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. Heretofore, 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 offering a direct measure of the radioactive Earth, both (1) revealing the Earth’s inner structure as probed by radionuclides, and (2) allowing for 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 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 downward vertical. We note that a measurement of the neutrino intensity in peripheral directions leads to a strong lower limit to the central intensity. We also note that there is some controversy about the abundance of potassium in the Earth’s core; different geophysical predictions lead to strongly varying, and hence distinguishable, central intensities (θ <∼ 30 from the downward vertical). Other uncertainties in the models, and prospects for observation of the geoneutrino angular distribution, are briefly discussed. We conclude by urging the development and construction of antineutrino experiments with angular sensitivity. ‡ [email protected] ∗ [email protected]