On Titanium Carbide Nanoparticles as the Origin of the 21 Micron Emission Feature in Post–asymptotic Giant Branch Stars

Titanium carbide (TiC) nanocrystals were recently proposed as the carrier of the mysterious 21 mm 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 Letter that the KramersKronig 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∼50, independent of the absolute value of the (unknown) ultraviolet/visibleabsorptivity of nano-TiC. The TiC model is therefore readily ruled out by the Kramers-Kronig physical principle. Subject headings: circumstellar matter — dust, extinction — infrared: stars — stars: AGB and post-AGB — stars: individual (HD 56126)