  The collisional evolution of debris disks is expected to result in a
characteristic wavy pattern of the grain size distributions, i.e., an
under/overabundance of particles of specific sizes. This perturbed grain size
distribution potentially leaves characteristic patterns in the spectral energy
distribution (SED) of the disk system. We aim to quantify and understand the
specific influence of discontinuous particle size distributions on the
appearance of debris disks. For this purpose, we consider dust emission models
based on two different grain size distributions, i.e., once with a single and
once with a broken power law. We compare the spectral index $\alpha$
($F_{\nu}\,\propto \nu^{\rm{\,\alpha}}$) in the case of a continuous grain size
distribution with that of a discontinuous grain size distribution. We perform
this comparison for central stars with different spectral types and two
different disk structures (e.g., slim and broad debris dust rings). Within the
considered parameter space, we find a characteristic difference between the
spectral slopes of the SED in the different scenarios. More specifically, the
overabundance of small grains leads to a steeper slope in the
far-infrared/submillimeter regime, while the spectral index in the mm regime is
hardly affected. On the other hand, the underabundance of medium-sized grains
results in a slight steepening of the far-infrared slope of SED, while its
primary effect is on the mm slope of SED, causing it to become shallower. We
also find that the impact of an overabundance of small dust particles is more
pronounced than that of an underabundance of medium-sized dust particles.
Furthermore, we find that the difference between the spectral indices for the
two different grain size distributions is largest for debris disks around
brighter central stars and broader disks.
