1. Probing Solar Magneto-Gravity Waves using Solar Neutrinos
What Can Solar Neutrino Oscillations Tell Us About the Solar Interior?
C.P. Burgess
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with N. Dzhalilov, T. Rashba, V. Semikoz, and J. Valle
hep-ph/ and astro-ph to appear

2. Outline Solar Neutrinos Properties of the Radiative Zone
Altering Neutrino Oscillations
Background properties vs fluctuations.
Properties of the Radiative Zone
Helioseismology
Magnetic Fields
Magneto-Gravity Waves
Helioseismological p- and g-modes.
The Alfvén/g-mode Resonance.
Conclusions
20/09/2018
Neutrinos and the Solar RZ

3. The Sun
GONG
Dedicated satellite measurements are allowing many of the Sun’s properties to be understood.
Most of these are restricted to measurements of the solar surface.
20/09/2018
Neutrinos and the Solar RZ

4. The Solar Interior
GONG
Solar structure is inferred by modelling, based on bulk properties.
Tsurf, L⊙, R⊙…
Now supplemented by two direct probes:
Helioseismology
Solar neutrinos
20/09/2018
Neutrinos and the Solar RZ

5. Solar Neutrinos
J. Bahcall
Solar neutrinos escape from the solar centre in seconds, have been observed on Earth, and so bring us direct immediate information about the deep solar interior.
20/09/2018
Neutrinos and the Solar RZ

6. Solar Neutrino Deficit
J. Bahcall
For decades the disagreement between observations of the solar neutrino flux and solar model predictions has prevented using neutrinos to infer the properties of the deep solar interior.
20/09/2018
Neutrinos and the Solar RZ

7. Neutrino Oscillations
SNO
This deficit is now understood as a consequence of neutrinos oscillating while en route from the solar core.
20/09/2018
Neutrinos and the Solar RZ

8. Terrestrial Evidence
KamLands
The evidence for neutrino oscillations is also now supported by direct terrestrial experiments, which measure a disappearance of ne’s while en route to a distant detector.
20/09/2018
Neutrinos and the Solar RZ

9. What Can We Learn About the Sun?
The success of the solar model prediction constrains thermal properties deep within the solar core.
The 8B flux is sensitive to the temperature at the production point.
The efficiency of oscillations depends on the environment encountered en route.
20/09/2018
Neutrinos and the Solar RZ

10. Sensitivity to Solar Fluctuations
Loreti, Qian, Fuller & Balantekin
Nunokawa, Rossi, Semikoz & Valle
CB & Michaud
Resonant neutrino oscillations can be sensitive to fluctuations in the solar environment.
Each neutrino is lucky to scatter even once on its way out.
Successive neutrinos ‘see’ different solar properties, and so can oscillate more or less efficiently.
20/09/2018
Neutrinos and the Solar RZ

11. Only Fluctuations at Resonance Count
CB, Bamert & Michaud
Oscillations are only sensitive to fluctuations which satisfy two criteria at resonance:
Their correlation length must be comparable to the neutrino oscillation length.
Their amplitude must be at least a few percent of the background values.
No known sources of solar oscillations seem to have the required properties.
20/09/2018
Neutrinos and the Solar RZ

12. Current Sensitivities
CB, Dzhalilov, Maltoni, Rashba, Semikoz, Tortola and Valle
Better knowledge of neutrino oscillation parameters allows better sensitivity to solar properties.
Fluctuations generically imply a reduced transition rate and a distortion of the energy spectrum.
20/09/2018
Neutrinos and the Solar RZ

13. Outline Solar Neutrinos Properties of the Radiative Zone
Altering Neutrino Oscillations
Background properties vs fluctuations.
Properties of the Radiative Zone
Helioseismology
Magnetic Fields
Magneto-Gravity Waves
Helioseismological p- and g-modes.
The Alfvén/g-mode Resonance.
Conclusions
20/09/2018
Neutrinos and the Solar RZ

14. Helioseismology
GONG
The solar interior supports numerous kinds of oscillations, whose motion on the solar surface can be detected.
Comparison of frequency and observed wavepattern with solar model predictions constrains the properties of the model as a function of depth below the surface.
l = 1, m = 1
l = 36, m = 24
20/09/2018
Neutrinos and the Solar RZ

15. Helioseismic Waves Observed
GONG
Wave patterns are observable by measuring Doppler shifts as a function of position on the solar surface.
Thousands of normal modes have been detected in this way.
20/09/2018
Neutrinos and the Solar RZ

16. Two Kinds of Waves Two kinds of waves are possible.
For p-modes pressure is the restoring force.
Higher frequency, closer to solar surface.
For g-modes buoyancy is the restoring force.
Lower frequency, confined to radiative zone.
20/09/2018
Neutrinos and the Solar RZ

17. Physical Properties vs Depth
GONG
Successful comparison between predicted and measured normal mode frequencies gives cs, r as functions of depth.
Can ‘see’ bottom of Convective Zone.
Accuracy has been sufficient to correct errors in opacity codes.
20/09/2018
Neutrinos and the Solar RZ

