.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "user-guide/model-gallery/spectral/plot_super_exp_cutoff_powerlaw_4fgl.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_user-guide_model-gallery_spectral_plot_super_exp_cutoff_powerlaw_4fgl.py>`
        to download the full example code. or to run this example in your browser via Binder

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_user-guide_model-gallery_spectral_plot_super_exp_cutoff_powerlaw_4fgl.py:


.. _super-exp-cutoff-powerlaw-4fgl-dr3-spectral-model:

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:

.. math::

    \phi(E) = \begin{cases} \phi_0 \cdot \left(\frac{E}{E_0}\right)^{\frac{a}{\Gamma_2} -\Gamma_1} \cdot \exp \left( \frac{a}{\Gamma_2^2}\left( 1 - \left(\frac{E}{E_0}\right)^{\Gamma_2} \right) \right) \\ \phi_0 \cdot \left(\frac{E}{E_0}\right)^{ -\Gamma_1 - \frac{a}{2} \ln \frac{E}{E_0} - \frac{a \Gamma_2}{6} \ln^2 \frac{E}{E_0} - \frac{a \Gamma_2^2}{24} \ln^3 \frac{E}{E_0}} & \text{for } \left| \Gamma_2 \ln \frac{E}{E_0} \right| < 10^{-2} \end{cases}

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

.. GENERATED FROM PYTHON SOURCE LINES 19-22

Example plot
------------
Here is an example plot of the model:

.. GENERATED FROM PYTHON SOURCE LINES 22-43

.. code-block:: Python


    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)




.. image-sg:: /user-guide/model-gallery/spectral/images/sphx_glr_plot_super_exp_cutoff_powerlaw_4fgl_001.png
   :alt: plot super exp cutoff powerlaw 4fgl
   :srcset: /user-guide/model-gallery/spectral/images/sphx_glr_plot_super_exp_cutoff_powerlaw_4fgl_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    (1e-24, 1e-10)



.. GENERATED FROM PYTHON SOURCE LINES 44-47

YAML representation
-------------------
Here is an example YAML file using the model:

.. GENERATED FROM PYTHON SOURCE LINES 47-52

.. code-block:: Python


    model = SkyModel(spectral_model=model, name="super-exp-cutoff-power-law-4fgl-dr3-model")
    models = Models([model])

    print(models.to_yaml())




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    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 1.3
        date: '2024-11-26T10:08:47.760921'
        origin: null






.. _sphx_glr_download_user-guide_model-gallery_spectral_plot_super_exp_cutoff_powerlaw_4fgl.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/gammapy/gammapy-webpage/v1.3?urlpath=lab/tree/notebooks/1.3/user-guide/model-gallery/spectral/plot_super_exp_cutoff_powerlaw_4fgl.ipynb
        :alt: Launch binder
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_super_exp_cutoff_powerlaw_4fgl.ipynb <plot_super_exp_cutoff_powerlaw_4fgl.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_super_exp_cutoff_powerlaw_4fgl.py <plot_super_exp_cutoff_powerlaw_4fgl.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_super_exp_cutoff_powerlaw_4fgl.zip <plot_super_exp_cutoff_powerlaw_4fgl.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_