PowerLaw2

class gammapy.spectrum.models.PowerLaw2(amplitude='1e-12 cm-2 s-1', index=2, emin='0.1 TeV', emax='100 TeV')[source]

Bases: gammapy.spectrum.models.SpectralModel

Spectral power-law model with integral as amplitude parameter.

See also: https://fermi.gsfc.nasa.gov/ssc/data/analysis/scitools/source_models.html

\[\phi(E) = F_0 \cdot \frac{\Gamma + 1}{E_{0, max}^{-\Gamma + 1} - E_{0, min}^{-\Gamma + 1}} \cdot E^{-\Gamma}\]
Parameters:

index : Quantity

Spectral index \(\Gamma\)

amplitude : Quantity

Integral flux \(F_0\).

emin : Quantity

Lower energy limit \(E_{0, min}\).

emax : Quantity

Upper energy limit \(E_{0, max}\).

Examples

This is how to plot the default PowerLaw2 model:

from astropy import units as u
from gammapy.spectrum.models import PowerLaw2

pwl2 = PowerLaw2()
pwl2.plot(energy_range=[0.1, 100] * u.TeV)
plt.show()

Methods Summary

__call__(energy) Call evaluate method of derived classes
copy() A deep copy.
energy_flux(emin, emax, **kwargs) Compute energy flux in given energy range.
energy_flux_error(emin, emax, **kwargs) Compute energy flux in given energy range with error propagation.
evaluate(energy, amplitude, index, emin, emax) Evaluate the model (static function).
evaluate_error(energy) Evaluate spectral model with error propagation.
from_dict(val) Create from dict.
integral(emin, emax, **kwargs) Integrate power law analytically.
integral_error(emin, emax, **kwargs) Integrate power law analytically with error propagation.
inverse(value) Return energy for a given function value of the spectral model.
plot(energy_range[, ax, energy_unit, …]) Plot spectral model curve.
plot_error(energy_range[, ax, energy_unit, …]) Plot spectral model error band.
spectral_index(energy[, epsilon]) Compute spectral index at given energy.
to_dict() Convert to dict.

Methods Documentation

__call__(energy)

Call evaluate method of derived classes

copy()

A deep copy.

energy_flux(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, emax : Quantity

Lower and upper bound of integration range.

**kwargs : dict

Keyword arguments passed to func:integrate_spectrum
energy_flux_error(emin, emax, **kwargs)

Compute energy flux in given energy range with error propagation.

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

emin, emax : Quantity

Lower bound of integration range.

**kwargs : dict

Keyword arguments passed to integrate_spectrum()
Returns:

energy_flux, energy_flux_error : tuple of Quantity

Tuple of energy flux and energy flux error.
static evaluate(energy, amplitude, index, emin, emax)[source]

Evaluate the model (static function).

evaluate_error(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(emin, emax, **kwargs)[source]

Integrate power law analytically.

\[F(E_{min}, E_{max}) = F_0 \cdot \frac{E_{max}^{\Gamma + 1} \ - E_{min}^{\Gamma + 1}}{E_{0, max}^{\Gamma + 1} \ - E_{0, min}^{\Gamma + 1}}\]
Parameters:

emin, emax : Quantity

Lower and upper bound of integration range.
integral_error(emin, emax, **kwargs)[source]

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(value)[source]

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

Parameters:

value : Quantity

Function value of the spectral model.
plot(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(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(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()

Convert to dict.