The Earth’s Interior: A New Frontier and a New Challenge for Earth Scientists

In this era of space exploration, deep expeditions to the ocean bottom and far viewing telescopes, the Earth's interior has emerged as one of the most challenging frontier areas for scientific investigation. Exploration of the crust, by seismic and other means, is well underway but our view of the underlying mantle and core is fuzzy. Plate tectonic theory has revolutionized Earth Science but we still do not understand the driving mechanism or why global processes change with time. The origins of the magnetic field, volcanism, earthquakes, mineral resources and mountain building processes are related to processes in the deep interior. Planetary exploration has opened up the new science of comparative planetology and yet, the most fundamental questions regarding the origin, evolution and composition of the Earth are unresolved because of our ignorance of the characteristics of most of our planet, the interior. The time is now ripe to make an integrated study of the Earth as a Planet or, in space age jargon, to undertake a mission to Planet Earth. There are several recent developments which make this timely

Neutrino oscillation probabilities: Sensitivity to parameters

We study in detail the sensitivity of neutrino oscillation probabilities to the fundamental neutrino parameters and their possible determination through experiments. The first part of the paper is devoted to the broad theme of isolating regions in the neutrino (and anti-neutrino) energy and propagation length that are sensitive to the oscillation parameters. Such a study is relevant to neutrinos both from the Earth's atmosphere or from a neutrino factory. For completeness we discuss the sensitivity, however small, to the parameters involved in a three-generation framework, and to the Earth matter density profile. We then study processes relevant to atmospheric neutrinos which are sensitive to and allow precision measurements of the mixing angle theta_23 and mass-squared difference delta_32 apart from the mixing angle theta_13. Crucial to this analysis is charge identification; detectors having this capability can isolate these matter effects. In particular, we address the issue of using matter effects to determine whether the mixing angle theta_23 is maximal, and, if not, to explore how well its octant can be determined. When realistic detector resolutions are included, we find that deviations of about 15% (20%) from a maximal value of sin^2 theta_23=1/2 can be measured at 95% (99%) CL provided theta_13 is non-zero, sin^2 theta_13 >= 0.015, and the neutrino mass ordering is normal, with fairly large exposures of 1000 kton-years.Comment: 37 pages Latex file, 30 eps figure files; minor typos fixe

Core-mantle boundary deformations and J2 variations resulting from the 2004 Sumatra earthquake

The deformation at the core-mantle boundary produced by the 2004 Sumatra earthquake is investigated by means of a semi-analytic theoretical model of global coseismic and postseismic deformation, predicting a millimetric coseismic perturbation over a large portion of the core-mantle boundary. Spectral features of such deformations are analysed and discussed. The time-dependent postseismic evolution of the elliptical part of the gravity field (J2) is also computed for different asthenosphere viscosity models. Our results show that, for asthenospheric viscosities smaller than 10^18 Pa s, the postseismic J2 variation in the next years is expected to leave a detectable signal in geodetic observations.Comment: 14 pages, 8 figures, 1 table. It will appear in Geophysical Journal Internationa

Thermal and electrical conductivity of iron at Earth's core conditions

The Earth acts as a gigantic heat engine driven by decay of radiogenic isotopes and slow cooling, which gives rise to plate tectonics, volcanoes, and mountain building. Another key product is the geomagnetic field, generated in the liquid iron core by a dynamo running on heat released by cooling and freezing to grow the solid inner core, and on chemical convection due to light elements expelled from the liquid on freezing. The power supplied to the geodynamo, measured by the heat-flux across the core-mantle boundary (CMB), places constraints on Earth's evolution. Estimates of CMB heat-flux depend on properties of iron mixtures under the extreme pressure and temperature conditions in the core, most critically on the thermal and electrical conductivities. These quantities remain poorly known because of inherent difficulties in experimentation and theory. Here we use density functional theory to compute these conductivities in liquid iron mixtures at core conditions from first principles- the first directly computed values that do not rely on estimates based on extrapolations. The mixtures of Fe, O, S, and Si are taken from earlier work and fit the seismologically-determined core density and inner-core boundary density jump. We find both conductivities to be 2-3 times higher than estimates in current use. The changes are so large that core thermal histories and power requirements must be reassessed. New estimates of adiabatic heat-flux give 15-16 TW at the CMB, higher than present estimates of CMB heat-flux based on mantle convection; the top of the core must be thermally stratified and any convection in the upper core driven by chemical convection against the adverse thermal buoyancy or lateral variations in CMB heat flow. Power for the geodynamo is greatly restricted and future models of mantle evolution must incorporate a high CMB heat-flux and explain recent formation of the inner core.Comment: 11 pages including supplementary information, two figures. Scheduled to appear in Nature, April 201

