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_bounds = [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_bounds)
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())

components:
-   name: power-law-model
    type: SkyModel
    spectral:
        type: PowerLawSpectralModel
        parameters:
        -   name: index
            value: 2.0
        -   name: amplitude
            value: 1.0e-12
            unit: cm-2 s-1 TeV-1
        -   name: reference
            value: 1.0
            unit: TeV
metadata:
    creator: Gammapy 2.0.dev155+g9309a089d
    date: '2024-12-18T16:14:22.171005'
    origin: null