Imaging the earth's interior: The angular distribution of terrestrial neutrinos

Decays of radionuclides throughout the earth's interior produce geothermal heat, but also are a source of antineutrinos; these geoneutrinos are now becoming observable in experiments such as KamLAND. The (angle-integrated) geoneutrino flux has been shown to provide a unique probe of geothermal heating due to decays, and an integral constraint on the distribution of radionuclides in the earth. In this paper, we calculate the angular distribution of geoneutrinos, which opens a window on the differential radial distribution of terrestrial radionuclides. We develop the general formalism for the neutrino angular distribution. We also present the inverse transformation which recovers the terrestrial radioisotope distribution given a measurement of the neutrino angular distribution. Thus, geoneutrinos not only allow a means to image the earth's interior, but offer a direct measure of the radioactive earth, both revealing the earth;s inner structure as probed by radionuclides, and allowing a complete determination of the radioactive heat generation as a function of radius. Turning to specific models, we emphasize the very useful approximation in which the earth is modeled as a series of shells of uniform density. Using this multishell approximation, we present the geoneutrino angular distribution for the favored earth model which has been used to calculate the geoneutrino flux. In this model the neutrino generation is dominated by decays of potassium, uranium, and thorium in the earth's mantle and crust; this leads to a very "peripheral" angular distribution, in which 2/ 3 of the neutrinos come from angles θ 60° away from the nadir. We note that a measurement of the neutrino intensity in peripheral directions leads to a strong lower limit to the central intensity. We briefly discuss the challenges facing experiments to measure the geoneutrino angular distribution. Currently available techniques using inverse beta decay of protons require a (for now) unfeasibly large number of events to recover with confidence the forward scattering signal from the background of subsequent elastic scatterings. Nevertheless, it is our hope that future large experiments, and/or more sensitive techniques, can resolve an image of the earth's radioactive interior.