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
        -   name: amplitude
            value: 1.0e-12
            unit: cm-2 s-1 TeV-1
        -   name: reference
            value: 1.0
            unit: TeV
            frozen: true
        -   name: lambda_
            value: 0.1
            unit: TeV-1
        -   name: alpha
            value: 1.0
            frozen: true