SIMBAD references

The non-steady-state formation of small clusters and the growth of grains accompanied by chemical reactions are formulated under the consideration that the collision of key gas species (key molecule) controls the kinetics of dust formation process. The formula allows us to evaluate the size distribution and condensation efficiency of dust formed in astrophysical environments. We apply the formulation to the formation of C and MgSiO₃ grains in the ejecta of supernovae, as an example, to investigate how the non-steady effect influences the formation process, condensation efficiency f_con, ∞_, and average radius a_ave, ∞_ of newly formed grains in comparison with the results calculated with the steady-state nucleation rate. We show that the steady-state nucleation rate is a good approximation if the collision timescale of key molecule τ_coll is much smaller than the timescale τ_sat with which the supersaturation ratio increases; otherwise the effect of the non-steady state becomes remarkable, leading to a lower f_con, ∞_ and a larger a_ave, ∞_. Examining the results of calculations, we reveal that the steady-state nucleation rate is applicable if the cooling gas satisfies Λ ≡ τ_sat/τ_coll ≳ 30 during the formation of dust, and find that f_con, ∞_ and a_ave, ∞_are uniquely determined by Λ_on at the onset time t_onof dust formation. The approximation formulae for f_con, ∞_ and a_ave, ∞_as a function of Λ_on could be useful in estimating the mass and typical size of newly formed grains from observed or model-predicted physical properties not only in supernova ejecta but also in mass-loss winds from evolved stars.