Shell spatial model#

This is a spatial model parametrizing a projected radiating shell.

The shell spatial model is defined by the following equations:

ϕ(lon,lat)=32π(rout3rin3){rout2θ2rin2θ2for θ<rinrout2θ2for rinθ<rout0for θ>rout

where θ is the sky separation and rout=rin + 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:

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)
plot shell
<WCSAxes: >

YAML representation#

Here is an example YAML file using the model:

pwl = PowerLawSpectralModel()
shell = ShellSpatialModel()

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

print(models.to_yaml())
components:
-   name: pwl-shell-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
    spatial:
        type: ShellSpatialModel
        frame: icrs
        parameters:
        -   name: lon_0
            value: 0.0
            unit: deg
        -   name: lat_0
            value: 0.0
            unit: deg
        -   name: radius
            value: 1.0
            unit: deg
        -   name: width
            value: 0.2
            unit: deg
metadata:
    creator: Gammapy 1.2
    date: '2024-02-29T10:21:49.578674'
    origin: null

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