.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "tutorials/analysis-1d/cta_sensitivity.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. or to run this example in your browser via Binder .. rst-class:: sphx-glr-example-title .. _sphx_glr_tutorials_analysis-1d_cta_sensitivity.py: Point source sensitivity ======================== Estimate the CTA sensitivity for a point-like IRF at a fixed zenith angle and fixed offset. Introduction ------------ This notebook explains how to estimate the CTA sensitivity for a point-like IRF at a fixed zenith angle and fixed offset, using the full containment IRFs distributed for the CTA 1DC. The significance is computed for a 1D analysis (ON-OFF regions) with the Li&Ma formula. We use here an approximate approach with an energy dependent integration radius to take into account the variation of the PSF. We will first determine the 1D IRFs including a containment correction. We will be using the following Gammapy class: - `~gammapy.estimators.SensitivityEstimator` .. GENERATED FROM PYTHON SOURCE LINES 24-33 .. code-block:: Python import numpy as np import astropy.units as u from astropy.coordinates import SkyCoord # %matplotlib inline from regions import CircleSkyRegion import matplotlib.pyplot as plt .. GENERATED FROM PYTHON SOURCE LINES 34-39 Setup ----- As usual, we’ll start with some setup … .. GENERATED FROM PYTHON SOURCE LINES 39-48 .. code-block:: Python from IPython.display import display from gammapy.data import FixedPointingInfo, Observation, observatory_locations from gammapy.datasets import SpectrumDataset, SpectrumDatasetOnOff from gammapy.estimators import FluxPoints, SensitivityEstimator from gammapy.irf import load_irf_dict_from_file from gammapy.makers import SpectrumDatasetMaker from gammapy.maps import MapAxis, RegionGeom from gammapy.maps.axes import UNIT_STRING_FORMAT .. GENERATED FROM PYTHON SOURCE LINES 49-51 Check setup ----------- .. GENERATED FROM PYTHON SOURCE LINES 51-55 .. code-block:: Python from gammapy.utils.check import check_tutorials_setup check_tutorials_setup() .. rst-class:: sphx-glr-script-out .. code-block:: none System: python_executable : /home/runner/work/gammapy-docs/gammapy-docs/gammapy/.tox/build_docs/bin/python python_version : 3.9.19 machine : x86_64 system : Linux Gammapy package: version : 1.3.dev283+g0ce322691 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 : 1.13.0 astropy : 5.2.2 regions : 0.8 click : 8.1.7 yaml : 6.0.1 IPython : 8.18.1 jupyterlab : not installed matplotlib : 3.8.4 pandas : not installed healpy : 1.16.6 iminuit : 2.25.2 sherpa : 4.16.0 naima : 0.10.0 emcee : 3.1.6 corner : 2.2.2 ray : 2.20.0 Gammapy environment variables: GAMMAPY_DATA : /home/runner/work/gammapy-docs/gammapy-docs/gammapy-datasets/dev .. GENERATED FROM PYTHON SOURCE LINES 56-63 Define analysis region and energy binning ----------------------------------------- Here we assume a source at 0.5 degree from pointing position. We perform a simple energy independent extraction for now with a radius of 0.1 degree. .. GENERATED FROM PYTHON SOURCE LINES 63-80 .. code-block:: Python energy_axis = MapAxis.from_energy_bounds(0.03 * u.TeV, 30 * u.TeV, nbin=20) energy_axis_true = MapAxis.from_energy_bounds( 0.01 * u.TeV, 100 * u.TeV, nbin=100, name="energy_true" ) pointing = SkyCoord(ra=0 * u.deg, dec=0 * u.deg) pointing_info = FixedPointingInfo(fixed_icrs=pointing) offset = 0.5 * u.deg source_position = pointing.directional_offset_by(0 * u.deg, offset) on_region_radius = 0.1 * u.deg on_region = CircleSkyRegion(source_position, radius=on_region_radius) geom = RegionGeom.create(on_region, axes=[energy_axis]) empty_dataset = SpectrumDataset.create(geom=geom, energy_axis_true=energy_axis_true) .. GENERATED FROM PYTHON SOURCE LINES 81-86 Load IRFs and prepare dataset ----------------------------- We extract the 1D IRFs from the full 3D IRFs provided by CTA. .. GENERATED FROM PYTHON SOURCE LINES 86-97 .. code-block:: Python irfs = load_irf_dict_from_file( "$GAMMAPY_DATA/cta-1dc/caldb/data/cta/1dc/bcf/South_z20_50h/irf_file.fits" ) location = observatory_locations["cta_south"] livetime = 50.0 * u.h obs = Observation.create( pointing=pointing_info, irfs=irfs, livetime=livetime, location=location ) .. rst-class:: sphx-glr-script-out .. code-block:: none /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) .. GENERATED FROM PYTHON