1. Geology from Geo-neutrino Flux Measurements Eugene Guillian / Queen’s University DOANOW March 24, 2007

2. Content of This Presentation KamLAND: The Pioneering Geo-neutrino Detector –Proved that geo-neutrinos can be detected, but under very unfavorable conditions How to proceed in the next generation –10  KamLAND (size  time) –Low background –Simple neighboring geology –Multiple sites How to extract geological information from flux measurements –1 site –2 sites Statistical sensitivity Effect of nuclear reactor background Possible applications

3. Geo-neutrinos Produced in the radioactive decay of unstable isotopes Isotope Half Life (billion years) 238 U4.47 232 Th14.1 40 K1.25 The flux of geo-neutrinos depends on: –Total mass of these isotopes in the earth –The distribution of the isotopes in the earth

4. Total Isotopic Mass in the Earth An educated guess: –CI carbonaceous chondrite meteorite Representative of the raw material from which the earth was formed Based on the isotopic abundances in this type of meteorite, estimate the initial elemental abundance Evolution of the early earth –Core separation –Bulk Silicate Earth (BSE) –Crust extraction from BSE

5. Element Concentration in Primitive Mantle Uranium20.3 ppb Thorium79.5 ppb Potassium240 ppm Isotope Percent of Natural Element 238 U99.3% 232 Th100% 40 K0.012%

6. Crust Extraction from the Mantle Uranium, thorium, and potassium are all lithophile elements –They have a strong tendency to leave the mantle and stay in the crust A good starting guess about isotope concentrations: Isotopic Abundance in Different Earth Structures 238 U 232 Th 40 K Crustppm Mantleppb~10 ppb Core~0 ~0?

7. More Detailed Earth Models Examples: –Mantovani et al., Phys. Rev. D 69, 013001 (2004) –S. Enomoto, Ph. D. Thesis, Tohoku University (2005) –Turcotte et al., J. Geophys. Res. 106, 4265-4276 (2001)

8. The Mantovani et al. Reference Model Layer Isotopic Concentration (ppb) 238 U 232 Th 40 K Ocean3.2048 Sediments170069002000 Oceanic Crust100220150 Contiental Crust Upper250098003100 Middle160061002000 Lower6203700860 Mantle Upper7179 Lower135219 Core000 Note: These are just educated guesses There is considerable spread in what could “reasonably” be assigned to these values

9. S. Enomoto Reference Model Layer Isotopic Concentration (ppb) 238 U 232 Th Sediments Continental280011000 Oceanic17007000 Oceanic Crust100220 Contiental Crust Upper280011000 Middle16006100 Lower2001200 Mantle Upper1248 Lower1248 Core Outer00 Inner00

10. Turcotte et al. Models Model I (Ur = 0.7) Layer Isotope Concentration (ppb) 238 U 232 Th Continental Crust 9806700 Upper Mantle 2256 Lower Mantle 34140 Model II (Ur = 0.5) Layer Isotope Concentration (ppb) 238 U 232 Th Continental Crust 12006200 Upper Mantle 1332 Lower Mantle 26110 These models argue for significant level of selective erosion of crustal uranium, and subsequent recycling into the upper mantle. Mantle convection boundary is deeper than the 660 km seismic discontinuity (1200 ± 200) km

11. The Overall Picture of Geo-neutrinos The models differ in: –The number of geological subdivision –The assignment of isotopic concentrations in each subdivision But, at the very basic level, similar (i.e. within a factor of several) geo-neutrino fluxes are predicted –The flux at the surface of the earth is ~10 6 cm -2 s -1 –The flux varies by a factor of several depending on the location

12. A Neutrino Flux Map: Example The color scale is Y = yield (number of detected events per unit of exposure)

13. A Note on Units: The Scale of Things Geo-neutrino flux units –Several  10 6 cm -2 s -1 Geo-neutrino detection rate (yield) –10 32 p-yr –The number of geo-neutrino events that can be detected with 10 32 free protons exposed for 1 year –For a typical target, 10 32 free protons is about 1000 tonne –The volume is about the size of a large room Several million geo- neutrinos stream through a penny every second

14. Detecting Geo-neutrinos with a Liquid Scintillator Detector Inverse Beta Decay Anti-neutrinoFree ProtonNeutronPositron 1.8 MeV energy threshold Mn - Mp = 1.3 MeV M(e+) = 0.5 MeV 1.8 MeV e + kinetic energy E - 1.8 MeV M(e+) = 0.5 MeV e + kinetic energy M(e-) = 0.5 MeV 1.0 MeV from e + -e - annhilation E - 1.8 MeV Energy InputDeposited Energy Prompt energy deposition E - 0.8 MeV

15. Detecting Geo-neutrinos Delayed energy deposition –Neutron thermalization & capture on free proton –~200 micro-second –2.2 MeV gamma rays Prompt-delayed correlation –Reduces background noise to a very low level Prompt Delayed

16. 1.8 MeV Energy Threshold Nature 436, 499-503 (28 July 2005) Only the highest-energy anti-neutrinos from 238 U and 232 Th are detectable 40 K is not detectable with this technology

17. Inverse Beta Decay Cross Section Cross section –The effective cross sectional area of a free proton from the point of view of a geo-neutrino –~10 -43 cm 2 Geo-neutrino flux: –~10 6 cm -2 s -1 = ~10 13 cm -2 yr -1 Probability that a particular free proton will be hit by a geo-neutrino in one year: ~10 -43 cm 2  ~10 13 cm -2 yr -1 = ~10 -30 per year This determines the necessary target size A detector with 10 32 free protons should see ~10 32  10 -30 = ~100 events Extremely small!

