On the Formation of Graphite Grains in Cool Stars

The conditions for the formation of graphite grains in cool stars have been examined on the basis of recently available molecular equilibrium data for stellar atmospheres. The Hoyle-Wickramasinghe mecha- nism for condensation in N stars has been re-examined taking into account the presence of hydrogen, oxygen, and nitrogen. From Tsuji's tables, we find that the partial pressure of free carbon in an N star exceeds the vapor pressure of bulk graphite when the temperature falls below 24000 K for a solar C/H ratio and at still lower temperatures for other abundances Formation of graphite grains requires nuclea- tion followed by crystal growth. Using classical nucleation theory, it is shown that the supersaturation P/Ps~t required for graphite condensation on pre-existing ions in the stellar atmosphere is only ~`2.2. Such a supersaturation is reached when the temperature falls to ,~..)22OO0 K in an N star with a solar C/H ratio 1O~, and at `-~-45OO° K if C/H = 1O-~. Crystal growth proceeds sufficiently fast at the free-carbon pressures appropriate for temperatures greater than 15000 K to produce grain sizes exceeding 10-6 cm. The actual size to which particles grow is, however, restricted by the amount of available carbon and the number of effective condensation nuclei. With an ion density -`10~ cm3, particle sizes /-%~/5 x 106 cm would arise Assuming a constant luminosity function, it is shown that 1O~ N stars in the Galaxy (at any time) operating over a time scale of 1O~ years would suffice to produce the required grain density to ex- plain the interstellar extinction. The possibility that graphite particles may condense in the outer atmospheres of ordinary M giants is also discussed. Graphite condensation may take place to a limited extent in a region of the stellar atmos- phere where the temperature falls to about 16000 K, provided that the effective C/O ratio is 1.3. Such a high effective dO ratio cannot be ruled out, because of uncertainties in the relevant equilibrium calcula- tion