# 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


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