Sim-B

Simplified Models for Photohadronic Interactions in cosmic accelerators

Authors : S. Hümmer, M. Rüger, F. Spanier, W. Winter

This notebook illustrates how to reproduce some results for model Sim - B of arXiv : 1002.1310. It calculates pion, kaon, neutron muon and neutrino spectra. Please cite arXiv: 1002.1310 if you use this notebook. The notebook can be downloaded here. Requires Mathematica 7.

General parameters

General note on units : All energies in this notebook are in GeV. All spectra are in units of (steady) or (injection) times the normalization factors, as given in App. C.

Input Proton spectrum as a function of energy (Eq. C2)

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Input Photon spectrum as a function of energy (Eq. C1)

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Energy range for which spectra are to be calculated

This notebook needs about 10 minutes to run through for the considered energy range chosen to be [1 ...10^11] GeV (logarithmically). The distance between the interpolation points is in this case deltae = 0.5 [GeV]. For smoother/better results, adjust this number to 0.1 (affects the computation time by a factor of five).

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Switches off the messages regarding slow converging and undeflows in computations. For our accuracy, this treatment is sufficient.

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Description of photohadronics

Here the response Functions (f) and the parameters are defined for the different interaction types.

Resonant production (see Sec. 4.2.2)

General version of f-functions in Eqs. (31) and (32):

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Parameters from Table 4 in the form {emin, emax, Ïƒ, Ï‡, , , } for different pion charges and interaction types {(LR; ),(LR; ),(HR; ),(HR; ),(HR; )}

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Direct production (see Sec. 4.3)

Functions :

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f-functions for single pion production (1) and 2-pion production (2) from Eq. (33):

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Parameters from Table 5 {emin, emax, Ï‡, , , , Z} for the different interaction types ,,,,,,};â€¨here Z=1 for single pion production and Z=2 for 2-pion production

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Multi-pion production (see Sec. 4.4.2)

f - function (see Eq. (40)) has the same general form as the one for resonant production

Parameters from Table 6 {emin, emax, Ïƒ, Ï‡, , , } for the different interaction types (see first column of Table 6):

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Kaon production (see Sec. 4.5)

f - function from Eq. (42):

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Computation of secondary spectra

Pion production; computed with Eq. (28) for the different interaction types; uses logarithmic integration and y as logarithmic variable

Pion spectra from resonant production

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Pion spectra from direct production

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Pion spectra from multi-pion production

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Total pion spectra

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Kaon production; see Eq. (28)

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Neutron production; see Eq. (B6)

Resonant production:

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Direct production:

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Multi-pion production:

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Total neutron spectra :

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Figures for secondary spectra

Function constructing interpolating functions (Parameters: data: table for which to define interpolating function, xmin, xmax and ymax: to define ranges for the plots, func: interpolating function object to be returned)

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Calculation of the interpoalting functions for pion, neutron and kaon spectra

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Contributions to the positive charged pion spectrum from resonant, direct and multi pion interactions (see Fig.5 top left corner)

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Pion and kaon spectra (see Fig. 6 left panel)

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Description of Weak Decays

Scaling functions for the decays of pions and muons

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Pion decays - Muon spectra

Here we compute the decays of the pions into left- and right-handed muons and construct the interpolating functions for the muon spectra (for explanation see module part1)

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Pion decays - Neutrino spectra

Here we compute the decay of the pions into neutrinos and construct the interpolating functions for the neutrino spectra (for explanation see module part1)

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Kaon decays - Neutrino spectrum

Here we compute the decay of the kaons into neutrinos and construct the interpolating functions for the neutrino spectrum

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Neutron decays - Neutrino spectrum

Here we compute the decay of the neutrons into neutrinos and construct the interpolating functions for the neutrino spectrum (for explanation see module part1)

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Muon decays - Neutrino spectra

Here we compute the decays of the left - and right - handed muons into neutrinos and construct the interpolating functions for the neutrino spectra taking into account the helicity of the muons (for explanation see module part1).

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