The bright end of the exo-Zodi luminosity function: disc evolution and implications for exo-Earth detectability

We present the first characterisation of the 12um warm dust ("exo-Zodi") luminosity function around Sun-like stars, focussing on the dustiest systems that can be identified by WISE. We detect six new warm dust candidates, five of which have unknown ages. We show that the dustiest old (>Gyr) systems like BD+20 307 are 1 in 10,000 occurrences. Bright warm dust is more common around young (<120Myr) systems, with a ~1% occurrence rate. We show that a two component in situ model where all stars have initially massive warm disks and in which warm debris is also generated at some random time along the stars' main-sequence lifetime, perhaps due to a collision, can explain the observations. However, if all stars only have initially massive warm disks these would not be visible at Gyr ages, and random collisions on the main-sequence are too infrequent to explain the high disk occurrence rate for young stars. That is, neither component can explain the observations on their own. Despite these conclusions, we cannot rule out an alternative model in which comets are scattered from outer regions because the distribution of systems with the appropriate dynamics is unknown. Our in situ model predicts the fraction of stars with exo-Zodi bright enough to cause problems for future exo-Earth imaging attempts is at least ~10%, and is higher for populations of stars younger than a few Gyr. This prediction of ~10% applies to old stars because bright systems like BD+20 307 imply a population of fainter systems that were once bright but are now decaying through fainter levels. Our prediction should be strongly tested by the Large Binocular Telescope Interferometer, providing valuable input for more detailed evolution models. A detection fraction lower than our prediction could indicate that the hot dust in systems like BD+20 307 has a cometary origin due to the quirks of the planetary dynamics.