18. The Fine Print Detection efficiency ≈ 70% Neutrino oscillation –When geo-neutrinos travel more than ~50 km, it becomes a mixture of undetectable types of anti-neutrinos –This effect reduces the detectable flux by about a factor of 0.57

19. Extracting Geological Information from a Geo-neutrino Flux Measurement Example: Flux at Sudbury Assumes the S. Enomoto reference model, which determines: –The total flux at Sudbury –The relative contributions from 238 U and 232 Th Region 1 Region 2 Region 1: –N 1 = N Th + 0.459·N U Region 2: –N 2 = 0.541·N U 0.541·N U 0.459·N U N Th

20. Extracting Geological Information from a Geo-neutrino Flux Measurement N 1 and N 2 are the measured quantities N U and N Th are quantities that carry geological information It is possible to separately measure the uranium and thorium flux

21. Upper Limit on the Sensitivity The statistical error sets the upper limit on the sensitivity to the geo- neutrino flux measurement Mantovani et al. Ref. Model, 10 33 p-yr The sensitivity scales with exposure as:

22. What Does the Flux Tell Us about the Earth? XU or Th  X (r 0 ) Flux of anti-neutrinos from X at detector position r 0 AXAX Frequency of radioactive decay of X per unit mass NXNX Number of anti-neutrinos produced per decay of X RR Earth radius a X (r)Concentration of X at position r  (r) Density of earth at position r

23. Analyzing the Flux Formula Constant (accurately known) Relatively well-determined through seismic tomography Earth models (not well known) The goal of neutrino geology is to learn about a X (r) from measurements of  X (r)

24. What Can We Learn about Isotope Concentrations from a 1-site Measurement? We can get the isotope concentration averaged over the entire earth But the information about the isotope distribution in the earth and the total amount of isotopes is poorly determined –One can distribute X between the mantle and crust to produce the same answer –The constraint on models is weak

25. Neutrino Geology in the Near Future KamLAND was the pioneering neutrino geology detector Characteristics of KamLAND as a Geo-neutrino Detector Exposure~10 32 p-yr Number of Sites1 Local geologyComplicated Background noiseIntense

26. Goals for the Coming Generation Characteristics of the Next-generation Geo-neutrino Detectors Exposure>10 33 p-yr Number of Sites≥ 2 Local geologySimple Background noiseLow

27. A 2-site Geo-neutrino Measurement: An Example Two measurements –Can solve for two unknowns The continental crust and mantle account for most of the observed geo-neutrinos, regardless of the detector location –The two unknowns: 1.Average isotope concentration in the continental crust 2.Average isotope concentration in the mantle –The small contribution from other geological subdivisions is approximated as being zero

28. An Example of a 2-Site Measurement The mantle contribution is the same at both sites –Assume that the mantle is spherically symmetric A large contrast in the continental crustal component exists The contribution from other geological structures is negligible

29. Flux vs. Concentration Equations Constant Factors (g -1 s -1 cm -1 ) CUCU 5.85  10 -5 C Th 1.27  10 -5 Geologic Integral (g/cm) Integrated over…. Evaluated at… I CC Sudbury Continental Crust Sudbury I CC Hawaii Hawaii IMIM Mantle Common to all surface locations Measured Quantities  X (Sudbury) Flux evaluated at Sudbury  X (Hawaii) Same as above, Hawaii Unknown Quantities  X (CC) Average concentration of isotope X in the continental crust  X (M) Same as above, mantle

30. Geologic Integrals Unit:g/cm Continental Crust (  10 16 g/cm) Mantle 148

31. Solving for the Concentrations Uranium Flux 2  2 Matrix Equation Solution of the unknown quantities in terms of the measured ones Geologic Integral Matrix  10 16

32. Statistical Sensitivity of 2-Site Measurements Exposure = 10 33 p-yr Model = Mantovani et al. Reference Oceanic site = Hawaii Vary the “continental” sites Upper CC Input Middle CC Input Lower CC Input Statistical Uncertainty ≈ 12% Lower Mantle Input Upper Mantle Input Statistical Uncertainty ≈ 24% Concentration / 238 U / Continental CrustConcentration / 238 U / Mantle

33. Statistical Sensitivity for Th Concentrations Concentration / 232 Th / Continental CrustConcentration / 232 Th / Mantle Upper CC Input Middle CC Input Lower CC Input Lower Mantle Input Upper Mantle Input Statistical Uncertainty ≈ 34%Statistical Uncertainty ≈ 77%

