N EUTRINO O SCILLATION W ORKSHOP Conca Specchiulla 9-16 Sept. 2006

1. NEUTRINOOSCILLATIONWORKSHOPConca Specchiulla 9-16 Sept. 2006 Geo-Neutrino: Theoretical Aspects Anna Maria Rotunno Dip. Di Fisica & Sez. INFN di Bari Based on: G.L. Fogli, E. Lisi, A. Palazzo, A.M. Rotunno, GeoNeutrinos: an approach to their uncertainties and correlations, to appear in Earth, Moon and Planets; & long preprint in preparation (2006)

2. Purpose of this Work Geo-Neutrinos emitted by heat producing elements (U, Th, K) can probe Earth interior. Their fluxes present large and correlated uncertainties. Handling them is difficult but necessary, if we want to quantify how future data can reduce errors. - We propose an approach in terms of covariance matrices. - We briefly discuss the construction of a tentative Geo-Neutrino Source Model (GNSM) describing U, Th, K abundances in Earth reservoirs. - We show predictions about several experiments (“forward approach”) and how future data can constrain the error matrix of the model (“backward approach”). • Contents • Introduction to Geo-Neutrinos • The Geo-Neutrino Source Model (GNSM) • Covariance and Correlation • Forward Analysis • Backward Analysis • Conclusions and Prospects

3. Introduction to Geo-Neutrinos

4. What do we know about Earth Interior? T = 4000 ºC T = 1500 ºC T = 3700 ºC T = 4300 ºC Fe-Ni, Si, S, O, H, etc. (Mg, Fe, Al) (Al,Si)O2 pervoskite CaSiO2 pervoskite, (Fe,Mg)O • Seismology: based on sound velocity • measurement from seismic data • - reconstructs density profile • throughout the Earth • - infers crust-mantle-core layer • structure • GeoChemistry: based • on direct sampling - gives direct information on chemical composition of crust and upper part of mantle - does not reach deep Earth

5. The mantle convects even though it is “solid”. • - Main issue today: Whole or layered mantle convection?

6. - Earth’s Global Heat: - 30 – 45 TW: not well constrained due to scarce oceanic sampling and model dependence - probably 40 – 60% has radiogenic origin: mainly from decays of 238U, 232Th, 40K (trace elements) inside crust and mantle Geo-Neutrinos from radioactive decays of 238U, 232Th, 40K trace elements in crust and mantle of Earth 238U series 232Th series 40K counts/MeV/parent • bring to surface information about: • the whole planet • its radioactive contents • energetics and thermal history anti-neutrino energy E (MeV) Where are radioactive elements located?

7. “Standard Model” of Earth Global Composition in Trace Elements 4.5 GY ago Original Earth global composition similar to Carbonaceous Chondrites (CI) Oldest meteorites ≡undifferentiated rock and metal mixture • Escape of volatile elements (e.g. K) • Crust/Mantle(Upper/Lower Mantle) • Differentiation • Refractory Lithophile elements • (e.g. U, Th) differently distributed • in crust and mantle Low (<1200 K) condensation temperature Planetary Evolution: High (>1400 K) condensation temperature Preferentially embedded in rocks rather than iron Today’s Earth composition is not CI ! i.e. before crust/mantle differentiation - “primitive mantle” - present crust+mantle system Bulk Silicate Earth (BSE) Model describes assumes -Earth Refractory Elements in chondritic proportions - U, Th, K absent in the Earth core Th/U abundance ratio is 3.9 Constraints: Direct sampling (crust & upper mantle) & Neutrino Geophysics (in the future)

8. A recent new field in Neutrino Physics: Geo-Neutrino detection by Liquid Scintillator Sea of Japan KamLAND 2005:first Geo–ne observation at KamLAND KamLAND Coll., Nature 436,499 (2005) JapanTrench • Some Important Facts: • Observable Geo-ne events: from U, Th decay only • - ne from K decay below threshold for detection • - FTh(ne) & FU(ne) in KamLAND weighted by 1/L2 • U, Th, K more abundant in the crust than in the mantle • - Assumptions on the relative Th, U (and K) abundances • needto be explicitly reported • - Earth science constraints • - Uncertainty evaluation Th/U = 3.8 our reanalysis of Kamland data In this context we illustrate our approach to uncertainties and correlations

