  Low- and intermediate-mass stars at the asymptotic giant branch (AGB) are
known to be prevalent dust providers to galaxies. However, the mechanisms
responsible for the formation and acceleration of dust in the cool extended
atmospheres of AGB stars are still open to debate. We present visible
polarimetric imaging observations of the oxygen-rich AGB star IK Tau obtained
with SPHERE-ZIMPOL (phase 0.27) as well as interferometric observations with
AMBER. IK Tau was observed with ZIMPOL at three wavelengths in the
pseudo-continuum (645, 748, and 820 nm), in the H$\alpha$ line at 656.3 nm, and
in the TiO band at 717 nm. The AMBER observations were carried out in the
wavelength region of the CO first overtone lines near 2.3 $\mu$m (R=12 000).
The polarimetric imaging capabilities of SPHERE-ZIMPOL have allowed us to
spatially resolve clumpy dust clouds at 20--50 mas from the central star, which
corresponds to 2--5 $R_{\star}$ when combined with a central star's angular
diameter of 20.7$\pm$1.53 mas measured with AMBER. The diffuse, asymmetric dust
emission extends out to $\sim$73 $R_{\star}$. We find that the TiO emission
extends to 150 mas (15 $R_{\star}$). The AMBER data in the CO lines also
suggest a molecular outer atmosphere extending to $\sim$1.5 $R_{\star}$. The
results of our 2-D Monte Carlo radiative transfer modelling of dust clumps
suggest that the polarized intensity and degree of linear polarization can be
reasonably explained by small-sized (0.1 $\mu$m) grains of Al$_{2}$O$_{3}$,
MgSiO$_{3}$, or Mg$_{2}$SiO$_{4}$ in an optically thin shell
($\tau_{550\mathrm{nm}}$=0.5$\pm$0.1) with an inner boundary radius of 3.5
$R_{\star}$. IK Tau's mass-loss rate is 20 to 50 times higher than the
previously studied AGB stars W Hya, R Dor, and $o$ Cet. Nevertheless, our
observations of IK Tau revealed that clumpy dust formation occurs close to the
star as seen in those low mass-rate AGB stars.
