Superposition model for energy reconstruction and mass identification in cosmic ray spectra

Abstract

The "knee" of cosmic ray spectra may reflect the maximum energy accelerated by galactic cosmic ray sources or the limit of the galaxy's ability to bind cosmic rays. Measurements of individual energy spectra are a crucial tool to understand the origin of the knee. Energy reconstruction and composition identification are foundations of the individual energy spectra measurements. One of the main scientific goals of Large High Altitude Air Shower Observatory (LHAASO) is measuring the cosmic ray energy spectra and composition from ~10 TeV to ~EeV. In this work, a novel method for reconstructing energy and logarithm mass (lnA) based on a superposition model is introduced. Energy and lnA are reconstructed using two universal, composition- and energy-independent calibration lines. For zenith angle below 40 degree, the energy and lnA biases are within +-5% and +-0.3, respectively, across all compositions. The method uses particle densities-measured by LHAASO's electromagnetic and muon detectors at a fixed distance from the shower axis-rather than integrated particle counts in annular bands. The density-based approach improves resolution for both energy and lnA, especially for heavy nuclei. The resulting energy resolution ranges from below 5% to ~15% above 1 PeV, the best mass resolution for iron achieved is below 25% above 10 PeV. The hadronic model dependencies of energy and lnA are also reported. These dependencies scale with lg(E/A) and are nearly independent of primary composition.

Figures (15)

• Figure 1: Lateral distribution (density vs r, r is the perpendicular distance to shower axis) reconstructed from ED (left) and MD (right), the primary particle is proton with energy equal to 1.3 PeV, the fitting result is also shown as the red line. The fitting formula for ED is equation \ref{['eq1']}, and the fitting formula for MD is equation \ref{['eq2']}.
• Figure 2: The resolution of density from ED ($\rho_{em}$) calculated from equation \ref{['eq1']} (left) and density from MD ($\rho_{\mu}$) calculated from equation \ref{['eq2']} (right) vs r (the perpendicular distance to the shower axis) for a CNO sample with zenith angle $\theta=28^{o}$. The resolution of density is defined as the sigma of fitted Gaussian function to distribution of logarithm density. Different lines correspond to different energy indicated in the legend of plot, the dashed vertical line indicates the chosen distance that have the best resolution of density, which is 100 m for ED and 150 m for MD, the results are similar for other primary particles and other zenith angles.
• Figure 3: The resolution comparison of several variables for ED (left) and MD (right) as a function of the true energy. The orange lines are the density at 100 m for ED (left) and density at 150 m for MD (right) respectively, the green lines are the shower size (the integration of lateral distribution function over area) of the fitted lateral function, all the other lines are the number of particles detected by ED and MD in an annular band indicated in the legend of the plot. The primary particle is CNO group, and the zenith angle is $\theta$=28$^{o}$, the results are similar for other primary particles and other zenith angles.
• Figure 4: The relationship between the reconstructed density for ED(left) and MD(right) from detector responded data (y axis) and the density counted from CORSIKA data (x axis) for the mixed-composition sample (normalized by H3a flux model Gaisser_Model). The $cos(\theta)$ in y axis is used for correcting the path-length effect in the detector. The red lines are a linear fit to data.
• Figure 5: The mean relationship between $lg(\rho_{ED}/A^{\alpha_{e}})$ and $lg(E/A)$ (panel a), mean relationship between $lg(\rho_{MD}/A^{\alpha_{\mu}})$ and $lg(E/A)$ (panel b), and mean relationship between $lg(\rho_{MD}/A^{\alpha_{\mu}})$ and $lg(\rho_{ED}/A^{\alpha_{e}})$ (panel c). Panels (d), (e), and (f) present the corresponding residuals.