  Context: Recent observations with the Atacama Large Millimeter Array (ALMA)
have shown that the large dust aggregates observed at millimeter wavelengths
settle to the midplane into a remarkably thin layer. Aims: We intend to find
out if the geometric thinness of these layers is evidence against the vertical
shear instability (VSI) operating in these disks. Methods: We performed
hydrodynamic simulations of a protoplanetary disk with a locally isothermal
equation of state, and let the VSI fully develop. We sprinkled dust particles
and followed their motion as they got stirred up by the VSI. We determined for
which grain size the layer becomes geometrically thin enough to be consistent
with ALMA observations. We then verified if, with these grain sizes, it is
still possible to generate a moderately optically thick layer at millimeter
wavelengths, as observations appear to indicate. Results: We found that even
very large dust aggregates with Stokes numbers close to unity get stirred up to
relatively large heights above the midplane by the VSI, which is in conflict
with the observed geometric thinness. For grains so large that the Stokes
number exceeds unity, the layer can be made to remain thin, but we show that it
is hard to make dust layers optically thick at ALMA wavelengths (e.g.,
tau(1.3mm)>=1) with such large dust aggregates. Conclusions: We conclude that
protoplanetary disks with geometrically thin midplane dust layers cannot be VSI
unstable, at least not down to the disk midplane. Explanations for the
inhibition of the VSI include a reduced dust-to-gas ratio of the small dust
grains that are responsible for the radiative cooling of the disk. A reduction
of small grains by a factor of between 10 and 100 is sufficient to quench the
VSI. Such a reduction is plausible in dust growth models, and still consistent
with observations at optical and infrared wavelengths.
