A debris disk is a constituent of any planetary system surrounding a main sequence star. We study whether close stellar encounters can disrupt and strip a debris disk of its planetesimals in the expanding open cluster of its birth with a decreasing star number density over 100 Myr. Such stripping would affect the dust production and hence detectability of the disk. We tabulated the fractions of planetesimals stripped off during stellar flybys of miss distances between 100 and 1000 AU and for several mass ratios of the central to passing stars. We then estimated the numbers of close stellar encounters over the lifetime of several expanding open clusters characterized by their initial star densities. We found that a standard disk, with inner and outer radii of 40 and 100 AU, suffers no loss of planetesimals over 100 Myr around a star born in a common embedded cluster with star density ≤1000 pc −3 . In contrast, we found that such a disk is severely depleted of its planetesimals around a star born in an Orion-type cluster where the star density is >20 000 pc −3 . In this environment, a disk loses >97% of its planetesimals around an M-dwarf, >63% around a solar-type star, and >42% around an A-dwarf, over 100 Myr. We roughly estimate that two-thirds of the stars may be born in such high star density clusters. This might explain in part why fewer debris disks are observed around lower mass stars.

Debris disks have been found primarily around intermediate and solar mass stars (spectral types A-K), but rarely around low-mass M-type stars. This scarcity of detections in M star surveys can be confronted with the predictions of the steady state collisional evolution model. First, we determine the parameters of the disk population evolved with this model and fit to the distribution of the fractional dust luminosities measured in the surveys of A-and FGK-type stars observed by the infrared satellite Spitzer. Thus, in our approach, we stipulate that the initial disk mass distribution is bimodal and that only high-mass collisionally-dominated disks are detected. The best determined parameter is the diameter D c of the largest planetesimals in the collisional cascade of the model, which ranges between 2 and 60 km, consistently for disks around both A-and FGK-type stars. Second, we assume that the same disk population surrounds the M dwarfs that have been the subjects of debris disk searches in the far-infrared with Spitzer and at submillimeter wavelengths with radiotelescopes. We find, in the framework of our study, that this disk population, which has been fit to the AFGK data, is still consistent with the observed lack of disks around M dwarfs with Spitzer.