Flux Profile Estimation

Learn how to estimate flux profiles on a Fermi-LAT dataset.

Prerequisites

Knowledge of 3D data reduction and datasets used in Gammapy, see for instance the first analysis tutorial.

Context

A useful tool to study and compare the spatial distribution of flux in images and data cubes is the measurement of flux profiles. Flux profiles can show spatial correlations of gamma-ray data with e.g. gas maps or other type of gamma-ray data. Most commonly flux profiles are measured along some preferred coordinate axis, either radially distance from a source of interest, along longitude and latitude coordinate axes or along the path defined by two spatial coordinates.

Proposed Approach

Flux profile estimation essentially works by estimating flux points for a set of predefined spatially connected regions. For radial flux profiles the shape of the regions are annuli with a common center, for linear profiles it’s typically a rectangular shape.

We will work on a pre-computed MapDataset of Fermi-LAT data, use SkyRegion to define the structure of the bins of the flux profile and run the flux profile extraction using the FluxProfileEstimator

import numpy as np
from astropy import units as u
from astropy.coordinates import SkyCoord

# %matplotlib inline
import matplotlib.pyplot as plt

Setup

from IPython.display import display
from gammapy.datasets import MapDataset
from gammapy.estimators import FluxPoints, FluxProfileEstimator
from gammapy.maps import RegionGeom
from gammapy.modeling.models import PowerLawSpectralModel

Check setup

from gammapy.utils.check import check_tutorials_setup
from gammapy.utils.regions import (
    make_concentric_annulus_sky_regions,
    make_orthogonal_rectangle_sky_regions,
)

check_tutorials_setup()

System:

        python_executable      : /home/runner/work/gammapy-docs/gammapy-docs/gammapy/.tox/build_docs/bin/python
        python_version         : 3.9.20
        machine                : x86_64
        system                 : Linux


Gammapy package:

        version                : 2.0.dev155+g9309a089d
        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                  : 1.13.1
        astropy                : 5.2.2
        regions                : 0.8
        click                  : 8.1.7
        yaml                   : 6.0.2
        IPython                : 8.18.1
        jupyterlab             : not installed
        matplotlib             : 3.9.4
        pandas                 : not installed
        healpy                 : 1.17.3
        iminuit                : 2.30.1
        sherpa                 : 4.16.1
        naima                  : 0.10.0
        emcee                  : 3.1.6
        corner                 : 2.2.3
        ray                    : 2.40.0


Gammapy environment variables:

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

Read and Introduce Data

dataset = MapDataset.read(
    "$GAMMAPY_DATA/fermi-3fhl-gc/fermi-3fhl-gc.fits.gz", name="fermi-dataset"
)

This is what the counts image we will work with looks like:

counts_image = dataset.counts.sum_over_axes()
counts_image.smooth("0.1 deg").plot(stretch="sqrt")
plt.show()

There are 400x200 pixels in the dataset and 11 energy bins between 10 GeV and 2 TeV:

print(dataset.counts)

WcsNDMap

        geom  : WcsGeom
        axes  : ['lon', 'lat', 'energy']
        shape : (400, 200, 11)
        ndim  : 3
        unit  :
        dtype : >i4

Profile Estimation

Configuration

We start by defining a list of spatially connected regions along the galactic longitude axis. For this there is a helper function make_orthogonal_rectangle_sky_regions. The individual region bins for the profile have a height of 3 deg and in total there are 31 bins. Its starts from lon = 10 deg and goes to lon = 350 deg. In addition, we have to specify the wcs to take into account possible projections effects on the region definition:

regions = make_orthogonal_rectangle_sky_regions(
    start_pos=SkyCoord("10d", "0d", frame="galactic"),
    end_pos=SkyCoord("350d", "0d", frame="galactic"),
    wcs=counts_image.geom.wcs,
    height="3 deg",
    nbin=51,
)

We can use the RegionGeom object to illustrate the regions on top of the counts image:

geom = RegionGeom.create(region=regions)
ax = counts_image.smooth("0.1 deg").plot(stretch="sqrt")
geom.plot_region(ax=ax, color="w")
plt.show()

