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Light curves

Prerequisites

• Knowledge of the high level interface to perform data reduction, see first gammapy analysis with the high level interface tutorial

Context

This tutorial presents how light curve extraction is performed in gammapy, i.e. how to measure the flux of a source in different time bins.

Cherenkov telescopes usually work with observing runs and distribute data according to this basic time interval. A typical use case is to look for variability of a source on various time binnings: observation run-wise binning, nightly, weekly etc.

Objective: The Crab nebula is not known to be variable at TeV energies, so we expect constant brightness within statistical and systematic errors. Compute per-observation and nightly fluxes of the four Crab nebula observations from the H.E.S.S. first public test data releaseoto check it.

Proposed approach

We will demonstrate how to compute a gammapy.estimators.LightCurve from 3D reduced datasets (gammapy.datasets.MapDataset) as well as 1D ON-OFF spectral datasets (gammapy.datasets.SpectrumDatasetOnOff).

The data reduction will be performed with the high level interface for the data reduction. Then we will use the gammapy.estimators.LightCurveEstimator class, which is able to extract a light curve independently of the dataset type.

Setup

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

%matplotlib inline
import matplotlib.pyplot as plt

import astropy.units as u
from astropy.coordinates import SkyCoord
import logging

from astropy.time import Time

log = logging.getLogger(__name__)

Now let’s import gammapy specific classes and functions

from gammapy.modeling.models import PowerLawSpectralModel
from gammapy.modeling.models import PointSpatialModel
from gammapy.modeling.models import SkyModel, Models
from gammapy.modeling import Fit
from gammapy.estimators import LightCurveEstimator
from gammapy.analysis import Analysis, AnalysisConfig

Analysis configuration

For the 1D and 3D extraction, we will use the same CrabNebula configuration than in the notebook analysis_1.ipynb using the high level interface of Gammapy.

From the high level interface, the data reduction for those observations is performed as followed

Building the 3D analysis configuration

conf_3d = AnalysisConfig()

Definition of the data selection

Here we use the Crab runs from the HESS DL3 data release 1

conf_3d.observations.obs_ids = [23523, 23526, 23559, 23592]

Definition of the dataset geometry

# We want a 3D analysis
conf_3d.datasets.type = "3d"

# We want to extract the data by observation and therefore to not stack them
conf_3d.datasets.stack = False

# Here is the WCS geometry of the Maps
conf_3d.datasets.geom.wcs.skydir = dict(
    frame="icrs", lon=83.63308 * u.deg, lat=22.01450 * u.deg
)
conf_3d.datasets.geom.wcs.binsize = 0.02 * u.deg
conf_3d.datasets.geom.wcs.width = dict(width=1 * u.deg, height=1 * u.deg)

# We define a value for the IRF Maps binsize
conf_3d.datasets.geom.wcs.binsize_irf = 0.2 * u.deg

# Define energy binning for the Maps
conf_3d.datasets.geom.axes.energy = dict(
    min=0.7 * u.TeV, max=10 * u.TeV, nbins=5
)
conf_3d.datasets.geom.axes.energy_true = dict(
    min=0.3 * u.TeV, max=20 * u.TeV, nbins=20
)

Run the 3D data reduction

analysis_3d = Analysis(conf_3d)
analysis_3d.get_observations()
analysis_3d.get_datasets()

Setting logging config: {'level': 'INFO', 'filename': None, 'filemode': None, 'format': None, 'datefmt': None}
Fetching observations.
Observations selected: 4 out of 4.
Number of selected observations: 4
Creating reference dataset and makers.
Creating the background Maker.
No background maker set. Check configuration.
Start the data reduction loop.
Computing dataset for observation 23523
Running MapDatasetMaker
Running SafeMaskMaker
Computing dataset for observation 23526
Running MapDatasetMaker
Running SafeMaskMaker
Computing dataset for observation 23559
Running MapDatasetMaker
Running SafeMaskMaker
Computing dataset for observation 23592
Running MapDatasetMaker
Running SafeMaskMaker

Define the model to be used

Here we don’t try to fit the model parameters to the whole dataset, but we use predefined values instead.

target_position = SkyCoord(ra=83.63308, dec=22.01450, unit="deg")
spatial_model = PointSpatialModel(
    lon_0=target_position.ra, lat_0=target_position.dec, frame="icrs"
)

spectral_model = PowerLawSpectralModel(
    index=2.702,
    amplitude=4.712e-11 * u.Unit("1 / (cm2 s TeV)"),
    reference=1 * u.TeV,
)

sky_model = SkyModel(
    spatial_model=spatial_model, spectral_model=spectral_model, name="crab"
)
# Now we freeze these parameters that we don't want the light curve estimator to change
sky_model.parameters["index"].frozen = True
sky_model.parameters["lon_0"].frozen = True
sky_model.parameters["lat_0"].frozen = True

We assign them the model to be fitted to each dataset

models = Models([sky_model])
analysis_3d.set_models(models)

