PowerLaw

class gammapy.spectrum.models.PowerLaw(index=2.0, amplitude='1e-12 cm-2 s-1 TeV-1', reference='1 TeV')

Bases: gammapy.spectrum.models.SpectralModel

Spectral power-law model.

\[\phi(E) = \phi_0 \cdot \left( \frac{E}{E_0} \right)^{-\Gamma}\]

Parameters:

index : Quantity

\(\Gamma\)

amplitude : Quantity

\(\phi_0\)

reference : Quantity

\(E_0\)

Examples

This is how to plot the default PowerLaw model:

from astropy import units as u
from gammapy.spectrum.models import PowerLaw

pwl = PowerLaw()
pwl.plot(energy_range=[0.1, 100] * u.TeV)
plt.show()

Attributes Summary

amplitude
index
parameters	Parameters (Parameters)
reference

Methods Summary

__call__(self, energy)	Call evaluate method of derived classes
copy(self)	A deep copy.
energy_flux(self, emin, emax)	Compute energy flux in given energy range analytically.
energy_flux_error(self, emin, emax, \*\*kwargs)	Compute energy flux in given energy range analytically with error propagation.
evaluate(energy, index, amplitude, reference)	Evaluate the model (static function).
evaluate_error(self, energy)	Evaluate spectral model with error propagation.
from_dict(val)	Create from dict.
integral(self, emin, emax, \*\*kwargs)	Integrate power law analytically.
integral_error(self, emin, emax, \*\*kwargs)	Integrate power law analytically with error propagation.
inverse(self, value)	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)	Convert to dict.

Attributes Documentation

amplitude

index

parameters

Parameters (Parameters)

reference

Methods Documentation

__call__(self, energy)

Call evaluate method of derived classes

copy(self)

A deep copy.

energy_flux(self, emin, emax)

Compute energy flux in given energy range analytically.

\[G(E_{min}, E_{max}) = \int_{E_{min}}^{E_{max}}E \phi(E)dE = \left. \phi_0 \frac{E_0^2}{-\Gamma + 2} \left( \frac{E}{E_0} \right)^{-\Gamma + 2} \right \vert _{E_{min}}^{E_{max}}\]

Parameters:

emin, emax : Quantity

Lower and upper bound of integration range.

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

Compute energy flux in given energy range analytically with error propagation.

Parameters:

emin, emax : Quantity

Lower and upper bound of integration range.

Returns:

energy_flux, energy_flux_error : tuple of Quantity

Tuple of energy flux and energy flux error.

static evaluate(energy, index, amplitude, reference)

Evaluate the model (static function).

evaluate_error(self, energy)

Evaluate spectral model with error propagation.

Parameters:

energy : Quantity

Energy at which to evaluate

Returns:

flux, flux_error : tuple of Quantity

Tuple of flux and flux error.

classmethod from_dict(val)

Create from dict.

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

Integrate power law analytically.

\[F(E_{min}, E_{max}) = \int_{E_{min}}^{E_{max}}\phi(E)dE = \left. \phi_0 \frac{E_0}{-\Gamma + 1} \left( \frac{E}{E_0} \right)^{-\Gamma + 1} \right \vert _{E_{min}}^{E_{max}}\]

Parameters:

emin, emax : Quantity

Lower and upper bound of integration range

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

Integrate power law analytically with error propagation.

Parameters:

emin, emax : Quantity

Lower and upper bound of integration range.

Returns:

integral, integral_error : tuple of Quantity

Tuple of integral flux and integral flux error.

inverse(self, value)

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

Parameters:

value : Quantity

Function value of the spectral model.

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.spectrum.models import ExponentialCutoffPowerLaw
from astropy import units as u

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

Parameters:

ax : Axes, optional

Axis

energy_range : Quantity

Plot range

energy_unit : str, Unit, optional

Unit of the energy axis

flux_unit : str, Unit, optional

Unit of the flux axis

energy_power : int, optional

Power of energy to multiply flux axis with

n_points : int, optional

Number of evaluation nodes

Returns:

ax : Axes, 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:

ax : Axes, optional

Axis

energy_range : Quantity

Plot range

energy_unit : str, Unit, optional

Unit of the energy axis

flux_unit : str, Unit, optional

Unit of the flux axis

energy_power : int, optional

Power of energy to multiply flux axis with

n_points : int, optional

Number of evaluation nodes

**kwargs : dict

Keyword arguments forwarded to matplotlib.pyplot.fill_between

Returns:

ax : Axes, optional

Axis

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

Compute spectral index at given energy.

Parameters:

energy : Quantity

Energy at which to estimate the index

epsilon : float

Fractional energy increment to use for determining the spectral index.

Returns:

index : float

Estimated spectral index.

to_dict(self)

Convert to dict.