Cherenkov light

Gamma rays correspond to the highest radiation in the Electromagnetic (EM) spectrum, which covers 20 energy decades (or orders of magnitude) between radio and the TeV regime. Most of the lowest energy emission can travel across the atmosphere reaching the ground (see Figure 2.1). However, this is not the case for the gamma rays, whose interaction with the molecules in the atmosphere prevents the most energetic radiation from penetrating and reaching us. In order to detect high-energy photons, detectors on-board satellites can be used. Nevertheless, due to weight limitations, they can only support detectors with small collection area and therefore, they cannot provide results for energies above 100 GeV, regime in which the photon fluxes are already low.

Figure 2.1: EM spectrum and its corresponding absorption level in the atmosphere. Credit: Wagner (2006), plot adapted from Longair (2011) and Moralejo (2000).

For energies> 50 GeV, the IACTs, with larger sensitive area, dominates the study of gamma rays. The technique is based on indirect detection. When a VHE gamma ray or CR interacts with the atmospheric nuclei, a particle cascade is initiated, the so-called EAS. If the resulting charged particles of this interaction travel faster than the speed of light in the atmosphere, Cherenkov light is emitted, whose wavelength ranges between 300 and 500 nm. The existence of this type of light was proposed by the Soviet physicist Pavel Alekseyevich Cherenkov (Cherenkov 1934) who, along with Ilya Frank and Igor Tamm, received the Nobel prize in 1958 for the discovery and interpretation of the Cherenkov effect.

Figure 2.2: Polarization on a medium when a charged particle travels with low velocity (v < c/n). Taken from http://mxp.physics.umn.edu.

Figure 2.3: Polarization on a medium when a charged particle travels faster than the speed of light on it (v > c/n). Taken from http://mxp.physics.umn.edu.

The atmosphere is a dielectric medium and therefore, the molecules in it are disrupted by the charged particles crossing, changing their polarization. If the particle velocity is low, v < c/n (wherec is the speed of light in vacuum and n is the refraction index of the medium), the po-larization is symmetrical (see Figure 2.2) and therefore, the electromagnetic field remains null.

However, when its velocity is higher than the speed of light in the medium (v > c/n), the parti-cle travels faster than its electric field leaving behind a non-symmetric perturbation (see Figure 2.3). To return to the equilibrium, Cherenkov radiation is emitted in the depolarization of the molecules.

The number of Cherenkov photons can be estimated as a function of unit track length of the charged particle and its own wavelength, following Yao et al. (2006):

d²N

dxdλ = 2πα

λ² 1− c²

v²n²(λ)

!

≈379sin²θ(λ)eV⁻¹cm⁻¹] (2.1) whereα≈ 1/137 is the known fine structure constant. Therefore, the number of Cherenkov photons is inversely proportional to the squared wavelength, dN/dλ∝ λ⁻². This is the reason why this radiation peaks at∼320 nm, i.e. in the UV band (see Figure 2.4). However, the emitted and observed Cherenkov radiation spectrum differ due to the transmission losses in the atmosphere.

The main sources of this attenuation are:

Rayleigh scattering:Scattering offair molecules, which a wavelength dependency ofλ⁻⁴. It affects mostly UV radiation.

Mie scattering: Scattering off aerosols, dust and droplets water. It does not show any strong wavelength dependency.

Ozone molecules: These molecules are responsible for the strong absorption of hard UV photons (< 300 nm).

H₂O and CO₂ molecules:They produce absorption in the IR band.

Zenith angle: The larger the zenith angle of the EAS, the higher the attenuation. This is due to the fact that at high zenith angle, the cascades develop in the highest layers of the atmosphere and hence, particles need to travel a larger path. Consequently, the probability of suffering absorption from some of the above mentioned processes increases.

Only EASs initiated by particles at the highest energies are significantly detected by the telescopes at high Zenith distance (Zd) range. Thus, at larger zenith ranges the peak of the Cherenkov radiation spectrum shifts to larger wavelengths. Figure 2.5 shows how the density of Cherenkov photons, as well as the peak of their spectrum, vary at different zenith angles.

Figure 2.4:Spectra of Cherenkov radiation produced by vertical EAS initiated by gamma rays at different energies. The solid lines corresponds to the unabsorbed spectra at 10 km altitude, while the dashed line are the observed spectra attenuated by Rayleigh and Mie scattering (see Section 2.1).

The shape of the Cherenkov radiation around the track of the charged particle is a cone with an aperture angleθ, (the so-called Cherenkov angle; see Figure 2.6), given by:

cosθ= c⁰ v = c

vn(λ) (2.2)

wherec⁰ =c/nis the speed of light in the medium andn(λ) is the refractive index of the medium, whose value varies with the wavelength (λ) of the Cherenkov light. The mean value ofθin air is

∼1^◦.

An ultrarelativistic particle propagating vertically through the atmosphere creates a doughnut ring of Cherenkov light in the ground. The contribution of all the involving particles in a EAS

Figure 2.5:Cherenkov spectra at different zenith angles.

Figure 2.6:Cherenkov radiation scheme.

that emit Cherenkov radiation leads to a full circle on the ground, the so-called Cherenkov light pool (Figure 2.7). If the cascade produced in the atmosphere does not propagates vertically but with some inclination, the superposition of the Cherenkov light rings illuminates an ellipse on the ground.

In the case of a vertical EAS initiated by a gamma ray, the Cherenkov photons density is approximately uniform in a circle from the core of the cascade up to . 120 m. There is a slightly increase on the density around this distance, which is known as hump, whose origin arises from an increase in the opening angle,θ, due to the changes in the refraction index as the

Figure 2.7: The superposition of the Cherenkov light rings produces a circle (or ellipse) in the ground, the so-called Cherenkov light pool.

particle penetrates the atmosphere. Beyond thehump, the density fades rapidly. The density of Cherenkov photons is proportional to the energy of the primary particle when this is a gamma ray, which is not true in case of different incident particle (see Figure 2.8). Therefore, this relation can be used to estimate the energy of the incident gamma ray.

Figure 2.8: Cherenkov photon density within a radius of 125 m from the core shower as a function of photons energy for different primary particles. Taken from Wagner (2006).

Although we are interesting in the EASs initiated by gamma rays, cascades induced by hadrons (mainly protons) are much more numerous. Even for strong gamma-ray sources, as it is the case of the Crab Nebula, the ratio between hadron-induced and gamma ray-induced cascades is considerably high, around 1000 hadronic cascades for each electromagnetic shower. There-fore, hadronic cascades represent the major source of background in our observations. The better we understand both types of shower, the better we can get rid of the background that embedded our observations.