Detecting Changing Polarization Structures in Sagittarius A* with High
  Frequency VLBI
  Sagittarius A* is the source of near infrared, X-ray, radio, and
(sub)millimeter emission associated with the supermassive black hole at the
Galactic Center. In the submillimeter regime, Sgr A* exhibits time-variable
linear polarization on timescales corresponding to <10 Schwarzschild radii of
the presumed 4 million solar mass black hole. In previous work, we demonstrated
the potential for total-intensity (sub)millimeter-wavelength VLBI to detect
time-variable -- and periodic -- source structure changes in the Sgr A* black
hole system using nonimaging analyses. Here we extend this work to include full
polarimetric VLBI observations. We simulate full-polarization (sub)millimeter
VLBI data of Sgr A* using a hot-spot model that is embedded within an accretion
disk, with emphasis on nonimaging polarimetric data products that are robust
against calibration errors. Although the source-integrated linear polarization
fraction in the models is typically only a few percent, the linear polarization
fraction on small angular scales can be much higher, enabling the detection of
changes in the polarimetric structure of Sgr A* on a wide variety of baselines.
The shortest baselines track the source-integrated linear polarization
fraction, while longer baselines are sensitive to polarization substructures
that are beam-diluted by connected-element interferometry. The detection of
periodic variability in source polarization should not be significantly
affected even if instrumental polarization terms cannot be calibrated out. As
more antennas are included in the (sub)mm-VLBI array, observations with full
polarization will provide important new diagnostics to help disentangle
intrinsic source polarization from Faraday rotation effects in the accretion
and outflow region close to the black hole event horizon.
