.. 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_broken_powerlaw.py:
.. _broken-powerlaw-spectral-model:
Broken Power Law Spectral Model
======================================
This model parametrises a broken power law spectrum.
It is defined by the following equation:
.. math::
\phi(E) = phi_0 \cdot \begin{cases}
\left( \frac{E}{E_0} \right)^{-\Gamma1} \rm{if} E < E_{break}\\
\left( \frac{E}{E_0} \right)^{-\Gamma2} \rm{otherwise}
\end{cases}
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 BrokenPowerLawSpectralModel, Models, SkyModel
energy_range = [0.1, 100] * u.TeV
model = BrokenPowerLawSpectralModel(
index1=1.5, index2=2.5, amplitude="1e-12 TeV-1 cm-2 s-1", ebreak="1 TeV",
)
model.plot(energy_range)
plt.grid(which="both")
.. image:: /modeling/gallery/spectral/images/sphx_glr_plot_broken_powerlaw_001.png
:alt: plot broken powerlaw
: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="broken-power-law-model")
models = Models([model])
print(models.to_yaml())
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
components:
- name: broken-power-law-model
type: SkyModel
spectral:
type: BrokenPowerLawSpectralModel
parameters:
- name: index1
value: 1.5
- name: index2
value: 2.5
- name: amplitude
value: 1.0e-12
unit: cm-2 s-1 TeV-1
- name: ebreak
value: 1.0
unit: TeV
.. _sphx_glr_download_modeling_gallery_spectral_plot_broken_powerlaw.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_broken_powerlaw.py `
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: plot_broken_powerlaw.ipynb `
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery `_