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Debris disks common around Sun-like stars carry dynamical imprints in their structure that are key to understanding the formation and evolution history of planetary systems. In this paper, we extend an algorithm (rave) originally developed to model edge-on disks to be applicable to disks at all inclinations. The updated algorithm allows for non-parametric recovery of the underlying (i.e., deconvolved) radial profile and vertical height of optically thin, axisymmetric disks imaged in either thermal emission or scattered light. Application to simulated images demonstrates that the de-projection and deconvolution performance allows for accurate recovery of features comparable to or larger than the beam or PSF size, with realistic uncertainties that are independent of model assumptions. We apply our method to recover the radial profile and vertical height of a sample of 18 inclined debris disks observed with ALMA. Our recovered structures largely agree with those fitted with an alternative visibility-space de-projection and deconvolution method (frank). We find that for disks in the sample with a well-defined main belt, the belt radius, fractional width and fractional outer edge width all tend to increase with age, but do not correlate in a clear or monotonic way with dust mass or stellar temperature. In contrast, the scale height aspect ratio does not strongly correlate with age, but broadly increases with stellar temperature. These trends could reflect a combination of intrinsic collisional evolution in the disk and the interaction of perturbing planets with the disk's own gravity., Comment: 23 pages, 17 figures, 1 table, accepted for publication in MNRAS

The Herschel open-time key program Disc Emission via a Bias-free Reconnaissance in the Infrared and Sub-millimeter (DEBRIS) is an unbiased survey of the nearest ~100 stars for each stellar type A-M observed with a uniform photometric sensitivity to search for cold debris disks around them. The analysis of the Photoconductor Array Camera and Spectrometer (PACS) photometric observations of the 94 DEBRIS M dwarfs of this program is presented in this paper, following upon two companion papers on the DEBRIS A-star and FGK-star subsamples. In the M-dwarf subsample, two debris disks have been detected, around the M3V dwarf GJ581 and the M4V dwarf FomalhautC (LP876-10). This result gives a disk detection rate of 2.1^{+2.7}_{-0.7}% at the 68% confidence level, significantly less than measured for earlier stellar types in the DEBRIS program. However, we show that the survey of the DEBRIS M-dwarf subsample is about ten times shallower than the surveys of the DEBRIS FGK subsamples when studied in the physical parameter space of the disk's fractional dust luminosity versus blackbody radius. Furthermore, had the DEBRIS K-star subsample been observed at the same shallower depth in this parameter space, its measured disk detection rate would have been statistically consistent with the one found for the M-dwarf subsample. Hence, the incidence of debris disks does not appear to drop from the K subsample to the M subsample of the DEBRIS program, when considering disks in the same region of physical parameter space. An alternative explanation is that the only two bright disks discovered in the M-dwarf subsample would not, in fact, be statistically representative of the whole population., Comment: 12 pages, long Table 3 included, accepted for publication in Astronomy & Astrophysics