Knee of the cosmic hydrogen and helium spectrum below 1 PeV measured by ARGO-YBJ and a Cherenkov telescope of LHAASO

The measurement of the cosmic ray energy spectrum, in particular for individual species of nuclei, is an important tool to investigate cosmic ray production and propagation mechanisms. The determination of the “knees” in the spectra of different species remains one of the main challenges in cosmic ray physics. In fact, experimental results are still conflicting. In this paper we report a measurement of the mixed proton and helium energy spectrum, obtained with the combined data of the ARGO-YBJ experiment and a wide field of view Cherenkov telescope, a prototype of the future LHAASO experiment. By means of a multiparameter technique, we have selected a high-purity proton plus helium sample. The reconstructed energy resolution is found to be about 25% throughout the investigated energy range from 100 TeV to 3 PeV, with a systematic uncertainty in the absolute energy scale of 9.7%. The found energy spectrum can be fitted with a broken power-law function, with a break at the energy ${\mathrm{E}}_k=700\pm 230(\mathrm{stat})\pm 70(\mathrm{sys})\mathrm{TeV}$, where the spectral index changes from $-2.56\pm 0.05$ to $-3.24\pm 0.36$. The statistical significance of the observed spectral break is 4.2 standard deviations.

Figure 1

The total number of photoelectrons $N_{pe}$ as a function of the impact parameter $R_p$ for primary protons. The color scale represents the shower energies in bins of $\mathrm{\Delta }{\log }_{10}(E/1\mathrm{TeV})=0.2$, covering primary energies from 30 TeV to 10 PeV.

Figure 2

The simulated distribution of $(E_{\text{true}}-E_{\text{reco}})/E_{\text{true}}$ for different mass groups in the energy range 500–800 TeV. The reconstructed energy is obtained from the look-up table built for primaries $\mathrm{p}+\mathrm{He}$ in $1:1$ ratio.

Figure 3

Distribution of the number of Cherenkov photoelectrons ($N_{pe}$) measured by the telescope (filled circles). The histograms represent the $N_{pe}$ distributions obtained by simulations according to the flux models [34, 36] and to the all-particle spectra and corresponding composition models reported by the Tibet ${\mathrm{AS}}_{\gamma }$ [35] and KASCADE[10] experiments. The bin size is 0.22 in ${\log }_{10}{N}_{pe}$.

Figure 4

The simulated largest number of particles in the RPC ($N_{\max }$) as a function of the simulated number of photoelectrons in the Cherenkov telescope ($N_0^{pe}$, normalized to $R_p=0$ and $\alpha =0°$). The separation between the different mass groups is visible.

Figure 5

The length to width ratio ($L/W$) of the shower Cherenkov image as a function of the impact parameter $R_p$, for showers with ${\log }_{10}{N}_0^{pe}$ between 5.0 and 5.3, according to simulations. The separation between the different mass groups is visible.

Figure 6

Composition-sensitive parameters $p_L$ and $p_C$ for two mass groups, H&He (solid contours) and heavier masses (dashed contours) including $1:1:1$ mixing of CNO, MgAlSi, and iron. The primary energy of the plotted events is between 100 TeV and 10 PeV. Numbers on the contours indicate the percentage of contained events.

Figure 7

Aperture of the hybrid experiment. Solid circles represent the aperture for all particles, solid squares for the selected H&He events, triangles for the H&He events obtained with stricter cuts for calibration purposes using the low-energy part of the spectrum [18].

Figure 8

The contamination fraction (%) of events of different heavy composition groups that survive through the H&He selection cuts. The Hörandel model is assumed in the simulation.

Figure 9

The energy resolution at $\sim 300\mathrm{TeV}$ (left), $\sim 1\mathrm{PeV}$ (middle) and $\sim 3\mathrm{PeV}$ (right) for a H&He sample. The distributions are fitted with a Gaussian function.

Figure 10

H&He spectrum obtained by the hybrid experiment with ARGO-YBJ and the imaging Cherenkov telescope. A clear knee structure is observed around 700 TeV. The H&He spectra by CREAM [7], ARGO-YBJ [16] and the hybrid experiment [18] below the knee, the spectra by Tibet ${\mathrm{AS}}_{\gamma }$ [9] and KASCADE [10] above the knee are shown for comparison. In our result, the error bar is the statistical error, and the shaded area represents the systematic uncertainty.

Figure 11

Comparison between the input H&He spectrum according to Ref. [34] and the reconstructed one. The slightly harder reconstructed spectrum shape is consistent with the contamination from heavier components shown in Fig. 8. The shaded area represents the systematic uncertainty caused by the contamination of heavy nuclei and boundary selection.