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Polluted white dwarfs are generally accreting terrestrial-like material thatmay originate from a debris belt like the asteroid belt in the solar system.The fraction of white dwarfs that are polluted drops off significantly forwhite dwarfs with masses $M_{\rm WD}\gtrsim 0.8\,\rm M_\odot$. This impliesthat asteroid belts and planetary systems around main-sequence stars with mass$M_{\rm MS}\gtrsim 3\,\rm M_\odot$ may not form because of the intenseradiation from the star. This is in agreement with current debris disc andexoplanet observations. The fraction of white dwarfs that show pollution alsodrops off significantly for low mass white dwarfs $(M_{\rm WD}\lesssim0.55\,\rm M_\odot)$. However, the low-mass white dwarfs that do show pollutionare not currently accreting but have accreted in the past. We suggest thatasteroid belts around main sequence stars with masses $M_{\rm MS}\lesssim2\,\rm M_\odot$ are not likely to survive the stellar evolution process. Thedestruction likely occurs during the AGB phase and could be the result ofinteractions of the asteroids with the stellar wind, the high radiation or, forthe lowest mass stars that have an unusually close-in asteroid belt, scatteringduring the tidal orbital decay of the inner planetary system.

Asteroid belt survival through stellar evolution: dependence on the stellar mass