Discriminating local sources of high-energy cosmic electrons and positrons by current and future anisotropy measurements

The Fermi-LAT detects no significant anisotropy of the cosmic-ray (CR) electrons and positrons ($e^-+e^+$) with seven years of data, which provides the strongest restriction to the $e^-+e^+$ anisotropy up to now. As next generation CR observatory, HERD is expected to have a better capability of anisotropy detection than Fermi-LAT. In this paper, we discuss several models aimed to explain the AMS-02 data by the present and future anisotropy measurements. We find that the upper limits of Fermi-LAT disfavor Vela SNR as the dominant source in sub-TeV, while other cases that remain safe under the constraint of Fermi-LAT are expected to be distinguished from each other by HERD. We then discuss the possibilities of remarkable TeV spectral features, and test the corresponding anisotropies. We find the conditions under which the TeV model can have a prominent spectral feature and avoid the constraint of Fermi-LAT at the same time. Furthermore, the expected performance of HERD is sensitive enough to detect the anisotropies of all these TeV models, and even for the case of a featureless TeV spectrum. Thus HERD may play a crucial part in the study of the origin of cosmic electrons and positrons.