Robust Geo-Neutrino Results
Steve Dye
University of Hawaii
Hawaii Pacific University

Borexino data through the years

Spectacular Achievements

KamLAND data through the years
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Geo-neutrino Observations

Borexino data (2015)
5.9σ detection

KamLAND data (2013)
4.6σ detection

Geo-neutrinos conclusively observed at Japan and Italy
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Assumptions and Model Dependence• Measured geo-neutrino rate (TNU) and spectrum (Th/U)• If Th/U not resolved, assume Th/U (3.9) to go from rate to flux
• If source reservoirs not resolved, assume no core and use crustmodel to get mantle flux
• Radiogenic heating from mantle flux for model distributions• Questions• Do assumptions and model dependence bias answers?
• Are there assumption-free and model-independent measurements?

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46-2 -1

U+Th Flux (x10 cm s )Observations and Predictions Compatible
7654

Predicted surface flux variation- AGM15
3Observation
2Geo-neutrino observationshave not yet independently
confirmed surface flux variation

Prediction
KamiokaGran Sasso

103.8

4

4.2

4.4

4.6

Th/U
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5Constant Surface Flux/Rate HypothesisFlux• Borexino 2015- 𝜙U+Th = 5.0 ± 1.3 cm-2𝜇s-1• KamLAND 2016- 𝜙U+Th = 3.9 ± 0.7 cm-2𝜇s-1• Weighted Average- 𝜙U+Th = 4.15 ± 0.62 cm-2𝜇s-1• 𝜙U = 2.25 ± 0.33 cm-2𝜇s-1; 𝜙Th = 1.90 ± 0.28 cm-2𝜇s-1 Predicted surface flux variation- AGM15Rate• Borexino 2015- RU+Th = 43.5 ± 11.8 TNU• KamLAND 2016- RU+Th = 34.9 ± 6.0 TNU• Weighted Average- RU+Th = 37.2 ± 5.5 TNU• RU = 29.6 ± 4.4 TNU; RTh = 7.6 ± 1.1 TNU
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Measured surface flux/rate variation
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Constant Surface Flux/Rate Hypothesis
Constant surface flux => constant HPE mass fractions
Uranium flux: 𝜙U = 2.25 ± 0.33 cm-2𝜇s-1
Uranium mass fraction: aU = 46 ± 7 ng/g*
Thorium mass fraction: aTh = aU Th/U (=3.9)
Potassium mass fraction: aK = aU K/U (=12000)
Radiogenic power: P = 44 ± 7 TW
Measured Heat Flux: P = 47 ± 2 TW
(Davies and Davies, 2010)

Constant surface flux hypothesis
is compatible with fullyradiogenic heat model of Earth*
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-1

Exposure (TNU )Measuring a Rate Different from Constant Rate
10Sudbury
KL 2016

Homestake
HimalayaPacific
Runi+/- 1σ1Predicted surface flux variation- AGM15
BX 2015-110Figure of merit
10 geo evts

0204060

Geo-neutrino Rate (TNU)
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Geo-neutrino observations ofabout 1 TNU-1 at selectedsites should resolve
surface rate variation
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Observing Geo-neutrino Spectrum
Gando et al. 2013

Bellini et al. 2015

KamLAND data (2013)
consistent with NTh= 0

Borexino data (2015)
consistent with STh= 0

Th geo-neutrinos certainly present but not yet resolved at 1 (1.6?)𝛔10/27/16

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9latitude (N)Crust model rate Th/U ratio
4.780

4.660

4.540

Number Events

Measuring Different Th/U

107

Himalaya
Chondritic

106105104

Pacific

4.4

20

4.3

0

4.2-20

4.1

-40

4-60

3.9-80-150-100-50050

100150Arbitrarylongitude (E)2Poisson statistics
𝛔 = √NTh/U = 4.7
Th/U = 3.9
Th/U = 3.1

1.5

3.5

3.6

3.7

3.8

3.9

4

4.1

4.2

4.3

4.4

4.5

4.6

Th/U
1

Geo-neutrino observations ofabout 100 TNU-1 at selectedsites should resolve Th/U variation

0.5

0

1.5

2

2.5

3

3.5

Geo-neutrino Energy (MeV)

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10Status of Geo-Neutrino Observations
U + ThKCrustMantle
LLSVP/ULVZCoreRate Spectrum
Flux
Variation Power Dir>5s Th/U < 17 Th/U=3.9
model
K/U
K/U
K/U
model
model
model
model
model
model

Demonstrated/Completed
Assumption and/or Model-dependent result
Opportunity

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Assumption-Free Model-Independent Results• Rule out constant surface rate hypothesis• Observations at selected sites (Himalaya, Pacific, …)• Exposure requirements not demanding (1 TNU-1)• Independently confirm fractionation of HPE between crust and mantle• Rule out constant spectral shape hypothesis• Observations at selected sites (Himalaya, Pacific, …)• Exposure requirements demanding (100 TNU-1)• Independently confirm differential fractionation of HPE between crust and mantle• Direction measurements• Imaging of inverse beta decay is scintillating liquid• Resolving elastic electron scattering in high pressure TPC

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Constant Mantle Assumption• Measure mantle and crust rates with multiple observations• Requires one crust estimate with small absolute error

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Rate Analysis•T=C+M+R+B• Total (T) = Crust (C) + Mantle (M) + Reactor (R) + Background (B)• R and B are estimated with good precision• Signal (S) = Total (T) – Reactor (R) – Background (B)• Signal (S) = Crust (C) + Mantle (M)•S=C+M

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Rate Analysis• S 1 = C1 + M• S 2 = C2 + M• C2 = C1 + (S2 – S1)• 𝛿C2 = { (𝛿C1)2 + (𝛿S2)2 + (𝛿S1)2 }1/2
• 𝛿M = { (𝛿S1)2 + (𝛿C1)2 }1/2
• 𝛿S1 and 𝛿S2 from Poisson statistics• If Number of events (N) is very high, then 𝛿M ≈ 𝛿C2 ≈ 𝛿C1

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Rate Analysis• 𝛿M ≅ 𝛿C2 ≅ 𝛿C1• Applies to any site C2, C3, C4 … CN
• Just minimize 𝛿C at one site
• Crust studies realize 15% - 20% error at continental sites• If Ccont ≈ 40 TNU, then 𝛿Ccont ≈ 𝛿M ≈ 𝛿CN ≈ 6 TNU• Model-dependent• What about ocean?

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Rate Analysis• Set Cocean ± 𝛿Cocean = 3 ± 1 TNU (error exaggerated)• 𝛿Cocean ≈ 𝛿M ≈ 𝛿CN ≈ 1 TNU• But statistics not infinitely large• Assume Nocean = 100 (10%)• 𝛿CN = { (𝛿Cocean)2 + (𝛿SN)2 + (𝛿Socean)2 }1/2
• If SN and CN continental, then 𝛿CN = { (1)2 + SN2/N + (1)2 }1/2 ⪅ 2.5 TNU• If NN = 400 and SN = 40 TNU, continental crust signals CN measured to ≈ 6%
• Mantle signal M measured to ≈ 25%• Precision improves as NN increases
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Conclusions• Geo-neutrino observations making spectacular progress• Most results use Th/U=3.9 signal shape assumption• Further analyses depend on crust modeling• Constant rate hypothesis still allowed- can rule out with modest exposuresat selected sites (Himalaya, Pacific, …)• Constant shape hypothesis still allowed- can rule out with demanding
expoures at selected sites (Himalaya, Pacific, …)• Direction measurements should really help
• Constant mantle assumption enables crust and mantle rate measurements• Future looks very good!
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