Constraining X-ray Coronal Size with Transverse Motion of AGN Ultra-Fast
  Outflows
  One of the canonical physical properties of ultra-fast outflows (UFOs) seen
in a diverse population of active galactic nuclei (AGNs) is its seemingly very
broad width (i.e. $\Delta v \sim 10,000$ km~s$^{-1}$) , a feature often
required for X-ray spectral modeling. While unclear to date, this condition is
occasionally interpreted and justified as internal turbulence within the UFOs
for simplicity. In this work, we exploit a transverse motion of a
three-dimensional accretion-disk wind, an essential feature of non-radial
outflow morphology unique to magnetohydrodynamic (MHD) outflows. We argue that
at least part of the observed line width of UFOs may reflect the degree of
transverse velocity gradient due to Doppler broadening around a putative
compact X-ray corona in the proximity of a black hole. In this scenario, line
broadening is sensitive to the geometrical size of the corona, $R_c$. We
calculate the broadening factor as a function of coronal radius $R_c$ and
velocity smearing factor $f_{\rm sm}$ at a given plasma position. We
demonstrate, as a case study of the quasar, PDS~456, that the spectral analysis
favors a compact coronal size of $R_c /R_g \lesssim 10$ where $R_g$ is
gravitational radius. Such a compact corona is long speculated from both X-ray
reverberation study and the lamppost model for disk emission also consistent
with microlensing results. Combination of such a transverse broadening around a
small corona can be a direct probe of a substantial rotational motion perhaps
posing a serious challenge to radiation-driven wind viewpoint.
