Neutrinos from San Marco and Below

Order of magnitude estimates of radiogenic heat and antineutrino production are given, using the San Marco cathedral as an example. Prospects of determining the radiogenic contribution to terrestrial heat by detection of antineutrinos from natural radioactivity (geoneutrinos) are discussed. A three kton scintillator detector in three years can clearly discriminate among different models of terrestrial heat production. In addition, the study of geoneutrinos offers a possibility of improving the determination of neutrino mass and mixing, by exploiting the knowledge of Th/U abundance in the Earth. 1. A few facts about San Marco After the visit of the San Marco cathedral, accompanied by a most interesting historical and artistic overview, nothing should be added but our gratitude to Milla Baldo Ceolin for organizing this most interesting and timely conference and for spicing it with exceptional events. Physicists however are tenacious, and we cannot resist adding a few additional information, some of these a touristic guide will never tell you. First of all, San Marco contains radioactive materials. The cathedral mass being in the range of 100 kton , we expect it contains about 100 kg of Uranium, as the typical Uranium abundance in rocks is in the range of one part per million, however with large variations. We also expect some 400 kg of Thorium, since almost everywhere in the solar system (meteorites, Moon, Venus and also Earth) the typical abundance ratio is Th/U ≃ 4. In addition, there are about 100 Kg of K, corresponding to the typical ratio K/U ≃ 10 which one finds in Earth rocks and to the natural abundance K/K = 1.2 · 10. San Marco is also a heat source. In fact, each decay chain releases energy over long time scales (e.g. for U ∆ = 52 MeV and τ1/2 = 4.5 Gyr ), the total heat flow being: H = 9.5M(U) + 2.7M(Th) + 3.6M(K) (1) with masses in 100 kg and H in mW. This gives 24 mW for San Marco, really a very weak heat source, although it does not matter in these sunny days. More interesting to people attending this conference, San Marco is an anti-neutrino source. Each decay chain releases antineutrinos together with heat, with a well fixed ratio. (e.g. U → Pb+ 8 He+ 6ν̄ + 52 MeV). The antineutrino luminosity is: L = 7.4M(U) + 1.6M(Th) + 27M(K) (2) where again M is in 100 Kg and L in 10ν̄/s. This gives about 4 · 10ν̄/s for San Marco. Antineutrinos from the progenies of Uranium (Emax = 3.3MeV ) and Thorium (Emax = 2.2MeV ) can be detected by means of inverse beta decay reaction: ν̄ + p → n + e − 1.804MeV (3) At least in principle, the two components can be discriminated, due to the different end points. Unfortunately, antineutrinos from β decay of K are below the threshold for (3), whereas neutrinos from electron capture are obscured by the Sun. The cross section of (3) for 2.5 MeV antineutrinos ( σ ≃ 5 · 10cm) corresponds to an interaction length in water λ = 7 · 10 m. There is plenty of water near the cathedral and San Marco square (S ≃ 10 m) is often covered with Acqua Alta (high water), a 10 cm height corresponding roughly to 1 kton, the size of KamLAND. Should Acqua Alta reach the clock of Torre dell’Orologio, the size of Superkamiokande is reached. With a height of 100m a megaton detector is obtained, the cathedral being now deeply submerged. A pointlike source emitting 10ν̄/s with E=2.5 MeV at the center of a megaton water sphere will produce one event every four years. Also in view of the environmental impact of such a project, better we look at some other direction. 2. The sources of terrestrial heat Earth re-emits in space the radiation coming from the sun (K⊙ = 1.4 kW/m ) adding to it a a tiny flux of heat produced from its interior (Φ ≃ 80mW/m). By integrating this latter over the Earth surface one gets a flow HE = 40TW , the equivalent of some 10 nuclear power plants. The origins of terrestrial heat are not understood in quantitative terms. In 1980 J. Verhoogen concluded a review of terrestrial heat sources by saying 1): “...what emerges from this morass of fragmentary and uncertain data is that radioactivity itself could possibly account for at least 60 per cent if not 100 per cent of the Earth’s heat output. If one adds the greater rate of radiogenic heat production in the past, possible release of gravitational energy (original heat, separation of the core...) tidal friction ... and possible meteoritic impact ... the total supply of energy may seem embarassingly large...”. One can appreciate the complexity of the problem by comparing Sun and Earth energy inventories. In fact, a constant heat flow H can be sustained by an energy source U for an age t provided that U ≥ Ht. For sustaining the sun over an age tsolar = 4.5 · 10 yr, gravitational and chemical energies are short by a factor 10 and 10 respectively and only nuclear energy can succeed, as beautifully demonstrated by Gallium experiments in the nineties. On the other hand, the terrestrial heat can be sustained over geological times by any energy source, be it nuclear, gravitational or chemical. Observational data on the amounts of Uranium, Thorium and Potassium in Earth interior are rather limited, since only the crust and the upper part of the mantle are accessible to geochemical analysis. As U, Th and K are lithofile elements, they accumulate in the continental crust (CC). Estimates for the Uranium mass in the crust are in the range2,3) Mc(U) = (0.2− 0.4)10 kg . (4) Concentrations in the mantle are much smaller, however the total amounts are comparable due to the much larger mass of the mantle. Estimates for the whole mantle are in the range1) Mm(U) = (0.4− 0.8)10 kg . (5) One