All-particle cosmic ray energy spectrum measured by the HAWC experiment from 10 to 500 TeV

We report on the measurement of the all-particle cosmic ray energy spectrum with the High Altitude Water Cherenkov (HAWC) Observatory in the energy range 10 to 500 TeV. HAWC is a ground-based air-shower array deployed on the slopes of Volcan Sierra Negra in the state of Puebla, Mexico, and is sensitive to gamma rays and cosmic rays at TeV energies. The data used in this work were taken over 234 days between June 2016 and February 2017. The primary cosmic-ray energy is determined with a maximum likelihood approach using the particle density as a function of distance to the shower core. Introducing quality cuts to isolate events with shower cores landing on the array, the reconstructed energy distribution is unfolded iteratively. The measured all-particle spectrum is consistent with a broken power law with an index of $-2.49\pm 0.01$ prior to a break at $(45.7\pm 0.1)\mathrm{TeV}$, followed by an index of $-2.71\pm 0.01$. The spectrum also represents a single measurement that spans the energy range between direct detection and ground-based experiments. As a verification of the detector response, the energy scale and angular resolution are validated by observation of the cosmic ray Moon shadow’s dependence on energy.

Figure 1

The left panel shows the layout of the entire HAWC detector. Each WCD is indicated by a large circle encompassing the smaller, darker circles which identify the PMTs. The right panel depicts the representation of a single WCD including the steel tank, the protective roof, and the four PMTs. The penetrating dark blue line represents a high-energy secondary air shower particle, which emits Cherenkov radiation indicated by the cyan rays inside the WCD volume.

Figure 2

Example air-shower events from the data sample, where the color scale indicates the logarithm of the measured signal in PEs. The core location is indicated by the red star, and the 40 meter circle shows the region used for $N_{\mathrm{r}40}$. The reconstructed energy of the events are 10 TeV (left) and 100 TeV (right), where the uncertainty on each is 0.1 in $\log E_{\text{reco}}$.

Figure 3

Difference between the logarithms of the reconstructed $E_{\text{reco}}$ and true energy $E$ for the bin centered at $E=100\mathrm{TeV}$, showing the definitions of energy bias, resolution, and efficiency. The values from simulation are indicated by the blue markers, while the black curve is a Gaussian fit to these points. The normalization condition includes events that were not selected as a result of the selection criteria, thus, the integral represents the efficiency $\epsilon (E)$ to reconstruct and select events in this energy bin.

Figure 4

Resulting energy bias (left) and resolution (right) for all particles and protons as a function of the true energy using the energy estimation method provided the event selection criteria. The vertical bars in the left panel represent the width of the bias distribution or the energy resolution, while the uncertainty in the bias value is comparatively miniscule. The uncertainties shown for the energy resolution are those estimated from the fit of a Gaussian to the bias. The bars in the coordinate represent the bin width in true energy.

Figure 5

Relative intensity of the Moon shadow at a mean energy of 4.3 TeV. The map has been smoothed with a top-hat function by 1° to enhance the shadow visually. A two-dimensional Gaussian was fit to the unsmoothed maps.

Figure 6

Top panel: Gaussian centroid offset in right ascension $\mathrm{\Delta }\alpha$, with expectations for pure proton and pure helium hypotheses. Fitting the data values to Eq. (5) shown by the black curve results in an estimated mean charge of $\overline{Z}=1.25\pm 0.06$. Bottom panel: angular resolution from simulation compared to that estimated from using the Moon shadow width. The Moon points represent the fit widths and are compared to the 46.6% containment fraction from the simulated angular deviation distribution. The uncertainties on the red data points are obtained from the fit to the two-dimensional Gaussian, while the coordinate bins represent the estimated mean and covariance in true energy of each map.

Figure 7

The left panel shows the efficiencies $\epsilon (E)$ for all combined cosmic ray particles and individually for proton, helium, and iron components. The energy response matrix $P(E_{\text{reco}}|E)$ for all species using the composition defined in Table 1 is shown on the right. The deviation from the diagonal and the width of $P(E_{\text{reco}}|E)$ are simply the bias and resolution, respectively, already presented in Fig. 4.

Figure 8

Reconstructed energy distribution $N(E_{\text{reco}})$ of the data sample used in this analysis. A subtle change in slope above $E_{\text{reco}}=2\mathrm{TeV}$ suggests a change in spectral index between 10–50 TeV in $E_{\text{reco}}$.

Figure 9

Unfolded all-particle differential energy spectrum scaled by $E^{2.5}$. The uncertainties visible on the data are the systematic uncertainties from the finite size of the simulated data set, while the statistical uncertainties are smaller than the marker size. Fits to the flux using single $\mathcal{F}(A,\gamma )$ and broken $\mathcal{F}(A,E_{\text{br}},{\gamma }_1,{\gamma }_2)$ power-law forms are also shown by the dashed lines. The broken power law is favored, as for $\mathrm{\Delta }{\chi }^2=29.2$ with a difference of two degrees of freedom gives a $p$-value of $4.6\times {10}^{-7}$.

Figure 10

The differential all-particle energy spectrum measured by HAWC (blue) compared with the spectra from the ARGO-YBJ [11], ATIC-2 [7], GRAPES-3 [12], IceTop [41], and Tibet-III [13] experiments. The CREAM [6] light component spectrum ($\mathrm{H}+\mathrm{He}$) is also included for comparison. The uncertainties on the ATIC-2 and CREAM measurements represent combined statistical and systematic uncertainties. For the HAWC, ARGO-YBJ, and IceTop spectra, the shaded regions represent the reported systematic uncertainties. Only ARGO-YBJ reports statistical uncertainties that are shown by visible vertical bars, while for the remaining air-shower array measurements, these are smaller than the respective marker size. The double-sided arrow indicates the shift in flux that would result from a $\pm 10\%$ shift in the energy scale. The GST4-gen [40] and Polygonato [39] all-particle flux models are shown by the red and black dashed lines, respectively.

Figure 11

Comparison of the HAWC spectrum to the all-particle measurement by ATIC-2 [7] and the light component (proton and helium) by CREAM [6]. The energy flux is scaled by $E^{2.75}$ for ease of viewing, and the dashed line is the best fit broken power law $\mathcal{F}(A,E_{\text{br}},{\gamma }_1,{\gamma }_2)$ to HAWC data from Fig. 9 to highlight the location of $E_{\text{br}}$. The double-sided arrow indicates the shift in flux that would result from a $\pm 10\%$ shift in the energy scale.