/home/runner/work/gammapy-docs/gammapy-docs/gammapy/.tox/build_docs/lib/python3.9/site-packages/regions/shapes/rectangle.py:207: UserWarning: Setting the 'color' property will override the edgecolor or facecolor properties.
  return Rectangle(xy=xy, width=width, height=height,

Next we create the FluxProfileEstimator. For the estimation of the flux profile we assume a spectral model with a power-law shape and an index of 2.3

flux_profile_estimator = FluxProfileEstimator(
    regions=regions,
    spectrum=PowerLawSpectralModel(index=2.3),
    energy_edges=[10, 2000] * u.GeV,
    selection_optional=["ul"],
)

/home/runner/work/gammapy-docs/gammapy-docs/gammapy/examples/tutorials/analysis-3d/flux_profiles.py:135: GammapyDeprecationWarning: "spectrum" was deprecated in version v1.3 and will be removed in a future version. Use argument "spectral_model" instead.
  flux_profile_estimator = FluxProfileEstimator(

We can see the full configuration by printing the estimator object:

print(flux_profile_estimator)

FluxProfileEstimator
--------------------

  energy_edges           : [  10. 2000.] GeV
  fit                    : <gammapy.modeling.fit.Fit object at 0x7ff3fccc8250>
  n_jobs                 : None
  n_sigma                : 1
  n_sigma_ul             : 2
  norm                   : Parameter(name='norm', value=1.0, factor=1.0, scale=1.0, unit=Unit(dimensionless), min=nan, max=nan, frozen=False, prior=None, id=0x7ff3fccc8ee0)
  null_value             : 0
  parallel_backend       : None
  reoptimize             : False
  selection_optional     : ['ul']
  source                 : 0
  spectral_model         : PowerLawSpectralModel
  sum_over_energy_groups : False

Run Estimation

Now we can run the profile estimation and explore the results:

profile = flux_profile_estimator.run(datasets=dataset)

print(profile)

FluxPoints
----------

  geom                   : RegionGeom
  axes                   : ['lon', 'lat', 'energy', 'projected-distance']
  shape                  : (1, 1, 1, 51)
  quantities             : ['norm', 'norm_err', 'norm_ul', 'ts', 'npred', 'npred_excess', 'stat', 'stat_null', 'counts', 'success']
  ref. model             : pl
  n_sigma                : 1
  n_sigma_ul             : 2
  sqrt_ts_threshold_ul   : 2
  sed type init          : likelihood

We can see the flux profile is represented by a FluxPoints object with a projected-distance axis, which defines the main axis the flux profile is measured along. The lon and lat axes can be ignored.

Plotting Results

Let us directly plot the result using plot:

ax = profile.plot(sed_type="dnde")
ax.set_yscale("linear")
plt.show()

Based on the spectral model we specified above we can also plot in any other sed type, e.g. energy flux and define a different threshold when to plot upper limits:

profile.sqrt_ts_threshold_ul = 2

plt.figure()
ax = profile.plot(sed_type="eflux")
ax.set_yscale("linear")
plt.show()

We can also plot any other quantity of interest, that is defined on the FluxPoints result object. E.g. the predicted total counts, background counts and excess counts:

quantities = ["npred", "npred_excess", "npred_background"]

fig, ax = plt.subplots()

for quantity in quantities:
    profile[quantity].plot(ax=ax, label=quantity.title())

ax.set_ylabel("Counts")
ax.legend()
plt.show()

Serialisation and I/O

The profile can be serialised using write, given a specific format:

profile.write(
    filename="flux_profile_fermi.fits",
    format="profile",
    overwrite=True,
    sed_type="dnde",
)

profile_new = FluxPoints.read(filename="flux_profile_fermi.fits", format="profile")

ax = profile_new.plot()
ax.set_yscale("linear")
plt.show()

