Super exponential cutoff power law model used for 3FGL

This model parametrises super exponential cutoff power-law model spectrum used for 3FGL.

It is defined by the following equation:

\[\phi(E) = \phi_0 \cdot \left(\frac{E}{E_0}\right)^{-\Gamma_1} \exp \left( \left(\frac{E_0}{E_{C}} \right)^{\Gamma_2} - \left(\frac{E}{E_{C}} \right)^{\Gamma_2} \right)\]

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 (
    Models,
    SkyModel,
    SuperExpCutoffPowerLaw3FGLSpectralModel,
)

energy_bounds = [0.1, 100] * u.TeV
model = SuperExpCutoffPowerLaw3FGLSpectralModel(
    index_1=1,
    index_2=2,
    amplitude="1e-12 TeV-1 s-1 cm-2",
    reference="1 TeV",
    ecut="10 TeV",
)
model.plot(energy_bounds)
plt.grid(which="both")
plt.ylim(1e-24, 1e-10)

YAML representation

Here is an example YAML file using the model:

model = SkyModel(spectral_model=model, name="super-exp-cutoff-power-law-3fgl-model")
models = Models([model])

print(models.to_yaml())

Out:

components:
-   name: super-exp-cutoff-power-law-3fgl-model
    type: SkyModel
    spectral:
        type: SuperExpCutoffPowerLaw3FGLSpectralModel
        parameters:
        -   name: amplitude
            value: 1.0e-12
            unit: cm-2 s-1 TeV-1
            is_norm: true
        -   name: reference
            value: 1.0
            unit: TeV
            frozen: true
            is_norm: false
        -   name: ecut
            value: 10.0
            unit: TeV
            is_norm: false
        -   name: index_1
            value: 1.0
            is_norm: false
        -   name: index_2
            value: 2.0
            is_norm: false