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High-metallicity pollution is common in white dwarf (WD) stars hostingremnant planetary systems. However, they rarely have detectable debrisaccretion discs, possibly because much of the influx is fast steeply-infallingdebris in star-grazing orbits, producing a more tenuous signature than a slowlyaccreting disk. Processes governing such deposition between the Roche radiusand photosphere have so far received little attention and we model them hereanalytically by extending recent work on sun-grazing comets to WD systems. Wefind that the evolution of cm-to-km size (a_0) infallers most strongly dependson two combinations of parameters, which effectively measure sublimation rateand binding strength. We then provide an algorithm to determine the fate ofinfallers for any WD, and apply the algorithm to four limiting combinations ofhot versus cool (young/old) WDs with snowy (weak, volatile) versus rocky(strong, refractory) infallers. We find: (i) Total sublimation above thephotosphere befalls all small infallers across the entire WD temperature (T_WD)range, the threshold size rising with T_WD and 100X larger for rock than snow.(ii) All very large objects fragment tidally regardless of T_WD: for rock, a_0>= 10^5 cm; for snow, a_0 >= 10^3 -- 3x10^4 cm across all WD cooling ages.(iii) A considerable range of a_0 avoids fragmentation and total sublimation,yielding impacts or grazes with cold WDs. This range narrows rapidly withincreasing T_WD, especially for snowy bodies. Finally, we discuss briefly howthe various forms of deposited debris may finally reach the photosphere surfaceitself.

Deposition of steeply infalling debris around white dwarf stars