18. Small-scale Features Unresolved
Christensen-Dalsgaard
Although helioseismology constrains deviations from solar models at better than the percent level, it cannot resolve fluctuations with small spatial sizes.
Must deconvolve spherical harmonics given only half of the Sun and experimental noise.
20/09/2018
Neutrinos and the Solar RZ

19. The Sun’s Magnetic Fields
Studies of the solar surface and corona also provide information about the Sun’s magnetic field.
Dynamic, changing fields believed responsible for sunspots, solar cycle, hot corona etc.
20/09/2018
Neutrinos and the Solar RZ

20. The Solar Dynamo
GONG
Solar magnetic fields have long been believed to be generated by a solar dynamo, in which the turbulent inner motion generates the magnetic fields we see.
Longstanding problem to understand this dynamo in detail.
20/09/2018
Neutrinos and the Solar RZ

21. New Progress from Helioseismology
GONG
Helioseismology now allows a more detailed 3-dimensional inference of the motion of the solar interior in the Convective Zone.
This new information is helping to pin down the nature of the solar dynamo.
Also new information from other stars, eg: the existence of large magnetic fields around convective brown dwarfs.
20/09/2018
Neutrinos and the Solar RZ

22. The Role of the Tachocline
GONG
The layer at the base of the Convective Zone is now believed to play an important role in the dynamo, due to the large shear stresses there.
The RZ rotates rigidly while the CZ rotates differentially.
RZ toroidal fields may be as large as 104 – 105 Gauss just below the CZ.
20/09/2018
Neutrinos and the Solar RZ

23. Constraints on RZ Magnetic Fields
Friedland & Gruzinov
Radiative Zone fields can persist over the age of the Sun.
High RZ conductivity reduces magnetic diffusion.
Radiative Zone fields cannot be larger than a few times 106 Gauss:
Magnetic pressure B2/8p would otherwise cause observable distortions to the solar oblateness.
Magnetic pressure in core would change densities and temperatures inconsistently with observed solar neutrino production and helioseismology.
Magnetic flux tubes would too rapidly rise out of the RZ into the CZ.
20/09/2018
Neutrinos and the Solar RZ

24. Outline Solar Neutrinos Properties of the Radiative Zone
Altering Neutrino Oscillations
Background properties vs fluctuations.
Properties of the Radiative Zone
Helioseismology
Magnetic Fields
Magneto-Gravity Waves
Helioseismological p- and g-modes.
The Alfvén/g-mode Resonance.
Conclusions
20/09/2018
Neutrinos and the Solar RZ

25. Linear Magneto-Gravity Waves
Can re-examine helioseismic waves in the RZ and see if magnetic fields can make a difference.
Restrict to plasma properties deep in RZ.
Restrict to geometry where B0 is approximately constant and is perpendicular to r and g etc.
Best near solar equator, not too close to solar centre.
20/09/2018
Neutrinos and the Solar RZ

26. Approximate MG Equations
Reduce coupled system to a single eigenvalue equation for bz.
20/09/2018
Neutrinos and the Solar RZ

27. Approximate Analytical Solutions
Eigenvalue equation may be put into Hypergeometric form using x  exp(r/H).
Spike occurs at singular point x = 1.
Analytic forms obtainable for wave profiles and for complex mode frequencies.
20/09/2018
Neutrinos and the Solar RZ

28. Normal Mode Frequencies
Real and imaginary parts of the Magneto-Gravity dispersion relation.
Frequency cannot be as small as 1/27 day = 4 x 10-7 Hz.
20/09/2018
Neutrinos and the Solar RZ

29. Surprisingly Large Magnetic Effects
Magneto-Gravity wave profiles show resonant spikes at specific radii.
Resonant position depends on mode number.
Resonant position depends on magnetic field strength.
Resonant width can be comparatively narrow.
20/09/2018
Neutrinos and the Solar RZ

30. Alfvén/g-mode Resonance
The eigenmodes are oscillatory between the Brunt-Väisälä and Alfvén frequencies, and spikes occur when their frequency equals the local Alfvén frequency.
Channel energy from g-modes along magnetic field lines.
20/09/2018
Neutrinos and the Solar RZ

31. Fluctuations on n Oscillation Scales.
For magnetic fields of order 10 kG, these density spikes can alter neutrino oscillations.
They are arise where the neutrinos oscillate.
Their spacing is comparable to the neutrino oscillation length.
What is their amplitude??
20/09/2018
Neutrinos and the Solar RZ

32. Observable Changes to Oscillations
If these modes are large enough and the magnetic fields are the right size, then observable dilution of neutrino oscillations arise:
Most efficient near solar equatorial plane: seasonal effect?
20/09/2018
Neutrinos and the Solar RZ

33. Conclusions and Outlook
Solar neutrino physics is entering a mature phase where neutrinos can be used to probe the deep solar interior.
Probes both the neutrino production point and the intervening neutrino oscillation history.
Solar fluctuations at the position of the resonant neutrino oscillations can be observable if their amplitude is a few percent and their correlation length is a few hundred km.
Under favourable circumstances, radiative zone magnetic fields may produce such fluctuations in the solar density due to a resonance between Alfvén waves and helioseismic g-modes.
20/09/2018
Neutrinos and the Solar RZ