Power Law Spectral Model

This model parametrises a power law spectrum.

It is defined by the following equation:

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

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, PowerLawSpectralModel, SkyModel

energy_range = [0.1, 100] * u.TeV
model = PowerLawSpectralModel(
    index=2, amplitude="1e-12 TeV-1 cm-2 s-1", reference=1 * u.TeV,
)
model.plot(energy_range)
plt.grid(which="both")

YAML representation

Here is an example YAML file using the model:

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

print(models.to_yaml())

Out:

components:
-   name: power-law-model
    type: SkyModel
    spectral:
        type: PowerLawSpectralModel
        parameters:
        - {name: index, value: 2.0, unit: '', min: .nan, max: .nan, frozen: false}
        - {name: amplitude, value: 1.0e-12, unit: cm-2 s-1 TeV-1, min: .nan, max: .nan,
            frozen: false}
        - {name: reference, value: 1.0, unit: TeV, min: .nan, max: .nan, frozen: true}