Stereo reconstruction

The next step in the analysis is to characterize EASs event-wise, inferring informa- tion of the primary particle from the images gathered by the triggered telescopes. The main characteristics to determine are the primary impinging direction, its energy and to discern if its nature is of γ-ray origin.

Figure 3.10: Schematics of the monoscopic parameterization using the first order Hillas parameters. Image corresponds to a simulated γ-ray of E ≈ 3 T eV seen by a LST.

Direction reconstruction: The primary particle direction is calculated from individual telescope images, determining the source position in the camera by minimizing Σnwid2i, where diis the distances between each shower direction and the

source location and withe weight of each telescope image. This weight accounts for

the quality of the reconstruction considering the shower geometry and the telescope type. It is extracted from a previously generated LUT from an independent set of simulated γ-rays, evaluating the reconstructed deviation (mismatch between reconstructed and real source position) as a function of size and width over length. Then, the core position and the shower maximum height are calculated using similar minimizations. Note only triggered telescopes with clean images (reduced Number of islands) and size larger than a certain threshold (50 phe) are used in the minimization.

• Core position: Position in the ground intersecting the projection of the pri- mary particle direction, corresponding to the center of the Cherenkov light pool.

• Maximum height : Estimated height (in cm) at which the maximum devel- opment of the shower was located. This parameter is used for the energy reconstruction and also by the background suppression algorithms.

• Reconstructed source position: Point projected in the sky (in degrees) which represents the estimated position of the source emitting the event (consider- ing the event as a γ-ray).

• Multiplicity: Number of telescopes used in the direction reconstruction.

• MinResultDir : Minimum value (in square degrees) obtained for the mini- mized function (Σnwid2i) during the direction reconstruction.

And the following monoscopic (source dependent) parameters are calculated image-wise:

• θ: Distance (in degrees) between the reconstructed source position and the position of the γ-ray source. This parameters squared, together with the hadroness, is the main background suppression cut generally applied in the IACT technique.

• Impact parameter : Distance projected in the ground (in cm) between the core position and the telescope observing the event.

• Dist : Angular distance (in degrees) between the center of gravity of the image (mean) and the reconstructed source position in the camera.

Energy estimation: Two different methods are implemented to estimate the energy of the primary particle, always considering them of γ-ray nature. The first method is analog to the one implemented for the direction reconstruction, and uses a Look-Up Table (LUT) (one per telescope type) evaluating reconstructed showers energy over size as a function of the impact parameter and the stereo

reconstructed maximum height. The second method used is a Random Forest (RF) (also one per telescope type) trained to evaluate the energy as a function of a list of parameters: The stereo reconstructed maximum height and the monoscopic size, impact parameter, width, length, concentration ratio, width∗length_size , dist2 and the angle between the positive x-axis and the line projected by the source position and the CoG of the shower. Both methods need a previous step computing the LUT or the RF using an independent set of generated γ-rays, and they are both used to estimate the energy of individual images independently. The primary particle energy estimation is calculated as the average of these values weighted with wi = _∆E12. The performance of these two methods is compared in Sec. 5.2.1.

Gamma-Hadron separation: Background rejection is performed by applying a RF algorithm for each telescope type, trained to discern between showers of electromagnetic or hadronic origin. This algorithm is applied to each triggered telescope image assigning a real number, defined between [0, 1], called hadroness (h). This variable indicates the likelihood of a shower to have hadronic origin corresponding h ≈ 1 to hadron-like showers and h ≈ 0 to γ-like ones. The RF is trained using both simulated γ-rays and hadrons, evaluating hadroness as a func- tion of the stereo estimated energy and maximum height, and individual telescope images energy, impact parameter, size, width, length and concentration ratio. The global hadroness value is calculated as the average of the calculated single values weighted with wi = size0.54 (expression obtained empirically).

Taking into account the methods just described, 4 different datasets are required. An initial set of γ-rays is needed to train the LUT involved in the direction re- construction. In principle, a training sample of ∼ 2 × 105 stereo triggered shower images would be enough for accurate direction reconstruction weighting. A sec- ond set of stereo reconstructed γ-rays is used for the LUT (or RF) involved in the energy reconstruction. This sample also needs > 2 × 105 telescope images to create a proper training. The third dataset corresponds to the γ-rays and hadrons needed for the RF training, responsible of the background suppression. The num- ber of telescope images needed for a decent cosmic-ray rejection is ∼ 1 × 105 _for

the different methods needed for the event characterization are computed, the last dataset (composed by the remaining MC simulated γ-rays, hadrons and electrons available) is used to estimate the CTA performance, explained in the next section. Note that in the last CTA MC production, stereoscopically triggered γ-ray events account roughly for a ∼ 0.3% of generated showers, generally observed by ∼ 4 tele- scopes (although this value increases significantly with the energy). In the case of generated hadrons, this number significantly decreases, accounting triggered events for less than the ∼ 0.02% of generated hadronic showers.

Instead of using all triggered telescopes to characterize an event, a set of quality cuts are applied to get rid of poorly reconstructed showers, significantly improving the characterization. Showers are required to exceed a minimum size, main island size over size ratio and width over length values, removing faint and scattered images. The dispersion from the 2-pass trace extraction time fit and the number of islands are also used to reject noise dominated events.