Energy spectra of gamma rays, electrons, and neutrinos produced at proton-proton interactions in the very high energy regime

By S. Kelner, F. Aharonian, V. V. Bugayov. 2006

634 citations recorded by the source corpus.

We present new parameterizations of energy spectra of secondary particles, $\ensuremath{\pi}$ mesons, gamma rays, electrons, and neutrinos produced in inelastic proton-proton collisions. The simple analytical approximations based on simulations of proton-proton interactions using the public available SIBYLL code provide very good accuracy for energy distributions of secondary products in the energy range above 100 GeV. Generally, the recommended analytical formulas deviate from the simulated distributions within a few percent over a large range of $x={E}_{i}/{E}_{p}$\char22{}the fraction of energy of the incident proton transferred to the secondaries. Finally, we describe an approximate procedure of continuation of calculations towards low energies, down to the threshold of $\ensuremath{\pi}$-meson production.

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Citations in the corpus

Observational Signatures of Particle Acceleration in Supernova Remnants (2012, background): “Since the pion production cross section is only mildly energy dependent (see Kelner et al., 2006, for approximate formulae), the spectral photon index is approximately that of the spectral index of the particles, Γ ≈ qp.”
Cosmic-ray propagation with DRAGON2: I. numerical solver and astrophysical ingredients (2016, methodology): “is energy loss has been described for the rst time in [134] and it has recently been revisited in [136], where the impact of the new parameterisations for the pion production cross section derived in [137,138] has been discussed. In our implementation of the energy loss due to pion production, we us”
Broad-band non-thermal emission from molecular clouds illuminated by cosmic rays from nearby supernova remnants (2009, methodology): “We calculate the spectrum of the injected secondary electrons Qe(t,E) by using the parameterization given by Kelner et al. (2006) and we follow the time evolution of the electron distribution function fe(t, E) by solving the equation: ∂fe(t, E) ∂t = ∂ ∂E [( dE dt ) e fe(t, E) ] + Qe(t, E) −…”
The 511 keV emission from positron annihilation in the Galaxy (2010, background): “New parameterizations of neutral and charged pion cross sections which provide an accurate description of the experimental data in a wide energy range from the pion production threshold up to 105 TeV are discussed in Kelner et al. (2006), Kamae et al. (2006, 2007).”
Background model systematics for the Fermi GeV excess (2014, background): “Rs that propagate in the Galaxy. Firstly, CR nuclei produce via inelastic nucleon-nucleon collisions with the interstellar gas neutral mesons (mainly ˇ0s), which subsequently decay to gamma-ray pairs [82,85,86]. This is typically, and throughout this work, referred to as the ˇ0 Galactic diuse compon”
Strong evidence for hadron acceleration in Tycho’s supernova remnant (2011, methodology): “Finally, flux and spectrum of the gamma rays produced by π0 decay are calculated following the analytical approximations by Kelner et al. (2006).”
Cosmic-ray energy spectrum and composition up to the ankle - the case for a second Galactic component (2016, background): “The inelastic interaction cross-section for protons is taken from Kelner et al. (2006), and for heavier nuclei, the cross-sections are taken from Letaw et al. (1983).”
Testing the nature of dark compact objects: a status report (2019, background): “Even without advocating new physics beyond the 10 TeV scale, extrapolation of known hadronic interactions to large energies suggests that about 20% of the collision energy goes into neutrinos, whose total energy is a sizable fraction of that of the photons emitted in the process [453].”
Star-forming galaxies as the origin of diffuse high-energy backgrounds: gamma-ray and neutrino connections, and implications for starburst history (2014, background): “However the relative flux of neutrinos and gamma rays depends on the ratio of charged to neutral pions, Nπ±/Nπ0 , and the relative neutrino flux per flavor depends on the initial mix of π+ to π [71, 72].”
Letter of intent for KM3NeT 2.0 (2016, methodology): “The neutrino flux adopted has been derived from the measured γ-ray spectrum and has been parameterised following [62]:”
CONSTRAINTS ON COSMIC-RAY PROPAGATION MODELS FROM A GLOBAL BAYESIAN ANALYSIS (2010, methodology): “Production of secondary positrons and electrons is calculated as described in Moskalenko & Strong (1998) with a correction by Kelner et al. (2006).”
Tests for the existence of black holes through gravitational wave echoes (2017, background): “Even without advocating new physics beyond the 10 TeV scale, extrapolation of known hadronic interactions to large energies suggests that about 20% of the collision energy goes into neutrinos, whose total energy is a sizeable fraction of that of the photons emitted in the process [151].”
NEUTRAL PION EMISSION FROM ACCELERATED PROTONS IN THE SUPERNOVA REMNANT W44 (2011, methodology): “The gamma-ray emission was derived assuming that protons interact with the nuclei of the ambient medium through pp interactions and then radiate through π0 decay (Kelner et al. 2006).”
Inverse Compton Origin of the Hard X-Ray and Soft Gamma-Ray Emission from the Galactic Ridge (2008, methodology): “…spectrum of interstellar turbulence or δ = 1/2 for a Kraichnan cascade, ρ is the magnetic rigidity, D0 is a constant, and β = v/c. Production of secondary positrons and electrons is calculated using a formalism described in Moskalenko & Strong (1998) with a correction by Kelner et al. (2006).”