Origins of sharp cosmic-ray electron structures and the DAMPE excess

Nearby sources may contribute to cosmic-ray electron (CRE) structures at high energies. Recently, the first DAMPE results on the CRE flux hinted at a narrow excess at energy ~1.4 TeV. We show that in general a spectral structure with a narrow width appears in two scenarios: I) "Spectrum broadening" for the continuous sources with a delta-function-like injection spectrum. In this scenario, a finite width can develop after propagation through the Galaxy, which can reveal the distance of the source. Well-motivated sources include mini-spikes and subhalos formed by dark matter (DM) particles $\chi_{s}$ which annihilate directly into e+e- pairs. II) "Phase-space shrinking" for burst-like sources with a power-law-like injection spectrum. The spectrum after propagation can shrink at a cooling-related cutoff energy and form a sharp spectral peak. The peak can be more prominent due to the energy-dependent diffusion. In this scenario, the width of the excess constrains both the power index and the distance of the source. Possible such sources are pulsar wind nebulae (PWNe) and supernova remnants (SNRs). We analysis the DAMPE excess and find that the continuous DM sources should be fairly close within ~0.3 kpc, and the annihilation cross sections are close to the thermal value. For the burst-like source, the narrow width of the excess suggests that the injection spectrum must be hard with power index significantly less than two, the distance is within ~(3-4) kpc, and the age of the source is ~0.16 Myr. In both scenarios, large anisotropies in the CRE flux are predicted. We identify possible candidates of mini-spike (PWN) sources in the current Fermi-LAT 3FGL (ATNF) catalog. The diffuse gamma-rays from these sources can be well below the Galactic diffuse gamma-ray backgrounds and less constrained by the Ferm-LAT data, if they are located at the low Galactic latitude regions.