.. only:: html
.. note::
:class: sphx-glr-download-link-note
Click :ref:`here ` to download the full example code
.. rst-class:: sphx-glr-example-title
.. _sphx_glr_modeling_gallery_spectral_plot_super_exp_cutoff_powerlaw_4fgl.py:
.. _super-exp-cutoff-powerlaw-4fgl-spectral-model:
Super Exponential Cutoff Power Law Model used for 4FGL
======================================================
This model parametrises super exponential cutoff power-law model spectrum used for 4FGL.
It is defined by the following equation:
.. math::
\phi(E) = \phi_0 \cdot \left(\frac{E}{E_0}\right)^{-\Gamma_1}
\exp \left(
a \left( E_0 ^{\Gamma_2} - E^{\Gamma_2} \right)
\right)
See Equation (3) in https://arxiv.org/pdf/1902.10045.pdf
Example plot
------------
Here is an example plot of the model:
.. code-block:: default
from astropy import units as u
import matplotlib.pyplot as plt
from gammapy.modeling.models import (
Models,
SkyModel,
SuperExpCutoffPowerLaw4FGLSpectralModel,
)
energy_range = [0.1, 100] * u.TeV
model = SuperExpCutoffPowerLaw4FGLSpectralModel(
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)
.. image:: /modeling/gallery/spectral/images/sphx_glr_plot_super_exp_cutoff_powerlaw_4fgl_001.png
:class: sphx-glr-single-img
YAML representation
-------------------
Here is an example YAML file using the model:
.. code-block:: default
model = SkyModel(spectral_model=model, name="super-exp-cutoff-power-law-4fgl-model")
models = Models([model])
print(models.to_yaml())
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
components:
- name: super-exp-cutoff-power-law-4fgl-model
type: SkyModel
spectral:
type: SuperExpCutoffPowerLaw4FGLSpectralModel
parameters:
- {name: amplitude, value: 1.0e-12, unit: cm-2 s-1 TeV-1, min: .nan, max: .nan,
frozen: false, error: 0}
- {name: reference, value: 1.0, unit: TeV, min: .nan, max: .nan, frozen: true,
error: 0}
- {name: expfactor, value: 0.01, unit: '', min: .nan, max: .nan, frozen: false,
error: 0}
- {name: index_1, value: 1.0, unit: '', min: .nan, max: .nan, frozen: false,
error: 0}
- {name: index_2, value: 2.0, unit: '', min: .nan, max: .nan, frozen: false,
error: 0}
.. _sphx_glr_download_modeling_gallery_spectral_plot_super_exp_cutoff_powerlaw_4fgl.py:
.. only :: html
.. container:: sphx-glr-footer
:class: sphx-glr-footer-example
.. container:: sphx-glr-download sphx-glr-download-python
:download:`Download Python source code: plot_super_exp_cutoff_powerlaw_4fgl.py `
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: plot_super_exp_cutoff_powerlaw_4fgl.ipynb `
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery `_