Helioseismic Evidence of Changes inside the Sun

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Helioseismic Evidence of Changes inside the Sun

• How do we determine what happens inside the Sun?
• The obvious, large, changes (solar dynamics)
• More subtle changes (structure).

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Sir Arthur Eddington in The internal
constitution of stars (1926)
At first sight it would seem that the deep
interior of the Sun and stars is less accessible
to scientific investigation than any other region
of the universe. Our telescopes may probe farther
and farther into the depths of space but how can
we ever obtain certain knowledge of that which is
being hidden behind substantial barriers? What
appliance can pierce through the outer layers of
a star and test the conditions within?
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A Crash Course in Helioseismology

• The Sun oscillates in millions of different
  modes.
• The oscillations are linear and adiabatic.
• All observed modes are acoustic i.e., p-modes or
  surface modes i.e. f-modes.
• Each mode is characterized by three numbers
  
• (1) n the radial order, the number of nodes
  in the radial direction
• (2) l the degree no. of nodal planes
• (3) m the azimuthal order. m goes from l to
  -l no. of node circles crossing a latitude
• .

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Ray paths within the Sun
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• If the Sun were spherically symmetric and did not
  rotate, all modes with the same l and n but
  different m would have the same frequency.
• Rotation lists this degeneracy, giving rise to
  rotational splittings of the modes
• It is convenient to parameterize the frequencies
  within a multiplet of given n and l in terms of
  a central frequency and a limited number (of coefficients aj, such that
• The basis functions used are generally
  polynomials related to Clebsch-Gordon
  coefficients.
• The central frequency is used to determine the
  spherically symmetric structure of the Sun.
• Odd order splitting coefficients (corresponding
  to the symmetric part of the splitting
  coefficients) are used to determine the rotation
  rate inside the Sun.
• Even-order splitting coefficients (corresponding
  to the antisymmetric part of the splitting
  coefficients) are used to determine asphericity.

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A sample of the data
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Relationship between structure and frequencies
A Hermitian Eigenvalue problem, therefore use the
variational principle
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What did we know at the start of solar cycle 23?
Solar structure
Model from Bahcall, Basu Serenelli (2005)
Solar properties YCZ 0.24850.0034 (Basu
Antia 1995,2004) RCZ0.7130.001R0 (Basu Antia
1997, 2004)
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Solar Rotation
From Basu Antia 1998
nHz
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Solar sound-speed distribution is not spherically
symmetric either
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So are there detectable solar-cycle related
changes inside the Sun?
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Solar frequencies change with change in Solar
Activity
Frequency differences are predominantly (but not
completely) a function of frequency
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Changes are correlated with activity
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Solar rotation and other motions show the largest
changes.
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Changes in solar rotation The zonal flows
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Solar zonal flows
Rises upwards at about 1 m/s
Bifurcation not seen earlier
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Radial Gradient
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Latitudinal Gradient
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The butterfly diagram and the gradients of
rotation
Most sunspots seen where the radial gradient is
larger than the average, but the latitudinal
gradient is smaller than average.
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Acceleration
m/s
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Oscillations in rotation rate at the CZ base?
Howe et al. (2006)
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Another view
MDI
Data from Antia, Basu Chitre 2008
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Changes in meridional flows
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Are there any changes in solar structure?
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At first sight, no!
Basu (2002)
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A detailed look a the outer layers shows changes.
First hints from active regions.
Basu Mandel 2004
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Signature of the He ionization zone
l l 28
Signs of change!
L l 29
More direct signs of change
Basu et al. (2007)
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What of the inner layers Position of the CZ base?
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More subtle signatures deep inside?
Chou Serebryanskiy (2005)
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How about preprocessing the frequencies in an
attempt to reduce errors? A PCA analysis of
solar frequency changes.
Principal Component Analysis (PCA) is a technique
whereby a set of observations is expressed as a
set of uncorrelated vectors. It is an efficient
linear representation of the data set. Our set
Scaled frequency differences for different
epochs.
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The first few vectors
Baldner Basu 2008
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The coefficients
Baldner Basu 2008
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Reconstructing the frequencies
Baldner Basu 2008
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What does the first vector imply?
Baldner Basu 2008
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Latitudinal changes
Baldner Basu 2008
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The coefficients
Baldner Basu 2008
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Inversion results
Baldner Basu 2008
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Conclusions

• Solar oscillation frequencies and frequency
  splittings change as in solar activity changes.
• Solar rotation and dynamics show large changes
  with time/activity.
• The structure of the outer layers of the Sun show
  significant changes as solar activity increases.
• The changes in the structure of the deep interior
  of the Sun are more subtle, but are detectable.