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$\text{mum}$ 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 $\text{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.