SOURCE LINES 98-103 Initiate and run the `~gammapy.makers.SpectrumDatasetMaker`. Note that here we ensure ``containment_correction=False`` which allows us to apply our own containment correction in the next part of the tutorial. .. GENERATED FROM PYTHON SOURCE LINES 103-110 .. code-block:: Python spectrum_maker = SpectrumDatasetMaker( selection=["exposure", "edisp", "background"], containment_correction=False, ) dataset = spectrum_maker.run(empty_dataset, obs) .. GENERATED FROM PYTHON SOURCE LINES 111-119 Now we correct for the energy dependent region size. **Note**: In the calculation of the containment radius, we use the point spread function which is defined dependent on true energy to compute the correction we apply in reconstructed energy, thus neglecting the energy dispersion in this step. Start by correcting the exposure: .. GENERATED FROM PYTHON SOURCE LINES 119-123 .. code-block:: Python containment = 0.68 dataset.exposure *= containment .. GENERATED FROM PYTHON SOURCE LINES 124-129 Next, correct the background estimation. Warning: this neglects the energy dispersion by computing the containment radius from the PSF in true energy but using the reco energy axis. .. GENERATED FROM PYTHON SOURCE LINES 129-137 .. code-block:: Python on_radii = obs.psf.containment_radius( energy_true=energy_axis.center, offset=offset, fraction=containment ) factor = (1 - np.cos(on_radii)) / (1 - np.cos(on_region_radius)) dataset.background *= factor.value.reshape((-1, 1, 1)) .. GENERATED FROM PYTHON SOURCE LINES 138-141 Finally, define a `~gammapy.datasets.SpectrumDatasetOnOff` with an alpha of 0.2. The off counts are created from the background model: .. GENERATED FROM PYTHON SOURCE LINES 141-147 .. code-block:: Python dataset_on_off = SpectrumDatasetOnOff.from_spectrum_dataset( dataset=dataset, acceptance=1, acceptance_off=5 ) .. GENERATED FROM PYTHON SOURCE LINES 148-157 Compute sensitivity ------------------- We impose a minimal number of expected signal counts of 10 per bin and a minimal significance of 5 per bin. The excess must also be larger than 5% of the background. We assume an alpha of 0.2 (ratio between ON and OFF area). We then run the sensitivity estimator. These are the conditions imposed in standard CTA sensitivity computations. .. GENERATED FROM PYTHON SOURCE LINES 157-165 .. code-block:: Python sensitivity_estimator = SensitivityEstimator( gamma_min=10, n_sigma=5, bkg_syst_fraction=0.05, ) sensitivity_table = sensitivity_estimator.run(dataset_on_off) .. GENERATED FROM PYTHON SOURCE LINES 166-176 Results ------- The results are given as a `~astropy.table.Table`, which can be written to disk utilising the usual `~astropy.table.Table.write` method. A column criterion allows us to distinguish bins where the significance is limited by the signal statistical significance from bins where the sensitivity is limited by the number of signal counts. This is visible in the plot below. .. GENERATED FROM PYTHON SOURCE LINES 176-180 .. code-block:: Python display(sensitivity_table) .. rst-class:: sphx-glr-script-out .. code-block:: none e_ref e_min e_max e2dnde excess background criterion TeV TeV TeV erg / (cm2 s) --------- --------- --------- ------------- ------- ---------- ------------ 0.0356551 0.03 0.0423761 8.0756e-12 1642.38 32847.7 bkg 0.0503641 0.0423761 0.0598579 4.33368e-12 825.3 16506 bkg 0.0711412 0.0598579 0.0845515 1.70634e-12 482.297 7567.56 significance 0.10049 0.0845515 0.119432 9.33055e-13 341.929 3765.63 significance 0.141945 0.119432 0.168702 6.71944e-13 237.265 1785.63 significance 0.200503 0.168702 0.238298 4.74542e-13 158.077 772.881 significance 0.283218 0.238298 0.336606 3.21236e-13 107.547 345.112 significance 0.400056 0.336606 0.475468 2.54721e-13 73.7922 154.188 significance 0.565095 0.475468 0.671616 1.81699e-13 52.9343 74.1691 significance 0.798218 0.671616 0.948683 1.53482e-13 37.9876 34.654 significance 1.12751 0.948683 1.34005 1.30015e-13 29.3536 18.6033 significance 1.59265 1.34005 1.89287 1.04939e-13 24.6823 11.9845 significance 2.24968 1.89287 2.67375 8.93128e-14 20.6464 7.43113 significance 3.17776 2.67375 3.77678 8.05637e-14 17.5411 4.66104 significance 4.48871 3.77678 5.33484 8.49078e-14 15.5144 3.196 significance 6.34047 5.33484 7.53566 9.4579e-14 13.2274 1.8669 significance 8.95615 7.53566 10.6444 1.00931e-13 10.843 0.845693 significance 12.6509 10.6444 15.0356 