The temperature of newly forming dust is controlled by the radiation field.
As dust forms around stars, stellar transients, quasars or supernovae, the
grains must grow through a regime where they are stochastically heated by
individual photons. Since evaporation rates increase exponentially with
temperature while cooling times decrease only as a power law, the evaporation
rates for these small grains are dominated by the temperature spikes. We
calculate effective evaporation temperatures for a broad range of input spectra
that are encapsulated in a series of simple interpolation formulae for both
graphitic and silicate grains. These can be easily used to first determine if
dust formation is possible and then to estimate the radius or time at which it
commences for a broad range of radiation environments. With these additional
physical effects, very small grains may form earlier than in standard models of
AGB winds. Even for very high mass loss rates, the hottest stars that can form
dust are G and F stars particularly in the case of silicate dusts. For hotter
stars, the higher fluxes of ultraviolet photons prevent dust formation. Thus,
episodic dust formation by OH/IR stars and LBVs is primarily driven by
fluctuations in their apparent temperatures rather than changes in luminosity
or mass loss rates.Comment: 13 pages, 10 figures, submitted to MNRA