Transcript Document

NEUTRINO OSCILLATION WORKSHOP
Conca 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)
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
Introduction to Geo-Neutrinos
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.
-Seismology: based on sound velocity
measurement from seismic data
- reconstructs density
profile
throughout the Earth
- infers crust-mantle-core layer
structure
(Mg, Fe, Al)
(Al,Si)O2 pervoskite
CaSiO2 pervoskite,
(Fe,Mg)O
-GeoChemistry: based
on direct sampling
- gives direct information on
chemical composition of crust
and upper part of mantle
- does not reach deep Earth
-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
bring to surface information about:
- the whole planet
- its radioactive contents
- energetics and thermal history
238U
232Th
counts/MeV/parent
from radioactive decays of
238U, 232Th, 40K trace elements
in crust and mantle of Earth
series
series
40K
anti-neutrino energy E (MeV)
Where are radioactive elements located?
“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
Planetary Evolution:
- Refractory Lithophile elements
(e.g. U, Th) differently distributed
in crust and mantle
Today’s Earth composition is not CI !
Bulk Silicate Earth
(BSE) Model
describes
assumes
Constraints:
- “primitive mantle”
- present crust+mantle system
- Earth Refractory Elements in chondritic
proportions
- U, Th, K absent in the Earth core
Direct sampling (crust & upper mantle)
Low (<1200 K)
condensation
temperature
High (>1400 K)
condensation
temperature
Preferentially
embedded in rocks
rather than iron
i.e. before
crust/mantle
differentiation
Th/U abundance
ratio is 3.9
& Neutrino Geophysics (in the future)
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)
Sea of Japan
KamLAND
Japan
Trench
Some Important Facts:
- Observable Geo-e events: from U, Th decay only
- e from K decay below threshold for detection
- FTh(e) & FU(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
Th/U = 3.8
- Earth science constraints
- Uncertainty evaluation
our reanalysis of Kamland data
In this context we illustrate our approach to uncertainties and correlations
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)
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
9 crustal tiles
- SNO
- LENA
Local composition may be ≠ from global composition
(in terms of U, Th, K)
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 ± i
and
[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 information is supplied by educated guesses, whenever possible, or arbitrary
but explicit assumptions, when unavoidable
-“local” abundance fluctuations
uncertainties
assumed to be decoupled from “global” abundance
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
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
Sources:
We obtain:
aTh
BSE
=
aTh
CI
(aAl
Al
BSE/a CI)
aUBSE = aUCI (aAlBSE/aAlCI)
U,ThBSE= 0.936 (U,Th) correlation
- 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
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
UM
CC = continental crust
OC = oceanic crust
UM = upper mantle
LM = lower mantle
LM
(core is excluded)
OC
Global
Reservoirs
(correlated)
CC
U
Th K
U
Local
Reservoirs
(uncorrelated)
i-th
reservoir
≡
Th
K
“local” fluctuations have nothing to do with
“global” estimates
LM abundances anti-correlated with the other reservoirs because of subtraction
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
± 1
U
Th
U
21.9×10-9
± 14 %
1
Th
82.1×10-9
± 14 %
K
26.3×10-5
± 21 %
U
1.46×10-6
± 17 %
Th
6.29×10-6
± 10 %
K
1.62×10-2
± 10 %
U
1.00×10-7
± 30 %
Th
2.20×10-7
± 30 %
K
1.25×10-3
± 28 %
U
3.95×10-9
± 30 %
Th
10.8×10-9
± 30 %
K
5.02×10-5
± 28 %
U
17.3×10-9
± 30 %
Th
60.4×10-9
± 30 %
K
21.7×10-5
± 28 %
Reser. Elem. Abund.
BSE
CC
OC
UM
LM
BSE
CC
OC
K
U
Th
K
U
Th
+ .936
+ .701
0
0
0
0
1
+ .648
0
0
0
0
1
0
0
0
1
+ .906
1
Similar to previous work by
Enomoto et al., Fiorentini et al.
UM
LM
K
U
Th
K
U
Th
K
0
0
0
0
0
+ .908
+ .893
+ .690
0
0
0
0
0
+ .850
+ .954
+ .638
0
0
0
0
0
0
+ .636
+ .618
+ .985
+ .906
0
0
0
0
0
0
- .409
- .263
- .146
+ .595
0
0
0
0
0
0
- .371
- .291
- .096
1
0
0
0
0
0
0
- .371
- .173
- .161
1
+ .906
+ .868
0
0
0
- . 012
- .007
- .007
1
+ .764
0
0
0
- .011
- .001
- .006
1
0
0
0
- .010
- .006
- .008
1
+ .906
+ .868
- .093
- .065
- .058
1
+ .764
- .084
- .071
- .051
1
- .081
- .054
- .066
1
+ .924
+ .692
1
+ .640
1
Qualifying result of our work
allows well-defined statistical analyses
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
RU (TNU)
1 TNU = 1 event/year/1032 protons
Negative correlation due to experimental sensitivity
to RU +RTh rather than RU and RTh separately
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.
Forward Analysis: Total Event Rates (including oscillations) with
errors and correlations at various detector sites
Site
Rate ± 1
(TNU)
Kamioka
31.6 ± 2.5
Gran Sasso
40.6 ± 2.9
Sudbury
47.9 ± 3.2
Pyhasalmi
49.9 ± 3.5
Baksan
50.7 ± 3.4
Hawaii
13.4 ± 2.2
Correlation Matrix of GNSM predictions
Kamioka
Gran Sasso
Sudbury
Phyasalmi
Baksan
Hawaii
1.00
0.72
0.65
0.63
0.62
0.83
1.00
0.71
0.73
0.70
0.64
1.00
0.69
0.65
0.55
1.00
0.69
0.48
1.00
0.51
1.00
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
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
1, 2, 3 
Within 3:
GNSM
- aLM
two-layered
homogeneous
aUM (left panel)
whole mantle convection
- aLM
aBSE (right panel)
two-layered mantle model
GNSM central values:
aUM < aLM < aBSE
partial mantle convection
The two extreme cases are
recovered at ± 3 in our GNSM
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).
Really relevant result in
geophysics and geochemistry
More realistic (or less optimistic)
simulations of prospective data
need to be performed.
partial convection
preferred
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.
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.