The profile can be serialised to a Table object using:

table = profile.to_table(format="profile", formatted=True)
display(table)

       x_min              x_max              x_ref        ... counts success
        deg                deg                deg         ...
------------------- ------------------ ------------------ ... ------ -------
-0.1960784313725492 0.1960784313725492                0.0 ...    0.0   False
 0.1960784313725492 0.5882352941176467  0.392156862745098 ...    0.0   False
 0.5882352941176467 0.9803921568627443 0.7843137254901955 ...  163.0    True
 0.9803921568627443 1.3725490196078436  1.176470588235294 ...  448.0    True
 1.3725490196078436  1.764705882352942 1.5686274509803928 ...  599.0    True
  1.764705882352942   2.15686274509804  1.960784313725491 ...  354.0    True
   2.15686274509804  2.549019607843138 2.3529411764705888 ...  367.0    True
  2.549019607843138  2.941176470588236  2.745098039215687 ...  339.0    True
  2.941176470588236 3.3333333333333344  3.137254901960785 ...  531.0    True
 3.3333333333333344  3.725490196078432  3.529411764705883 ...  458.0    True
                ...                ...                ... ...    ...     ...
 15.882352941176466 16.274509803921596  16.07843137254903 ...  321.0    True
 16.274509803921596 16.666666666666696 16.470588235294144 ...  421.0    True
 16.666666666666696 17.058823529411775 16.862745098039234 ...  431.0    True
 17.058823529411775   17.4509803921569 17.254901960784338 ...  374.0    True
   17.4509803921569 17.843137254902004 17.647058823529452 ...  370.0    True
 17.843137254902004 18.235294117647083 18.039215686274545 ...  410.0    True
 18.235294117647083 18.627450980392158  18.43137254901962 ...  336.0    True
 18.627450980392158  19.01960784313726  18.82352941176471 ...  172.0    True
  19.01960784313726  19.41176470588239 19.215686274509824 ...    0.0   False
  19.41176470588239 19.803921568627494 19.607843137254942 ...    0.0   False
Length = 51 rows

No we can also estimate a radial profile starting from the Galactic center:

regions = make_concentric_annulus_sky_regions(
    center=SkyCoord("0d", "0d", frame="galactic"),
    radius_max="1.5 deg",
    nbin=11,
)

Again we first illustrate the regions:

geom = RegionGeom.create(region=regions)
gc_image = counts_image.cutout(
    position=SkyCoord("0d", "0d", frame="galactic"), width=3 * u.deg
)
ax = gc_image.smooth("0.1 deg").plot(stretch="sqrt")
geom.plot_region(ax=ax, color="w")
plt.show()

/home/runner/work/gammapy-docs/gammapy-docs/gammapy/.tox/build_docs/lib/python3.9/site-packages/regions/core/compound.py:160: UserWarning: Setting the 'color' property will override the edgecolor or facecolor properties.
  patch = mpatches.PathPatch(path, **mpl_kwargs)

This time we define two energy bins and include the fit statistic profile in the computation:

flux_profile_estimator = FluxProfileEstimator(
    regions=regions,
    spectrum=PowerLawSpectralModel(index=2.3),
    energy_edges=[10, 100, 2000] * u.GeV,
    selection_optional=["ul", "scan"],
)

/home/runner/work/gammapy-docs/gammapy-docs/gammapy/examples/tutorials/analysis-3d/flux_profiles.py:269: GammapyDeprecationWarning: "spectrum" was deprecated in version v1.3 and will be removed in a future version. Use argument "spectral_model" instead.
  flux_profile_estimator = FluxProfileEstimator(

The configuration of the fit statistic profile is done throught the norm parameter:

flux_profile_estimator.norm.scan_values = np.linspace(-1, 5, 11)

Now we can run the estimator,

profile = flux_profile_estimator.run(datasets=dataset)

and plot the result:

profile.plot(axis_name="projected-distance", sed_type="flux")
plt.show()

However because of the powerlaw spectrum the flux at high energies is much lower. To extract the profile at high energies only we can use:

profile_high = profile.slice_by_idx({"energy": slice(1, 2)})
plt.show()

And now plot the points together with the likelihood profiles:

fig, ax = plt.subplots()
profile_high.plot(ax=ax, sed_type="eflux", color="tab:orange")
profile_high.plot_ts_profiles(ax=ax, sed_type="eflux")
ax.set_yscale("linear")
plt.show()

# sphinx_gallery_thumbnail_number = 2