flux-sensitivity-sebastian-achim-mueller 0.0.6

Instrument Response Function

To be precise: This response-function is what I (as a non CTA-member) extracted from the provided documentation. To extract these quantities I interpolate and/or average over e.g. solid angle. The script flux_sensitivity/scripts/read_irf_and_estimate_differential_sensitivity.py reads CTA’s instrument-response and writes the differential sensitivity for the various scenarios.

We use e for true gamma-ray-energy and e' for reconstructed gamma-ray-energy.

Rate of background R[e']

The rate of background (the sum of all contributions) w.r.t. to reconstructed gamma-ray-energy.

Area for signal A[e]

The effective area to collect gamma-rays w.r.t. the true gamma-ray-energy.

Probability to confuse energy M_\gamma[e, e']

The probabilty to confuse the true with the reconstructed gamma-ray-energy. This is also called energy-migration.

Scenarios

This package offeres multiple scenarios how to handle the instrument’s non perfec reconstruction in energy. Each scenario results in a different estimate for the instrument’s differential sensitivity. The scenarios are named using colors to point out their differences while not implying a hierachy. We compiled this list of scenarios from what we found in the wild. We do not think that any of the shown scenarios is superior, we just want to raise awareness.

The figure below shows the settle differences of the scenarios.

Fortunately, we found a way to represent each scenario by using the two matrices G and B. Matrix G defines how a scenario takes the effective area for the signal into account

and matrix B defines how a scenario takes the rate of background into account

Here A^k[e'] is the area of the signal and R^k[e'] is the rate of background used in scenario k.

Algorithm C to Estimate the Critical Number of Signal-Counts N_S

Independent of the different scenarios, there are additional degrees of freedom when computing a differential sensitivity. One additional source of differences is: The algorithm C to compute the critical rate which is required in order to claim a detection. After one has estimated the number of background-counts in the on-region \hat{N}_B, one uses algorithm C to estimate the minimal number of signal-counts in the on-region

which is required to claim a detection. A possible input to C might be:

• The number of background-counts in the on-region \hat{N}_B.

• The minimal significance S a signal has to have in order to be considered unlikely to be a fluctuation in the background. S is commonly chosen to be 5\sigma, (std.,dev.).

• A method to estimate S based on the counts in the on- and off-regions. Here commonly Equation,17 in cite{li1983analysis} is used.

• An estimate for the systematic uncertainties of the instrument. This commonly demands N_S / \hat{N}_B > \approx 5\%. When our instrument runs into this limit, more observation-time T_\text{obs} will no longer decrease the required flux to claim a detection.

• A limit on the minimal amount of statistics. This is commonly used to make sure that the estimator for S operates in a valid range of inputs. This might require the counts in the on- and off-regions to be above a minimal threshold e.g. N_\text{on} > 10.