  The origin of the disks around Be stars is still not known. Further progress
requires a proper parametrization of their structure, both spatially and
kinematically. This is challenging as the disks are very small. Here we assess
whether a novel method is capable of providing these data. We obtained spectro
astrometry around the Pa beta line of two bright Be stars, alpha Col and zeta
Tau, to search for disk signatures. The data, with a pixel to pixel precision
of the centroid position of 0.3..0.4 milliarcsecond is the most accurate such
data to date. Artefacts at the 0.85 mas level are present in the data, but
these are readily identified as they were non-repeatable in our redundant
datasets. This does illustrate the need of taking multiple data to avoid
spurious detections. The data are compared with simple model simulations of the
spectro astrometric signatures due to rotating disks around Be stars. The upper
limits we find for the disk radii correspond to disk sizes of a few dozen
stellar radii if they rotate Keplerian. This is very close to observationally
measured and theoretically expected disk sizes, and this paper therefore
demonstrates that spectro-astrometry, of which we present the first such
attempt, has the potential to resolve the disks around Be stars.
