Astronomy and Astrophysics – Astrophysics
Scientific paper
2003-11-04
Astrophys.J. 599 (2003) L45-L48
Astronomy and Astrophysics
Astrophysics
To appear in The Astrophysical Journal Letters; 10 pages, 3 figures
Scientific paper
10.1086/381137
Titanium carbide (TiC) nanocrystals were recently proposed as the carrier of the mysterious 21$\mum$ emission feature observed in post-asymptotic giant branch stars, based on their close spectral match and the presolar nature of meteoritic TiC nanograins (which reveals their stellar ejecta origin). But we show in this {\it Letter} that the Kramers-Kronig dispersion relations, which relate the wavelength-integrated extinction cross section to the total dust mass, would impose a lower bound on the TiC mass. This Kramers-Kronig lower limit exceeds the maximum available TiC mass by a factor of at least $\simali$50, independent of the absolute value of the ultraviolet/visible absorptivity of nano TiC. The TiC model is therefore readily ruled out by the Kramers-Kronig physical principle.
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