1.33013e-13 10 0.447552 gamma 17.8699 15.0356 21.2384 1.59254e-13 10 0.266192 gamma 25.2419 21.2384 30 2.25162e-13 10 0.126585 gamma .. GENERATED FROM PYTHON SOURCE LINES 181-183 Plot the sensitivity curve .. GENERATED FROM PYTHON SOURCE LINES 183-212 .. code-block:: Python from cycler import cycler fig, ax = plt.subplots() ax.set_prop_cycle(cycler("marker", "s*v") + cycler("color", "rgb")) for criterion in ("significance", "gamma", "bkg"): mask = sensitivity_table["criterion"] == criterion t = sensitivity_table[mask] ax.errorbar( t["e_ref"], t["e2dnde"], xerr=0.5 * (t["e_max"] - t["e_min"]), label=criterion, linestyle="", ) ax.loglog() ax.set_xlabel(f"Energy [{t['e_ref'].unit.to_string(UNIT_STRING_FORMAT)}]") ax.set_ylabel(f"Sensitivity [{t['e2dnde'].unit.to_string(UNIT_STRING_FORMAT)}]") ax.legend() plt.show() .. image-sg:: /tutorials/analysis-1d/images/sphx_glr_cta_sensitivity_001.png :alt: cta sensitivity :srcset: /tutorials/analysis-1d/images/sphx_glr_cta_sensitivity_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 213-219 We add some control plots showing the expected number of background counts per bin and the ON region size cut (here the 68% containment radius of the PSF). Plot expected number of counts for signal and background. .. GENERATED FROM PYTHON SOURCE LINES 219-242 .. code-block:: Python fig, ax1 = plt.subplots() ax1.plot( sensitivity_table["e_ref"], sensitivity_table["background"], "o-", color="black", label="blackground", ) ax1.loglog() ax1.set_xlabel(f"Energy [{t['e_ref'].unit.to_string(UNIT_STRING_FORMAT)}]") ax1.set_ylabel("Expected number of bkg counts") ax2 = ax1.twinx() ax2.set_ylabel( f"ON region radius [{on_radii.unit.to_string(UNIT_STRING_FORMAT)}]", color="red" ) ax2.semilogy(sensitivity_table["e_ref"], on_radii, color="red", label="PSF68") ax2.tick_params(axis="y", labelcolor="red") ax2.set_ylim(0.01, 0.5) plt.show() .. image-sg:: /tutorials/analysis-1d/images/sphx_glr_cta_sensitivity_002.png :alt: cta sensitivity :srcset: /tutorials/analysis-1d/images/sphx_glr_cta_sensitivity_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 243-252 Obtaining an integral flux sensitivity -------------------------------------- It is often useful to obtain the integral sensitivity above a certain threshold. In this case, it is simplest to use a dataset with one energy bin while setting the high energy edge to a very large value. Here, we simply squash the previously created dataset into one with a single energy .. GENERATED FROM PYTHON SOURCE LINES 252-261 .. code-block:: Python dataset_on_off1 = dataset_on_off.to_image() sensitivity_estimator = SensitivityEstimator( gamma_min=5, n_sigma=3, bkg_syst_fraction=0.10 ) sensitivity_table = sensitivity_estimator.run(dataset_on_off1) print(sensitivity_table) .. rst-class:: sphx-glr-script-out .. code-block:: none e_ref e_min e_max e2dnde excess background criterion TeV TeV TeV erg / (cm2 s) -------- ----- ----- ------------- ------- ---------- --------- 0.948683 0.03 30 1.44749e-12 6390.29 63902.9 bkg .. GENERATED FROM PYTHON SOURCE LINES 262-265 To get the integral flux, we convert to a `~gammapy.estimators.FluxPoints` object that does the conversion internally. .. GENERATED FROM PYTHON SOURCE LINES 265-274 .. code-block:: Python flux_points = FluxPoints.from_table( sensitivity_table, sed_type="e2dnde", reference_model=sensitivity_estimator.spectrum ) print( f"Integral sensitivity in {livetime:.2f} above {energy_axis.edges[0]:.2e} " f"is {np.squeeze(flux_points.flux.quantity):.2e}" ) .. rst-class:: sphx-glr-script-out .. code-block:: none Integral sensitivity in 50.00 h above 3.00e-02 TeV is 3.01e-11 1 / (cm2 s) .. GENERATED FROM PYTHON SOURCE LINES 275-282 Exercises --------- - Compute the sensitivity for a 20 hour observation - Compare how the sensitivity differs between 5 and 20 hours by plotting the ratio as a function of energy. .. _sphx_glr_download_tutorials_analysis-1d_cta_sensitivity.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: binder-badge .. image:: images/binder_badge_logo.svg :target: https://mybinder.org/v2/gh/gammapy/gammapy-webpage/main?urlpath=lab/tree/notebooks/dev/tutorials/analysis-1d/cta_sensitivity.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: cta_sensitivity.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: cta_sensitivity.py ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_