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Point Spatial Model

This model is a delta function centered in lon_0 and lat_0 parameters provided:

$$\phi(lon, lat) = \delta{(lon - lon_0, lat - lat_0)}$$

The model is defined on the celestial sphere in the coordinate frame provided by the user.

If the point source is not centered on a pixel, the flux is re-distributed across 4 neighbouring pixels. This ensured that the center of mass position is conserved.

Example plot

Here is an example plot of the model:

from astropy.coordinates import SkyCoord
from gammapy.maps import WcsGeom
from gammapy.modeling.models import (
    Models,
    PointSpatialModel,
    PowerLawSpectralModel,
    SkyModel,
)

model = PointSpatialModel(lon_0="0.01 deg", lat_0="0.01 deg", frame="galactic",)

geom = WcsGeom.create(
    skydir=SkyCoord("0d 0d", frame="galactic"), width=(1, 1), binsz=0.1
)
model.plot(geom=geom, add_cbar=True)

YAML representation

Here is an example YAML file using the model:

pwl = PowerLawSpectralModel()
point = PointSpatialModel()

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

print(models.to_yaml())

Out:

components:
-   name: pwl-point-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: PointSpatialModel
        frame: icrs
        parameters:
        -   name: lon_0
            value: 0.0
            unit: deg
        -   name: lat_0
            value: 0.0
            unit: deg