# Licensed under a 3-clause BSD style license - see LICENSE.rst
import numpy as np
from astropy import units as u
from gammapy.modeling import Parameter
from .spectral import (
ExpCutoffPowerLawSpectralModel,
LogParabolaSpectralModel,
PowerLawSpectralModel,
SpectralModel,
)
__all__ = [
"create_crab_spectral_model",
"MeyerCrabSpectralModel",
]
[docs]class MeyerCrabSpectralModel(SpectralModel):
"""Meyer 2010 log polynomial Crab spectral model.
Reference: https://ui.adsabs.harvard.edu/abs/2010A%26A...523A...2M, Appendix D
"""
norm = Parameter("norm", value=1, frozen=True)
norm._is_norm = True
coefficients = [-0.00449161, 0, 0.0473174, -0.179475, -0.53616, -10.2708]
[docs] @staticmethod
def evaluate(energy, norm):
"""Evaluate the model."""
polynomial = np.poly1d(MeyerCrabSpectralModel.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 norm * flux / energy**2
[docs]def create_crab_spectral_model(reference="meyer"):
"""Create a Crab nebula reference 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', https://ui.adsabs.harvard.edu/abs/2010A%26A...523A...2M, Appendix D
* 'hegra', https://ui.adsabs.harvard.edu/abs/2000ApJ...539..317A
* 'hess_pl' and 'hess_ecpl': https://ui.adsabs.harvard.edu/abs/2006A%26A...457..899A
* 'magic_lp' and 'magic_ecpl': https://ui.adsabs.harvard.edu/abs/2015JHEAp...5...30A
Parameters
----------
reference : {'meyer', 'hegra', 'hess_pl', 'hess_ecpl', 'magic_lp', 'magic_ecpl'}, optional
Which reference to use for the spectral model. Default is 'meyer'.
Examples
--------
Let's first import what we need::
>>> import astropy.units as u
>>> from gammapy.modeling.models import PowerLawSpectralModel, create_crab_spectral_model
Plot the 'hess_ecpl' reference Crab spectrum between 1 TeV and 100 TeV::
>>> crab_hess_ecpl = create_crab_spectral_model('hess_ecpl')
>>> crab_hess_ecpl.plot([1, 100] * u.TeV) #doctest: +SKIP
Use a reference crab spectrum as unit to measure a differential flux (at 10 TeV)::
>>> pwl = PowerLawSpectralModel(
... index=2.3, amplitude=1e-12 * u.Unit('1 / (cm2 s TeV)'), reference=1 * u.TeV
... )
>>> crab = create_crab_spectral_model('hess_pl')
>>> energy = 10 * u.TeV
>>> dnde_cu = (pwl(energy) / crab(energy)).to('%')
>>> print(dnde_cu)
6.196991563774588 %
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)
3.535058216604496 %
"""
if reference == "meyer":
return MeyerCrabSpectralModel()
elif reference == "hegra":
return PowerLawSpectralModel(
amplitude=2.83e-11 * u.Unit("1 / (cm2 s TeV)"),
index=2.62,
reference=1 * u.TeV,
)
elif reference == "hess_pl":
return PowerLawSpectralModel(
amplitude=3.45e-11 * u.Unit("1 / (cm2 s TeV)"),
index=2.63,
reference=1 * u.TeV,
)
elif reference == "hess_ecpl":
return ExpCutoffPowerLawSpectralModel(
amplitude=3.76e-11 * u.Unit("1 / (cm2 s TeV)"),
index=2.39,
lambda_=1 / (14.3 * u.TeV),
reference=1 * u.TeV,
)
elif reference == "magic_lp":
return LogParabolaSpectralModel(
amplitude=3.23e-11 * u.Unit("1 / (cm2 s TeV)"),
alpha=2.47,
beta=0.24 / np.log(10),
reference=1 * u.TeV,
)
elif reference == "magic_ecpl":
return ExpCutoffPowerLawSpectralModel(
amplitude=3.80e-11 * u.Unit("1 / (cm2 s TeV)"),
index=2.21,
lambda_=1 / (6.0 * u.TeV),
reference=1 * u.TeV,
)
else:
raise ValueError(f"Invalid reference: {reference!r}")