9. Question 1: What do we really know about U, Th, K abundances? Question 2: What do we expect to know from geo- data? Usually advertised Goal: measure the Earth Radiogenic Heat But…. … based on future U and Th geo- flux measurements, we might say something more (e.g., about mantle convection) We report about a systematic approach to include U, Th and K abundance uncertainties and correlations in reservoirs (“Geo-Neutrino Source Model”)

10. The Geo-Neutrino Source Model (GNSM)

11. GNSM Structural Details • Purpose: to incorporate the best available knowledge of U, Th and K distributions inside Earth. • Our GNSM geometry is based on: • PREM model (Dziewonsky & Anderson, 1981): spherical symmetry of Earth below crust • CRUST 2.0 model (G. Laske et al., 2001): crustal characterization on a 2° 2° grid. Global reservoirs: • - core • lower mantle • - upper mantle • continental crust • oceanic crust Local reservoirs: lower/middle/upper crust around detector sites that are: - Japan (KamLAND) 13 crustal tiles - Hawaii - BOREXINO - SNO - LENA 9 crustal tiles Local composition may be ≠ from global composition (in terms of U, Th, K)

12. GNSM geochemical details: {aiS}i=1,…N (S=U,Th,K) a = {ai}i=1,…3N , N = number of reservoirs set of abundances (i.e. abundance vector) of reservoirs, ai: ai = ai± iand [2]ij = ij i j where ai = central value, 2 = covariance matrix,  = error correlation matrix. • Entries for the above equations: • BSE Model:gives global constraints on elemental abundances (“mass balance constraints”) • Vertical crust structure:relevant within local reservoirs • Missing informationis supplied by educated guesses, whenever possible, or arbitrary • but explicit assumptions, when unavoidable • “local” abundance fluctuationsassumed to be decoupled from “global” abundance • uncertainties For abundance values and references, we refer to G.L. Fogli, E. Lisi, A. Palazzo, GeoNeutrinos: an approach to their uncertainties and correlations, to appear in Earth, Moon and Planets

13. An example: U, Th, K uncertainties and correlations in BSE • For Uranium, Thorium: • aBSE/aCI expected to be the same for all Refractory Lithophile • Elements not volatilized during Earth formation • (e.g. U, Th, Al) • - Benchmark: Alluminium more abundant than trace elements U, Th We obtain: aThBSE = aThCI (aAlBSE/aAlCI) aUBSE = aUCI (aAlBSE/aAlCI) U,ThBSE= 0.936 (U,Th) correlation • Sources: • CI meteoritic data (1988-2003) • recent BSE models: McDonough & Sun (1995) • Allegre et al. (2001) • Palme & O’Neill (2003) • relative U & Th abundances in CI from • Ref. Rochall & Jochum (1993), Goreva & Burnett (2001) • For Potassium: • K not constrained by meteorites, because moderately volatile • we conservatively increase the K/U ratio error usually quoted in the geochemical literature • (Ref.Jochum et al, 1983) because unrealistic We obtain aKBSE ,K,ThBSE = 0.648 & K,UBSE = 0.701 Similarly, we survey all the available literature for upper mantle (UM), continental crust (CC) and oceanic crust (OC) to estimate abundances (central values), errors and correlation

14. Lower Mantle (LM) not accessible! Derived by mass balance constraints Qualifying result of our work - LM abundance obtained by subtraction: LM = BSE–UM–CC–OC - Derivation of errors (by propagation) and correlations Structure of correlation matrix of abundance OC CC UM LM CC = continental crust OC = oceanic crust UM = upper mantle LM = lower mantle (core is excluded) OC CC UM LM Global Reservoirs (correlated) U Th K U Th K i-th reservoir ≡ Local Reservoirs (uncorrelated) “local” fluctuations have nothing to do with “global” estimates LM abundances anti-correlated with the other reservoirs because of subtraction

15. Numerical Results Geo-Neutrino Source Model (GNSM): Abundances, errors and correlations of radiogenic elements (U, Th, K) in global reservoirs Geo-Neutrino Source Model for Global Reservoirs BSE CC OC UM LM Reser. Elem. Abund.± 1 U Th K U Th K U Th K U Th K U Th K BSE CC OC UM LM NEW Similar to previous work by Enomoto et al., Fiorentini et al. Qualifying result of our work allows well-defined statistical analyses

