N EUTRINO O SCILLATION W ORKSHOP Conca Specchiulla 9-16 Sept. 2006 Anna Maria Rotunno Dip. Di Fisica & Sez. INFN di Bari Geo-Neutrino: Theoretical Aspects.

NEUTRINO OSCILLATION WORKSHOP

Conca Specchiulla 9-16 Sept. 2006

Anna Maria Rotunno

Dip. Di Fisica & Sez. INFN di Bari

Geo-Neutrino: Theoretical Aspects

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)

Contents

- Introduction to Geo-Neutrinos

- The Geo-Neutrino Source Model (GNSM)

- Covariance and Correlation

- Forward Analysis

- Backward Analysis

- Conclusions and Prospects

Purpose of this Work

- We show predictions about several experiments (“forward approach”) and how future data can constrain the error matrix of the model (“backward approach”).

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.

Introduction to Geo-Neutrinos

T = 1500 ºC

(Mg, Fe, Al)(Al,Si)O2 pervoskiteCaSiO2 pervoskite,

(Fe,Mg)O

Fe-Ni, Si, S, O, H,

etc.

T = 4300 ºC

T = 3700 ºC

T = 4000 ºC

What do we know about Earth Interior?

-Seismology: based on sound velocity measurement from seismic data - reconstructs density profile throughout the Earth - infers crust-mantle-core layer structure - does not reach deep Earth

-GeoChemistry: based on direct sampling - gives direct information on chemical composition of crust and upper part of mantle

-The mantle convects even though it is “solid”.

- Main issue today: Whole or layered mantle convection?

- 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

bring to surface information about:- the whole planet- its radioactive contents- energetics and thermal history

Where are radioactive elements located?

anti-neutrino energy E (MeV)

238U series232Th series 40K

coun

ts/M

eV/p

aren

t

“Standard Model” of Earth Global Composition in Trace Elements

Original Earth global composition similar to Carbonaceous Chondrites (CI)

- 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

Oldest meteorites ≡ undifferentiated rock and metal mixture

Today’s Earth composition is not CI !

Planetary Evolution:

Low (<1200 K) condensation temperature

High (>1400 K) condensationtemperature

Preferentially embedded in rocks

rather than iron

Bulk Silicate Earth (BSE) Model

Th/U abundance ratio is 3.9

i.e. before crust/mantle differentiation

- “primitive mantle” - present crust+mantle system

describes

- Earth Refractory Elements in chondritic proportions - U, Th, K absent in the Earth core

assumes

Constraints: Direct sampling (crust & upper mantle) & Neutrino Geophysics (in the future)

4.5 GY ago

A recent new field in Neutrino Physics: Geo-Neutrino detection by Liquid Scintillator

2005: first Geo–e observation at KamLAND

KamLAND Coll., Nature 436,499 (2005)

Some Important Facts:

- Observable Geo-e events: from U, Th decay only

- e from K decay below threshold for detection

- Th(e) & U(e) 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 need to be explicitly reported

- Earth science constraints

- Uncertainty evaluation

Sea of Japan

JapanTrench

KamLAND

our reanalysis of Kamland data

In this context we illustrate our approach to uncertainties and correlations

Th/U = 3.8

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”)

The Geo-Neutrino Source Model (GNSM)

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:

around detector sites that are:

- Japan (KamLAND) 13 crustal tiles

- Hawaii

- BOREXINO

- SNO

- LENA

9 crustal tiles

GNSM Structural Details

- core- lower mantle

- upper mantle- continental crust- oceanic crust

Local reservoirs: lower/middle/upper crust

Local composition may be ≠ from global composition(in terms of U, Th, K)

{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 ± i and [2]ij = ij i j

where ai = central value, 2 = covariance matrix, = error correlation matrix.

