  Isolated Herbig Ae stars can be divided into two groups (Meeus et al. 2001):
those with an almost flat spectral energy distribution in the mid-infrared
(`group I'), and those with a strong decline towards the far-infrared (`group
II'). In this paper we show that the group I vs. II distinction can be
understood as arising from flaring vs. self-shadowed disks. We show that these
two types of disks are natural solutions of the 2-D radiation-hydrostatic
structure equations. Disks with high optical depth turn out to be flaring and
have a strong far-IR emission, while disks with an optical depth below a
certain threshold drop into the shadow of their own puffed-up inner rim and are
weak in the far-IR. In spite of not having a directly irradiated surface layer,
self-shadowed disks still display dust features in emission, in agreement with
observations of group II sources. We propose an evolutionary scenario in which
a disk starts out with a flaring shape (group I source), and then goes through
the process of grain growth, causing the optical depth of the disk to drop and
the disk to become self-shadowed (group II source). We show that this scenario
predicts that the (sub-)millimeter slope of the disk changes from steep (small
grains) to Rayleigh-Jeans-like (large grains) in the early stages of evolution,
so that all group II sources are expected to have Rayleigh-Jeans-like slopes,
while some group I sources may still have steep (sub-)millimeter slopes.
