Introduction¶

The predicted flux in reconstructed energy is defined via the product of model flux, effective area and livetime.

Including energy dispersion means that the predicted flux in reconstructed energy has to be derived via summing over the flux predicted in each true energy bin weighted with the energy dispersion relating true and reconstructed energy.

Including energy threshold means that, on the one hand, the observed counts spectra should be cutted below the threshold and, on the other hand, it should be ensured that the predicted counts spectra in reconstructed energy should contain no counts below threshold.
The easiest way to deal with the latter is to modify the energy dispersion so that a redistribution of true energies to reconstructed energies below threshold is prevented.

In cta on/off the application of the energy threshold is mainly done in GCTAOnOffObservation::apply_ebounds().

My frame¶

Joint on/off analysis of H.E.S.S. data using the latest ctools dev (Aug03) / gammapy dev (Aug04) versions.

The problem¶

Including energy dispersion, you will aggree that model flux for true energies below the threshold has a nonzero probability to be reconstructed above threshold.
In order to ensure that this flux is considered, an effective area is needed for computation that features reasonable values over the whole energy range, including regimes beyond the threshold.

Obviously in ctools the effective area is set to zero beyond the threshold.
(See GCTAAeff2D::operator() which basically applies the energy threshold via an energy bounds check.)

That reduces the number of events predicted in the reconstructed energy range in the vicinity of the threshold and affects the model fitting.

Validation¶

Removing the check for the energy bounds in GCTAAeff2D::operator() (which of course is just a temporary kludge for validation and not a solution at all!) basically leaves the effective area like it is and does not set it to zero beyond threshold.

A test with H.E.S.S. PDR data on pks2155 now results in spectral parameters which are very good comparable to what we obtain with the internal H.E.S.S. analysis tool and with gammapy:

                    | ctools: native       | ctools: Aeff without threshold check | H.E.S.S. analysis tool | gammapy
--------------------+----------------------+--------------------------------------+------------------------+----------------------
Norm [/TeV /s /cm2] | 2.236 +- 0.2421 e-11 | 1.816 +- 0.1906 e-11                 | 1.804 +- 0.2096 e-11   | 1.718 +- 0.1814 e-11
Index [1]           | 3.758 +- 0.265       | 3.431 +- 0.231                       | 3.464 +- 0.2389        | 3.422 +- 0.2096