[Paper Review] Correlating prompt GRB photons with neutrinos

I. Taboada, M. V. D’Agostino|ArXiv.org|Nov 14, 2007

Gamma-ray bursts and supernovae1 references3 citations

TL;DR

This paper demonstrates that standard broken power law approximations of the GRB Band function overestimate high-energy photon contributions, leading to a ~2× overestimation of expected neutrino event rates in km³ neutrino telescopes like IceCube. It introduces a refined approximation (approximation B) that correctly models the Band function, yielding a higher characteristic neutrino energy (~10¹⁵ eV) and more accurate event rate predictions, with Earth's column density modulating the overestimation factor.

ABSTRACT

It is standard in theoretical neutrino astrophysics to use a broken power law approximation, based on the Band function, to describe the average photon flux of the prompt emission of Gamma-Ray Bursts. We will show that this approximation overestimates the contribution of high energy gamma-rays (and underestimates low energy gamma-rays). As a consequence models that rely on this approximation overestimate neutrino event rate by a factor of approx 2 depending on Earth's column density in the direction of the GRB. Furthermore the characteristic energy of neutrinos that trigger a km^3 detector is typically 10^{16} eV, higher than previously predicted. We also provide a new broken power law approximation to the Band function and show that it properly represents the photon spectra.

Motivation & Objective

• To identify and correct systematic errors in neutrino event rate predictions from GRBs caused by approximating the Band function with a broken power law.
• To quantify how the overestimation of high-energy photons affects expected neutrino detection rates in km³-scale telescopes like IceCube and KM3NET.
• To derive a new, accurate broken power law approximation (approximation B) to the Band function that preserves spectral shape and improves neutrino spectrum modeling.
• To determine the true characteristic energy of detectable neutrinos from GRBs, correcting prior estimates that were too low by factors of 10–e.
• To assess the implications for neutrino flavor ratios and experimental searches, particularly regarding muon range and Earth attenuation effects.

Proposed method

• Uses the Band function (dNγ/dEγ) as the true photon spectrum, with parameters αγ ≈ -2, βγ ≈ -1, E_pk ≈ 300 keV, and εbγ = 300 keV for a GRB at z = 1 with Γ = 300.
• Compares two broken power law approximations: standard approximation A (incorrectly assumes power-law behavior at all energies) and a new approximation B derived from the Band function’s effective break energy (ε̄γ = εbγ / e).
• Applies the photo-pion production process (p + γ → Δ⁺ → π⁺ → μ⁺ → e⁺ + νμ + ν̄μ + νe) to compute neutrino spectra from proton-photon interactions.
• Calculates neutrino event rates using the full detector response: effective area (1 km²), muon threshold (100 GeV), muon range, and Earth attenuation via column density and total cross-section (σT).
• Computes the attenuation factor S(Eν, θ) using Earth’s column density from the Preliminary Earth Reference Model and neutrino cross-sections from CTEQ5.
• Normalizes all neutrino spectra to the same fluence and compares event rates across approximations A, B, and the true Band function for varying viewing angles (cosθ).

Experimental results

Research questions

• RQ1 Does the standard broken power law approximation of the GRB Band function systematically overestimate high-energy photon flux, leading to inflated neutrino event rate predictions?
• RQ2 How does the characteristic energy of detectable neutrinos from GRBs compare to prior estimates, and what is its dependence on the true photon spectrum?
• RQ3 To what extent does Earth’s column density modulate the overestimation factor in neutrino event rates when using the standard approximation?
• RQ4 Can a new broken power law approximation to the Band function be derived that accurately reflects the spectral shape and avoids overestimating low-energy neutrino contributions?
• RQ5 What are the implications of the corrected neutrino energy spectrum for neutrino flavor ratios and experimental detection strategies in km³ neutrino telescopes?

Key findings

• The standard broken power law approximation (approximation A) overestimates the contribution of high-energy photons by a factor of ~2, leading to a corresponding overestimation of expected neutrino event rates in km³ detectors.
• The new approximation B to the Band function correctly models the effective break energy as ε̄γ = εbγ / e, which is independent of spectral indices and provides a more accurate spectral representation.
• The characteristic energy of detectable neutrinos is ~10¹⁵ eV, a factor of e (~2.7) higher than previous estimates based on approximation A, and a factor of 10 higher than the average value used in Waxman & Bahcall (1997).
• The overestimation factor of ~2 depends on the Earth’s column density along the line of sight; it increases for steeper angles due to enhanced attenuation in approximation B.
• The corrected neutrino spectrum implies that muon energy loss and flavor ratio effects (as discussed by Kashti & Waxman, 2005) are more relevant than previously thought, since the characteristic energy is now closer to the synchrotron break energy.
• For back-of-the-envelope calculations, the paper provides a new, accurate broken power law approximation (approximation B) that should replace the standard approach in future GRB neutrino modeling.