# Licensed under a 3-clause BSD style license - see LICENSE.rst
import numpy as np
from astropy import units as u
from ..utils.fitting import Parameters
from .models import PowerLaw, LogParabola, ExponentialCutoffPowerLaw, SpectralModel
__all__ = ["CrabSpectrum"]
# HESS publication: 2006A&A...457..899A
hess_pl = {
"amplitude": 3.45e-11 * u.Unit("1 / (cm2 s TeV)"),
"index": 2.63,
"reference": 1 * u.TeV,
}
hess_ecpl = {
"amplitude": 3.76e-11 * u.Unit("1 / (cm2 s TeV)"),
"index": 2.39,
"lambda_": 1 / (14.3 * u.TeV),
"reference": 1 * u.TeV,
}
# HEGRA publication : 2004ApJ...614..897A
hegra = {
"amplitude": 2.83e-11 * u.Unit("1 / (cm2 s TeV)"),
"index": 2.62,
"reference": 1 * u.TeV,
}
# MAGIC publication: 2015JHEAp...5...30A
# note that in the paper the beta of the LogParabola is given as negative in
# Table 1 (pag. 33), but should be positive to match gammapy LogParabola expression
# Also MAGIC uses log10 in the LogParabola expression, gammapy uses ln, hence
# the conversion factor
magic_lp = {
"amplitude": 3.23e-11 * u.Unit("1 / (cm2 s TeV)"),
"alpha": 2.47,
"beta": 0.24 / np.log(10),
"reference": 1 * u.TeV,
}
magic_ecpl = {
"amplitude": 3.80e-11 * u.Unit("1 / (cm2 s TeV)"),
"index": 2.21,
"lambda_": 1 / (6.0 * u.TeV),
"reference": 1 * u.TeV,
}
class MeyerCrabModel(SpectralModel):
"""Meyer 2010 log polynomial Crab spectral model.
See 2010A%26A...523A...2M, Appendix D.
"""
coefficients = np.array([-0.00449161, 0, 0.0473174, -0.179475, -0.53616, -10.2708])
@staticmethod
def evaluate(energy):
polynomial = np.poly1d(MeyerCrabModel.coefficients)
log_energy = np.log10(energy.to_value("TeV"))
log_flux = polynomial(log_energy)
flux = u.Quantity(np.power(10, log_flux), "erg / (cm2 s)", copy=False)
return flux / energy ** 2
[docs]class CrabSpectrum:
"""Crab nebula spectral model.
The Crab nebula is often used as a standard candle in gamma-ray astronomy.
Fluxes and sensitivities are often quoted relative to the Crab spectrum.
The following references are available:
* 'meyer', http://adsabs.harvard.edu/abs/2010A%26A...523A...2M, Appendix D
* 'hegra', http://adsabs.harvard.edu/abs/2000ApJ...539..317A
* 'hess_pl' and 'hess_ecpl': http://adsabs.harvard.edu/abs/2006A%26A...457..899A
* 'magic_lp' and 'magic_ecpl': http://adsabs.harvard.edu/abs/2015JHEAp...5...30A
Parameters
----------
reference : {'meyer', 'hegra', 'hess_pl', 'hess_ecpl', 'magic_lp', 'magic_ecpl'}
Which reference to use for the spectral model.
Examples
--------
Let's first import what we need::
import astropy.units as u
from gammapy.spectrum import CrabSpectrum
from gammapy.spectrum.models import PowerLaw
Plot the 'hess_ecpl' reference Crab spectrum between 1 TeV and 100 TeV::
crab_hess_ecpl = CrabSpectrum('hess_ecpl')
crab_hess_ecpl.model.plot([1, 100] * u.TeV)
Use a reference crab spectrum as unit to measure a differential flux (at 10 TeV)::
>>> pwl = PowerLaw(index=2.3, amplitude=1e-12 * u.Unit('1 / (cm2 s TeV)'), reference=1 * u.TeV)
>>> crab = CrabSpectrum('hess_pl').model
>>> energy = 10 * u.TeV
>>> dnde_cu = (pwl(energy) / crab(energy)).to('%')
>>> print(dnde_cu)
6.19699156377 %
And the same for integral fluxes (between 1 and 10 TeV)::
>>> # compute integral flux in crab units
>>> emin, emax = [1, 10] * u.TeV
>>> flux_int_cu = (pwl.integral(emin, emax) / crab.integral(emin, emax)).to('%')
>>> print(flux_int_cu)
3.5350582166 %
"""
references = ["meyer", "hegra", "hess_pl", "hess_ecpl", "magic_lp", "magic_ecpl"]
"""Available references (see class docstring)."""
def __init__(self, reference="meyer"):
if reference == "meyer":
model = MeyerCrabModel()
elif reference == "hegra":
model = PowerLaw(**hegra)
elif reference == "hess_pl":
model = PowerLaw(**hess_pl)
elif reference == "hess_ecpl":
model = ExponentialCutoffPowerLaw(**hess_ecpl)
elif reference == "magic_lp":
model = LogParabola(**magic_lp)
elif reference == "magic_ecpl":
model = ExponentialCutoffPowerLaw(**magic_ecpl)
else:
fmt = "Invalid reference: {!r}. Choices: {!r}"
raise ValueError(fmt.format(reference, self.references))
self.model = model
self.reference = reference