Broken Power Law Spectral Model

This model parametrises a broken power law spectrum.

It is defined by the following equation:

\[\begin{split}\phi(E) = phi_0 \cdot \begin{cases} \left( \frac{E}{E_0} \right)^{-\Gamma1} \rm{if} E < E_{break}\\ \left( \frac{E}{E_0} \right)^{-\Gamma2} \rm{otherwise} \end{cases}\end{split}\]

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_range = [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_range)
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())

Out:

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: cm-2 s-1 TeV-1
        -   name: ebreak
            value: 1.0
            unit: TeV