Light Propagation in Ice

The optical properties of the glacial ice govern the light intensity and arrival time profile of the Cherenkov photons. For the simulation one needs an accurate modeling of the processes involved. Since an analytic description of scattering is not possible [106] the photonicssoftware was developed to perform a random walk simulation of light propagation in ice or water [112].

photonicsis used for the simulation and recently also for the reconstruction of events in theIceCube detector. It uses a medium described by depth and wavelength dependent absorption and scattering coefficients. For I^ceCube the ice model described in the previous section is employed.

Due to the large number of photons emitted from a single particle, it is not possible to perform a dedicated ray tracing for each photon. photonics produces a set of photon flux density tables describing the evolution of the light field around a source in a cellular grid. In case of a Cherenkov light source, photons are injected from a single point in space according to the Cherenkov wavelength spectrum and angular emission profile. For simulation and reconstruction the photon flux tables are converted to the mean number

of photons detected in each detector module, as well as the arrival time distribution of these photons. The source is specified by type (e.g. muon or cascade), location ~r_source and orientation θ, φ. The module by its spatial coordinates ~r_DOM. In order to save disk space, the photon wavelength and arrival orientation are folded with the wavelength and angular acceptance of the detector modules. For the use in reconstructions, a multidimensional interpolation between the discrete coordinates used in the photon tracking is performed. Details can be found in [106].

The photon arrival time is a composite of the travel time of an un-scattered photon, called geometrical time, and the time delay due to scat-tering. The geometrical time is given by t_geo = ∆x/c_g, where ∆x is the distance between the point of light emission and the sensor, and cg is the group velocity of light in the medium. The delay time is governed by a stochastic process and the underlying probability distributionP(∆t) is com-puted in the simulation. The probability distribution depends strongly on the distance between emitter and detector, as well as on the composition of the medium. Figure 4.13a shows a 2-dimensional plot of the delay time dis-tribution for different distances obtained by querying the photonicstables using a cascade-like emitter at a depth of 1950 m. At short distances, the time distribution has a concise peak at very small delay times. However, with increasing distance, scattering becomes more important and the delay time distribution becomes wider and the most likely delay becomes larger. The right plot (b) shows the delay time distribution for a fixed distance of 100 m at different depths. The change in the distribution is caused by different dust concentrations in the ice layers. In particular, at z = −100 m, which corresponds to a depth of ∼2050 m, the delay time distribution is widened dramatically. This is caused by the dense dust layer labeled with ’D’ in Figure 4.12.

The evolution of the light distribution for a cascade-like emitter is shown in Figure 4.14. At different times after the cascade appeared, the mean number of photon-electrons is shown in the x −z plane. The cascade is located at a depth of z =−120 m below the detector center, with direction pointing downward and an energy of 100 PeV. It is important to notice that photonics ignores the extension of the cascade in space and time. The plots on the left show the light distribution as obtained from photonics using a point-like cascade, whereas plots on the right are obtained using the simulation described in the Section 3.4.3 to take into account the longitudinal development of the shower.

The light distribution in the left plot after 20 ns (a) reflects the emission pattern used in photonics. Most of the light is emitted in the forward di-rection, in particular in the direction of the Cherenkov angle. The plot on

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(a) Delay time probability versus distance for a cascade located at the center of theIceCube^detector.

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∆t [ns]

(b) Delay time distribution at 100 m horizontal distance in different depths (in detector coordinates) Figure 4.13: Delay time distributions obtained fromphotonicssimulations.

the right clearly shows the impact of the shower development. The emis-sion pattern is stretched as a result of the overlay of multiple sub-cascades constituting the complete shower.

After 150 ns (b) the emission pattern is washed out due to scattering. For the point-like emitter, the distribution is almost isotropic and all directional information is lost. This is different in plot on the right, the longitudinal development of the cascade creates a light cone as can be expected from a moving particle.

Even at 300 ns (c) the light distribution in the plot on the right shows the influence of the cascade development, but starts to vanish. The distortions at the top of the light pattern in both plots are due to high dust concentrations at z ≈ −100 m, which introduces some ambiguity in the interpretation of directional information of the light pattern. In particular, one could argue the cascade is pointing upwards, in both plots. This illustrates that it is hardly possible to reconstruct the direction of cascades.

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(a)Light distribution after 20 ns

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(b) Light distribution after 150 ns

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(c) Light distribution after 300 ns

Figure 4.14: Cherenkov light distribution after 20 ns (a), 150 ns (b) and 300 ns (c) for a 100 PeV cascade at a depth ofz=−120 m pointing downward. The left plots are for point-like cascades as provided byphotonics, the plots on the right are obtained taking the longitudinal development of the shower into account.