16. Covariance approach relevant for GeoNeutrino physics because: - All relevant observables and constraints can be expressed as linear functions of such abundances (with known coefficients) - (U,Th,K) abundances within a given reservoir are typically positively correlated - (U,Th,K) correlations among different reservoirs can take any value > 0 local abundances ij < 0 complementary reservoirs ~ 0 decoupled reservoirs - Measured Geo-Neutrino event rates (RU, RTh) are anticorrelated our reanalysis of Kamland data Solid line: KamLAND data fit Dashed line: Adapted Gaussian RU = 12.5 ± 48.9 TNU RTh = 34.7 ± 28.5 TNU (U,Th) = - 0.645 RTh (TNU) Negative correlation due to experimental sensitivity to RU +RTh rather than RU and RTh separately RU (TNU) 1 TNU = 1 event/year/1032 protons

17. Forward Analysis: Event Rates at KamLAND Dashed Line: KamLAND data RU = 12.5±48.9 TNU RTh = 34.7±28.5 TNU (U,Th) = -0.645 Solid Line: GNSM RU = 24.9±2.0 TNU RTh = 6.7±0.5 TNU (U,Th) = 0.901 - GNSM compatible with data at 1. - Data do not constrain model yet. - Background reduction and much higher statistics required. Th/U = 3.8

18. Forward Analysis: Total Event Rates (including oscillations) with errors and correlations at various detector sites Site Rate ± 1 Correlation Matrix of GNSM predictions (TNU) all positively correlated (they measure in part the same flux)

19. Forward Analysis: Total Radiogenic Heat vs Total Event Rate at KamLAND GNSM RU+Th = 31.6 ± 2.5 TNU HU+Th+K = 21.1 ± 3.0 TW (R,H) = +0.858 The ellipse selects the allowed band of total radiogenic heat around GNSM prediction

20. Mantle Convection Problem: still debated today Two extremes: 1) homogeneous mantle: whole mantle convection, i.e. aLM= aUM 2) two-layered model: geochemically decoupled UM and LM LM with primitive abundances aLM= aBSE Within 3: - aLM aUM (left panel) whole mantle convection - aLM aBSE (right panel) two-layered mantle model 1, 2, 3  GNSM two-layered homogeneous GNSM GNSM central values: aUM < aLM < aBSE partial mantle convection The two extreme cases are recovered at ± 3 in our GNSM

21. Backward Analysis:Hypothetical future Results about Mantle Convection In an optimistic future scenario with: - 6 detectors operative - U, Th event separate collection for 20 kton years - no background - no systematics + DATA In principle, it might allow to reject at >> 3 the case aLM = aUM (global mantle convection). partial convection preferred Really relevant result in geophysics and geochemistry More realistic (or less optimistic) simulations of prospective data need to be performed.

22. We expect that a network of detectors in different points of the Earth’s continental and oceanic crust would be useful to:- REDUCE THE EXPERIMENTAL ERROR;- CONSTRAIN THE GNSM PARADIGM NEW EXPERIMENTS in sites with both LOWER & HIGHER FLUX - BOREXINO - LENA - Sudbury - Hawaii - Baksan We are currently studying the synergy of a world detector network from a quantitative viewpoint.

23. Conclusions and Prospects • We have presented a tentative Geo-Neutrino Source Model (GNSM) embedding a full error • matrix for the (U, Th, K) abundances in relevant local and global reservoirs. It is based on • published data (when available) and on supplementary assumptions (when needed). • Covariance analysis may provide a useful template for current and future studies. • Applications of our approach have been given in terms of predictions for future • experiments (forward propagations of errors) and of GNSM error reduction through • prospective data (backward update). • We are still far from a satisfactory approach of this kind in (U, Th, K) geochemistry, • due to intrinsic difficulties (large uncertainties, incomplete data, sometimes conflicting • estimates, ecc.) • Interdisciplinary studies of more refined geochemical and geophysical Earth models • and of future possible observations of Geo-Neutrino signals will be beneficial to • Earth sciences.