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

Entries for the above equations:

-BSE Model: gives global constraints on elemental abundances (“mass balance constraints”)

-Vertical crust structure: relevant within local reservoirs

-Missing information is supplied by educated guesses, whenever possible, or arbitrary but explicit assumptions, when unavoidable

-“local” abundance fluctuations assumed to be decoupled from “global” abundance uncertainties

GNSM geochemical details:

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 = aTh

CI (aAlBSE/aAl

CI)

aUBSE = aU

CI (aAlBSE/aAl

CI)

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,Th

BSE = 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

- LM abundance obtained by subtraction: LM = BSE–UM–CC–OC

- Derivation of errors (by propagation) and correlations Qualifying result

of our work

Global Reservoirs

(correlated)

OC CC UM LM

OC

CC

UM

LM

CC = continental crustOC = oceanic crustUM = upper mantleLM = lower mantle

(core is excluded)

Local Reservoirs(uncorrelated)

i-threservoir

U Th K

U

Th

K

≡

LM abundances anti-correlated with the other reservoirs because of subtraction

Structure of correlation matrix of abundance

Lower Mantle (LM) not accessible! Derived by mass balance constraints

“local” fluctuations have nothing to do with“global” estimates

Geo-Neutrino Source Model for Global Reservoirs BSE CC OC UM LM

U 21.9×10-9 ± 14 % 1 + .936 + .701 0 0 0 0 0 0 0 0 0 + .908 + .893 + .690

Th 82.1×10-9 ± 14 % 1 + .648 0 0 0 0 0 0 0 0 0 + .850 + .954 + .638

K 26.3×10-5 ± 21 % 1 0 0 0 0 0 0 0 0 0 + .636 + .618 + .985

U 1.46×10-6 ± 17 % 1 + .906 + .906 0 0 0 0 0 0 - .409 - .263 - .146

Th 6.29×10-6 ± 10 % 1 + .595 0 0 0 0 0 0 - .371 - .291 - .096

K 1.62×10-2 ± 10 % 1 0 0 0 0 0 0 - .371 - .173 - .161

U 1.00×10-7 ± 30 % 1 + .906 + .868 0 0 0 - . 012 - .007 - .007

Th 2.20×10-7 ± 30 % 1 + .764 0 0 0 - .011 - .001 - .006

K 1.25×10-3 ± 28 % 1 0 0 0 - .010 - .006 - .008

U 3.95×10-9 ± 30 % 1 + .906 + .868 - .093 - .065 - .058

Th 10.8×10-9 ± 30 % 1 + .764 - .084 - .071 - .051

K 5.02×10-5 ± 28 % 1 - .081 - .054 - .066

U 17.3×10-9 ± 30 % 1 + .924 + .692

Th 60.4×10-9 ± 30 % 1 + .640

K 21.7×10-5 ± 28 % 1

Reser. Elem. Abund. ± 1 U Th K U Th K U Th K U Th K U Th K

BSE

CC

OC

UM

LM

Geo-Neutrino Source Model (GNSM): Abundances, errors and correlations of radiogenic elements(U, Th, K) in global reservoirs

Qualifying result of our workNEW

Similar to previous work by

Enomoto et al., Fiorentini et al.

Numerical Results

allows well-defined statistical analyses

- 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

RT

h (T

NU

)

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

1 TNU = 1 event/year/1032 protons

RU (TNU)

our reanalysis of Kamland data

Negative correlation due to experimental sensitivity to RU +RTh rather than RU and RTh separately

Covariance approach relevant for GeoNeutrino physics because:

Forward Analysis: Event Rates at KamLAND

- GNSM compatible with data at 1.

- Data do not constrain model yet.

- Background reduction and much higher statistics required.

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

Th/U = 3.8

Kamioka Gran Sasso Sudbury Phyasalmi Baksan Hawaii

Kamioka 31.6 ± 2.5 1.00 0.72 0.65 0.63 0.62 0.83

Gran Sasso 40.6 ± 2.9 1.00 0.71 0.73 0.70 0.64

Sudbury 47.9 ± 3.2 1.00 0.69 0.65 0.55

Pyhasalmi 49.9 ± 3.5 1.00 0.69 0.48

Baksan 50.7 ± 3.4 1.00 0.51

Hawaii 13.4 ± 2.2 1.00

Site Rate ± 1 Correlation Matrix of GNSM predictions (TNU)

Forward Analysis: Total Event Rates (including oscillations) with errors and correlations at various detector sites

all positively correlated

(they measure in part the same flux)

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

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

The two extreme cases are recovered at ± 3 in our GNSM

GNSM central values: aUM < aLM < aBSE

partial mantle convection

Mantle Convection Problem: still debated today

1, 2, 3

homogeneous

two-layered

GNSM

GN

SM

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).

Really relevant result in geophysics and geochemistry

More realistic (or less optimistic) simulations of prospective dataneed to be performed.

Backward Analysis: Hypothetical future Results about Mantle Convection

partial convectionpreferred

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.

- 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.

Conclusions and Prospects