Solution to the Cosmic Ray Anisotropy Problem

In the standard diffusive picture for transport of cosmic rays (CRs), a gradient in the CR density induces a typically small, dipolar anisotropy in their arrival directions. This is being widely advertised as a tool for finding nearby sources. However, the predicted dipole amplitude at TeV and PeV energies exceeds the measured one by almost 2 orders of magnitude. Here, we critically examine the validity of this prediction, which is based on averaging over an ensemble of turbulent magnetic fields. We focus on (1) the deviations of the dipole in a particular random realization from the ensemble average, and (2) the possibility of a misalignment between the regular magnetic field and the CR gradient. We find that if the field direction and the gradient direction are close to $\sim 90°$, the dipole amplitude is considerably suppressed and can be reconciled with observations, which sheds light on a long-standing problem. Furthermore, we show that the dipole direction in general does not coincide with the gradient direction, thus hampering the search for nearby sources.

Figure 1

The dipole anisotropy in the arrival directions of CRs, as predicted by an isotropic diffusion model [25] (dotted line) and measured by a variety of experiments [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. The black filled circles, connected by solid lines, mark the dipole anisotropy predicted in five random realizations of the turbulent magnetic field and assuming a misalignment between the background magnetic field and CR gradient close to 90°.

Figure 2

Sky map of dipole directions in 50 random realizations of the local turbulent magnetic field ($\eta =1$) at 1 PV. The center and radius of each black circle shows the dipole direction and amplitude in one random realization, respectively. The yellow star shows the direction of the assumed CR gradient, the green diamond the predicted value from an isotropic diffusion model, and the red square the average of the 50 magnetic field configurations.

Figure 3

The distribution of dipole amplitudes as a function of the longitude of the CR gradient at 1 PV for $\eta =1$. Each vertical slice is the normalized histogram for a gradient direction. We also show the median (orange dashed line) and amplitude of the (vectorial) mean (red solid line), together with the prediction for isotropic diffusion (green dashed line). The cyan solid line and gray band show the KASCADE upper limit and the EAS-TOP measurement at $\sim 1\mathrm{PeV}$, respectively.

Figure 4

Same as Fig. 2, but for a small turbulent field on top of a regular field ($\eta =0.1$), indicated by the blue cross.

Figure 5

Same as Fig. 3, but for a small turbulent field on top of a regular field ($\eta =0.1$).