2D map fitting#

Source modelling and fitting in stacked observations using the high level interface.

Prerequisites#

  • To understand how a general modelling and fitting works in gammapy, please refer to the 3D detailed analysis tutorial.

Context#

We often want the determine the position and morphology of an object. To do so, we don’t necessarily have to resort to a full 3D fitting but can perform a simple image fitting, in particular, in an energy range where the PSF does not vary strongly, or if we want to explore a possible energy dependence of the morphology.

Objective#

To localize a source and/or constrain its morphology.

Proposed approach#

The first step here, as in most analysis with DL3 data, is to create reduced datasets. For this, we will use the Analysis class to create a single set of stacked maps with a single bin in energy (thus, an image which behaves as a cube). This, we will then model with a spatial model of our choice, while keeping the spectral model fixed to an integrated power law.

# %matplotlib inline
import astropy.units as u
import matplotlib.pyplot as plt

Setup#

As usual, we’ll start with some general imports…

from IPython.display import display
from gammapy.analysis import Analysis, AnalysisConfig

Check setup#

from gammapy.utils.check import check_tutorials_setup

check_tutorials_setup()
System:

        python_executable      : /home/runner/work/gammapy-docs/gammapy-docs/gammapy/.tox/build_docs/bin/python
        python_version         : 3.9.18
        machine                : x86_64
        system                 : Linux


Gammapy package:

        version                : 1.3.dev60+ge5aecb334
        path                   : /home/runner/work/gammapy-docs/gammapy-docs/gammapy/.tox/build_docs/lib/python3.9/site-packages/gammapy


Other packages:

        numpy                  : 1.26.4
        scipy                  : 1.12.0
        astropy                : 5.2.2
        regions                : 0.8
        click                  : 8.1.7
        yaml                   : 6.0.1
        IPython                : 8.18.1
        jupyterlab             : not installed
        matplotlib             : 3.8.3
        pandas                 : not installed
        healpy                 : 1.16.6
        iminuit                : 2.25.2
        sherpa                 : 4.16.0
        naima                  : 0.10.0
        emcee                  : 3.1.4
        corner                 : 2.2.2
        ray                    : 2.9.3


Gammapy environment variables:

        GAMMAPY_DATA           : /home/runner/work/gammapy-docs/gammapy-docs/gammapy-datasets/dev

Creating the config file#

Now, we create a config file for out analysis. You may load this from disc if you have a pre-defined config file.

Here, we use 3 simulated CTA runs of the galactic center.

config = AnalysisConfig()
# Selecting the observations
config.observations.datastore = "$GAMMAPY_DATA/cta-1dc/index/gps/"
config.observations.obs_ids = [110380, 111140, 111159]

Technically, gammapy implements 2D analysis as a special case of 3D analysis (one bin in energy). So, we must specify the type of analysis as 3D, and define the geometry of the analysis.

config.datasets.type = "3d"
config.datasets.geom.wcs.skydir = {
    "lon": "0 deg",
    "lat": "0 deg",
    "frame": "galactic",
}  # The WCS geometry - centered on the galactic center
config.datasets.geom.wcs.width = {"width": "8 deg", "height": "6 deg"}
config.datasets.geom.wcs.binsize = "0.02 deg"

# The FoV radius to use for cutouts
config.datasets.geom.selection.offset_max = 2.5 * u.deg
config.datasets.safe_mask.methods = ["offset-max"]
config.datasets.safe_mask.parameters = {"offset_max": "2.5 deg"}
config.datasets.background.method = "fov_background"
config.fit.fit_range = {"min": "0.1 TeV", "max": "30.0 TeV"}

# We now fix the energy axis for the counts map - (the reconstructed energy binning)
config.datasets.geom.axes.energy.min = "0.1 TeV"
config.datasets.geom.axes.energy.max = "10 TeV"
config.datasets.geom.axes.energy.nbins = 1

config.datasets.geom.wcs.binsize_irf = "0.2 deg"

print(config)
AnalysisConfig

    general:
        log: {level: info, filename: null, filemode: null, format: null, datefmt: null}
        outdir: .
        n_jobs: 1
        datasets_file: null
        models_file: null
    observations:
        datastore: /home/runner/work/gammapy-docs/gammapy-docs/gammapy-datasets/dev/cta-1dc/index/gps
        obs_ids: [110380, 111140, 111159]
        obs_file: null
        obs_cone: {frame: null, lon: null, lat: null, radius: null}
        obs_time: {start: null, stop: null}
        required_irf: [aeff, edisp, psf, bkg]
    datasets:
        type: 3d
        stack: true
        geom:
            wcs:
                skydir: {frame: galactic, lon: 0.0 deg, lat: 0.0 deg}
                binsize: 0.02 deg
                width: {width: 8.0 deg, height: 6.0 deg}
                binsize_irf: 0.2 deg
            selection: {offset_max: 2.5 deg}
            axes:
                energy: {min: 0.1 TeV, max: 10.0 TeV, nbins: 1}
                energy_true: {min: 0.5 TeV, max: 20.0 TeV, nbins: 16}
        map_selection: [counts, exposure, background, psf, edisp]
        background:
            method: fov_background
            exclusion: null
            parameters: {}
        safe_mask:
            methods: [offset-max]
            parameters: {offset_max: 2.5 deg}
        on_region: {frame: null, lon: null, lat: null, radius: null}
        containment_correction: true
    fit:
        fit_range: {min: 0.1 TeV, max: 30.0 TeV}
    flux_points:
        energy: {min: null, max: null, nbins: null}
        source: source
        parameters: {selection_optional: all}
    excess_map:
        correlation_radius: 0.1 deg
        parameters: {}
        energy_edges: {min: null, max: null, nbins: null}
    light_curve:
        time_intervals: {start: null, stop: null}
        energy_edges: {min: null, max: null, nbins: null}
        source: source
        parameters: {selection_optional: all}

Getting the reduced dataset#

We now use the config file and create a single MapDataset containing counts, background, exposure, psf and edisp maps.