Reading model.
Models

Component 0: SkyModel

  Name                      : crab
  Datasets names            : None
  Spectral model type       : PowerLawSpectralModel
  Spatial  model type       : PointSpatialModel
  Temporal model type       :
  Parameters:
    index                 (frozen):      2.702
    amplitude                     :   4.71e-11   +/- 0.0e+00 1 / (cm2 s TeV)
    reference             (frozen):      1.000       TeV
    lon_0                 (frozen):     83.633       deg
    lat_0                 (frozen):     22.015       deg

Component 1: FoVBackgroundModel

  Name                      : MC_6mfCo-bkg
  Datasets names            : ['MC_6mfCo']
  Spectral model type       : PowerLawNormSpectralModel
  Parameters:
    norm                          :      1.000   +/-    0.00
    tilt                  (frozen):      0.000
    reference             (frozen):      1.000       TeV

Component 2: FoVBackgroundModel

  Name                      : XRKs3EVL-bkg
  Datasets names            : ['XRKs3EVL']
  Spectral model type       : PowerLawNormSpectralModel
  Parameters:
    norm                          :      1.000   +/-    0.00
    tilt                  (frozen):      0.000
    reference             (frozen):      1.000       TeV

Component 3: FoVBackgroundModel

  Name                      : BF3KNxcT-bkg
  Datasets names            : ['BF3KNxcT']
  Spectral model type       : PowerLawNormSpectralModel
  Parameters:
    norm                          :      1.000   +/-    0.00
    tilt                  (frozen):      0.000
    reference             (frozen):      1.000       TeV

Component 4: FoVBackgroundModel

  Name                      : NHA6yjbb-bkg
  Datasets names            : ['NHA6yjbb']
  Spectral model type       : PowerLawNormSpectralModel
  Parameters:
    norm                          :      1.000   +/-    0.00
    tilt                  (frozen):      0.000
    reference             (frozen):      1.000       TeV

Light Curve estimation by observation

We can now create the light curve estimator.

We pass it the list of datasets and the name of the model component for which we want to build the light curve. We can optionally ask for parameters reoptimization during fit, that is most of the time to fit background normalization in each time bin.

If we don’t set any time interval, the gammapy.estimators.LightCurveEstimator is determines the flux of each dataset and places it at the corresponding time in the light curve. Here one dataset equals to one observing run.

lc_maker_3d = LightCurveEstimator(
    energy_edges=[1, 10] * u.TeV, source="crab", reoptimize=False
)
lc_3d = lc_maker_3d.run(analysis_3d.datasets)

The LightCurve object contains a table which we can explore.

lc_3d.plot(axis_name="time")

<AxesSubplot:xlabel='Time [iso]', ylabel='dnde (1 / (cm2 s TeV))'>

table = lc_3d.to_table(format="lightcurve", sed_type="flux")
table["time_min", "time_max", "e_min", "e_max", "flux", "flux_err"]

Table length=4

time_min	time_max	e_min [1]	e_max [1]	flux [1]	flux_err [1]
		TeV	TeV	1 / (cm2 s)	1 / (cm2 s)
float64	float64	float64	float64	float64	float64
53343.922340092584	53343.94186555555	1.191457161449437	10.000000000000002	2.0380210271197794e-11	2.1205833943560366e-12
53343.954215092584	53343.97369425925	1.191457161449437	10.000000000000002	2.061095350246212e-11	2.1406685689437862e-12
53345.96198129629	53345.98149518518	1.191457161449437	10.000000000000002	2.1806916394335914e-11	2.78937151632376e-12
53347.91319657407	53347.932710462956	1.191457161449437	10.000000000000002	2.5084878816023824e-11	2.914172443640524e-12

Running the light curve extraction in 1D

Building the 1D analysis configuration

conf_1d = AnalysisConfig()

Definition of the data selection

Here we use the Crab runs from the HESS DL3 data release 1

conf_1d.observations.obs_ids = [23523, 23526, 23559, 23592]

Definition of the dataset geometry

# We want a 1D analysis
conf_1d.datasets.type = "1d"

# We want to extract the data by observation and therefore to not stack them
conf_1d.datasets.stack = False

# Here we define the ON region and make sure that PSF leakage is corrected
conf_1d.datasets.on_region = dict(
    frame="icrs",
    lon=83.63308 * u.deg,
    lat=22.01450 * u.deg,
    radius=0.1 * u.deg,
)
conf_1d.datasets.containment_correction = True

# Finally we define the energy binning for the spectra
conf_1d.datasets.geom.axes.energy = dict(
    min=0.7 * u.TeV, max=10 * u.TeV, nbins=5
)
conf_1d.datasets.geom.axes.energy_true = dict(
    min=0.3 * u.TeV, max=20 * u.TeV, nbins=20
)

Run the 1D data reduction

analysis_1d = Analysis(conf_1d)
analysis_1d.get_observations()
analysis_1d.get_datasets()

Setting logging config: {'level': 'INFO', 'filename': None, 'filemode': None, 'format': None, 'datefmt': None}
Fetching observations.
Observations selected: 4 out of 4.
Number of selected observations: 4
Reducing spectrum datasets.
Creating the background Maker.
No background maker set. Check configuration.

