Context. Sagittarius A*, the supermassive black hole at the center of our Galaxy, exhibits episodic near-infrared flares. The recent monitoring of three such events with the GRAVITY instrument has shown that some flares are associated with orbital motions in the close environment of the black hole. The GRAVITY data analysis indicates a super-Keplerian azimuthal velocity, while (sub-) Keplerian velocity is expected for the hot flow surrounding the black hole. Aims. We develop a semi-analytic model of the Sagittarius A* flares based on an ejected large plasmoid, inspired by recent particle-in-cell global simulations of black hole magnetospheres. We model the infrared astrometric and photometric signatures associated with this model. Methods. We considered a spherical macroscopic hot plasma region that we call a large plasmoid. This structure was ejected along a conical orbit in the vicinity of the black hole. This plasmoid was assumed to be formed by successive mergers of smaller plasmoids produced through magnetic reconnection that we did not model. Nonthermal electrons were injected into the plasmoid. We computed the evolution of the electron-distribution function under the influence of synchrotron cooling. We solved the radiative transfer problem associated with this scenario and transported the radiation along null geodesics of the Schwarzschild space time. We also took the quiescent radiation of the accretion flow into account, on top of which the flare evolves. Results. For the first time, we successfully account for the astrometric and flux variations of the GRAVITY data with a flare model that incorporates an explicit modeling of the emission mechanism. The prediction of our model and recent data agree well. In particular, the azimuthal velocity of the plasmoid is set by the magnetic field line to which it belongs, which is anchored in the inner parts of the accretion flow, hence the super-Keplerian motion. The astrometric track is also shifted with respect to the center of mass due to the quiescent radiation, in agreement with the difference measured with the GRAVITY data. Conclusions. These results support the hypothesis that magnetic reconnection in a black hole magnetosphere is a viable model for the infrared flares of Sagittarius A*.