/home/runner/work/gammapy-docs/gammapy-docs/gammapy/.tox/build_docs/lib/python3.9/site-packages/astropy/units/core.py:2097: UnitsWarning: '1/s/MeV/sr' did not parse as fits unit: Numeric factor not supported by FITS If this is meant to be a custom unit, define it with 'u.def_unit'. To have it recognized inside a file reader or other code, enable it with 'u.add_enabled_units'. For details, see https://docs.astropy.org/en/latest/units/combining_and_defining.html
  warnings.warn(msg, UnitsWarning)
/home/runner/work/gammapy-docs/gammapy-docs/gammapy/.tox/build_docs/lib/python3.9/site-packages/astropy/units/core.py:2097: UnitsWarning: '1/s/MeV/sr' did not parse as fits unit: Numeric factor not supported by FITS If this is meant to be a custom unit, define it with 'u.def_unit'. To have it recognized inside a file reader or other code, enable it with 'u.add_enabled_units'. For details, see https://docs.astropy.org/en/latest/units/combining_and_defining.html
  warnings.warn(msg, UnitsWarning)
/home/runner/work/gammapy-docs/gammapy-docs/gammapy/.tox/build_docs/lib/python3.9/site-packages/astropy/units/core.py:2097: UnitsWarning: '1/s/MeV/sr' did not parse as fits unit: Numeric factor not supported by FITS If this is meant to be a custom unit, define it with 'u.def_unit'. To have it recognized inside a file reader or other code, enable it with 'u.add_enabled_units'. For details, see https://docs.astropy.org/en/latest/units/combining_and_defining.html
  warnings.warn(msg, UnitsWarning)
MapDataset
----------

  Name                            : stacked

  Total counts                    : 85625
  Total background counts         : 85624.99
  Total excess counts             : 0.01

  Predicted counts                : 85625.00
  Predicted background counts     : 85624.99
  Predicted excess counts         : nan

  Exposure min                    : 8.46e+08 m2 s
  Exposure max                    : 2.14e+10 m2 s

  Number of total bins            : 120000
  Number of fit bins              : 96602

  Fit statistic type              : cash
  Fit statistic value (-2 log(L)) : nan

  Number of models                : 0
  Number of parameters            : 0
  Number of free parameters       : 0

The counts and background maps have only one bin in reconstructed energy. The exposure and IRF maps are in true energy, and hence, have a different binning based upon the binning of the IRFs. We need not bother about them presently.

print(analysis.datasets["stacked"].counts)

print(analysis.datasets["stacked"].background)

print(analysis.datasets["stacked"].exposure)
WcsNDMap

        geom  : WcsGeom
        axes  : ['lon', 'lat', 'energy']
        shape : (400, 300, 1)
        ndim  : 3
        unit  :
        dtype : float32

WcsNDMap

        geom  : WcsGeom
        axes  : ['lon', 'lat', 'energy']
        shape : (400, 300, 1)
        ndim  : 3
        unit  :
        dtype : float32

WcsNDMap

        geom  : WcsGeom
        axes  : ['lon', 'lat', 'energy_true']
        shape : (400, 300, 16)
        ndim  : 3
        unit  : m2 s
        dtype : float32

We can have a quick look of these maps in the following way:

analysis.datasets["stacked"].counts.reduce_over_axes().plot(vmax=10, add_cbar=True)
plt.show()
modeling 2D

Modelling#

Now, we define a model to be fitted to the dataset. The important thing to note here is the dummy spectral model - an integrated powerlaw with only free normalisation. Here, we use its YAML definition to load it:

model_config = """
components:
- name: GC-1
  type: SkyModel
  spatial:
    type: PointSpatialModel
    frame: galactic
    parameters:
    - name: lon_0
      value: 0.02
      unit: deg
    - name: lat_0
      value: 0.01
      unit: deg
  spectral:
    type: PowerLaw2SpectralModel
    parameters:
    - name: amplitude
      value: 1.0e-12
      unit: cm-2 s-1
    - name: index
      value: 2.0
      unit: ''
      frozen: true
    - name: emin
      value: 0.1
      unit: TeV
      frozen: true
    - name: emax
      value: 10.0
      unit: TeV
      frozen: true
"""

analysis.set_models(model_config)

We will freeze the parameters of the background

analysis.datasets["stacked"].background_model.parameters["tilt"].frozen = True

# To run the fit
analysis.run_fit()

# To see the best fit values along with the errors
display(analysis.models.to_parameters_table())
   model    type    name      value      unit   ... frozen is_norm link prior
----------- ---- --------- ----------- -------- ... ------ ------- ---- -----
       GC-1      amplitude  4.1496e-11 cm-2 s-1 ...  False    True
       GC-1          index  2.0000e+00          ...   True   False
       GC-1           emin  1.0000e-01      TeV ...   True   False
       GC-1           emax  1.0000e+01      TeV ...   True   False
       GC-1          lon_0 -4.7613e-02      deg ...  False   False
       GC-1          lat_0 -5.3570e-02      deg ...  False   False
stacked-bkg           norm  9.9445e-01          ...  False    True
stacked-bkg           tilt  0.0000e+00          ...   True   False
stacked-bkg      reference  1.0000e+00      TeV ...   True   False

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