Radial Earth Density Profile by Neutrino Mapping

C. Kuo, H. Crawford, R. Jeanloz, B. Romanowicz, G. Shapiro, M.L. Stevenson


The recent discovery of a number of very high-energy extra-galactic gamma-ray sources, and the current installation of neutrino detectors on the Earth ( Antarctic Muon And Neutrino Detector Array (AMANDA), NEutrinos from Supernovae and Tev sources, Ocean Range (NESTOR), Neutrino Telescope, Lake Baikal, Siberia (NT)) reopens the case for imaging the density structure of the Earth using neutrinos. Determining the density profile of the Earth in such a manner would complement and refine the seismological constraints on the Earth's radial density profile. This possibility had previously been imagined (DeRujula 1981, Wilson 1984, Nicolaidis 1991) but rapidly abandoned for lack of appropriate geometries using artificial, accelerator-based neutrino sources. High-energy astrophysical gamma-ray sources, on the other hand, are now believed to also emit neutrinos, and would contribute to an advantageous neutrino source-receiver configuration. By measuring the attenuation of the neutrino flux, originating from the astrophysical sources, then passing through the Earth, constraints on the radial density structure of the planet can be obtained. More than one neutrino source are expected to be observed. Obtaining further details on the 3D density structure would be possible, depending on the observation of adequate numbers of neutrinos at several detectors placed around the world.

Geophysics, the physics of the Earth, covers a wide variety of topics concerning the Earth system, in regions spanning from the interior to the magnetosphere. In investigations of the deep interior, it would be impossible to be physically extract samples from the deep interior--the deepest drilled hole is only two one-thousandths of the radius of the Earth. The composition of the minerals at depth is of great interest; dynamic processes occurring in the interior give rise to the variation of compounds and mixtures at depth. The density of minerals is a quality which could help identify them. Lateral deviations in density from equilibrium drives geodynamics--mantle material flows to reach states of equilibrium. Mantle convection is believed to be the driving force of plate tectonics, manifested on the surface of the Earth by earthquakes, volcanic activity, and mountain ranges, etc. The deep structure of the Earth must be inferred from non-evasive density imaging techniques conducted at the Earth's surface.

Studies of the normal modes of the Earth, complemented by studies of propagation of body waves, have until now been the primary source of constraints on the density profile of the Earth. Although current reference models, such as the Preliminary Reference Earth Model (Dziewonski and Anderson 1981), represent good first approximations, a number of uncertainties still remain, in particular concerning density jumps at the major structural boundaries, for example, at the core-mantle boundary or at the inner core-outer core boundary. This is due to the fact that seismic wave velocities are dependent not only on the density but also on the elastic properties of the medium, the effect of the latter being dominant. In contrast, density is the only material property to which neutrino absorption is sensitive. The neutrino method could measure the density directly, whereas measurements based on seismology depends on inferred elastic properties as well. The possibility of imaging the boundaries of density contrast using absorption of extraterrestrial neutrinos by the Earth is imminent and would provide an independent complement to profiles indirectly obtained from seismological data. High-energy neutrinos are already being sought by physicists in the astrophysics community. With the installation of high-energy neutrino detector arrays built for astrophysical research, and the recent discovery of a number of very high-energy gamma-ray sources in the celestial sky, the potential to image the Earth from observing neutrino absorption looks promising. Natural neutrino sources, such as astrophysical bodies, which could provide a number of neutrino paths through the Earth, had been considered previously, but until recently, these neutrino sources were not believed to generate neutrinos of sufficient energies for this purpose (Wilson 1984). High-energy gamma-ray sources are sought as neutrino sources of equivalent energies because the gamma rays are believed to be products of hadronic collisions, from which neutrinos also are emitted as daughter products. By using these very high-energy gamma-ray sources as neutrino sources and acquiring data from various neutrino detectors placed around the world, the location of radial density boundaries may be extricated directly by measuring the attenuation of the extraterrestrial neutrino flux by the Earth. The detail to which the imaging can be resolved will be dependent upon the number of neutrinos detected.

The absorption of high-energy extraterrestrial neutrinos by the Earth will be used in this technique to image the Earth's density profile. The attenuated flux of neutrinos passing through certain regions of the Earth will be compared to the unattenuated flux of neutrinos reaching the detector unobstructed. A muon-neutrino is absorbed by the Earth when it interacts with a nucleon N by charged-current interaction and changes into a muon : . Since the neutrino-nucleon scattering cross section (probability of neutrino interaction with a nucleon) rises with energy, the cross section is sufficiently high for neutrinos of TeV ( electron Volts) energies to be absorbed by the Earth. The much lower energy solar or supernovae neutrinos, which are in the electron Volt energy range, tend to pass through the Earth without being stopped.

The pertinent interaction in the neutrino 'absorption' is one in which a neutrino changes into a muon via charged current weak interaction: . Since this interaction involves quarks, the neutrino absorption is dependent on the integrated nucleon number density along the chord of the neutrino's path or, in other words, the integrated atomic mass density along the chord. The coefficient of neutrino absorption by the Earth is defined as the product of the neutrino-nucleon scattering cross section and the integrated nucleon number density n: (Wilson 1984) where n is the total number of nucleons in a column of unit area through which the neutrino passes. The muon continues along the neutrino trajectory, either eventually loses energy and stops within the Earth, or if it has enough energy, escapes from the solid Earth. The muons escaping the solid Earth and traversing through the effective area of the detector in an 'upward' direction will be detected and interpreted as a neutrino-generated muon.

As a consequence of the Earth's rotation, only one extraterrestrial source and one detector are necessary to obtain a number of neutrino paths through the Earth. The detector is fixed on the surface of the Earth as the Earth rotates, and in the detector's rest frame, the neutrino source will sweep across the detector's celestial sky, intersecting the Earth in a continuous set of chord paths. Assuming spherical symmetry of the interior, the Earth's density structure can be unfolded, provided there is appropriate sampling at all depths. The imaging can in principle be increased to three dimensions if more sources at different declinations are found, and if more than one detector is used. The detection of neutrinos from a diffuse spectrum, in which case neutrinos impinge on the Earth isotropically, would provide the required source geometry for three-dimensional imaging.

If the attenuation of neutrinos is measured over a continuous range of paths through the Earth, and if the density is assumed to be spherically symmetric, then the density as a function of radius is uniquely determined by the measurements. The ability to measure the radial distribution of density in the Earth by neutrino absorption may soon be possible with the recent discoveries of high-energy gamma-ray sources which are potential neutrino emitters, and the installation of several detectors built for astrophysical research.

References

DeRujula, A., et al, Physics Reports , 99, 341 (1983).
Dziewonski, A.M. and D.L. Anderson, Physics of the Earth and Planetary Interiors, 25, 297 (1981).
Nicolaidis, A., Physics Letters B, 200, 553 (1988).
Wilson, T.L., Nature, 309, 38 (1984).