The Most Compact Bright Radio-loud AGN -- II. VLBA Observations of Ten
  Sources at 43 and 86~GHz
  Radio-loud active galactic nuclei (AGNs), hosting powerful relativistic jet
outflows, provide an excellent laboratory for studying jet physics. Very long
baseline interferometry (VLBI) enables high-resolution imaging on
milli-arcsecond (mas) and sub-mas scales, making it a powerful tool to explore
the inner jet structure, shedding light on the formation, acceleration and
collimation of AGN jets. In this paper, we present Very Long Baseline Array
(VLBA) observations of ten radio-loud AGNs at 43 and 86~GHz, which were
selected from the {\it Planck} catalogue of compact sources and are among the
brightest in published VLBI images at and below 15 GHz. The image noise levels
in our observations are typically 0.3 mJy beam$^{-1}$ and 1.5 mJy beam$^{-1}$
at 43 and 86 GHz, respectively. Compared with the VLBI data observed at lower
frequencies from the literature, our observations with higher resolution (the
highest resolution up to 0.07 mas at 86 GHz and 0.18 mas at 43 GHz) and at
higher frequencies detected new jet components at sub-parsec scales, offering
valuable data for studies of the physical properties of innermost jets. These
include compactness factor of the radio structure (the ratio of core flux
density to total flux density), and core brightness temperature ($T_{\rm b}$).
In all these sources, the compact core accounts for a significant fraction ($>
60\%$) of the total flux density. Their correlated flux density at the longest
baselines is higher than 0.16 Jy. The compactness of these sources make them
good phase calibrators of mm-wavelength ground-based and space VLBI.
