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Calibration of the air shower energy scale of the water and air Cherenkov techniques in the LHAASO experiment

F. Aharonian et al. (LHAASO Collaboration)
Phys. Rev. D 104, 062007 – Published 15 September 2021
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  • INTRODUCTION
  • THE LHAASO WCDA AND WFCTA ARRAYS
  • DETERMINATION OF THE ENERGY SCALE OF…
  • DETERMINATION OF THE ENERGY SCALE OF…
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
    • References

    Abstract

    The Wide Field-of-View Cherenkov Telescope Array (WFCTA) and the Water Cherenkov Detector Array (WCDA) of LHAASO are designed to work in combination for measuring the energy spectra of the cosmic ray species over a very wide energy range from a few TeV to 10 PeV. The energy calibration can be achieved with a proven technique of measuring the westward shift of the Moon shadow cast by galactic cosmic rays due to the geomagnetic field. This deflection angle Δ is inversely proportional to the cosmic ray rigidity. The precise measurement of the shifts by WCDA allows us to calibrate its energy scale for energies as high as 35 TeV. Through a set of commonly triggered events, the energy scales can be propagated to WFCTA. The energies of the events can be derived both by WCDA-1 and WFCTA with the median energies 23.4±0.1±1.3  TeV and (21.9±0.1  TeV), respectively, which are consistent within uncertainties. In addition, the propagation of the energy scale is also validated by the Moon shadow based on the same data selection criteria of the commonly triggered events. This paper reports, for the first time, an observational measurement of the absolute energy scale of the primary cosmic rays generating showers observed by air Cherenkov telescopes.

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    • Received 2 June 2021
    • Accepted 11 August 2021

    DOI:https://doi.org/10.1103/PhysRevD.104.062007

    © 2021 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Cosmic ray composition & spectra
    Gravitation, Cosmology & Astrophysics

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    Vol. 104, Iss. 6 — 15 September 2021

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    Images

    • Figure 1
      Figure 1

      The displacement of the Moon shadow from the real direction of the Moon as a function of Nhit.

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    • Figure 2
      Figure 2

      The LHAASO layout. The three ponds of WCDA are represented by the cyan rectangles at the center of the site. The 6 WFCTA telescopes, positioned near the southwest core of WCDA-1, can be seen in the zoomed view at the bottom right. The remaining KM2A extends over an area of about 1  km2, instrumented with the electromagnetic detector (ED) array of scintillation counters (small red dots) and the muon detector array (big blue dots).

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    • Figure 3
      Figure 3

      A typical event that triggered both WCDA-1 and WFCTA. The two panels on the left-hand side show the images recorded by two of the WFCTA telescopes, both in vertical view, but with different orientations of 15° and 45°, respectively, from north toward west. The two panels on the right, instead, show the maps of hits in WCDA-1 units, where the color scale indicates the number of recorded photo-electrons (Npe). The top right panel shows the map for the 8′′ PMTs, which exhibit a clear saturation in the central region of the shower. The lower right panel shows the map for the same event as recorded by the 1.5′′ PMTs. The corresponding lateral distributions of Npe are shown in the lower panel in the middle column. Here, the red dots represent the 8′′ PMT and the blue ones the 1.5′′ PMTs, which are also scaled (green dots) and overlaid on the previous one to reconstruct the profile over the full range. The upper panel in the middle column shows the arrival time (in ns) of shower secondary particles as recorded by the WCDA-1.

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    • Figure 4
      Figure 4

      The distribution of the total number of photoelectrons, Npe, for shower events coming from a region around the normal Moon position. The black solid line indicates a power law ∝Npe−2.6, which fits the histograms for Npe>50,000. The two vertical magenta lines indicate the range used for the energy calibration using the Moon shadow.

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    • Figure 5
      Figure 5

      The significance map of the Moon shadow for shower events detected by WCDA-1 of the six Npe intervals. The coordinates are centered on the Moon position. The color scale represents the statistical significance of the deficit in terms of standard deviations.

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    • Figure 6
      Figure 6

      The westward shift of the Moon shadow as a function of the inverse of the CR particle energy for pure protons (blue dot-dashed line) and pure Helium nuclei (black dashed line) according to the ray-tracing simulations. The pink solid line indicates the westward shift of the Moon shadow based on formula (2). The blue squares indicate the westward shifts of the Moon shadows with their statistical errors and the corresponding median energies obtained by formula (2). The uncertainty in the composition is represented by the shaded area around the pink solid line, however so small to be barely visible.

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    • Figure 7
      Figure 7

      The average shower energy measured using the Moon shadow shift versus Npe, the total number of photoelectrons detected by WCDA-1 detector.

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    • Figure 8
      Figure 8

      Upper: distribution of Npe for the events with cores inside WCDA-1 with zenith angle 22°<θz<38° (by the blue solid line) compared to the Npe distribution for the commonly triggered events (by the red solid line). In the selected region of Npe, denoted by the vertical lines, the selection efficiency is high enough to have almost the same ratio protons: Helium nuclei =2: 1. Lower: distribution of the zenith angles for the commonly triggered events.

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    • Figure 9
      Figure 9

      Distribution of reconstructed energies for the commonly triggered events. The black dashed line shows the energy distribution reconstructed by WCDA-1 using the estimator E[GeV]=1.33·Npe0.95. The vertical black dashed line indicates the median energy (23.4±0.1±1.3  TeV) of the distribution. The continuous red solid line shows the distribution of the energies reconstructed by the WFCTA telescopes. The vertical red solid line indicates the median energy (21.9±0.1  TeV) of the distribution. The median energies 21.0−4.8+9.0  TeV and 16.2−4.5+10.1  TeV obtained from the Moon shadow data are shown by a red square and a blue dot, respectively. The first energy is related to the selection Nhit>200, 20,000<Npe<60,000, 22°<θz<38°, the second one by requiring in addition the shower core falling inside WCDA-1.

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    • Figure 10
      Figure 10

      Upper: the distribution of zenith angles of all events with Nhit>200 used in the WCDA-1 Moon shadow analysis. The shaded areas represent the zenith range not covered by WFCTA telescopes. Lower: the significance map of the Moon shadows, for events with Npe between 20,000 and 60,000 and in the zenith angle range covered by the WFCTA telescopes, i.e., 22°≤θz≤38°. The color scale represents the statistical significance of the deficit in terms of standard deviations.

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    • Figure 11
      Figure 11

      The relation in the energy range 10–300 TeV between the energy estimator EWFCTA of WFCTA and the energy E0 of primary protons and Helium nuclei sample according to the ratio protons: Helium nuclei =1: 1, based on the simulations of WFCTA telescopes. The red line represents the median energy of the EWFCTA distribution. The black square indicates the corresponding value of the energy, 21.0−4.8+9.0  TeV, determined by WCDA-1 from the Moon shadow shift. The color scale gives the number of events in each bin. The width bin is dlog10E0=0.05.

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