The Endgame in Numbers: When the Wind Overtakes Accretion, How Long the Inner Disc Survives, and Why a Tenth of Discs Have Holes

Disc dispersal has two timescales — a long life and a rapid death — and the standard explanation is a handover: once the accretion rate through the disc falls to the photoevaporative wind rate, the wind opens a gap, the inner disc drains, and the outer disc follows. This paper computes the handover with a similarity-solution accretion decline and the wind rates of the companion calculation. Against an X-ray wind of 6e-9 solar masses per year, the switch fires at 3.3 Myr; against an EUV wind of 4e-10 it would not fire until 20 Myr, after essentially all discs are already gone — EUV alone cannot run the endgame. The inner disc inside 5 AU holds 0.0046 solar masses and drains in 0.07 Myr at alpha = 1e-2 or 0.72 Myr at alpha = 1e-3, so the predicted fraction of discs caught with holes is 2 to 18 per cent — bracketing the observed transition-disc fraction of about ten per cent. Once the hole opens it expands at about 16 AU per Myr at 10 AU, reaching the observed hole sizes of tens of AU within the endgame duration. The two-timescale structure, the hole fraction and the hole sizes all fall out of three rates and one profile. Computed from stated assumptions, not measured.