Every Nearby Energetic Pulsar Is Surrounded by a Region of Inhibited Diffusion

The H.E.S.S. telescope has recently detected the total electron-plus-positron ($e^+e^-$) flux up to 40 TeV, finding it to be a featureless and steeply-falling power-law above 1 TeV. This result is in stark tension with standard one-zone models of pulsar $e^+e^-$ injection and diffusion, which predict a hard-spectrum signal above $\sim$10 TeV. We model the local pulsar population, and find 20 sources that would each $individually$ overproduce the H.E.S.S. $e^+e^-$ flux in a one-zone diffusion model. We conclude that $every$ energetic pulsar younger than $\sim$500 kyr must be surrounded by a region of inhibited diffusion ($e.g.$, a supernova remnant, pulsar wind nebula, or TeV halo) that prevents the transport of these $e^+e^-$ to Earth. Because the high-electron density in these regions produces bright synchrotron and inverse-Compton emission, we conclude that all nearby pulsars are detectable as (potentially unassociated) radio, x-ray or $\gamma$-ray sources.