Onset scale of the memory-burden regime in black hole evaporation

Determine the mass scale, expressed as a fraction q of the primordial black hole mass at formation M_F, at which the semi-classical Hawking evaporation description ceases to be valid and the memory-burden regime begins for an evaporating black hole. Establishing this onset scale is necessary to model the transition between phases of evaporation and to quantify resulting dark-matter emission and cosmological signatures.

Background

The analysis assumes that semi-classical evaporation must break down before the black hole reaches Planckian mass, but the precise point at which this occurs is unknown. The authors therefore parametrize the onset by a dimensionless fraction q of the initial mass. Theoretical arguments suggest that memory burden should start no later than after half the mass has been lost, but a general determination of q remains open.

The value of q impacts the timing and spectra of particles emitted during evaporation and thus affects the phase-space distribution of non-cold dark matter and the corresponding structure-formation constraints derived from the Lyman-α forest.

References

Since the associated scale has not yet been determined, in this work, we will remain general and denote the mass scale at which the SC approach is no longer valid as $q\,M_\mathrm{F}$. However, note that in Refs., it was argued that the MB should set in at the latest when the BH has lost half of its mass, i.e.~for $ q \geq 0.5$.

— Non-Cold Dark Matter from Memory-Burdened Primordial Black Holes  (2604.00090 - Thoss et al., 31 Mar 2026) in Section 2.2, The Memory-Burden Effect