Black Hole Polarimetry I. A Signature of Electromagnetic Energy Extraction

In 1977, Blandford and Znajek showed that the electromagnetic field surrounding a rotating black hole can harvest its spin energy and use it to power a collimated astrophysical jet, such as the one launched from the center of the elliptical galaxy M87. Today, interferometric observations with the Event Horizon Telescope (EHT) are delivering high-resolution, event-horizon-scale, polarimetric images of the supermassive black hole M87* at the jet launching point. These polarimetric images offer an unprecedented window into the electromagnetic field structure around a black hole. In this paper, we show that a simple polarimetric observable-the phase angle beta 2 of the second azimuthal Fourier mode of the linear polarization in a near-horizon image-depends on the sign of the electromagnetic energy flux and therefore provides a direct probe of black hole energy extraction. In Boyer-Lindquist coordinates, the Poynting flux for axisymmetric electromagnetic fields is proportional to the product B phi B r . The phase angle beta 2 likewise depends on the ratio B phi /B r , thereby enabling an observer to determine the direction of electromagnetic energy flow in the near-horizon environment experimentally. Data from the 2017 EHT observations of M87* are consistent with electromagnetic energy outflow. Currently envisioned multifrequency observations of M87* will achieve higher dynamic range and angular resolution, and hence deliver measurements of angle beta 2 closer to the event horizon as well as better constraints on Faraday rotation. Such observations will enable a definitive test for energy extraction from the black hole M87*.