Define the model to be used

Here we don’t try to fit the model parameters to the whole dataset, but we use predefined values instead.

target_position = SkyCoord(ra=83.63308, dec=22.01450, unit="deg")

spectral_model = PowerLawSpectralModel(
    index=2.702,
    amplitude=4.712e-11 * u.Unit("1 / (cm2 s TeV)"),
    reference=1 * u.TeV,
)

sky_model = SkyModel(spectral_model=spectral_model, name="crab")
# Now we freeze these parameters that we don't want the light curve estimator to change
sky_model.parameters["index"].frozen = True

We assign the model to be fitted to each dataset. We can use the same gammapy.modeling.models.SkyModel as before.

models = Models([sky_model])
analysis_1d.set_models(models)

Reading model.
Models

Component 0: SkyModel

  Name                      : crab
  Datasets names            : None
  Spectral model type       : PowerLawSpectralModel
  Spatial  model type       :
  Temporal model type       :
  Parameters:
    index                 (frozen):      2.702
    amplitude                     :   4.71e-11   +/- 0.0e+00 1 / (cm2 s TeV)
    reference             (frozen):      1.000       TeV

Extracting the light curve

lc_maker_1d = LightCurveEstimator(
    energy_edges=[1, 10] * u.TeV, source="crab", reoptimize=False
)
lc_1d = lc_maker_1d.run(analysis_1d.datasets)

lc_1d.geom.axes.names

['energy', 'time']

lc_1d.to_table(sed_type="flux", format="lightcurve")

Table length=4

time_min	time_max	e_ref [1]	e_min [1]	e_max [1]	flux [1]	flux_err [1]	ts [1]	sqrt_ts [1]	npred [1,4]	npred_excess [1,4]	stat [1]	is_ul [1]	counts [1,4]	success [1]
		TeV	TeV	TeV	1 / (cm2 s)	1 / (cm2 s)
float64	float64	float64	float64	float64	float64	float64	float64	float64	float64	float64	float64	bool	float64	bool
53343.922340092584	53343.94186555555	3.4517490659800822	1.191457161449437	10.000000000000002	2.2143915082283826e-11	2.46043438709985e-12	9669.93681384043	98.3358368746635	80.99951140280142 .. nan	80.99950408935547 .. nan	-344.46719038026515	False	81.0 .. nan	True
53343.954215092584	53343.97369425925	3.4517490659800822	1.191457161449437	10.000000000000002	1.8788302509399298e-11	2.2297607397555523e-12	8464.484921386465	92.00263540457124	nan .. nan	nan .. nan	-290.30784403249163	False	nan .. nan	True
53345.96198129629	53345.98149518518	3.4517490659800822	1.191457161449437	10.000000000000002	2.1553175393191787e-11	3.0180475449692493e-12	6065.962232361473	77.88428745492554	nan .. nan	nan .. nan	-194.37024721988715	False	nan .. nan	True
53347.91319657407	53347.932710462956	3.4517490659800822	1.191457161449437	10.000000000000002	2.485367385298985e-11	3.2356719941454455e-12	7019.342401645411	83.78151587101662	nan .. 58.99955742868726	nan .. 58.99955749511719	-226.71637961887058	False	nan .. 59.0	True

Compare results

Finally we compare the result for the 1D and 3D lightcurve in a single figure:

ax = lc_1d.plot(marker="o", label="1D")
lc_3d.plot(ax=ax, marker="o", label="3D")
plt.legend()

<matplotlib.legend.Legend at 0x16cbf05e0>

Night-wise LC estimation

Here we want to extract a night curve per night. We define the time intervals that cover the three nights.

time_intervals = [
    Time([53343.5, 53344.5], format="mjd", scale="utc"),
    Time([53345.5, 53346.5], format="mjd", scale="utc"),
    Time([53347.5, 53348.5], format="mjd", scale="utc"),
]

To compute the LC on the time intervals defined above, we pass the LightCurveEstimator the list of time intervals.

Internally, datasets are grouped per time interval and a flux extraction is performed for each group.

lc_maker_1d = LightCurveEstimator(
    energy_edges=[1, 10] * u.TeV,
    time_intervals=time_intervals,
    source="crab",
    reoptimize=False,
    selection_optional="all",
)

nightwise_lc = lc_maker_1d.run(analysis_1d.datasets)

nightwise_lc.plot(color="tab:orange")
ax = nightwise_lc.plot_ts_profiles()
ax.set_ylim(1e-12, 3e-12);

What next?

When sources are bright enough to look for variability at small time scales, the per-observation time binning is no longer relevant. One can easily extend the light curve estimation approach presented above to any time binning. This is demonstrated in the following tutorial which shows the extraction of the lightcurve of an AGN flare.