  Atoms subject to weak coherent incident light can be treated as coupled
classical linear oscillators, supporting subradiant and superradiant collective
excitation eigenmodes. We identify the limits of validity of this \emph{linear
classical oscillator model} at increasing intensities of the drive by solving
the quantum many-body master equation for coherent and incoherent scattering
from a chain of trapped atoms. We show that deviations from the linear
classical oscillator model depend sensitively on the resonance linewidths
$\upsilon_\alpha$ of the collective eigenmodes excited by light, with the
intensity at which substantial deviation occurs scaling as a powerlaw of
$\upsilon_\alpha$. The linear classical oscillator model then becomes
inaccurate at much lower intensities for subradiant collective excitations than
superradiant ones, with an example system of seven atoms resulting in critical
incident light intensities differing by a factor of 30 between the two cases.
By individually exciting eigenmodes we find that this critical intensity has a
$\upsilon_\alpha^{2.5}$ scaling for narrower resonances and more strongly
interacting systems, while it approaches a $\upsilon_\alpha^3$ scaling for
broader resonances and when the dipole-dipole interactions are reduced. The
$\upsilon_\alpha^3$ scaling also corresponds to the semiclassical result
whereby quantum fluctuations between the atoms have been neglected. We study
both the case of perfectly mode-matched drives and the case of standing wave
drives, with significant differences between the two cases appearing only at
very subradiant modes and positions of Fano resonances.
