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/mergers). Most study has focused on 'isolated' galaxies, where seed asymmetries may represent realistic cosmological substructure, but subsequent evolution ignores galaxy growth. Large-scale modes in the disk then grow on a timescale of order a disk rotation period (0.1-1 Gyr). If, however, galaxies evolve cosmologically on a shorter timescale, then it may not be appropriate to consider them 'isolated.' We outline simple scalings to ask whether the timescale for secular evolution is shorter than the timescale for cosmological accretion and mergers. This is the case in a narrow, but important range of perturbation amplitudes corresponding to substructure or mode/bar fractional amplitudes 0.01-0.1, a range of interest for observed strong bars and pseudobulges. At smaller amplitudes <<0.1, systems are not isolated: typical disks will grow by accretion at a comparable level over even a single dynamical time. At larger amplitudes >>0.1, the evolution is no longer secular; direct gravitational evolution of the seed swamps the internal disk response. We derive criteria for when disks can be well-approximated as 'isolated' as a function of mass, redshift, and disk stability. The relevant parameter space shrinks at higher mass, higher disk stability, and higher-z as accretion rates increase. Cosmological rates of galaxy evolution also define a maximum bar/mode lifetime of practical interest, of ~0.1/H(z). Longer-lived modes will de-couple from their drivers (if driven) and encounter cosmological effects.