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Exponential Cutoff Powerlaw Spectral Model

This model parametrises a cutoff power law spectrum.

It is defined by the following equation:

$$\phi(E) = \phi_0 \cdot \left(\frac{E}{E_0}\right)^{-\Gamma} \exp(- {(\lambda E})^{\alpha})$$

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 ExpCutoffPowerLawSpectralModel, Models, SkyModel

energy_range = [0.1, 100] * u.TeV
model = ExpCutoffPowerLawSpectralModel(
    amplitude=1e-12 * u.Unit("cm-2 s-1 TeV-1"),
    index=2,
    lambda_=0.1 * u.Unit("TeV-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="exp-cutoff-power-law-model")
models = Models([model])

print(models.to_yaml())

Out:

components:
-   name: exp-cutoff-power-law-model
    type: SkyModel
    spectral:
        type: ExpCutoffPowerLawSpectralModel
        parameters:
        - {name: index, value: 2.0, 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: reference, value: 1.0, unit: TeV, min: .nan, max: .nan, frozen: true,
            error: 0}
        - {name: lambda_, value: 0.1, unit: TeV-1, min: .nan, max: .nan, frozen: false,
            error: 0}
        - {name: alpha, value: 1.0, unit: '', min: .nan, max: .nan, frozen: true,
            error: 0}