Relaxation of gas during dynamical black-hole growth

Determine whether gas in dense feeding flows associated with Little Red Dots and early quasars can relax while the central black hole grows dynamically, particularly beyond the regime in which the quasi-steady fixed-mass similarity description remains valid.

Background

The paper establishes an exact similarity transformation for atomic gas accreting onto a point mass when the black-hole mass is fixed, the ambient temperature and composition are fixed, and the relevant microphysical and feedback laws scale appropriately. Under this transformation, black-hole mass, radii, and times scale together while ambient density scales inversely with mass.

When the black hole grows rapidly, the Bondi radius expands and the dimensionless growth loading, defined as the fractional mass gained in one Bondi time, can approach unity. At this sonic-dilation boundary, the small parameter supporting a quasi-steady sequence of fixed-mass solutions disappears, and the black hole, its capture region, and the gas flow must be treated as a coupled dynamical system. The paper demonstrates the obstruction to a nontrivial stationary growing profile but does not determine whether the gas can nevertheless relax dynamically in the dense environments relevant to Little Red Dots and early quasars.