Flares of Sagittarius A*: Variability Sizes and Energy Budgets From the Light-Travel Limit

A variable source cannot be larger than the distance light travels during its variation, and that single fact sizes the flares of Sagittarius A* without any image. This paper applies the light-travel limit across the published range of flare timescales. Variability as fast as 600 seconds confines the emitting region to 14 Schwarzschild radii; the hour-scale duration of a typical bright flare corresponds to 85 Schwarzschild radii as an upper envelope, and claimed substructure at 100 seconds would imply 2.4 Schwarzschild radii. A bright flare radiating at 1e+35 erg per second for an hour releases 3.6e+38 erg, some 4e+06 times the energy of a large solar flare, yet still only 1.8e-10 of the Eddington power. The magnetic energy stored in a region five Schwarzschild radii across at a field of thirty gauss exceeds the radiated flare energy by a factor of 106, so the energy supply is comfortable; the puzzle of the flares is their triggering, not their budget. Computed from published timescales and luminosities.