.. 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_powerlaw2.py:
.. _powerlaw2-spectral-model:
Power Law 2 Spectral Model
==========================
This model parametrises a power law spectrum with integral as amplitude parameter.
It is defined by the following equation:
.. math::
\phi(E) = F_0 \cdot \frac{\Gamma + 1}{E_{0, max}^{-\Gamma + 1}
- E_{0, min}^{-\Gamma + 1}} \cdot E^{-\Gamma}
See also: https://fermi.gsfc.nasa.gov/ssc/data/analysis/scitools/source_models.html
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, PowerLaw2SpectralModel, SkyModel
energy_range = [0.1, 100] * u.TeV
model = PowerLaw2SpectralModel(
amplitude=u.Quantity(1e-12, "cm-2 s-1"), index=2.3, emin=1 * u.TeV, emax=10 * u.TeV,
)
model.plot(energy_range)
plt.grid(which="both")
.. image:: /modeling/gallery/spectral/images/sphx_glr_plot_powerlaw2_001.png
:alt: plot powerlaw2
: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="power-law2-model")
models = Models([model])
print(models.to_yaml())
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
components:
- name: power-law2-model
type: SkyModel
spectral:
type: PowerLaw2SpectralModel
parameters:
- name: amplitude
value: 1.0e-12
unit: cm-2 s-1
- name: index
value: 2.3
- name: emin
value: 1.0
unit: TeV
frozen: true
- name: emax
value: 10.0
unit: TeV
frozen: true
.. _sphx_glr_download_modeling_gallery_spectral_plot_powerlaw2.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_powerlaw2.py `
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: plot_powerlaw2.ipynb `
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery `_