Radio jet structures at ~100 parsec and larger scales of the
  $\gamma$-ray-emitting narrow-line Seyfert 1 galaxy PMN J0948+0022
  The narrow-line Seyfert 1 (NLS1) galaxy PMN J0948+0022 is an archetype of
gamma-ray-emitting NLS1s in active galactic nuclei (AGNs). In this study, we
investigate its radio structures using archival data obtained using the Karl
G.~Jansky very large array (VLA) and the very long baseline array (VLBA). The
new VLA images reveal an outermost radio emission separated by 9.1 arcsec. Its
resolved structure and steep spectrum suggest a terminal shock in a radio lobe
energized by the jet from the PMN J0948+0022 nucleus. This large-scale radio
component is found at almost the same position angle as that of the pc-scale
jet, indicating a stable jet direction up to ~1 Mpc. Its apparent one-sidedness
implies a moderate advancing speed ($\beta>0.27$). The kinematic age of 1 x
10^7 year of the jet activity is consistent with the expected NLS1 phase of
~10^7 year in the AGN lifetime. The VLBA image reveals the jet structure at
distances ranging from r=0.82 milliarcsec to 3.5 milliarcsec, corresponding to
approximately 100 pc, where superluminal motions were found. The jet width
profile ($\propto r^{1.12}$) and flux-density profile ($\propto r^{-1.44}$)
depending on the distance $r$ along the jet suggest that the jet kinetic energy
is converted into internal energy in this region. The jet is causally connected
in a nearly conical streamline, which is supported by ambient pressure at 100
pc scales in the host galaxy of PMN J0948+0022.
