Cosmic star-formation decline, the first galaxies and early black holes from the energy cascade of dark matter and gas
Year: 2026
Type: preprint
Abstract: Three puzzles in galaxy evolution follow from the energy cascade in haloes and galaxy centres: the steep decline of cosmic star formation since $z\simeq2$, the excess of UV-bright galaxies at $z>10$, and over-massive early black holes. Haloes of fixed mass collapse at a fixed density contrast until a crossover at $a_*\simeq0.5$--0.64, then grow denser. Gas instead radiates its random energy; if it keeps a fixed contrast, the cascade rate shared by all galaxy cores rises as $(1+z)^{5/2}$. Like haloes, galaxies have two levels: cores share a rate and boundaries a contrast, so the rate at the effective radius lies below the core rate by $F\propto M^{-2/3}$, about 1 in spheroids and $\sim10^2$ in low-mass discs. (i) \emph{Late decline.} Infalling gas reaches the galaxy only if the core radiates its heat fast enough. After $a_*$ this cooling fraction falls as $(1+z)^{5/4}$, steepening the local slope of the star-formation density from 1.5 to 2.7 with no added parameter. (ii) \emph{First galaxies.} Core densities at a given scale are the same in every host, so the threshold for feedback-free star formation is crossed in all haloes at once. A sharp onset at $z\simeq10.5$ fits the JWST densities and luminosity functions better than bursty or feedback-free alternatives ($\Delta{\rm AIC}\ge42$). (iii) \emph{Black holes.} Luminosity is limited by the pressure of the dense core gas, which rises with redshift, rather than by electron scattering. The resulting ceiling, $L/L_{\rm Edd}\propto(1+z)^2M_{\rm BH}^{-1/5}$, encloses all but 24 of $1.5\times10^5$ quasars\fix{ and the little red dots with revised masses}{}. Because the core sets the black hole, $M_{\rm BH}/\sigma^5$ stays constant, while dynamical masses at the effective radius of disc-dominated hosts lie a factor $F\simeq70$--90 below the core level, nearly cancelling the rise of the core rate, $(1+z)^{5/2}\simeq88$ at $z\simeq5$. This is why JADES black holes lie 1--2 dex above the local relation with stellar mass but near those with dispersion and dynamical mass. Against local disc hosts measured alike, the JADES hosts lie higher in $\sigma^3/R_e$ by $+1.18$ dex at fixed $\sigma$ and $+1.98$ dex at fixed dynamical mass, as predicted.
Source: Research Square
Author: Zhijie Xu
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225631998
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