Polluted white dwarfs are generally accreting terrestrial-like material that may originate from a debris belt like the asteroid belt in the solar system .
The fraction of white dwarfs that are polluted drops off significantly for white dwarfs with masses M _ { WD } \gtrsim 0.8 M _ { \odot } .
This implies that asteroid belts and planetary systems around main-sequence stars with mass M _ { MS } \gtrsim 3 M _ { \odot } may not form because of the intense radiation from the star .
This is in agreement with current debris disc and exoplanet observations .
The fraction of white dwarfs that show pollution also drops off significantly for low mass white dwarfs ( M _ { WD } \lesssim 0.55 M _ { \odot } ) .
However , the low-mass white dwarfs that do show pollution are not currently accreting but have accreted in the past .
We suggest that asteroid belts around main sequence stars with masses M _ { MS } \lesssim 2 M _ { \odot } are not likely to survive the stellar evolution process .
The destruction likely occurs during the AGB phase and could be the result of interactions of the asteroids with the stellar wind , the high radiation or , for the lowest mass stars that have an unusually close-in asteroid belt , scattering during the tidal orbital decay of the inner planetary system .