SkyShell

class gammapy.image.models.SkyShell(lon_0, lat_0, radius, width, frame='galactic')

Bases: gammapy.image.models.SkySpatialModel

Shell model.

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

where \(\theta\) is the sky separation and \(r_{\text{out}} = r_{\text{in}}\) + width

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

Parameters:

lon_0 : Longitude

\(lon_0\)

lat_0 : Latitude

\(lat_0\)

radius : Angle

Inner radius, \(r_{in}\)

width : Angle

Shell width

frame : {“galactic”, “icrs”}

Coordinate frame of lon_0 and lat_0.

Attributes Summary

evaluation_radius	Returns the effective radius of the sky region where the model evaluates to non-zero.
frame
lat_0
lon_0
parameters	Parameters (Parameters)
position	Spatial model center position
radius
width

Methods Summary

__call__(self, lon, lat)	Call evaluate method
copy(self)	A deep copy.
evaluate(lon, lat, lon_0, lat_0, radius, width)	Evaluate the model (static function).

Attributes Documentation

evaluation_radius

Returns the effective radius of the sky region where the model evaluates to non-zero.

Given by \(r_\text{out}\).

Returns:

radius : Angle

Radius in angular units

frame

lat_0

lon_0

parameters

Parameters (Parameters)

position

Spatial model center position

radius

width

Methods Documentation

__call__(self, lon, lat)

Call evaluate method

copy(self)

A deep copy.

static evaluate(lon, lat, lon_0, lat_0, radius, width)

Evaluate the model (static function).