Broken power law spectral model

This model parametrises a broken power law spectrum.

It is defined by the following equation:

\[\begin{split}\phi(E) = \phi_0 \cdot \begin{cases} \left( \frac{E}{E_{\mathrm{break}}} \right)^{-\Gamma1} & \text{if } E < E_{\mathrm{break}} \\ \left( \frac{E}{E_{\mathrm{break}}} \right)^{-\Gamma2} & \text{otherwise} \end{cases}\end{split}\]

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 BrokenPowerLawSpectralModel, Models, SkyModel

energy_bounds = [0.1, 100] * u.TeV
model = BrokenPowerLawSpectralModel(
    index1=1.5,
    index2=2.5,
    amplitude="1e-12 TeV-1 cm-2 s-1",
    ebreak="1 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="broken-power-law-model")
models = Models([model])

print(models.to_yaml())

components:
-   name: broken-power-law-model
    type: SkyModel
    spectral:
        type: BrokenPowerLawSpectralModel
        parameters:
        -   name: index1
            value: 1.5
        -   name: index2
            value: 2.5
        -   name: amplitude
            value: 1.0e-12
            unit: TeV-1 s-1 cm-2
        -   name: ebreak
            value: 1.0
            unit: TeV
metadata:
    creator: Gammapy 2.1
    date: '2026-04-02T13:57:47.034477'
    origin: null