  The major-axis density profiles of bars are known to be either exponential or
'flat'. We develop an automated non-parametric algorithm to detect flat
profiles and apply it to a suite of simulations (with and without gas). We
demonstrate that flat profiles are a manifestation of a bar's secular growth,
producing a 'shoulder' region (an overdensity above an exponential) in its
outskirts. Shoulders are not present when bars form, but develop as the bar
grows. If the bar does not grow, shoulders do not form. Shoulders are often
accompanied by box/peanut bulges, but develop separately from them and are
independent tracers of a bar's growth. They can be observed at a wide range of
viewing orientations with only their slope varying significantly with
inclination. We present evidence that shoulders are produced by looped x1
orbits. Since the growth rate of the bar moderately correlates with the growth
rate of the shoulder strength, these orbits are probably recently trapped.
Shoulders therefore are evidence of bar growth. The properties of the shoulders
do not, however, establish the age of a bar, because secondary buckling or
strong spirals may destroy shoulders, and also because shoulders do not form if
the bar does not grow much. In particular, our results show that an exponential
profile is not necessarily an indication of a young bar.
