGs or shifting the peak location. This discrepancy highlights the sensitivity of massive‑halo BCG growth to the implementation of AGN feedback and to halo assembly histories.

Methodologically, the paper demonstrates that X‑ray spectral stacking can reliably recover average gas temperatures and thus halo masses for systems that are individually undetectable in X‑rays. The bidirectional binning strategy (by stellar mass and by optical halo proxy) validates that the derived M⋆–Mhalo relation is robust against selection biases. The authors also discuss systematic uncertainties, including the fixed metallicity assumption and the choice of the M–Tₓ calibration, and show that these do not qualitatively alter the main conclusions.

Finally, the study outlines prospects for extending this work with deeper eROSITA data (eRASS4) and forthcoming large‑scale optical/infrared surveys (DESI, LSST). Such data will enable higher‑precision SHMR measurements, exploration of redshift evolution, and tighter constraints on galaxy formation models, particularly the physics of feedback in massive halos.