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Calculating the Flux of Solar Neutrinos

Calculating the Flux of Solar Neutrinos. By: Carrie A. Gill Advisors: Dr. Andrea Erdas & Dr. Mary Lowe CS AAPT Conference November 5, 2005. Outline. Subatomic Particles & Forces Solar Properties Solar Neutrino Problem Formulas Results & Conclusion References.

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Calculating the Flux of Solar Neutrinos

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  1. Calculating the Flux of Solar Neutrinos By: Carrie A. Gill Advisors: Dr. Andrea Erdas & Dr. Mary Lowe CS AAPT Conference November 5, 2005

  2. Outline • Subatomic Particles & Forces • Solar Properties • Solar Neutrino Problem • Formulas • Results & Conclusion • References

  3. SUBATOMIC PARTICLES & FORCES

  4. Forces • Gravitational Force • Electromagnetic Force • Strong Force • Weak Force

  5. Forces- Short Range • Strong Force ← - binds quarks inside neutrons and protons - binds nuclei together - cannot change quark type • Weak Force → - changes one type of quark into a different type - responsible for beta decay - n → p + e- + νe-

  6. Neutrinos • 3 types of neutrinos and 3 types of anti-neutrinos • Thought to be massless (still controversial) • No electric charge • Only produced by the weak force • Only interact through the weak force • Stable, fundamental particles About 1 trillion neutrinos pass through your thumb every second!!!

  7. Neutrino Production • Produced in nuclear fusion reactions in the solar core • Exit Sun in about 2 seconds • Almost never interact with other particles in space or in our atmosphere • Can be painstakingly detected on Earth • Flux can provide current information about the solar interior and nuclear reactions!!

  8. SOLAR PROPERTIES

  9. Standard Solar Model (SSM) • Begins with homogeneous composition • Solar core is modeled as an ideal plasma • Hydrogen burning- supplies luminosity and pressure to balance gravity • Energy is transported by photons • Chemical composition slowly changes with nuclear reactions

  10. Reaction Chains • Proton- Proton Chain - overall: 4p → 1He + 2e+ + 2ve + 25 MeV - reactions produce larger atoms - includes sub-chains involving 7Be and 8B - accounts for 99.6% of the Sun’s energy • CNO Cycle - accounts for 0.4% of the Sun’s energy - occurs more often in older stars

  11. SOLAR NEUTRINO PROBLEM

  12. Predicting Neutrino Flux • correct and complete→ able to predict the amount of neutrinos hitting Earth from the Sun • prediction is wrong→ either SSM incorrect or new physics

  13. Neutrino Detectors • Located almost 1 mi underground • Used 100,000 gallons of tetrachloroethylene (C2Cl4) • 37Cl + ve→ 37Ar + e- • Total number of 37Ar atoms collected reflects flux of neutrinos Homestake Gold Mine Neutrino Experiment

  14. Solar Neutrino Problem • Observed flux ≈ predicted flux for low energy neutrinos (PP) • Observed flux << predicted flux for high energy neutrinos (7Be, 8B) • There is some other source of power in the Sun • Scientists calculated the reaction rates inaccurately • Evidence that neutrinos can change “type” en route to Earth (detectors can only detect one type)

  15. FORMULAS

  16. Summary of Equations: Maxwell-Boltzmann Maxwell-Boltzmann Distribution

  17. Tsallis Distribution • Changed the normalized energy distribution from Maxwell-Boltzmann to Tsallis • Vary parameter empirically to match known data

  18. Change in Equation

  19. RESULTS & CONCLUSION

  20. A Comparison • pp neutrino flux using the Maxwell-Boltzmann distribution • total flux = 6.2 X 1010 cm-2 s-1 4x1012 2x1012 dFlux/d(R/R0) cm-2 s-1 • Bahcall’s value for pp neutrino flux = 6.0 X 1010 cm-2 s-1

  21. PP- Maxwell-Boltzmann vs. Tsallis Neutrino Production as a function of Solar Radius Maxwell-Boltzmann 5x1012 4x1012 3x1012 2x1012 1x1012 Tsallis: δ=0.0005 Tsallis: δ=0.0018 dFlux/d(R/R0) cm-2 s-1 Φ(δ=0.0018)=6.004 X 1010 cm-2 s-1 R/R0

  22. What Now? • Find flux for neutrinos from other reactions using the Tsallis distribution • Vary parameter (δ) so that predicted data matches observed data • Check that the Tsallis model using the parameter’s value still yields a close result for the pp reaction • Implies that the Sun’s core is not an ideal plasma (although it is very close)

  23. REFERENCES

  24. References • Neutrino Astrophysics by: John N. Bahcall • Principles of Stellar Evolution and Nucleosynthesis by: Donald D. Clayton • Cauldrons in the Cosmos- Nuclear Astrophysics by: Claus E. Rolfs & William S. Rodney • Quantum Physics of Atoms, Molecules, Solids, Nuclei, & Particles by: Robert Eisberg & Robert Resnick • A Tour of the Subatomic Zoo- A Guide to Particle Physics by: Cindy Shwarz • The Discovery of Subatomic Particles by: Steven Weinberg • Programming with Fortran 77 by: William E. Mayo & Martin Cwiakala • Numerical Recipes in Fortran 77 by: Flanney, Press, Teuolsky, & Vetterling

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