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Abstract

Cosmic ray electrons and positrons are tracers of particle propagation in the
interstellar medium (ISM). A recent measurement performed using H.E.S.S.
extends the all-electron (electron+positron) spectrum up to 20~TeV, probing
very local sources and transport due to the $\sim$10~kyr cooling time of these
particles. An additional key local measurement was the recent estimation of the
ISM diffusion coefficient around Geminga performed using HAWC. The inferred
diffusion coefficient is much lower than typically assumed values. It has been
argued that if this diffusion coefficient is representative of the local ISM,
pulsars would not be able to account for the all-electron spectrum measured at
the Earth. Here we show that a low diffusion coefficient in the local ISM is
compatible with a pulsar wind nebula origin of the highest energy electrons, if
a so far undiscovered pulsar with spin-down power $\sim 10^{33-34}$ erg/s
exists within 30 to 80~pc of the Earth. The existence of such a pulsar is
broadly consistent with the known population and may be detected in near future
survey observations.