Probing the magnetic field structure in Sgr A* on Black Hole Horizon Scales with Polarized Radiative Transfer Simulations

Magnetic fields are believed to drive accretion and relativistic jets in black hole accretion systems, but the magnetic-field structure that controls these phenomena remains uncertain. We perform general relativistic (GR) polarized radiative transfer of time-dependent three-dimensional GR magnetohydrodynamical (MHD) simulations to model thermal synchrotron emission from the Galactic Center source Sagittarius A$^\ast$ (Sgr A*). We compare our results to new polarimetry measurements by the Event Horizon Telescope (EHT) and show how polarization in the visibility (Fourier) domain distinguishes and constrains accretion flow models with different magnetic field structures. These include models with small-scale fields in disks driven by the magnetorotational instability (MRI) as well as models with large-scale ordered fields in magnetically-arrested disks (MAD). We also consider different electron temperature and jet mass-loading prescriptions that control the brightness of the disk, funnel-wall jet, and Blandford-Znajek-driven funnel jet. Our comparisons between the simulations and observations favor models with ordered magnetic fields near the black hole event horizon in Sgr A*, although both disk- and jet-dominated emission can satisfactorily explain most of the current EHT data. We show that stronger model constraints should be possible with upcoming circular polarization and higher frequency ($349~{\rm GHz}$) measurements.