34. S. Enomoto Reference Model ≈ 12%≈ 22% ≈ 36% ≈ 68%

35. Turcotte et al. Model I ≈ 22% ≈ 14% ≈ 38% ≈ 49%

36. Turcotte et al. Model II ≈19% ≈17% ≈ 40%≈58%

37. Radiogenic Heat Measurement The radiogenic heat is derived from the concentrations Heat from continental crust Heat from mantle 40 K term a U (CC), a U (M), a Th (CC), a Th (M) Measured isotope concentrations, continental crust & mantle Heat per Unit Isotope Mass (W/kg) HUHU 9.71  10 -5 H Th 2.69  10 -5 HKHK 3.58  10 -9 Mass (kg) M(CC) Continental Crust 2.2  10 22 M(M)Mantle 4.06  10 24

38. Heat Measurements ≈18% ≈19% ≈36% ≈16% ≈25% ≈24% ≈15% ≈23% ≈28% ≈16% Mantovani Enomoto Turcotte ITurcotte II Continental Crust Mantle Total ≈40% ≈17% Dashed blue line: Estimated 40 K contribution

39. Background Noise KamLAND from several years ago tells us a lot about background noise Nature 436, 499-503 (28 July 2005) Internal background – 13 C( ,n) 16 O (radon gas contamination) External background –Anti-neutrinos from nuclear reactors Nuclear Reactor 13 C( ,n) 16 O N = 152 Number of Events Total152 Geo-neutrino25 +19 -18 Background127 ± 13 Background Noise Nuclear Reactor80.4 ± 7.2 13 C( ,n) 16 O 42 ± 11

40. Internal Background A lot of R & D by the KamLAND team and others have taken place since the first geo-neutrino measurement Make use of the R & D results, and learn from experience: –Make sure the liquid scintillator and other internal detector components have minimal exposure to radon gas –Use newly developed purification techniques to remove 210 Pb (radioactive lead) from the liquid scintillator Assume that the internal background can be reduced to a negligible level

41. Reactor Anti-neutrino Background The only way to minimize this is to place the detector as far as possible from nuclear reactors Map of heat production by world-wide nuclear reactors ≈ 478 nuclear reactors world-wide Total generated heat ≈ 1.1 TW t ~30 to 40 TW t total heat ~20 to 30 TW t radiogenic heat

42. Reactor Anti-neutrino Background Rate Log-scale background rate (arbitrary units) Exposure = 10 33 p-yr Detection Efficciency = 0.70 Reactor Duty Cycle = 0.80

43. Subtracting the Reactor Background E - 0.8 MeV Region 1Region 2 Region 3 Region 1Region 2Region 3 N 1 = N Th + (1-f)·N U + r 1 ·RN 2 = f·N U + r 2 ·RN 3 = R f = 0.541r 1 = 0.0514r 2 = 0.303

44. Sensitivity with Reactor Background

45. Sensitivity with and without Reactor Background Example: Mantovani et al. Ref. Model No ReactorWith Reactor

46. Change in Sensitivity: Concentrations

47. Change in Sensitivity: Heat Red Points: No Reactor Blue Points: With Reactor Vertical Axis: Sensitivity (%) Horizontal Axis: Location

48. Testing Geological Models Examples of what kind of sensitivity the next-generation geo-neutrino measurements might have to geological models 1.Distinguishing the Turcotte et al. models from the “Reference” models 2.What can we say about the Th/U ratio? 3.How well can we constrain radiogenic heat?

49. The Turcotte et al. Models  = Th/U concentration ratio –BSE:  = 4 –Continental Crust:  = 5-6 –Upper Mantle:  = 2.5 –Lower Mantle:  = 4 Mass balance of 238 U between CC and UM  for CC and UM combined must be 4 Oxidized atmosphere (2 Ga) made U soluble in H 2 O, but not Th. U gets recycled into the upper mantle. Mantle convection occurs only in UM. Mass of UM ≈ 0.5 times total mantle mass. Primitive value Model I (Ur = 0.7) Layer Isotope Concentration (ppb) 238 U 232 Th Continental Crust9806700 Upper Mantle2256 Lower Mantle34140 Model II (Ur = 0.5) Layer Isotope Concentration (ppb) 238 U 232 Th Continental Crust12006200 Upper Mantle1332 Lower Mantle26110

50. Concentration Measurements for Different Models 2 sites = Hawaii & Sudbury 10 33 p-yr 238 U/CC 238 U/Mantle 232 Th/CC 232 Th/Mantle We can distinguish the mantle concentration of 238 U of Turcotte I from those of “Reference” models

51. Th/U Ratio Mantovani Ref. Model Turcotte Model I CC Mantle

52. Radiogenic Heat Boxes @ bottom: Estimated 40 K Contribution

53. Conclusions Next generation geo-neutrino experiments: –Exposure > 10 33 p-yr –2 sites: continental & oceanic location –Low background We can begin to distinguish models –Separate information about continental crust & mantle – 238 U concentration in the mantle Can separate reference models from Turcotte model I at 4-5 sigma level –Radiogenic heat 15-20% uncertainty in total radiogenic heat But extra uncertainty due to unknown 40 K heat