Cosmic star-formation decline, the first galaxies and early black holes from the energy cascade of dark matter and gas

Manuscript and CSV data behind the figures and tables of Xu (2026), Cosmic star-formation decline, the first galaxies and early black holes from the energy cascade of dark matter and gas, Research Square preprint, doi:10.21203/rs.3.rs-11556357/v1. Contents: the manuscript (P01_revised.pdf) and the folder csv/ with 30 CSV files holding the data behind Figs. 2 to 8, Figs. B1, Tables 1, 3, 4, 5, D1 and F1, and the numbers of Sections 2 to 5. Companion dataset: the 177 bulges of Table B1 and the black-hole masses of Xu (2025), doi:10.1093/mnras/stae2766, arXiv: arXiv:2501.07608. Major findings (Illustris-1-Dark and observed galaxies, 0 ≤ z ≤ 20): Haloes of fixed mass collapse at a fixed density contrast until a crossover at a* ≈ 0.5–0.64, after which they grow denser; the characteristic mass mh* ∝ a3θ, with θ falling from 1 to 1/2 at a*. Gas radiates its random energy; if its contrast stays fixed, the cascade rate shared by all galaxy cores rises as (1+z)5/2. The rate at the effective radius lies below the core rate by a factor F ∝ M-2/3: about 1 in spheroids and about 102 in low-mass discs. Late decline: after a*, the fraction of infalling gas that cools efficiently 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. First galaxies: a sharp onset of feedback-free star formation at z ≈ 10.5 fits the JWST UV densities and luminosity functions better than bursty or feedback-free alternatives (ΔAIC ≥ 42). Black holes: the luminosity ceiling L/LEdd ∝ (1+z)2 MBH-1/5 encloses all but 24 of 1.5×105 quasars, and MBH/σ5 stays constant. JADES black-hole hosts lie higher in σ3/Re than local disc hosts measured alike, by +1.18 dex at fixed σ and +1.98 dex at fixed dynamical mass.