Exponential Cutoff Powerlaw Spectral Model used for 3FGL

This model parametrises a cutoff power law spectrum used for 3FGL.

It is defined by the following equation:

\[\phi(E) = \phi_0 \cdot \left(\frac{E}{E_0}\right)^{-\Gamma} \exp \left( \frac{E_0 - E}{E_{C}} \right)\]

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 ExpCutoffPowerLaw3FGLSpectralModel, Models, SkyModel

energy_range = [0.1, 100] * u.TeV
model = ExpCutoffPowerLaw3FGLSpectralModel(
    index=2.3 * u.Unit(""),
    amplitude=4 / u.cm ** 2 / u.s / u.TeV,
    reference=1 * u.TeV,
    ecut=10 * 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-3fgl-model")
models = Models([model])

print(models.to_yaml())

Out:

components:
-   name: exp-cutoff-power-law-3fgl-model
    type: SkyModel
    spectral:
        type: ExpCutoffPowerLaw3FGLSpectralModel
        parameters:
        -   name: index
            value: 2.3
        -   name: amplitude
            value: 4.0
            unit: cm-2 s-1 TeV-1
        -   name: reference
            value: 1.0
            unit: TeV
            frozen: true
        -   name: ecut
            value: 10.0
            unit: TeV