.. only:: html

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

        Click :ref:`here <sphx_glr_download_modeling_gallery_spatial_plot_shell.py>`     to download the full example code
    .. rst-class:: sphx-glr-example-title

    .. _sphx_glr_modeling_gallery_spatial_plot_shell.py:


.. _shell-spatial-model:

Shell Spatial Model
===================

This is a spatial model parametrizing a projected radiating shell.

The shell spatial model is defined by the following equations:

.. math::
    \phi(lon, lat) = \frac{3}{2 \pi (r_{out}^3 - r_{in}^3)} \cdot
            \begin{cases}
                \sqrt{r_{out}^2 - \theta^2} - \sqrt{r_{in}^2 - \theta^2} &
                             \text{for } \theta \lt r_{in} \\
                \sqrt{r_{out}^2 - \theta^2} &
                             \text{for } r_{in} \leq \theta \lt r_{out} \\
                0 & \text{for } \theta > r_{out}
            \end{cases}

where :math:`\theta` is the sky separation and :math:`r_{\text{out}} = r_{\text{in}}` + width

Note that the normalization is a small angle approximation,
although that approximation is still very good even for 10 deg radius shells.

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


.. code-block:: default


    from gammapy.modeling.models import (
        Models,
        PowerLawSpectralModel,
        ShellSpatialModel,
        SkyModel,
    )

    model = ShellSpatialModel(
        lon_0="10 deg", lat_0="20 deg", radius="2 deg", width="0.5 deg", frame="galactic",
    )

    model.plot(add_cbar=True)




.. image:: /modeling/gallery/spatial/images/sphx_glr_plot_shell_001.png
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none

    /Users/terrier/Code/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/astropy/units/quantity.py:1032: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.
      out = super().__getitem__(key)
    /Users/terrier/Code/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/astropy/units/quantity.py:1054: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.
      self.view(np.ndarray).__setitem__(i, self._to_own_unit(value))




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


.. code-block:: default


    pwl = PowerLawSpectralModel()
    shell = ShellSpatialModel()

    model = SkyModel(spectral_model=pwl, spatial_model=shell, name="pwl-shell-model")
    models = Models([model])

    print(models.to_yaml())




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

 Out:

 .. code-block:: none

    components:
    -   name: pwl-shell-model
        type: SkyModel
        spectral:
            type: PowerLawSpectralModel
            parameters:
            - {name: index, value: 2.0, unit: '', min: .nan, max: .nan, frozen: false,
                error: 0}
            - {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}
        spatial:
            type: ShellSpatialModel
            frame: icrs
            parameters:
            - {name: lon_0, value: 0.0, unit: deg, min: .nan, max: .nan, frozen: false,
                error: 0}
            - {name: lat_0, value: 0.0, unit: deg, min: -90.0, max: 90.0, frozen: false,
                error: 0}
            - {name: radius, value: 1.0, unit: deg, min: .nan, max: .nan, frozen: false,
                error: 0}
            - {name: width, value: 0.2, unit: deg, min: .nan, max: .nan, frozen: false,
                error: 0}






.. _sphx_glr_download_modeling_gallery_spatial_plot_shell.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_shell.py <plot_shell.py>`



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

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


.. only:: html

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

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