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.
