IS COSMIC RAY ELECTRON EXCESS FROM PULSARS SPIKY OR SMOOTH?: CONTINUOUS AND MULTIPLE ELECTRON/POSITRON INJECTIONS

We investigate the observed spectrum of cosmic ray electrons and positrons from astrophysical sources, especially pulsars, and the physical processes for making the spectrum spiky or smooth via continuous and multiple electron/positron injections. We find that (1) the average electron spectrum predicted from nearby pulsars is consistent with PAMELA, Fermi, and H.E.S.S. data. However, the ATIC/PPB-BETS peak around 500 GeV is hard to produce by the sum of multiple pulsar contributions and requires a single (or a few) energetic pulsar(s). (2) A continuous injection produces a broad peak and a high-energy tail above the peak, which can constrain the source duration (∼<105 years with the current data). (3) The H.E.S.S. data in the TeV range suggest that young sources with age less than ∼6 x 104 years are less energetic than ∼1048 erg. (4) We also expect a large dispersion in the TeV spectrum due to the small number of sources that may cause the high-energy cutoff inferred by H.E.S.S. and potentially provide a smoking gun for the astrophysical origin. These spectral diagnostics can be refined in the near future by the CALET experiments to discriminate different astrophysical and dark matter origins.