.. 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_spatial_plot_disk.py:
.. _disk-spatial-model:
Disk Spatial Model
==================
This is a spatial model parametrising a disk.
By default, the model is symmetric, i.e. a disk:
.. math::
\phi(lon, lat) = \frac{1}{2 \pi (1 - \cos{r_0}) } \cdot
\begin{cases}
1 & \text{for } \theta \leq r_0 \
0 & \text{for } \theta > r_0
\end{cases}
where :math:`\theta` is the sky separation. To improve fit convergence of the
model, the sharp edges is smoothed using `~scipy.special.erf`.
In case an eccentricity (`e`) and rotation angle (:math:`\phi`) are passed,
then the model is an elongated disk (i.e. an ellipse), with a major semiaxis of length :math:`r_0`
and position angle :math:`\phi` (increaing counter-clockwise from the North direction).
The model is defined on the celestial sphere, with a normalization defined by:
.. math::
\int_{4\pi}\phi(\text{lon}, \text{lat}) \,d\Omega = 1\,.
Example plot
------------
Here is an example plot of the model:
.. code-block:: default
import numpy as np
from astropy.coordinates import Angle
from gammapy.modeling.models import (
DiskSpatialModel,
Models,
PowerLawSpectralModel,
SkyModel,
)
phi = Angle("30 deg")
model = DiskSpatialModel(
lon_0="2 deg", lat_0="2 deg", r_0="1 deg", e=0.8, phi="30 deg", frame="galactic",
)
ax = model.plot(add_cbar=True)
# illustrate size parameter
region = model.to_region().to_pixel(ax.wcs)
artist = region.as_artist(facecolor="none", edgecolor="red")
ax.add_artist(artist)
transform = ax.get_transform("galactic")
ax.scatter(2, 2, transform=transform, s=20, edgecolor="red", facecolor="red")
ax.text(1.7, 1.85, r"$(l_0, b_0)$", transform=transform, ha="center")
ax.plot([2, 2 + np.sin(phi)], [2, 2 + np.cos(phi)], color="r", transform=transform)
ax.vlines(x=2, color="r", linestyle="--", transform=transform, ymin=0, ymax=5)
ax.text(2.15, 2.3, r"$\phi$", transform=transform)
.. image:: /modeling/gallery/spatial/images/sphx_glr_plot_disk_001.png
:alt: plot disk
:class: sphx-glr-single-img
YAML representation
-------------------
Here is an example YAML file using the model:
.. code-block:: default
pwl = PowerLawSpectralModel()
gauss = DiskSpatialModel()
model = SkyModel(spectral_model=pwl, spatial_model=gauss, name="pwl-disk-model")
models = Models([model])
print(models.to_yaml())
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
components:
- name: pwl-disk-model
type: SkyModel
spectral:
type: PowerLawSpectralModel
parameters:
- name: index
value: 2.0
- name: amplitude
value: 1.0e-12
unit: cm-2 s-1 TeV-1
- name: reference
value: 1.0
unit: TeV
frozen: true
spatial:
type: DiskSpatialModel
frame: icrs
parameters:
- name: lon_0
value: 0.0
unit: deg
- name: lat_0
value: 0.0
unit: deg
- name: r_0
value: 1.0
unit: deg
- name: e
value: 0.0
frozen: true
- name: phi
value: 0.0
unit: deg
frozen: true
- name: edge
value: 0.01
unit: deg
frozen: true
.. _sphx_glr_download_modeling_gallery_spatial_plot_disk.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_disk.py `
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: plot_disk.ipynb `
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery `_