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 disk then grow on a timescale of order a disk rotation period ( \sim 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 , under realistic conditions , the timescale for secular evolution is shorter than the timescale 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 \delta \sim 0.01 - 0.1 , the range of most interest for observed strong bars and most pseudobulges .
At smaller amplitudes \delta \ll 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 \delta \gg 0.1 , the evolution is no longer secular ; the direct gravitational evolution of the seed substructure 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 .
The cosmological rate of galaxy evolution also defines a maximum bar/mode lifetime of practical interest , of \sim 0.1 t _ { Hubble } ( z ) .
Longer-lived modes will encounter cosmological effects and will de-couple from their drivers ( if they are driven ) .