A study of the polarization of Cherenkov Radiation in Extensive Air Showers of Energy around 1 TeV


J.L.Contreras, I. de la Calle, J.Cortina


Abstract


It is known that the Cherenkov radiation produced in EAS ( Extensive Air Showers ) has a net polarization, oriented along the line which joins the impact point of the photon and the core of the shower ( Hillas 1994 ). Cherenkov radiationfrom EAS is usually analyzed by means of Imaging Atmospheric Cherenkov Telescopes ( IACTs ). We propose a setup where polarizers are placed on the IACT camera, aligned with the radial direction, by which this polarization feature could exploited, and show some results about its performance, derived from Monte Carlo simulations.


1- Cherenkov light polarization in EAS


The Cherenkov radiation emitted by a charged particle is distributed along a cone whose apex moves with the particle and whose axis coincides with the particle path. The angle of the Cherenkov cone in air is of the order of one degree. Cherenkov radiation shows an intrinsic polarization. It is such that the electric vector is contained in the plane defined by the electron and photon paths (Figure 1a).

The existence of a net polarization in the radiation coming from an EAS can be readily understood within a simple limiting case. Lets take a shower of normal incidence and an observer located at a certain distance from the core of the shower at ground. Cherenkov photons can reach the observation point if it lays in the Cherenkov cone. For particles traveling along the shower axis the polarization pattern on ground will be a superposition of circles centered in the core, with the polarization vectors over it oriented towards the core.

The above arguments will still hold approximately when the distance of the observer to the core is big compared with the distance of the emitting particle tothe shower axis, and the direction of the particle is close to that of the shower axis.Therefore we expect a net polarization in the radial direction, growingwith the distance to the shower axis, until the effects of scattering become important, as then the direction of the particles which emitted the light differs from the direction of the shower. As an illustration Figure 1b shows the distribution of the directions of the photon polarizations at three different distances from the core, for a Monte Carlo generated event.

There is also a difference between gamma and proton EAS, shown in Figure 2a, as already noted in reference ( Hillas 1994 ). EAS initiated by hadrons have a lower polarization degree than those of electro-magnetic origin. This difference can be explained taking into account the higher transverse momentum generated in hadronic interactions. The directions of secondary particles in hadronic showers are further away from the shower direction than in electro-magnetic ones. This turns into a difference in the polarization vector distribution on ground as discussed in section 2.

Figure 2a also shows that the degree of polarization reaches a maximum at around 120 meters, decreasing afterwards. It can be understood as an effect of multiple scattering. Particle whose light reaches distances greater than 120 meters ( the so called hump ) are further from the ideal case depicted above. Either their position or their direction must be incompatible with those of the shower axis.

Finally, it must be noted that due to the same arguments, light coming from theupper parts of the shower possesses a higher degree of polarization than that coming from the lower parts. Early in the shower development particles are closer to the ideal case since they have suffered less scattering. A related argument links the time of arrival of the photons and their polarization. These fact appears clearly in the plots of Monte Carlo simulations; unfortunately we do not have space to show them here.


2- Application to IACTs


Cherenkov Telescopes focus light on a camera, made of photo-multiplier tubes, placed on its focal plane. As they point towards the source being observed and their angular fields are of a few degree the angles of incidence of the Cherenkov photons on the mirrors are close to zero. In this approximation of normal incidence the state of polarization is preserved after the reflection ( Sanchez Almeida and Martinez Pillet 1992 ) and carriedon to the camera.

Furthermore, for showers coming from the source direction, the corresponding image on the focal plane will have an elliptical shape with the mayor axis oriented towards the center of the camera. The major axis of this ellipse will lay along the line which joins the center of the telescope and the shower core. Finally, the projection of the light density on the ellipse major axis corresponds with the longitudinal development of the shower.

The above considerations show that the radial polarization on the ground translates in a radial polarization on the camera for showers coming from the source direction. The degree of polarization should increase slightly towards the center of the telescope where light comes mainly from higher up in the atmosphere .

An scheme of the setup we propose to take advantage from this situation is depicted in Figure 3, together with the image of an event in the camera extracted from the Monte Carlo simulations which will be described later. It consists in placing polarizers on each photo-multiplier with their transmitting axis oriented towards the center of the camera.

An immediate consequence of this setup is the suppression of the 50% of the unpolarized components of the night sky background. It is also worth noting that, off-axis showers will partially occupyregions of the camera which do not correspond to their dominant polarization. Other important remark is that the tail and the outer zones of the image will suffer more and the image will get more compact ( see Figure 3 ).


3- Monte Carlo Simulations


We have used CORSIKA 4.06 ( Capdevielle et al. 1992 ), corrected with regard to errors, to simulate a handful of events to test the ideas exposed above. The IACT telescopes characteristics included in the simulation are those of the telescopes which compose the HEGRA system, with drastic simplifications. The mirror is assumed to be a single parabola. We considered a 10% efficiency which takes into account the atmospheric absorption, mirror reflectivity, funnel transmission and quantum efficiency. The trigger threshold is set at 50 photons/image. Finally, we also assume that the polarization vector suffers no change in the state of polarization upon reflection on the mirror, which should be a very good approximation.

With this setup we have generated 40 gamma events at 0 degree zenith angle withenergy of 1 TeV, and 50 proton events of zenital angles distributed according to the solid angle between 0 degrees and 3 degrees and energy of 3 TeV ( in order to have approximately the same light intensity per unit of area as for the gamma events ). No Night Sky Background was included in the simulation.

To increase the sample statistics we simulate the same event in many non-overlapping telescopes covering an area of 150 meters of radius centered on the core.In this way we have a sample of the order of 10^5 gamma and 10^5 hadron events,highly correlated. Our results should be correct with respect to sampling fluctuations, but not to fluctuations of physical origin.

The results, standard image cuts were appplied, can be summarized as follows.

Night Sky Background is reduced by 50%, a priori .

The light output is reduced by 50% for protons and, around 30% for gammas depending on the distance to the core. See Figure 2b.

The image shrinks. The distributions of the Hillas parameters length and width , are shifted towards smaller values.

The ellipse orientation angle alpha distribution change slightly.


4- Conclusion


The use of radially aligned polarizers in the cameras of IACTs allows to take advantage from the natural polarization of the Cherenkov light present in EAS. Background is is reduced, while image parameters show little change.


5- List of Figures (in .eps format)


Figure 1a: Electron and Photon path view.

Figure 1b: Polarization vector distribution on ground is ilustrated for a 1 TeV gamma induced shower at three different core distance.

Figure 2a: Ratio of transverse to radial polarizations on the ground versus the distance to the core.

Figure 2b: Absorption of the polarizers versus distance of the telescope center to the core.

Figure 3: Camera Image.


6- Acknowledgements


We are in debt with our colleagues from the HEGRA collaboration and the departments of Astrphysics and Optics of the UCM, and with V. Martinez Pillet for fruitful discussions and comments. This work is partially supported by the CICYT under project number AEN-96-1676.


7- References


1- A.M. Hillas Space Science Reviews 75 vol 1, pp 17-30 ( 1994 ).

2- J.Sanchez Almeida and V. Martinez Pillet A&A 260, pp 543-555 ( 1992 ).

3- J.N. Capdevielle et al., KfK Report 4998 ( 1992 ).




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