SkyGaussian

class gammapy.image.models.SkyGaussian(lon_0, lat_0, sigma, frame='galactic')

Bases: gammapy.image.models.SkySpatialModel

Two-dimensional symmetric Gaussian model

\[\phi(\text{lon}, \text{lat}) = N \times \text{exp}\left\{-\frac{1}{2} \frac{1-\text{cos}\theta}{1-\text{cos}\sigma}\right\}\,,\]

where \(\theta\) is the angular separation between the center of the Gaussian and the evaluation point. This angle is calculated on the celestial sphere using the function angular.separation defined in astropy.coordinates.angle_utilities. The Gaussian is normalized to 1 on the sphere:

\[N = \frac{1}{4\pi a\left[1-\text{exp}(-1/a)\right]}\,,\,\,\,\, a = 1-\text{cos}\sigma\,.\]

The normalization factor is in units of \(\text{sr}^{-1}\). In the limit of small \(\theta\) and \(\sigma\), this definition reduces to the usual form:

\[\phi(\text{lon}, \text{lat}) = \frac{1}{2\pi\sigma^2} \exp{\left(-\frac{1}{2} \frac{\theta^2}{\sigma^2}\right)}\]

Parameters:

lon_0 : Longitude

\(\text{lon}_0\)

lat_0 : Latitude

\(\text{lat}_0\)

sigma : Angle

\(\sigma\)

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
sigma

Methods Summary

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

Attributes Documentation

evaluation_radius

Returns the effective radius of the sky region where the model evaluates to non-zero. For a Gaussian source, we fix it to \(5\sigma\).

Returns:

radius : Angle

Radius in angular units

frame

lat_0

lon_0

parameters

Parameters (Parameters)

position

Spatial model center position

sigma

Methods Documentation

__call__(self, lon, lat)

Call evaluate method

copy(self)

A deep copy.

static evaluate(lon, lat, lon_0, lat_0, sigma)

Evaluate the model (static function).