Stellar to Halo Mass Relation

The stellar-to-halo mass relation — the ratio of stellar mass to total gravitational mass as a function of halo mass — has a characteristic peaked shape: the conversion of baryons into stars is most efficient at halo masses near 10^{12} solar masses, and falls steeply both toward lower-mass halos (where supernova feedback is efficient) and toward higher-mass halos (where AGN feedback quenches star formation). This double-power-law shape and its specific peak location require fine-tuned feedback prescriptions in ΛCDM simulations that have no first-principles derivation; the feedback parameters must be empirically tuned to reproduce the observed relation. Successive Collision Theory provides a physically grounded origin for the peak location without feedback fine-tuning. The peak at 10^{12} solar masses corresponds to the halo mass scale where the centrifugal barrier from inherited angular momentum and the gravitational depth from frame superposition are simultaneously optimized for efficient gas cooling and confinement.

Below this mass scale, the inherited specific angular momentum is sufficient to prevent efficient gas infall into the center — the centrifugal barrier keeps gas in extended, diffuse orbits with long cooling times. Above this mass scale, the gravitational potential is deep enough to retain gas but the virial temperature of the infalling gas exceeds the cooling threshold for atomic hydrogen, suppressing further star formation after the initial high-redshift burst. The result is a natural peak in star formation efficiency that does not require fine-tuned AGN or supernova feedback — although these processes do operate in SCT as they do in ΛCDM, they are not the primary regulators of the stellar-to-halo mass peak. Instead, the angular momentum barrier and the virial temperature threshold — both rooted in GR and the collision's angular momentum deposition — define the peak scale, and feedback processes modulate the shape of the wings of the relation around this physically grounded peak.