Power law 2 spectral model

This model parametrises a power law spectrum with integral as amplitude parameter.

It is defined by the following equation:

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

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

Example plot

Here is an example plot of the model:

from astropy import units as u
import matplotlib.pyplot as plt
from gammapy.modeling.models import Models, PowerLaw2SpectralModel, SkyModel

energy_bounds = [0.1, 100] * u.TeV
model = PowerLaw2SpectralModel(
    amplitude=u.Quantity(1e-12, "cm-2 s-1"),
    index=2.3,
    emin=1 * u.TeV,
    emax=10 * u.TeV,
)
model.plot(energy_bounds)
plt.grid(which="both")

YAML representation

Here is an example YAML file using the model:

model = SkyModel(spectral_model=model, name="power-law2-model")
models = Models([model])

print(models.to_yaml())

Out:

components:
-   name: power-law2-model
    type: SkyModel
    spectral:
        type: PowerLaw2SpectralModel
        parameters:
        -   name: amplitude
            value: 1.0e-12
            unit: cm-2 s-1
        -   name: index
            value: 2.3
        -   name: emin
            value: 1.0
            unit: TeV
            frozen: true
        -   name: emax
            value: 10.0
            unit: TeV
            frozen: true