Monitoreo de plagas (Spodoptera sp J.E Smith, Tagasodes oryzicolus Muir y Oebalus insularis Stal)

As discussed in Section 1.4.3 the overwhelming majority of air showers are initiated by a cosmic ray incident on the atmosphere rather than a γ-ray photon. Despite this, very high energy γ- ray astronomy has been able to flourish thanks to work reported in Hillas (1985) which made it possible to distinguish between the two forms of air shower with a high degree of accuracy (achieving greater than 98% rejection of proton-initiated air showers). It had been noted that a number of astrophysical objects appeared to be potential point sources of TeV cosmic rays,

presumed to be γ-rays, but that they did not stand out clearly from the isotropic cosmic ray background; however, it was hoped that if any differences between air showers initiated by TeV photons and those initiated by protons could be documented, it might be possible to reject the background cosmic rays. Hillas used a Monte Carlo simulation to model the development of air showers with both proton and γ-ray primaries, using a program that had been previously used to model other interactions. The Cherenkov light released in these showers was assumed to be received by a collector, 10 m in diameter, and the predicted images were recorded. To describe these images Hillas used a total of six image parameters, which are described mathematically in Fegan (1997) and reproduced here. The first two parameters are the length, l, and width, w, of the ellipsoid, defined as:

l =r σx2+ σy2+ s 2 w = r σx2+ σ_y2− s 2 (2.1) where: σx2 = hx2i − hxi2 σ_y2 = hy2i − hyi2 (2.2) and s = q (σy2− σx2)2+ 4(σxy)2 (2.3) where σxy= hxyi − hxihyi (2.4)

σx2, σ_y2 and σxy are the spreads of the image in different directions defined in terms of the

image moments. These image moments are related to the number of counts in a pixel, ni, and

the position of this pixel, described, to second order, using the Cartesian coordinates xi and yi,

hxi = Σnixi Σni hyi = Σniyi Σni (2.5) hx2i = Σnix 2 i Σni hy2i =Σniy 2 i Σni (2.6) hxyi = Σnixiyi Σni (2.7) The third parameter is the distance, d, from the centroid of the image to the centre of the field of view, this is calculated using:

d =phxi2_{+ hyi}2 _(2.8)

Fourth is the miss, m, the perpendicular distance between the major axis of the image and the centre of the field of view of the camera, evaluated as:

m = s  uhxi2_{+ vhyi}2₎ 3  − 2σxyhxihyi s  (2.9) where u = 1 +σy2− σx2 s (2.10) and v = 2 − u (2.11) Fifth is the azimuthal width, Aw, which is the rms spread of light perpendicular to the line

connecting the centroid of the image to the centre of the field of view, defined mathematically: Aw=

r

hxi2_hy2_{i − 2hxihyihxyi + hx}2_ihyi2

d2 (2.12)

The final parameter is the degree of light concentration determined using the ratio of the two largest pixel signals to the sum of all signals. The length, width and distance are shown in Figure 2.1.

It was found that the images of hadronic showers tend to be longer and wider (due to the emission angles of pions, not present in γ-ray showers), fluctuate more in intensity across the image, and are not systematically aligned with the source. Using the parameters described above,

Figure 2.1: Diagram illustrating simple Hillas parameters, calculated for a γ-ray image, approx- imated as an ellipse. An image from a second telescope is superimposed to demonstrate the geometrical technique for source position reconstruction. The magnitude of the angular offset in shower direction reconstruction is the parameter, θ. Taken from Aharonian et al. (2006a). Hillas was able to define a region of parameter space containing showers mostly initiated by a γ-ray primary and only a small percentage of proton-initiated showers. By requiring that any four out of the six parameters for a shower lie in this region, Hillas found that it was possible to accept 60%- 70% of γ-ray-initiated air showers while rejecting more than 98% of background proton-initiated showers.

In practical situations, the image must be “cleaned” before the Hillas parameters can be calcu- lated. This involves selecting only the pixels which contain Cherenkov light while rejecting those containing only night-sky background (Aharonian et al., 2006a). For the H.E.S.S. telescopes, a two-level filter is used: pixels in the image are required to be above 5 photoelectrons with a neigh- bour above 10 photoelectrons and vice versa. This method successfully selects spatially correlated features which correspond to air shower light and smooths out shower fluctuations in a simple and repeatable manner. After this the Hillas parameters can then be calculated.

For arrays of more than one telescope, hadron-like events are primarily separated from γ-ray- like events using mean-scaled parameters, psc, for both the width and length of the detected air

shower (Aharonian et al., 2006a). A lookup table, calculated using Monte Carlo simulations, is used to predict the mean value and scatter expected for the parameter being considered in the case of a γ-ray-initiated air shower, as a function of the amplitude of the shower image on the camera, the impact parameter (the projected distance of the extrapolated shower track to a telescope) and the zenith angle. The value of psc is then calculated using:

psc=

(p − hpi) σp

(2.13) where hpi is the mean value of the parameter from the lookup tables, σp is the scatter taken

from the lookup tables and p is the measured value of the parameter from the air shower. The smaller the calculated value for psc, the more likely the event is to be a γ-ray initiated air shower.

Using the calculated value for psc the mean reduced scaled width (MRSW) and mean reduced

scaled length (MRSL) are then calculated by averaging over those telescope images which pass the image-amplitude selection cut for each event.