Super Exponential Cutoff Power Law Model used for 4FGL-DR3#

This model parametrises super exponential cutoff power-law model spectrum used for 4FGL.

It is defined by the following equation:

ϕ(E)={ϕ0(EE0)aΓ2Γ1exp(aΓ22(1(EE0)Γ2))ϕ0(EE0)Γ1a2lnEE0aΓ26ln2EE0aΓ2224ln3EE0for |Γ2lnEE0|<102

See Equation (2) and (3) in https://arxiv.org/pdf/2201.11184.pdf

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,
    SuperExpCutoffPowerLaw4FGLDR3SpectralModel,
)

energy_range = [0.1, 100] * u.TeV
model = SuperExpCutoffPowerLaw4FGLDR3SpectralModel(
    index_1=1,
    index_2=2,
    amplitude="1e-12 TeV-1 cm-2 s-1",
    reference="1 TeV",
    expfactor=1e-2,
)
model.plot(energy_range)
plt.grid(which="both")
plt.ylim(1e-24, 1e-10)
plot super exp cutoff powerlaw 4fgl
(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-4fgl-dr3-model")
models = Models([model])

print(models.to_yaml())
components:
-   name: super-exp-cutoff-power-law-4fgl-dr3-model
    type: SkyModel
    spectral:
        type: SuperExpCutoffPowerLaw4FGLDR3SpectralModel
        parameters:
        -   name: amplitude
            value: 1.0e-12
            unit: cm-2 s-1 TeV-1
        -   name: reference
            value: 1.0
            unit: TeV
        -   name: expfactor
            value: 0.01
        -   name: index_1
            value: 1.0
        -   name: index_2
            value: 2.0
metadata:
    creator: Gammapy 1.2
    date: '2024-02-29T10:21:57.973386'
    origin: null

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