The Geometry of Ultra-Fast Outflows Probed by Soft X-ray Variability in PDS 456

Constraining the location and geometry of ultra-fast outflows (UFOs) is essential for identifying where they are launched and how they are accelerated. We investigate the soft X-ray variability of the luminous quasar PDS 456 using simultaneous March 2024 observations with XRISM/Xtend and NuSTAR. A model-independent comparison between the flare and quiescent phases reveals spectral variability around 1 keV in the rest frame, while the hard X-ray spectral shape remains nearly unchanged. Broadband spectral fitting shows that the soft X-ray structure is well described by a partial-covering low-ionization UFO with (ξ/(erg cm s-1)) 3.1 and v out 0.30c. Time-sliced spectral analysis further reveals significant variability in the covering fraction of this absorber. Interpreting this variability as transverse motion across the X-ray source, we constrain the crossing velocity to be v cross 5 times 10-3c and derive a lower limit on the absorber distance of r 4 times 10 cubed R g. This location is substantially farther out than the high-ionization UFO previously inferred at 200-600 R g, while the two phases have comparable outflow velocities. The resulting velocity-distance structure disfavors a self-similar magnetocentrifugal wind and instead suggests either radiation-pressure acceleration following a Castor-Abbott-Klein-like velocity law or compact magnetic acceleration through magnetic reconnection. These results demonstrate that soft X-ray partial-covering variability can provide a geometrical probe of UFOs and directly connect spectral variability to wind acceleration.