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Infrared excesses around metal polluted white dwarfs have been associatedwith the accretion of dusty, planetary material. This work analyses theavailable infrared data for an unbiased sample of white dwarfs and demonstratesthat no more than 3.3% can have a wide, flat, opaque dust disc, extending tothe Roche radius, with a temperature at the disc inner edge of $T_{in} =1,400$K, the standard model for the observed excesses. This is in starkcontrast to the incidence of pollution of about 30%. We present four potentialreasons for the absence of an infrared excess in polluted white dwarfs,depending on their stellar properties and inferred accretion rates: i) theirdust discs are opaque, but narrow, thus evading detection if more than 85% ofpolluted white dwarfs have dust discs narrower than $\delta r< 0.04r$, ii)their dust discs have been fully consumed, which only works for the oldestwhite dwarfs with sinking timescales longer than hundreds of years, iii) theirdust is optically thin, which can supply low accretion rates of $<10^7$gs$^{-1}$ if dominated by PR-drag, and higher accretion rates, if inwardstransport of material is enhanced, for example due to the presence of gas, iv)their accretion is supplied by a pure gas disc, which could result from thesublimation of optically thin dust for T* > 20, 000K. Future observationssensitive to faint infrared excesses or the presence of gas, can test thescenarios presented here, thereby better constraining the nature of thematerial fuelling accretion in polluted white dwarfs.

Infrared observations of white dwarfs and the implications for the accretion of dusty planetary material