The probability that a lepton exits the Earth’s surface for emergence angles between 0.1° (Earth skimming) and 50° given a 4-km thick layer of ice with standard cross-sections and energy-loss models. The feature at emergence angle of 2° corresponds to the trajectory tangential to the rock layer beneath the 4-km thick layer of ice.
The exiting lepton energies corresponding to some of the energies shown in Fig. 5. The red line shows the most probable exiting tau lepton energy. The dark (light) gray band shows the 68% (95%) densest probability interval. The features in the curves are caused by regions where various interaction processes dominate. See Fig. 7 and text for details.
The mean number of CC, NC interactions, and tau lepton decays as a function of emergence angle for various incident neutrino energies corresponding to Figs. 5 and 6. Top panel: the mean number of CC interaction must be at least one since we are selecting for particles resulting in a lepton exiting the Earth’s surface. Middle Panel: The mean number of neutral current interactions. The sharp transition at emergence angle corresponds to the direction tangential to the subsurface rock beneath a 4-km thick layer of ice. Bottom panel: the mean number of lepton decays also show a feature at . Note that for the particle traverse ice only while for the particle traverses a combination of rock and ice, which affects the behavior of lepton and interactions.
The probability that a lepton exits Earth’s surface including and excluding the effect of regeneration given a 4-km thick layer of ice and standard neutrino cross-section and tau lepton energy-loss models. Excluding regeneration significantly underestimates the probability of exiting leptons for , where the trajectories propagate through rock rather than pure ice.
The probability that a lepton exits the Earth’s surface for various energies and ice thicknesses, including bare rock, assuming standard cross-section and energy-loss models. From top to bottom, the input neutrino energies are , , , and . A layer of ice is favorable to exiting leptons for neutrino energies while bare rock is favorable for neutrino energies . See text for details.
The probability that a lepton exits the Earth’s surface for various combinations of neutrino cross section and lepton energy-loss models given a 4-km thick ice layer for a injected . Lowering the cross section has the general effect of reducing the lepton exit probability for emergence angles below where the trajectory is tangential to the subsurface rock layer while increasing the probability for larger emergence angles. The ASW energy loss rate model, which is suppressed compared to the more standard ALLM model, results in an overall increase lepton exit probability.
The exiting lepton energies for various models corresponding to Fig. 11. On each panel, the cross-section model and energy loss rate models are labeled on the top left corner. The variance in exiting lepton energies tends to increase as the cross section increases for trajectories that traverse mostly rock. The energy loss model changes the range of emergence angles where the most probable energies plateaus.
The range of cosmogenic neutrino fluxes from Kotera 2010 [3] and the resulting flux of leptons for emergence angles , 5°, and 10° (see Fig. 2). The results use the middle neutrino-nucleon cross-section curve (Fig. 3), ALLM energy loss rate (Fig. 4) and thick ice.
The resulting flux of leptons for a cosmogenic neutrino flux in the middle of the flux ranges from Kotera 2010 [3] (Grey band Fig. 13). The different line colors indicate the interaction history that led to the exiting leptons (see text for more details). We show the effect of a 4-km thick ice layer (solid lines) versus bare rock (dashed lines) for 4 different emergence angles as indicated on the panels. These results are obtained using the middle neutrino-nucleon cross-section curve and ALLM energy loss rate.