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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

Results conclusion

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