has to remark, however, that these estimates are much more uncertain than for the crust as they are obtained by: i)collecting data for upper mantle (hu = 600km), ii)extrapolating them to the completely unexplored lower mantle (hl = 3000km). Concerning the abundance ratios, one has generally Th/U ≃ 4, consistent with the meteoritic value. A remarkable exception is the oceanic crust where Th/U ≃ 2, however both U and Th abundances are an order of magnitude smaller with respect to CC, which is also much thicker. Concerning Potassium, generally one finds K/U ≃ 10, 000. Earth looks thus significantly impoverished in Potassium with respect to Carbonaceous Chondrites, and also to other meteorites. This has long been known as the Potassium problem4,5). In fact, elements as heavy as Potassium should not have escaped from a planet as big as Earth. It has been suggested that at high pressure Potassium behaves as a metal and thus it could have been buried in the Earth core, where it could provide the energy source of the terrestrial magnetic field. However, Potassium depletion is also observed in Moon and Venus rocks. The most reasonable assumption is that it volatized in the formation of planetesimals from which Earth has accreted. In conclusion, the determination of the Uranium, Thorium and Potassium in the Earth is an important scientific problem, as it can fix the radiogenic contribution to terrestrial heat production. 3. Antineutrinos from below “If there are more things in heaven and Earth than are dreamt of in our natural philosphy, it is partly because electromagnetic detection alone is inadequate”. With these words in 1984, Krauss, Glashow and Schramm6) proposed a program of antineutrino astronomy and geophysics, which could open vast new windows for exploration above us and below. Now that we understand the fate of neutrinos it is time to tackle the program (including Earth energetics, a detailed study of the solar core, neutrinos from past supernovae...) Determination of the radiogenic contribution to terrestrial heat production is the first step. One can build several models for the radiogenic heat production. Since for any element there is a well fixed ratio heat/(anti)neutrinos each model also provides a prediction for the antineutrino luminosities, the basic equations being (1) and (2), where the same numerical coefficients can be used when masses are in units of 10 kg, powers are in TW and luminosities in 10/s. At this level, everything is fixed in terms of three inputs. The range of plausible models is covered in fig.1, which deserves the following comments: i)In a simple chondritic model one assumes that Earth is obtained by assembling together the same material as we find in these meteorites, without loss of heavy enough elements. The amounts of U , Th and K are determined from their ratio to Si in meteorites, by rescaling to the known abundance of this latter element in the Earth. This simple model easily accounts for 3/4 of HE , mainly supplied from K, however it implies K/U = 7 · 10, a factor seven larger than the value observed in Earth rocks. ii) In the standard model of geochemists, the so called Bulk Silicate Earth (BSE) model, with K/U = 1 · 10, the radiogenic production is about one half of the terrestrial heat flow, being supplied mainly from U and Th. iii) A fully radiogenic model, where the BSE abundances are rescaled imposing by imposing Hrad = 40 TW, is not excluded by observational data. In all models, see fig.2, antineutrino production is dominated by K decays. Th and U anti-neutrino luminosities are in the range (10− 20) · 10/s. By dividing over the earth surface, one gets fluxes of order 10 cms, in the same range as that of solar boron neutrinos. Clearly, in order to estimate fluxes at a specific site one needs assumptions about Figure 1: Contributions to terrestrial heat production (TW), as estimated in different models of Earth interior. CON= chondritic, BSE=bulk silicate Earth, RAD= fully radiogenic. The non radiogenic contribution is indicated as NR. the distribution of the radioactive materials, the total amounts being an insufficient information. In a paper submitted on December 2002 we provided estimates corresponding to different models for several sites7). The numbers of predicted events for Kamland (normalized to an exposure of 0.14 ·10p ·yr, a detection efficiency ǫ = 78% and a survival probability Pee = 0.55) are 3.5, 4 and 6 for the chondritic, BSE and fully radiogenic model respectively. The paper ended with: “The determination of the radiogenic component of terrestrial heat is an important and so far unanswered question.... , the first fruit we can get from neutrinos, and Kamland will get the firstlings very soon”. A few days later the first results from Kamland appeared8), containing a first glimpse of Earth interior in addition to important information on neutrino oscillation. Out of a total of 32 counts, in the prompt energy region below 2.6 MeV, 20 events are associated with antineutrinos from reactors and 3 correspond to the estimated background. The remaining 9 counts are the first indication of geo-neutrinos! Clearly the uncertainty is large, since the expected statistical fluctuations are about √ 32. Within this error, the result is consistent with any model for the radiogenic contribution to terrestrial heat, from 0 to 100 TW. One has to remind that data have been collected in just six months and that significant accumulation can be achieved Figure 2: Neutrino luminosity. Antineutrinos production rates from U, Th and K according to different models of Earth interior. In the last column neutrinos from e.c. of K are shown. Units are 10s.