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Modeling of the tau and muon neutrino-induced optical Cherenkov signals from upward-moving extensive air showers

A. L. Cummings, R. Aloisio, and J. F. Krizmanic
Phys. Rev. D 103, 043017 – Published 25 February 2021
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  • INTRODUCTION
  • NEUTRINO INTERACTIONS IN EARTH
  • UPWARD EXTENSIVE AIR SHOWER MODELING
  • APERTURE AND SENSITIVITY
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
    • References

    Abstract

    We present a detailed modeling and computation methodology to determine the optical Cherenkov signals produced by upward-moving extensive air showers (EASs) induced by τ-leptons and muons, sourced from the interaction of high-energy astrophysical neutrinos interacting in the Earth. Following and extending the physics modeling and Cherenkov signal simulations performed in M. H. Reno et al. [Phys. Rev. D 100, 063010 (2019)], this scheme encompasses a new, state-of-the-art computation of the muon neutrino propagation inside the Earth and the contribution to the τ-lepton muon decay channel. The modeling takes into account all possible τ-lepton decay and muon energy loss channels that feed the optical Cherenkov emission, produced by both tau and muon initiated EASs. The EAS modeling uses the electron energy, angular, and lateral distributions in the EAS and their evolution as well as the wavelength dependence of the Cherenkov emission and its atmospheric attenuation. The results presented here are focused on the detection capabilities of suborbital (balloon-borne) and orbital (satellite) based instruments. The latter case was calculated for POEMMA [The Probe Of Extreme MultiMessenger Astrophysics] to compare to that presented in M. H. Reno et al. [Phys. Rev. D 100, 063010 (2019)], specifically including the muon-decay channel of τ-leptons and the muonic EAS Cherenkov signal from muon neutrino interactions in the Earth. By detailing all these individual contributions to the optical Cherenkov emission and detection, we show how the ensemble that includes muonic channels provides a large detection capability for space-based, high-energy cosmic neutrino detection. Specifically, we show that for neutrino energies ≲10  PeV, the upward-EAS sensitivity due to muon neutrino interactions in the Earth begin to dominate over that for tau neutrino interactions, effectively extending the neutrino sensitivity to lower energies.

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    • Received 19 November 2020
    • Accepted 1 February 2021

    DOI:https://doi.org/10.1103/PhysRevD.103.043017

    © 2021 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Cosmic ray & astroparticle detectorsExtrasolar neutrino astronomyParticle astrophysics
    Gravitation, Cosmology & Astrophysics

    Authors & Affiliations

    A. L. Cummings1,2, R. Aloisio1,2, and J. F. Krizmanic3,4

    • 1Gran Sasso Science Institute (GSSI), Via F. Crispi 7, 67100 L’Aquila, Italy
    • 2INFN-Laboratori Nazionali del Gran Sasso, Via G. Acitelli 22, 67100 Assergi (AQ), Italy
    • 3CRESST/NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA
    • 4University of Maryland, Baltimore County, Baltimore, Maryland 21250, USA

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    Issue

    Vol. 103, Iss. 4 — 15 February 2021

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    Images

    • Figure 1
      Figure 1

      Upper panel: tau emergence probability as a function of Earth emergence angle (in degrees) for energies ranging from 1015  eV to 1021  eV as labeled. Lower panel: muon emergence probability for the same parameter space above.

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    • Figure 2
      Figure 2

      Upper panel: energy distribution of emergent τ-leptons from ντ (blue histograms) and muons from νμ (orange histograms) produced by a mono-energetic flux of 108 neutrinos with energy 1015  eV and an Earth emergence angle of 1°. Lower panel: the same as in upper panel with a flux of 106 neutrinos with 1017  eV energy. Note the small number of tau leptons in the 1 PeV distribution.

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    • Figure 3
      Figure 3

      Fractional energy distribution of a relativistic τ-lepton decay with negative polarization. The hadronic channel is the sum of the fractional energies of all hadrons in a given decay. These values are calculated using 100,000 pythia τ-lepton decays [76].

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    • Figure 4
      Figure 4

      Muon differential cross sections for nuclear and electronic bremsstrahlung [77], electron-positron pair production [74], and photonuclear interactions (we show the two primary models as described by [74, 80]) as a function of fractional energy deposition for a 100 PeV muon in air.

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    • Figure 5
      Figure 5

      Muon-air interaction lengths as a function of the fractional energy deposition v=E/Eμ for various muon energies as labelled. Note that a full atmosphere ranges from 1030gcm2 (perfectly vertical) to 34000gcm2 (perfectly horizontal).

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    • Figure 6
      Figure 6

      Cumulative 100 PeV muon-air interaction probability as a function of atmospheric depth for various fractional energy depositions. Dashed lines correspond to maximum depth of the Earth atmosphere for emergence angles 30°, 20°, 10°, 5°, 1°, and 0° (perfectly horizontal).

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    • Figure 7
      Figure 7

      Electron-Positron longitudinal profile as a function of shower age for an upwards 100 PeV proton shower as simulated in corsika and fit with appropriate Gaisser-Hillas parameters (assuming fixed λ) compared to the Greisen parametrization for an electromagnetic shower [88].

