Debris discs around M stars: non-existence versus non-detection

Motivated by the reported dearth of debris discs around M stars, we use survival models to study the occurrence of planetesimal discs around them. These survival models describe a planetesimal disc with a small number of parameters, determine if it may survive a series of dynamical processes and compute the associated infrared excess. For the Wide-field Infrared Survey Explorer (WISE) satellite, we demonstrate that the dearth of debris discs around M stars may be attributed to the small semimajor axes generally probed if either: (1) the dust grains behave like blackbodies emitting at a peak wavelength coincident with the observed one; (2) or the grains are hotter than predicted by their blackbody temperatures and emit at peak wavelengths that are shorter than the observed one. At these small distances from the M star, planetesimals are unlikely to survive or persist for time-scales of 300 Myr or longer if the disc is too massive. Conversely, our survival models allow for the existence of a large population of low-mass debris discs that are too faint to be detected with current instruments. We gain further confidence in our interpretation by demonstrating the ability to compute infrared excesses for Sun-like stars that are broadly consistent with reported values in the literature. However, our interpretation becomes less clear and large infrared excesses are allowed if only one of these scenarios holds: (3) the dust grains are hotter than blackbody and predominantly emit at the observed wavelength; (4) or are blackbody in nature and emit at peak wavelengths longer than the observed one. Both scenarios imply that the parent planetesimals reside at larger distances from the star than inferred if the dust grains behaved like blackbodies. In all scenarios, we show that the infrared excesses detected at 22 μm (via WISE) and 70 μm (via Spitzer) from AU Mic are easily reconciled with its young age (12 Myr). Conversely, the existence of the old debris disc (2–8 Gyr) from GJ 581 is due to the large semimajor axes probed by the Herschel PACS instrument. We elucidate the conditions under which stellar wind drag may be neglected when considering dust populations around M stars. The WISE satellite should be capable of detecting debris discs around young M stars with ages ∼10 Myr.