When should we treat galaxies as isolated?

Traditionally, secular evolution is defined as evolution of systems where the internal growth of structure and instabilities dominates the growth via external drivers (e.g. accretion and mergers). Most study has focused on 'isolated' galaxies, where seed asymmetries may represent realistic cosmological substructure, but subsequent evolution ignores galaxy growth and interactions. Large-scale modes in the disc then grow on a time-scale of the order of a disc rotation period (∼0.1-1 Gyr). If, however, galaxies evolve cosmologically on a shorter time-scale, then it may not be appropriate to consider them 'isolated'. We outline simple scalings to ask whether, under realistic conditions, the time-scale for secular evolution is shorter than the time-scale for cosmological accretion and mergers. We show that this is the case in a relatively narrow but important range of perturbation amplitudes corresponding to substructure or mode/bar fractional amplitudes δ ∼ 0.01-0.1, the range of most interest for observed strong bars and most pseudo-bulges. At smaller amplitudes δ ≪ 0.1, systems are not isolated: typical discs will grow by accretion at a comparable level over even a single dynamical time. At larger amplitudes δ ≫ 0.1, the evolution is no longer secular; the direct gravitational evolution of the seed substructure swamps the internal disc response. We derive criteria for when discs can be well approximated as 'isolated' as a function of mass, redshift and disc stability. The relevant parameter space shrinks at higher mass, higher disc stability and higher z as accretion rates increase. The cosmological rate of galaxy evolution also defines a maximum bar/mode lifetime of practical interest, of ∼0.1 t _Hubble(z). Longer lived modes will encounter cosmological effects and will decouple from their drivers (if they are driven).