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    • Figure 8
      Figure 8

      Index of refraction (n-1) as a function of altitude for wavelengths 270 nm to 1000 nm. Because the difference is small in this wavelength range, dispersion effects are ignored.

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    • Figure 9
      Figure 9

      Maximum optical depth as a function of wavelength for different trajectory angles (where 90° corresponds to horizontal and 0° corresponds to perfectly vertical).

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    • Figure 10
      Figure 10

      Fraction of e± above energy E for various shower ages, as parametrized in [95].

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    • Figure 11
      Figure 11

      Normalized angular distributions of electrons as a function of the angle off shower axis for electron energies from 1 MeV to 1 GeV for shower age s=1.0. As parametrized by Hillas [95] and Lafebre [96]. The former is used for the work presented in this paper.

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    • Figure 12
      Figure 12

      Average electron scale angle (dashed) versus local Cherenkov angle as a function of shower age for a 100 PeV proton shower with 10° Earth emergence angle initiated at the listed altitudes.

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    • Figure 13
      Figure 13

      Normalized electron lateral distributions for electron energies 1 MeV to 1 GeV at shower maximum.

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    • Figure 14
      Figure 14

      Moliere radius as a function of altitude for the standard US atmosphere.

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    • Figure 15
      Figure 15

      Cherenkov spatial distributions for an upward (90° Earth emergence angle) 10 TeV proton shower as observed at 400 km altitude, with λ range 300 nm to 450 nm, simulated with corsika [upper panel] and this work [lower panel]. Color bar represents Nγch/m2 and is scaled by 110 to decrease computation time in corsika for projecting photons from top of the atmosphere to 400 km. corsika run provided by F. Bisconti.

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    • Figure 16
      Figure 16

      Cherenkov spatial distributions for an upward 100 PeV proton air shower at 10° Earth emergence angle for starting altitudes from 0 km to 22 km, as observed by a space based instrument at 525 km [upper panel] and a balloon based instrument at 33 km [lower panel]. The spatial distribution for the balloon based instrument is plotted in logarithmic scale to better demonstrate the differences between the curves.

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    • Figure 17
      Figure 17

      Upper panel: Cherenkov light distribution for 100 PeV proton shower with 10° Earth emergence angle initiated at 0 km altitude as seen by POEMMA, with profile fits described in the text. Vertical lines show the transition from constant to power law to exponential behaviors. Lower panel: Shower initiated at 17 km altitude.

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    • Figure 18
      Figure 18

      Parameter fits to the Cherenkov spatial distribution from a 100 PeV upward proton shower initiated at starting altitudes 0 km to 25 km and Earth emergence angles 0° to 50° as observed by a space based instrument at 525 km altitude. Plots are central intensity ρ0 [upper panel], central width θch [middle panel], and power law scale β [lower panel] using the 5 parameter fit model described in the text.

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    • Figure 19
      Figure 19

      Parameter fits to the Cherenkov spatial distribution from a 100 PeV upward proton shower initiated at starting altitudes 0 km to 25 km and Earth emergence angles 0° to 50° as observed by a balloon based instrument at 33 km altitude. Plots are central intensity ρ0 [upper panel], central width θch [middle panel], and power law scale β [lower panel] using the 5 parameter fit model described in the text.

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    • Figure 20
      Figure 20

      Geometry of a neutrino induced upward going air shower as observed by a detector at altitude h (see text for details).

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    • Figure 21
      Figure 21

      Emerging τ-lepton energy distribution for a 1017  eV parent neutrino as a function of Earth emergence angle calculated using 3-dimensional kernel density estimation. The center blue line represents the mean τ-lepton energy and the dash-dotted and dotted lines represent the 1σ and 2σ deviations, respectively.

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    • Figure 22
      Figure 22

      Geometric aperture as a function of primary neutrino energy for the primary tau neutrino, primary and secondary muon neutrino detection channels for POEMMA-360° [upper panel] and EUSO-SPB2-360° [lower panel].

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    • Figure 23
      Figure 23

      Neutrino sensitivity scaled by neutrino energy squared for POEMMA [upper panel] and EUSO-SPB2 [lower panel], assuming duty cycle 20% and flight times of 5 y and 100 d, respectively. Solid lines correspond to ΔϕE=360° azimuthal field of view while dashed lines correspond to ΔϕE=30° (POEMMA) and ΔϕE=12.8° (EUSO-SPB2). The red and purple shaded regions represent the cosmogenic neutrino flux expected respectively in the case of a pure proton composition of UHECR and in the case of the mixed composition observed by Auger [53]. Different neutrino fluxes correspond to different choices for the cosmological evolution of the UHECR sources as discussed in [7] (see text).

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    • Figure 24
      Figure 24

      Total sensitivity, summed over all detection channels shown in Fig. 23, of a POEMMA like experiment with 2π azimuth range and different choices for ρthr. The solid blue line is the nominal case of the POEMMA design ρthr=ρthr0, while the solid orange line corresponds to the case ρthr=ρthr0/2 and the solid green line corresponds to the case ρthr=ρthr0/10.

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