Study of Galactic interactions and propagation properties of ultrahigh energy cosmic rays using the precision spectrum from the Pierre Auger Observatory

The Auger Collaboration has recently published the precise energy spectrum of cosmic rays above 1 EeV, which exhibits rich and interesting features. These features provide an opportunity to investigate the Galactic propagation and interaction of ultrahigh energy cosmic rays (UHECRs). While the classic dip model, which describes the UHECR propagation and interaction with cosmic microwave background in extragalactic space by theoretical calculation, well explains the cutoff behavior of the highest high energy spectrum of Auger, it fails to describe the low energy features. It indicates that the Galactic propagation and interaction of UHECRs might play an important role in modulating the low energy side of the Auger spectrum. With the disk-halo diffusion model, this work demonstrates excellent agreement with the energy spectrum measured by Auger and supports that the diffusion coefficient follows a power law with an index of ${1.81}_{-0.04}^{+0.05}$ in the Galaxy, at least above $5\times {10}^{18}\mathrm{eV}$. The inferred diffusion coefficient is 1 to 2 orders of magnitude smaller than these extrapolated from low energy studies when conventional model parameters are adopted. The study of the modulation effect at a cluster of the Galaxy level might be needed.

Figure 1

Two-dimensional correlation distributions of parameters and different contours represent different confidence intervals, namely $1\text{−}\sigma$, $2\text{−}\sigma$, and $3\text{−}\sigma$. The blue line in the figure indicates the starting position of the parameters. (a) Shows the distribution in the LTE scenario, and Fig. 2(b) shows the distribution in the high transmission energy (HTE) scenario.

Figure 2

(a) Fitted spectrum of different scenarios comparing to the measurement from Auger. The scale of the $y$ axis is multiplied with $E^3$. The green line shows that extragalactic cosmic rays dominate above 1 EeV, and the blue line shows that extragalactic cosmic rays dominate above 5 EeV. The corresponding dot-dashed lines and dashed lines refer to the source spectrum and the spectrum with only the dip model in fitting parameters, respectively. (b) The spectrum of $K(E)/hL\mathrm{\Gamma }$: the blue line and green line represent the LTE and HTE scenarios, respectively. We also present the extrapolation spectra of $K(E)/hL\mathrm{\Gamma }$ predicted by two low-energy models, with the orange line from [48] and the gray line from [8]. The parameters for these two lines are fixed at $L=7\mathrm{kpc}$ or $L=15\mathrm{kpc}$, ${\mathrm{\Gamma }}_0=0.13{\mathrm{Myr}}^{-1}$ or ${\mathrm{\Gamma }}_0=0.26{\mathrm{Myr}}^{-1}$ and $h=0.15\mathrm{kpc}$.