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 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 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 similar to50, independent of the absolute value of the ( unknown) ultraviolet/visible absorptivity of nano-TiC. The TiC model is therefore readily ruled out by the Kramers-Kronig physical principle.