Iron under Earth's core conditions: Liquid-state thermodynamics and high-pressure melting curve

{\em Ab initio} techniques based on density functional theory in the projector-augmented-wave implementation are used to calculate the free energy and a range of other thermodynamic properties of liquid iron at high pressures and temperatures relevant to the Earth's core. The {\em ab initio} free energy is obtained by using thermodynamic integration to calculate the change of free energy on going from a simple reference system to the {\em ab initio} system, with thermal averages computed by {\em ab initio} molecular dynamics simulation. The reference system consists of the inverse-power pair-potential model used in previous work. The liquid-state free energy is combined with the free energy of hexagonal close packed Fe calculated earlier using identical {\em ab initio} techniques to obtain the melting curve and volume and entropy of melting. Comparisons of the calculated melting properties with experimental measurement and with other recent {\em ab initio} predictions are presented. Experiment-theory comparisons are also presented for the pressures at which the solid and liquid Hugoniot curves cross the melting line, and the sound speed and Gr\"{u}neisen parameter along the Hugoniot. Additional comparisons are made with a commonly used equation of state for high-pressure/high-temperature Fe based on experimental data.Comment: 16 pages including 6 figures and 5 table

More Straightforward Extraction of the Fundamental Lepton Mixing Parameters from Long-Baseline Neutrino Oscillations

We point out the simple reversibility between the fundamental neutrino mixing parameters in vacuum and their effective counterparts in matter. The former can therefore be expressed in terms of the latter, allowing more straightforward extraction of the genuine lepton mixing quantities from a variety of long-baseline neutrino oscillation experiments. In addition to the parametrization-independent results, we present the formulas based on the standard parametrization of the lepton flavor mixing matrix and give a typical numerical illustration.Comment: RevTex 10 pages. Minor changes. Phys. Rev. D in printin

Breaking Eight-fold Degeneracies in Neutrino CP Violation, Mixing, and Mass Hierarchy

We identify three independent two-fold parameter degeneracies (\delta, \theta_{13}), sgn(\delta m^2_{31}) and (\theta_{23}, \pi/2-\theta_{23}) inherent in the usual three-neutrino analysis of long-baseline neutrino experiments, which can lead to as much as an eight-fold degeneracy in the determination of the oscillation parameters. We discuss the implications these degeneracies have for detecting CP violation and present criteria for breaking them. A superbeam facility with a baseline at least as long as the distance between Fermilab and Homestake (1290 km) and a narrow band beam with energy tuned so that the measurements are performed at the first oscillation peak can resolve all the ambiguities other than the (\theta_{23}, \pi/2-\theta_{23}) ambiguity (which can be resolved at a neutrino factory) and a residual (\delta, \pi-\delta) ambiguity. However, whether or not CP violation occurs in the neutrino sector can be ascertained independently of the latter two ambiguities. The (\delta,\pi-\delta) ambiguity can be eliminated by performing a second measurement to which only the \cos\delta terms contribute. The hierarchy of mass eigenstates can be determined at other oscillation peaks only in the most optimistic conditions, making it necessary to use the first oscillation maximum. We show that the degeneracies may severely compromise the ability of the proposed SuperJHF-HyperKamiokande experiment to establish CP violation. In our calculations we use approximate analytic expressions for oscillation probabilitites that agree with numerical solutions with a realistic Earth density profile.Comment: Revtex (singlespaced), 35 pages, 15 postscript figures, uses psfig.st

