Inhomogeneity in the Supernova Remnant Distribution as the Origin of the PAMELA Anomaly

Abstract

Recent measurements of the positron/electron ratio in the cosmic ray (CR) flux exhibits an apparent anomaly, whereby this ratio increases between 10 and 100 GeV. We show that inhomogeneity of CR sources on a scale of order a kpc, can naturally explain this anomaly. If the nearest major CR source is about a kpc away, then low energy electrons ($\sim 1$ GeV) can easily reach us. At higher energies ($\gtrsim 10$ GeV), the source electrons cool via synchrotron and inverse-Compton before reaching Earth. Pairs formed in the local vicinity through the proton/ISM interactions can reach Earth also at high energies, thus increasing the positron/electron ratio. A natural origin of source inhomogeneity is the strong concentration of supernovae in the galactic spiral arms. Assuming supernova remnants (SNRs) as the sole primary source of CRs, and taking into account their concentration near the galactic spiral arms, we consistently recover the observed positron fraction between 1 and 100 GeV. ATIC's electron excess at $\sim 600$ GeV is explained, in this picture, as the contribution of a few known nearby SNRs. The apparent coincident similarity between the cooling time of electrons at 10 GeV (where the positron/electron ratio upturn), $\sim 10$ Myr, and the CRs protons cosmogenic age at the same energy is predicted by this model.

Figures (2)

• Figure 1: The galaxy is modeled as a slab of width $2 l_H$, with $l_H = 1$ kpc, inside of which the CR components diffuse. Beyond $y = \pm l_H$, the CRs escape at a negligible time. CR sources are located in both cylinder shaped arms with a Gaussian cross-section of width $\sigma = 300$ pc, and disk sources, with a vertical scale height of 100 pc. The assumption of straight cylinders is permissible given the small spiral arm pitch angle. This also makes the problem effectively two dimensional. We model the Milky Way as having four spiral arms, with a pitch angle of $i \approx 15^\circ$Vallee, implying that the arm separation (in the direction perpendicular to the arm axis) is $d \approx (\pi /2) R_\odot \sin i \approx 3$ kpc, while the Sun is at a distance $x \approx 1$ kpc from the nearest spiral arm. Due to the motion of the arms, there is a small drift term carrying the CRs away from them. For a spiral arm periodicity of $P_s \sim 150$ Myr ShavivNewAstronomy, one obtains a velocity of $v_s \approx (\pi/2)(R_\odot \sin i/P_s) \approx 20$ km/s, which is slower than the two comparable diffusion times $l_H/\tau_e \approx x/\tau_x \approx 100$ km/s. A second component resides in the disk, with an exponential vertical decay. Because nearby sources are considered, the The smooth disk distribution is truncated for $r<0.5$ kpc and $t<0.5$ Myr.
• Figure 2: Bottom Panel: Model results and the measured PAMELA points for the positron fraction. The shaded region is the variability expected from solar modulation effects Clem. Top Panel: The expected electron and positron spectra -- Primary arm electrons (long dashed purple), primary disk electrons with nearby sources excluded (short dashed green), nearby SNRs (dot-dashed black), secondary positrons (dot-dashed red), and their sum (blue). The hatched region describes the solar modulation range (from 200 MV to 1200 MV). The three data sets plotted are of HEAT HEAT (circles), ATIC ATIC (triangles) and HESS HESS (open squares).