Effect of Electromagnetic Interaction on Galactic Center Flare Components

Recently, near-infrared GRAVITY@ESO observations at $2.2\,\mu{\rm m}$ have announced the detection of three bright "flares" in the vicinity of the Galactic center supermassive black hole (SMBH) that exhibited orbital motion at a distance of about $6 - 11$ gravitational radii from an $\sim 4\times 10^6\, M_{\odot}$ black hole. There are indications of the presence of a large-scale, organized component of the magnetic field at the Galactic center. Electromagnetic effects on the flare dynamics were previously not taken into account despite the relativistic motion of a plasma in magnetic field leading to the charge separation and nonnegligible net charge density in the plasma. Applying various approaches, we find the net charge number density of the flare components of the order of $10^{-3} - 10^{-4}$ cm$^{-3}$, while the particles' total number density is of the order of $10^{6} - 10^{8}$ cm$^{-3}$. However, even such a tiny excess of charged particles in the quasi-neutral plasma can significantly affect the dynamics of flare components, which can then lead to the degeneracy in the measurements of spin of the SMBH. Analyzing the dynamics of recent flares in the case of the rapidly rotating black hole, we also constrain the inclination angle between the magnetic field and spin axis to $\alpha < 50^{\circ}$, as for larger angles, the motion of the hot spot is strongly chaotic.