Waking the Belt: Self-Stirring Times, the Case for Planetary Stirrers, and the Maximum Luminosity a Debris Disc Can Show

A planetesimal belt is dark until something stirs it: collision velocities must be raised to disruptive levels before the cascade can begin. This paper computes when a belt can stir itself — by growing its own Pluto-sized stirrers — and what luminosity it can then show, for belts at 45 AU. The self-stirring time is 2851 Myr for a one-Earth-mass belt, 285 Myr for ten Earth masses and 95 Myr for thirty. Bright debris discs are already shining at 10 to 20 Myr (the beta Pictoris system is the type example), which self-stirring at these masses cannot do: an external stirrer, most plausibly a planet, is required for the young bright population, while self-stirring suffices for belts that switch on at hundreds of Myr. Once stirred, a ten-Earth-mass belt shows fractional luminosity 1.8e-04 at 500 Myr, 1.1e-04 at 1 Gyr and 2.5e-05 at 5 Gyr — the familiar 1/t fading — and cannot exceed its full-stock value at any age, which caps how bright an old debris disc can be without a recent event. The debris sky's brightness distribution is thus a record of two clocks: stirring, which sets the onset, and collisional grinding, which sets the decay. Computed from stated assumptions, not measured.