Classical IACT On/Off analysis

The traditional technique that is widely used by the IACT community for spectral analysis consists in selecting the source events from an On region and estimating the background events from one or several signal-free Off regions. The events are put into On and Off spectra, and the effective response is computed for the On region that allows to turn the event spectrum into flux points.

The cscript csphagen generates all files that are necessary for an On/Off spectral analysis and saves them in the OGIP format that is normally used in X-ray astronomy and that is compliant with the XSPEC spectral fitting package. This format is composed of Pulse Height Analyzer spectral files (PHA), an Auxiliary Response File (ARF) and a Redistribution Matrix File (RMF).

PHA files are generated for the On and the Off region by binning the events in both regions as function of reconstructed energy and storing the corresponding vectors $n_i^{\mathrm{on}}$ and $n_i^{\mathrm{off}}$, where $i$ is the index of the energy bin.

The ARF is computed using

$$ARF(E)={\int }_{\mathrm{on}}{\int }_p{A}_{\mathrm{e}\mathrm{f}\mathrm{f}}(p,E)\times PSF(p^{\prime }|p,E)\times M_s(p,E)dpd{p}^{\prime }$$

where $A_{\mathrm{e}\mathrm{f}\mathrm{f}}(p,E)$ is the effective area, $PSF(p^{\prime }|p,E)$ is the point spread function, $M_s(p,E)$ is the source model, $p$ and $p^{\prime }$ are the true and reconstructed photon arrival directions, respectively, and $E$ is the true energy. The integration in $p^{\prime }$ is done over the On region, the integration in $p$ is done over all $p$ that contribute events within the On region. These integrations assure the correct computation of the number of source events within the On region, even if the emission is not fully contained within that region.

Note

The source model is normalised to unity,

$${\int }_p{M}_s(p,E)dp=1$$

where the integral over $p$ is taken over the full sky.

Note

The convolution with the PSF is skipped and the model $M_s(p,E)$ ignored if the IRFs are calculated for the events surviving a directional cut around the assumed source position, which is specified by the RAD_MAX keyword in the IRF files. The user must take care of specifying an On region compatible with this directional cut. In that case

$$ARF(E)=\frac{{\int }_{\mathrm{on}}{A}_{\mathrm{e}\mathrm{f}\mathrm{f}}(p^{\prime },E)d{p}^{\prime }}{{\int }_{\mathrm{on}}d{p}^{\prime }}$$

which is the mean effective area over the On region.

The RMF is computed using

$$RM{F}_i(E)=\frac{{\int }_{\mathrm{on}}{\int }_{E^{\prime }}{A}_{\mathrm{e}\mathrm{f}\mathrm{f}}(p,E)\times E_{\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{p}}(E^{\prime }|p,E)d{E}^{\prime }dp}{{\int }_{\mathrm{on}}{A}_{\mathrm{e}\mathrm{f}\mathrm{f}}(p,E)dp}$$

where $E_{\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{p}}(E^{\prime }|p,E)$ is the energy dispersion. The integration in $p$ is done over the On region to accommodate for possible variations of the energy dispersion over that region. The integration over reconstructed energy $E^{\prime }$ is done over the width of the energy bin $i$.

csphagen also computes the background scaling factors ${\alpha }_i$ and background response vectors $b_i$.

The background scaling factors ${\alpha }_i$ are stored in the BACKSCAL column of the On PHA file and are computed using

$${\alpha }_i=\frac{{\int }_{\mathrm{on}}{M}_b(p^{\prime },E^{\prime })d{p}^{\prime }}{{\int }_{\mathrm{off}}{M}_b(p^{\prime },E^{\prime })d{p}^{\prime }}$$

where $M_b(p^{\prime },E^{\prime })$ is a background acceptance model, specified either using a model definition XML file, or the template background found in the IRF. If no background acceptance model is provided, $M_b(p^{\prime },E^{\prime })=1$, and ${\alpha }_i$ gives the solid angle ratio between On and Off regions.

The background response vectors $b_i$ are stored in the BACKRESP column of each Off PHA file and are computed using

$$b_i={\int }_{\mathrm{off}}{M}_b(p^{\prime },E^{\prime })d{p}^{\prime }$$

where $M_b(p^{\prime },E^{\prime })$ are evaluated at the reconstructed energy bins $i$. If no background acceptance model is provided, $M_b(p^{\prime },E^{\prime })=1$, and $b_i$ gives the solid angle of the Off region.