  The formation of silicate dust in oxygen-rich envelopes of evolved stars is
thought to be initiated by formation of seed particles that can withstand the
high temperatures close to the stellar photosphere and act as condensation
cores farther away from the star. Candidate species considered as first
condensates are TiO and TiO$_2$. We aim to identify and characterize the
circumstellar gas-phase chemistry of titanium that leads to the formation of
solid titanium compounds in the envelope of $o$ Cet, the prototypical Mira, and
seek an observational verification of whether titanium oxides play a major role
in the onset of dust formation in M-type AGB stars. We present high
angular-resolution ALMA observations at submillimeter (submm) wavelengths
supplemented by APEX and Herschel spectra of the rotational features of TiO and
TiO$_2$. In addition, circumstellar features of TiO and TiI are identified in
optical spectra which cover multiple pulsation cycles of $o$ Cet. The submm
ALMA data reveal TiO and TiO$_2$ bearing gas within the extended atmosphere of
Mira. While TiO is traceable up to a radius (FWHM/2) of 4.0 R$_{\star}$,
TiO$_2$ extends as far as 5.5 R$_{\star}$ and unlike TiO appears to be
anisotropically distributed. Optical spectra display variable emission of TiI
and TiO from inner parts of the extended atmosphere (<3 R$_{\star}$). Chemical
models which include shocks are in general agreement with the observations of
gas-phase titanium-bearing molecules. It is unlikely that substantial amounts
of titanium is locked up in solids because the abundance of the gaseous
titanium species is very high. In particular, formation of hot titanium-rich
condensates is very improbable because we find no traces of their hot precursor
species in the gas phase. It therefore appears unlikely that the formation of
dust in Mira, and possibly other M-type AGB stars, is initiated by titanium
oxides.
