A Similarity Theorem and Its Breakdown in Atomic Black Hole Accretion
Abstract
Inferring black-hole mass and growth from radiation processed by dense atomic gas requires connecting the emitting atmosphere to its feeding flow. We derive an exact similarity for point-mass accretion and use its limits to identify spectral information and dynamical consistency tests. At fixed temperature and composition, scaling mass, radius, and time together while scaling density inversely preserves the dimensionless flow, optical depths, and normalized spectra within a specified class of two-body microphysics, radiation, and boundary laws. Luminosity scales with mass, and the full atomic cooling curve is retained. Within this class the fixed-velocity power-law rescaling is unique. Density-sensitive populations and thermal radiation break the symmetry; public models of Little Red Dots illustrate the resulting density information. Even with luminosity and density normalization known, a prescribed spherical inflow retains an exact degeneracy between central mass and inward drift. A proposed feeding model nevertheless supplies growth and inventory tests. For point-mass Bondi feeding at fixed ambient sound speed, luminosity and its conversion to retained growth determine the ratio of adjustment to growth time independently of black-hole mass. For the critical isothermal Bondi profile with full retention, comparable times require gas mass comparable to the hole's mass. More generally, steady spherical continuity links luminosity and gas transit time to a required reservoir mass and minimum radial column. Lower retention slows growth while leaving this inventory unchanged at fixed supply and transit time.
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BibTeX
@misc{dupont2026similarity,
title = {{A Similarity Theorem and Its Breakdown in Atomic Black Hole Accretion}},
author = {Marcus DuPont},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.28587},
eprint = {2608.28587},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28587},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Similarity Theorem and Its Breakdown in Atomic Black Hole Accretion
AU - Marcus DuPont
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2608.28587
UR - https://arxiv.org/abs/2608.28587
AB - Inferring black-hole mass and growth from radiation processed by dense atomic gas requires connecting the emitting atmosphere to its feeding flow. We derive an exact similarity for point-mass accretion and use its limits to identify spectral information and dynamical consistency tests. At fixed temperature and composition, scaling mass, radius, and time together while scaling density inversely preserves the dimensionless flow, optical depths, and normalized spectra within a specified class of two-body microphysics, radiation, and boundary laws. Luminosity scales with mass, and the full atomic cooling curve is retained. Within this class the fixed-velocity power-law rescaling is unique. Density-sensitive populations and thermal radiation break the symmetry; public models of Little Red Dots illustrate the resulting density information. Even with luminosity and density normalization known, a prescribed spherical inflow retains an exact degeneracy between central mass and inward drift. A proposed feeding model nevertheless supplies growth and inventory tests. For point-mass Bondi feeding at fixed ambient sound speed, luminosity and its conversion to retained growth determine the ratio of adjustment to growth time independently of black-hole mass. For the critical isothermal Bondi profile with full retention, comparable times require gas mass comparable to the hole's mass. More generally, steady spherical continuity links luminosity and gas transit time to a required reservoir mass and minimum radial column. Lower retention slows growth while leaving this inventory unchanged at fixed supply and transit time.
ER -