Energy–mass relation of emitted quanta in the memory-burden phase

Ascertain the functional relationship between black-hole mass and the typical energy of emitted quanta after the semi-classical description breaks down and the memory-burden phase begins, specifically whether the effective emission temperature remains fixed (no-burst scenario) or continues to increase with decreasing mass (burst scenario).

Background

Predictions for the dark-matter momentum distribution depend sensitively on how the emission temperature behaves during the memory-burden phase. The authors study two prescriptions: a constant-temperature ‘no burst’ model and a time-evolving ‘burst’ model where temperature increases as mass decreases, analogous to the semi-classical regime.

The lack of a definitive description of the energy–mass relation in the memory-burden regime introduces substantial uncertainty into the high-energy tail and overall shape of the dark-matter velocity distribution, with direct consequences for Lyman-α forest constraints.