Evidence of the $Gaia$--VLBI position differences being related to radio
  source structure
  We report the relationship between the $Gaia$--VLBI position differences and
the magnitudes of source structure effects in VLBI observations. Because the
$Gaia$--VLBI position differences are statistically significant for a
considerable number of common sources, we attempt to discuss and explain these
position differences based on VLBI observations and available source images at
cm-wavelengths. Based on the derived closure amplitude root-mean-square
(CARMS), which quantifies the magnitudes of source structure effects in the
VLBI observations used for building the third realization of the International
Celestial Reference Frame, the arc lengths and normalized arc lengths of the
position differences are examined in detail. The radio jet directions and the
directions of the $Gaia$--VLBI position differences are investigated for a
small sample of sources. Both the arc lengths and normalized arc lengths of the
$Gaia$ and VLBI positions are found to increase with the CARMS values. The
majority of the sources with statistically significant position differences are
associated with the sources having extended structure. Radio source structure
is the one of the major factors of these position differences, and it can be
the dominate factor for a number of sources. The vectors of the $Gaia$ and VLBI
position differences are parallel to the radio-jet directions, which is
confirmed with stronger evidence.
