# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""Simple models for cosmic ray spectra at Earth.
For measurements, the "Database of Charged Cosmic Rays (CRDB)" is a great resource:
http://lpsc.in2p3.fr/cosmic-rays-db/
"""
from __future__ import absolute_import, division, print_function, unicode_literals
import numpy as np
from astropy.units import Quantity
__all__ = ["cosmic_ray_flux"]
def _power_law(E, N, k):
E = Quantity(E, "TeV")
E0 = Quantity(1, "TeV")
N = Quantity(N, "m^-2 s^-1 TeV^-1 sr^-1")
flux = N * (E / E0) ** (-k)
return flux
def _log_normal(E, L, E_p, w):
E = Quantity(E, "TeV")
E_p = Quantity(E_p, "TeV")
L = Quantity(L, "m^-2 s^-1 sr^-1")
term1 = L / (E * w * np.sqrt(2 * np.pi))
term2 = np.exp(-np.log(E / E_p) ** 2 / (2 * w ** 2))
return term1 * term2
def _electron_spectrum(E, N, k, L, E_p, w):
flux = _power_law(E, N, k)
flux += _log_normal(E, L, E_p, w)
return flux
[docs]def cosmic_ray_flux(energy, particle="proton"):
"""Cosmic ray flux at Earth.
These are the spectra assumed in this CTA study:
Table 3 in http://adsabs.harvard.edu/abs/2013APh....43..171B
The hadronic spectra are simple power-laws, the electron spectrum
is the sum of a power law and a log-normal component to model the
"Fermi shoulder".
Parameters
----------
energy : `~astropy.units.Quantity`
Particle energy
particle : {'electron', 'proton', 'He', 'N', 'Si', 'Fe'}
Particle type
Returns
-------
flux : `~astropy.units.Quantity`
Cosmic ray flux in unit ``m^-2 s^-1 TeV^-1 sr^-1``
"""
pars = {
"electron": {"N": 6.85e-5, "k": 3.21, "L": 3.19e-3, "E_p": 0.107, "w": 0.776},
"proton": {"N": 0.096, "k": 2.70},
"N": {"N": 0.0719, "k": 2.64},
"Si": {"N": 0.0284, "k": 2.66},
"Fe": {"N": 0.0134, "k": 2.63},
}
if particle == "electron":
return _electron_spectrum(energy, **pars["electron"])
elif particle in ["proton", "He", "N", "Si", "Fe"]:
return _power_law(energy, **pars[particle])
else:
raise ValueError("Invalid argument for particle: {}".format(particle))