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 \mathrel { \raise 2.15 pt \hbox { $ > $ } \mkern - 14.0 mu \lower 2.58 pt \hbox { $ \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 _ { 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 .