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Complex Analysis of Askaryan Radiation: UHE-$ν$ Identification and Reconstruction using the Hilbert Envelope of Observed Signals

J. C. Hanson, R. Hartig

Abstract

The detection of ultra-high energy neutrinos (UHE-$ν$), with enegies above 10 PeV, has been a long-time goal in astroparticle physics. Autonomous, radio-frequency (RF) UHE-$ν$ detetectors have been deployed in polar regions that rely on the Askaryan effect in ice for the neutrino signal. The Askaryan effect occurs when the excess negative charge within a UHE-$ν$ cascade radiates in a dense medium. UHE-$ν$ can induce cascades that radiate in the RF bandwidth above thermal backgrounds. To identify UHE-$ν$ signals in data from Askaryan-class detectors, analytic models of the Askaryan electromagnetic field have been created and matched to simulations and laboratory measurements. These models describe the Askaryan electromagnetic field, but leave the effects of signal propagation through polar ice and RF channel response to simulations. In this work, a fully analytic Askaryan model that accounts for these effects is presented. First, formulas for the observed voltage trace and its Hilbert envelope are calculated. Second, the analytic model is compared to UHE-$ν$ signals at 100 PeV from NuRadioMC, a key Monte Carlo toolset in the field. Correlation coefficients between the analytic signal envelope and MC data in excess of $0.94$ are found, and 99.99% of UHE-$ν$ signals pass a correlation threshold of $ρ\geq 0.4$. Analysis of RF thermal noise reveals that just 0.2 background events have $ρ\geq 0.4$ in 5 years at a 1 Hz thermal trigger rate. Finally, we describe future work related to the measurement of the logarithm of the UHE-$ν$ cascade energy.

Complex Analysis of Askaryan Radiation: UHE-$ν$ Identification and Reconstruction using the Hilbert Envelope of Observed Signals

Abstract

The detection of ultra-high energy neutrinos (UHE-), with enegies above 10 PeV, has been a long-time goal in astroparticle physics. Autonomous, radio-frequency (RF) UHE- detetectors have been deployed in polar regions that rely on the Askaryan effect in ice for the neutrino signal. The Askaryan effect occurs when the excess negative charge within a UHE- cascade radiates in a dense medium. UHE- can induce cascades that radiate in the RF bandwidth above thermal backgrounds. To identify UHE- signals in data from Askaryan-class detectors, analytic models of the Askaryan electromagnetic field have been created and matched to simulations and laboratory measurements. These models describe the Askaryan electromagnetic field, but leave the effects of signal propagation through polar ice and RF channel response to simulations. In this work, a fully analytic Askaryan model that accounts for these effects is presented. First, formulas for the observed voltage trace and its Hilbert envelope are calculated. Second, the analytic model is compared to UHE- signals at 100 PeV from NuRadioMC, a key Monte Carlo toolset in the field. Correlation coefficients between the analytic signal envelope and MC data in excess of are found, and 99.99% of UHE- signals pass a correlation threshold of . Analysis of RF thermal noise reveals that just 0.2 background events have in 5 years at a 1 Hz thermal trigger rate. Finally, we describe future work related to the measurement of the logarithm of the UHE- cascade energy.
Paper Structure (9 sections, 56 equations, 6 figures, 2 tables)

This paper contains 9 sections, 56 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Units, Definitions, and Conventions
  3. Calculation of the Main Results
  4. Comparison between Analytic Calculations and NuRadioMC
  5. Measurement of $\log_{10}E_{\rm C}$
  6. Conclusion
  7. Python3 Code for $\mathcal{L}\lbrace D(u-x)\rbrace_k$
  8. Python3 Example Code for $\mathcal{E}_{\rm s * r}(t)$
  9. Python3 Example Code for $s(t) * r(t)$

Figures (6)

  • Figure 1: (Top) The thin black line represents $s * r$ from Eq. \ref{['eq:final3']}. The gray envelope represents the envelope of Eq. \ref{['eq:final3']} computed with the Python3 SciPy function scipy.special.hilbert. The black envelope represents $\mathcal{E}_{r * s}(t)$ from Eqs. \ref{['eq:final']}-\ref{['eq:final2']}. (Bottom) Same as top, different parameters.
  • Figure 2: (Top) The thin black line represents $s(t)$ from Eq. \ref{['eq:s']} convolved with $r(t)$ from Eq. \ref{['eq:r']}, using the Python3 SciPy function scipy.signal.convolve. The gray line represents $s * r$ from Eq. \ref{['eq:final3']}. (Bottom) Same as top, different parameters.
  • Figure 3: (Black circles) Noise distribution. (Gray dashed line) Fitting function to noise distribution. (Solid gray line) UHE-$\nu$ signal distribution. (Dashed black line) Correlation threshold.
  • Figure 4: The correlation versus SNR (dB) for UHE-$\nu$ signals (upper distribution) and RF thermal noise (lower distribution). Color scale: normalized histogram value, with five equally spaced contours between 0.0 and 0.002.
  • Figure 5: A single-pulse CSW signal (black dots) from a 100 PeV UHE-$\nu$, matched to an analytic envelope (thick black line) with a correlation coefficient $\rho = 0.951$.
  • ...and 1 more figures