A Study of the Day - Night Effect for the Super - Kamiokande Detector: I. Time Averaged Solar Neutrino Survival Probability

This is the first of two articles aimed at providing comprehensive predictions for the day-night (D-N) effect for the Super-Kamiokande detector in the case of the MSW \nu_e \to \numt transition solution of the solar neutrino problem. The one-year averaged probability of survival of the solar \nue crossing the Earth mantle, the core, the inner 2/3 of the core, and the (core + mantle) is calculated with high precision (better than 1%) using the elliptical orbit approximation (EOA) to describe the Earth motion around the Sun. Results for the survival probability in the indicated cases are obtained for a large set of values of the MSW transition parameters $\Delta m^2$ and $sin^22\theta_{V}$ from the ``conservative'' regions of the MSW solution, derived by taking into account possible relatively large uncertainties in the values of the $^{8}$B and $^{7}$Be neutrino fluxes. Our results show that the one-year averaged D-N asymmetry in the $\nu_e$ survival probability for neutrinos crossing the Earth core can be, in the case of $sin^22 \theta_{V} \leq 0.13$, larger than the asymmetry in the probability for (only mantle crossing + core crossing) neutrinos by a factor of up to six. The enhancement is larger in the case of neutrinos crossing the inner 2/3 of the core. This indicates that the Super-Kamiokande experiment might be able to test the $sin^22\theta_{V} \leq 0.01$ region of the MSW solution of the solar neutrino problem by performing selective D-N asymmetry measurements.Comment: LaTeX2e - 18 Text Pages + 21 figures = 39 Pages. - Figures in PS + text file sk1b14.tex requires two auxiliary files (included

Neutrino oscillation parameters from MINOS, ICARUS and OPERA combined

We perform a detailed analysis of the capabilities of the MINOS, ICARUS and OPERA experiments to measure neutrino oscillation parameters at the atmospheric scale with their data taken separately and in combination. MINOS will determine $\Delta m^2_{32}$ and $\sin^2 2\theta_{23}$ to within 10% at the 99% C.L. with 10 kton-years of data. While no one experiment will determine $\sin^2 2\theta_{13}$ with much precision, if its value lies in the combined sensitivity region of the three experiments, it will be possible to place a lower bound of O(0.01) at the 95% C.L. on this parameter by combining the data from the three experiments. The same bound can be placed with a combination of MINOS and ICARUS data alone.Comment: Version to appear in PR

Mass hierarchy discrimination with atmospheric neutrinos in large volume ice/water Cherenkov detectors

Large mass ice/water Cherenkov experiments, optimized to detect low energy (1-20 GeV) atmospheric neutrinos, have the potential to discriminate between normal and inverted neutrino mass hierarchies. The sensitivity depends on several model and detector parameters, such as the neutrino flux profile and normalization, the Earth density profile, the oscillation parameter uncertainties, and the detector effective mass and resolution. A proper evaluation of the mass hierarchy discrimination power requires a robust statistical approach. In this work, the Toy Monte Carlo, based on an extended unbinned likelihood ratio test statistic, was used. The effect of each model and detector parameter, as well as the required detector exposure, was then studied. While uncertainties on the Earth density and atmospheric neutrino flux profiles were found to have a minor impact on the mass hierarchy discrimination, the flux normalization, as well as some of the oscillation parameter (\Delta m^2_{31}, \theta_{13}, \theta_{23}, and \delta_{CP}) uncertainties and correlations resulted critical. Finally, the minimum required detector exposure, the optimization of the low energy threshold, and the detector resolutions were also investigated.Comment: 23 pages, 16 figure