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The collisional evolution of debris disks is expected to result in acharacteristic wavy pattern of the grain size distributions, i.e., anunder/overabundance of particles of specific sizes. This perturbed grain sizedistribution potentially leaves characteristic patterns in the spectral energydistribution (SED) of the disk system. We aim to quantify and understand thespecific influence of discontinuous particle size distributions on theappearance of debris disks. For this purpose, we consider dust emission modelsbased on two different grain size distributions, i.e., once with a single andonce with a broken power law. We compare the spectral index $\alpha$($F_{\nu}\,\propto \nu^{\rm{\,\alpha}}$) in the case of a continuous grain sizedistribution with that of a discontinuous grain size distribution. We performthis comparison for central stars with different spectral types and twodifferent disk structures (e.g., slim and broad debris dust rings). Within theconsidered parameter space, we find a characteristic difference between thespectral slopes of the SED in the different scenarios. More specifically, theoverabundance of small grains leads to a steeper slope in thefar-infrared/submillimeter regime, while the spectral index in the mm regime ishardly affected. On the other hand, the underabundance of medium-sized grainsresults in a slight steepening of the far-infrared slope of SED, while itsprimary effect is on the mm slope of SED, causing it to become shallower. Wealso find that the impact of an overabundance of small dust particles is morepronounced than that of an underabundance of medium-sized dust particles.Furthermore, we find that the difference between the spectral indices for thetwo different grain size distributions is largest for debris disks aroundbrighter central stars and broader disks.

Impact of discontinuous grain size distributions on the spectral energy distribution of debris disks