Undiscovered Pulsar in the Local Bubble as an Explanation of the Local High Energy Cosmic Ray All-Electron Spectrum

Cosmic ray electrons and positrons are tracers of particle propagation in the interstellar medium (ISM). A recent measurement performed using the High Energy Stereoscopic System extends the all-electron ($\mathrm{electron}+\mathrm{positron}$) spectrum up to 20 TeV, probing very local sources and transport due to the $\sim 10\mathrm{kyr}$ cooling time of these particles. An additional key local measurement was the recent estimation of the ISM diffusion coefficient around Geminga performed using the High-Altitude Water Cherenkov Observatory. 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 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 $\sim 10^{33–34}\mathrm{erg}/\mathrm{s}$ exists within 30–80 pc of Earth. The existence of such a pulsar is broadly consistent with the known population and may be detected in near future survey observations.

Figure 1

Maximum contribution of a single source to the total cosmic ray electron spectrum as a function of energy for three diffusion coefficients with an energy dependence of $\delta =0.33$. Generated from 1000 realizations of a source population and simple propagation model. Solid lines correspond to the median of the distribution, and the bands correspond to the 16th and 84th percentiles.

Figure 2

Required spectral index $\alpha$ vs pulsar distance for different magnetic fields (top line, $B=3\mu \mathrm{G}$; middle line, $B=4\mu \mathrm{G}$; bottom line, $B=5\mu \mathrm{G}$). The color scale gives the energy into accelerated electrons needed to match the local electron flux in the range 1–20 TeV as measured by H.E.S.S.

Figure 3

All-electron spectrum measured at the Earth with Alpha Magnetic Spectrometer [22] and preliminary H.E.S.S. [9] data points compared to predictions for a single PWN. The colored lines correspond to the LAES contribution of a single pulsar located at 50 pc, $\dot{E}=1.3\times {10}^{33}\mathrm{erg}/\mathrm{s}$, $\alpha =2.4$, an ISM magnetic field of $B=3\mu \mathrm{G}$, and a range of values for $P_0$.

Figure 4

Positron fraction measured at Earth using Alpha Magnetic Spectrometer [23] and PAMELA (Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics) [3]. The blue solid line corresponds to the predicted positron fraction due to secondary production from Ref. [19]. The colored lines correspond to the positron fraction with this level of secondaries plus a single PWN as for Fig. 3.

Figure 5

Expected anisotropy due to the single local source simulated in Figs. 3 and 4. Fermi upper limits are shown as blue arrows. The color code for the single pulsar contribution is the same as in the aforementioned figures.