Background cube

A background cube is a 3-dimensional cube spanned by reconstructed Right Ascension or Galactic longitude, reconstructed Declination or Galactic latitude, and reconstructed photon energy. The background cube \(B(p', E')\) is computed using

\[B(p', E') = \frac{\sum_i B_i(p', E') \times \tau_i}
{\sum_i \tau_i}\]

where \(B_i(p', E')\) is the background rate estimate for observation \(i\), \(p'\) is the reconstruction photon arrival direction, \(E'\) is the reconstruction photon energy, and \(\tau_i\) is the livetime of observation \(i\). The sum is taken over all observations.

Counts cube

A counts cube is a 3-dimensional data cube spanned by reconstructed Right Ascension or Galactic longitude, reconstructed Declination or Galactic latitude, and reconstructed energy.

Energy Dispersion cube

An energy dispersion cube is a 4-dimensional cube spanned by true Right Ascension or Galactic longitude, true Declination or Galactic latitude, true photon energy, and migration which is the ratio between reconstructed and true photon energy. The energy dispersion cube \(E_{\rm disp}(E'| p, E)\) is computed using

\[E_{\rm disp}(E'| p, E) =
\frac{\sum_i E_{\rm disp,i}(E'| p, E) \times A_{\rm eff,i}(p, E) \times \tau_i}
{\sum_i E_{\rm disp,i}(E'| p, E) \times \tau_i}\]

where \(E_{\rm disp,i}(E'| p, E)\) is the energy dispersion for observation \(i\), \(E'\) is the reconstruction photon energy, \(p\) is the true photon arrival direction, \(E\) is the true photon energy, and \(\tau_i\) is the livetime of observation \(i\). The sum is taken over all observations.

Event list

An event list is a table comprising the reconstructed properties of the observed events. Each row of the table corresponds to an event. The columns of the table provide event characteristics, such as trigger time, reconstructed arrival direction (in Right Ascension and Declination), and the reconstructed event energy.

Exposure cube

An exposure cube is a 3-dimensional cube spanned by true Right Ascension or Galactic longitude, true Declination or Galactic latitude, and true photon energy. The exposure \(X(p, E)\) is computed using

\[X(p, E) = \sum_i A_{\rm eff,i}(p, E) \times \tau_i\]

where \(A_{\rm eff,i}(p, E)\) is the effective area for observation \(i\), \(p\) is the true photon arrival direction, \(E\) is the true photon energy, and \(\tau_i\) is the livetime of observation \(i\). The sum is taken over all observations.

First CTA Data Challenge

The goal of the first CTA Data Challenge is to enable the CTA Consortium Science Working Groups to derive science benchmarks for the CTA Key Science objectives.

The first CTA Data Challenge should provide quantitative estimates of CTA’s science capabilities that will enable the CTA Consortium Science Working Groups to evaluate science trade-offs in the future. The first CTA Data Challenge should also result in numerous show cases, including for example images, spectra and light curves, that can be used to illustrate CTA’s science case, and that should enrich the CTA outreach material. And the first CTA Data Challenge should also stimulate the enrichment of the CTA Science Case.

Good Time Interval

A Good Time Interval is a contiguous time period, defined by a start and a stop time, during which the events can be used for a scientific analysis.

Instrument Response Functions

The instrument response functions provide a mathematical description that links the measured quantities of an event to the physical quantities of the incident photon. The instrument response functions for CTA are factorised into the effective area \(A_{\rm eff}(p, E, t)\) (units \(cm^2\)), the point spread function \(PSF(p' | p, E, t)\), and the energy dispersion \(E_{\rm disp}(E' | p, E, t)\) following:

\[R(p', E', t' | p, E, t) =
A_{\rm eff}(p, E, t) \times
PSF(p' | p, E, t) \times
E_{\rm disp}(E' | p, E, t)\]

Model definition file

Source and background model components are defined in ctools by a model definition file. The model definition file is an ASCII file in XML format. The format of the model definition file is inspired from, and is compatible with, the format used by the Fermi-LAT Science Tools. The general structure of a model definition file is

```
<?xml version="1.0" standalone="no"?>
<source_library title="source library">
<source name="Crab" type="PointSource">
<spectrum type="PowerLaw">
<parameter name="Prefactor" scale="1e-16" value="5.7" min="1e-07" max="1000.0" free="1"/>
<parameter name="Index" scale="-1" value="2.48" min="0.0" max="+5.0" free="1"/>
<parameter name="PivotEnergy" scale="1e6" value="0.3" min="0.01" max="1000.0" free="0"/>
</spectrum>
<spatialModel type="SkyDirFunction">
<parameter name="RA" scale="1.0" value="83.6331" min="-360" max="360" free="0"/>
<parameter name="DEC" scale="1.0" value="22.0145" min="-90" max="90" free="0"/>
</spatialModel>
</source>
<source name="Background" type="CTAIrfBackground" instrument="CTA">
<spectrum type="PowerLaw">
<parameter name="Prefactor" scale="1.0" value="1.0" min="1e-3" max="1e+3" free="1"/>
<parameter name="Index" scale="1.0" value="0.0" min="-5.0" max="+5.0" free="1"/>
<parameter name="PivotEnergy" scale="1e6" value="1.0" min="0.01" max="1000.0" free="0"/>
</spectrum>
</source>
</source_library>
```

Each model component is described by the `<source>` tag. Each source has
an mandatory spectral and a spatial component (tags `<spectrum>` and
`<spatialModel>`) and an optional temporal component (tag `<temporal>`).
Parameters that should be adjusted in a maximum likelihood fit should be
set to `free="1"`; otherwise they are hold fixed.

Observation

The data are split into observations. Each observation is characterised by a stable instrument configuration that can be described by an instrument response function. Observations are also known as runs.

Observation definition file

Observations are combined in ctools using an observation definition file. The observation definition file is an ASCII file in XML format. The format of the observation definition file is illustrated below:

```
<?xml version="1.0" standalone="no"?>
<observation_list title="observation library">
<observation name="Crab" id="00001" instrument="CTA">
<parameter name="EventList" file="events1.fits"/>
</observation>
<observation name="Crab" id="00002" instrument="CTA">
<parameter name="EventList" file="events2.fits"/>
</observation>
</observation_list>
```

Point Spread Function cube

A point spread function cube is a 4-dimensional cube spanned by true Right Ascension or Galactic longitude, true Declination or Galactic latitude, true photon energy, and offset angle between true and reconstructed arrival direction of a photon. The point spread function cube \(PSF(\delta | p, E)\) is computed using

\[PSF(\delta | p, E) = \frac{\sum_i PSF_i(p' | p, E) \times A_{\rm eff,i}(p, E) \times \tau_i}
{\sum_i A_{\rm eff,i}(p, E) \times \tau_i}\]

where \(\delta\) is the angular separation between the true and measured photon directions \(p\) and \(p'\), respectively, \(A_{\rm eff,i}(p, E)\) is the effective area for observation \(i\), \(E\) is the true photon energy, and \(\tau_i\) is the livetime of observation \(i\). The sum is taken over all observations.