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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

Calculating the Flux of Solar Neutrinos

By: Carrie A. Gill

Advisors: Dr. Andrea Erdas

& Dr. Mary Lowe

CS AAPT Conference

November 5, 2005

  • Subatomic Particles & Forces
  • Solar Properties
  • Solar Neutrino Problem
  • Formulas
  • Results & Conclusion
  • References
  • Gravitational Force
  • Electromagnetic Force
  • Strong Force
  • Weak Force
forces short range
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-

  • 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!!!

neutrino production
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!!
standard solar model ssm
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
reaction chains
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

predicting neutrino flux
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
neutrino detectors
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

solar neutrino problem1
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)
summary of equations maxwell boltzmann
Summary of Equations: Maxwell-Boltzmann

Maxwell-Boltzmann Distribution

tsallis distribution
Tsallis Distribution
  • Changed the normalized energy distribution from Maxwell-Boltzmann to Tsallis
  • Vary parameter empirically to match known data
a comparison
A Comparison
  • pp neutrino flux using the Maxwell-Boltzmann distribution
  • total flux = 6.2 X 1010 cm-2 s-1



dFlux/d(R/R0) cm-2 s-1

  • Bahcall’s value for pp neutrino flux = 6.0 X 1010 cm-2 s-1
pp maxwell boltzmann vs tsallis
PP- Maxwell-Boltzmann vs. Tsallis

Neutrino Production as a function of Solar Radius







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


what now
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)
  • 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