We present ATCA continuum observations at a wavelength of 6.8 mm of five debris disks: $beta$ Pictoris, q$^1$ Eridani, HD 107146, HD 181327, and HD 95086. These observations provide the detection at the longest wavelengths obtained to date for all these debris disks. By combining our 6.8 mm data with previous detections at shorter sub-millimeter/millimeter wavelengths we measure the long wavelength spectral index of these sources. We then use previous estimates for the temperature of the emitting dust to derive the spectral index of the dust emissivity. Under the assumption that all the detected flux comes from dust only, we constrain the slope of the solid size distribution, assumed to be a power-law. The values that we infer for the slope of the size distribution range between about 3.36 and 3.50. We compare our findings with the case of the Fomalhaut debris disk and use these results to test the predictions of collisional cascades of planetesimal belts.
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