NaimaSpectralModel

class gammapy.modeling.models.NaimaSpectralModel(radiative_model, distance=<Quantity 1. kpc>, seed=None)

Bases: gammapy.modeling.models.SpectralModel

A wrapper for Naima models.

This class provides an interface with the models defined in the models module. The model accepts as a positional argument a Naima radiative model instance, used to compute the non-thermal emission from populations of relativistic electrons or protons due to interactions with the ISM or with radiation and magnetic fields.

One of the advantages provided by this class consists in the possibility of performing a maximum likelihood spectral fit of the model’s parameters directly on observations, as opposed to the MCMC fit to flux points featured in Naima. All the parameters defining the parent population of charged particles are stored as Parameter and left free by default. In case that the radiative model is ` ~naima.radiative.Synchrotron`, the magnetic field strength may also be fitted. Parameters can be freezed/unfreezed before the fit, and maximum/minimum values can be set to limit the parameters space to the physically interesting region.

Parameters

radiative_modelBaseRadiative

An instance of a radiative model defined in models

distanceQuantity, optional

Distance to the source. If set to 0, the intrinsic differential luminosity will be returned. Default is 1 kpc

seedstr or list of str, optional

Seed photon field(s) to be considered for the radiative_model flux computation, in case of a InverseCompton model. It can be a subset of the seed_photon_fields list defining the radiative_model. Default is the whole list of photon fields

Attributes Summary

default_parameters
parameters	Parameters (Parameters)
tag

Methods Summary

__call__(self, energy)	Call self as a function.
copy(self)	A deep copy.
create(tag, \*args, \*\*kwargs)	Create a model instance.
energy_flux(self, emin, emax, \*\*kwargs)	Compute energy flux in given energy range.
evaluate(self, energy, \*\*kwargs)	Evaluate the model.
evaluate_error(self, energy[, epsilon])	Evaluate spectral model with error propagation.
from_dict(data)
integral(self, emin, emax, \*\*kwargs)	Integrate spectral model numerically.
inverse(self, value[, emin, emax])	Return energy for a given function value of the spectral model.
plot(self, energy_range[, ax, energy_unit, …])	Plot spectral model curve.
plot_error(self, energy_range[, ax, …])	Plot spectral model error band.
spectral_index(self, energy[, epsilon])	Compute spectral index at given energy.
to_dict(self)	Create dict for YAML serialisation

Attributes Documentation

default_parameters = <gammapy.modeling.parameter.Parameters object>

parameters

Parameters (Parameters)

tag = 'NaimaSpectralModel'

Methods Documentation

__call__(self, energy)

Call self as a function.

copy(self)

A deep copy.

static create(tag, *args, **kwargs)

Create a model instance.

Examples

>>> from gammapy.modeling import Model
>>> spectral_model = Model.create("PowerLaw2SpectralModel", amplitude="1e-10 cm-2 s-1", index=3)
>>> type(spectral_model)
gammapy.modeling.models.spectral.PowerLaw2SpectralModel

energy_flux(self, emin, emax, **kwargs)

Compute energy flux in given energy range.

\[G(E_{min}, E_{max}) = \int_{E_{min}}^{E_{max}} E \phi(E) dE\]

Parameters

emin, emaxQuantity

Lower and upper bound of integration range.

**kwargsdict

Keyword arguments passed to func:integrate_spectrum

evaluate(self, energy, **kwargs)

Evaluate the model.

evaluate_error(self, energy, epsilon=0.0001)

Evaluate spectral model with error propagation.

Parameters

energyQuantity

Energy at which to evaluate

epsilonfloat

Step size of the gradient evaluation. Given as a fraction of the parameter error.

Returns

dnde, dnde_errortuple of Quantity

Tuple of flux and flux error.

classmethod from_dict(data)

integral(self, emin, emax, **kwargs)

Integrate spectral model numerically.

\[F(E_{min}, E_{max}) = \int_{E_{min}}^{E_{max}} \phi(E) dE\]

If array input for emin and emax is given you have to set intervals=True if you want the integral in each energy bin.

Parameters

emin, emaxQuantity

Lower and upper bound of integration range.

**kwargsdict

Keyword arguments passed to integrate_spectrum()

inverse(self, value, emin=<Quantity 0.1 TeV>, emax=<Quantity 100. TeV>)

Return energy for a given function value of the spectral model.

Calls the scipy.optimize.brentq numerical root finding method.

Parameters

valueQuantity

Function value of the spectral model.

eminQuantity

Lower bracket value in case solution is not unique.

emaxQuantity

Upper bracket value in case solution is not unique.

Returns

energyQuantity

Energies at which the model has the given value.

plot(self, energy_range, ax=None, energy_unit='TeV', flux_unit='cm-2 s-1 TeV-1', energy_power=0, n_points=100, **kwargs)

Plot spectral model curve.

kwargs are forwarded to matplotlib.pyplot.plot

By default a log-log scaling of the axes is used, if you want to change the y axis scaling to linear you can use:

from gammapy.modeling.models import ExpCutoffPowerLawSpectralModel
from astropy import units as u

pwl = ExpCutoffPowerLawSpectralModel()
ax = pwl.plot(energy_range=(0.1, 100) * u.TeV)
ax.set_yscale('linear')

Parameters

axAxes, optional

Axis

energy_rangeQuantity

Plot range

energy_unitstr, Unit, optional

Unit of the energy axis

flux_unitstr, Unit, optional

Unit of the flux axis

energy_powerint, optional

Power of energy to multiply flux axis with

n_pointsint, optional

Number of evaluation nodes

Returns

axAxes, optional

Axis

plot_error(self, energy_range, ax=None, energy_unit='TeV', flux_unit='cm-2 s-1 TeV-1', energy_power=0, n_points=100, **kwargs)

Plot spectral model error band.

Note

This method calls ax.set_yscale("log", nonposy='clip') and ax.set_xscale("log", nonposx='clip') to create a log-log representation. The additional argument nonposx='clip' avoids artefacts in the plot, when the error band extends to negative values (see also https://github.com/matplotlib/matplotlib/issues/8623).

When you call plt.loglog() or plt.semilogy() explicitely in your plotting code and the error band extends to negative values, it is not shown correctly. To circumvent this issue also use plt.loglog(nonposx='clip', nonposy='clip') or plt.semilogy(nonposy='clip').

Parameters

axAxes, optional

Axis

energy_rangeQuantity

Plot range

energy_unitstr, Unit, optional

Unit of the energy axis

flux_unitstr, Unit, optional

Unit of the flux axis

energy_powerint, optional

Power of energy to multiply flux axis with

n_pointsint, optional

Number of evaluation nodes

**kwargsdict

Keyword arguments forwarded to matplotlib.pyplot.fill_between

Returns

axAxes, optional

Axis

spectral_index(self, energy, epsilon=1e-05)

Compute spectral index at given energy.

Parameters

energyQuantity

Energy at which to estimate the index

epsilonfloat

Fractional energy increment to use for determining the spectral index.

Returns

indexfloat

Estimated spectral index.

to_dict(self)

Create dict for YAML serialisation