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Smooth Broken Power Law Spectral Model

This model parametrises a smooth broken power law spectrum.

It is defined by the following equation:

\[\phi(E) = \phi_0 \cdot \left( \frac{E}{E_0} \right)^{-\Gamma1}\left(1 + \frac{E}{E_{break}}^{\frac{\Gamma2-\Gamma1}{\beta}} \right)^{-\beta}\]

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, SkyModel, SmoothBrokenPowerLawSpectralModel

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

print(models.to_yaml())

Out:

components:
-   name: smooth-broken-power-law-model
    type: SkyModel
    spectral:
        type: SmoothBrokenPowerLawSpectralModel
        parameters:
        - {name: index1, value: 1.5, unit: '', min: .nan, max: .nan, frozen: false,
            error: 0}
        - {name: index2, value: 2.5, unit: '', min: .nan, max: .nan, frozen: false,
            error: 0}
        - {name: amplitude, value: 1.0e-12, unit: cm-2 s-1 TeV-1, min: .nan, max: .nan,
            frozen: false, error: 0}
        - {name: ebreak, value: 1.0, unit: TeV, min: .nan, max: .nan, frozen: false,
            error: 0}
        - {name: reference, value: 1.0, unit: TeV, min: .nan, max: .nan, frozen: true,
            error: 0}
        - {name: beta, value: 1.0, unit: '', min: .nan, max: .nan, frozen: true, error: 0}