Friday, 3 February 2017

Heliseismology - Introduction

I remember attending a lecture many years ago about the physics of stellar interiors with particular emphasis on the sun. It is amusing that the lecturer noted that one of the reasons for his interest was his freedom to construct models in the knowledge that it was very difficult to come up with the experimental evidence to verify the models! The field of helioseisomology and neutrino observations are changing this idea and we are gleening more information about the interior of our nearest star and other stars too.

Reka Jain gave an excellent presentation, her experience in this area is great and covers many levels of expertise including information inspiring young people [ref. 6]. Reka provided an overview of Helioseismology and  briefly discussed some recent successes of global and local Helioseismology.

My interest  in this area relates to the link between excitations in the solar atmosphere and the solar global oscillations see reference 13 and 14.

Helioseismology is the study of wave oscillations in the Sun. Observations of acoustic wave oscillations are used to make helioseismic studies of the interior of the Sun even though helioseismic techniques operate slightly differently on different length scales.The diagram below illustrates the variety of reflections and refractions occuring when acoustic waves propagate in the solar interior.

The helioseismic vibrations arise from convective and turbulent motions within the solar interior. We can identify two types of modes, pressure driven p-modes and gravity driven g-modes. Solving spherically symmetric equations of hydrodynamics (see our wobbling star) the modes can be understood in terms of spherical harmonics illustrated in the figure below. The predicted power spectrum gives rise to a series of distinct ridges 200000  modes have been detected of a possible million.



Reka's talk was particularly interesting because not only did she provide a clear overview  we heard about exciting advances including applications of helioseismology for studying
  • sunspot growth and evolution,
  • flux tubes convecting to the surface and the study of
  • neutrino observations to determine characteristics of g-mode oscillations.
  • neutrino propagation in stellar interiors to determine the properties of dark matter
Deubner [ref. 7] explained the p-mode oscillations using  the phase and group velocity of fluctuations of different solar spectral lines. Agreement with theoretical estimates was shown for acoustic waves trapped in the sun. With increasingly accurate models of the sun from helioseismology it is possible to use this higher quality data to study the propagation of neutrinos such probes can be used in studies of the difficult to find g-mode oscillations. One possibility is to use the sun as a probe for fundamental physics and cosmology. An important idea is the detection of dark matter and to understand the impact that this has onthe formation of stars [ref 8


ref. 8 Neutrion propagation in the interior
The Sun as a probe of Fundamental Physics and Cosmology The high quality data provided by helioseismology, solar neutrino flux measurements, spectral determination of solar abundances, nuclear reactions rates coefficients among other experimental data, leads to the highly accurate prediction of the internal structure of the present Sun - the standard solar model. In this talk, I have discussed how the standard solar model, the best representation of the real Sun, can be used to study the properties of dark matter, for which two complementary approaches have been developed: - to limit the number of theoretical candidates proposed as the dark matter particles, this analysis complements the experimental search of dark matter, and - as a template for the study of the impact of dark matter in the evolution of stars, which possibly occurs for stellar populations formed in regions of high density of dark matter, such as stars formed in the centre of galaxies and the first generations of stars.

 ref. 9 Predictions of solar cycle  changes in p-mode frequencies change with the solar cycle
The Sun's activity measured through many of its proxies varies in a periodic manner with an average duration of about 11 years. The empirical relations based on the periodicity are considered as the first generation methods to predict the maximum amplitude of the next solar cycle. These methods which are statistical in nature fall into two different categories: precursor methods and extrapolation methods and has been widely used in the later part of the 20th century. Recent advances include predictions based on non-linear methods and dynamo models, where the later predicts not only the maximum amplitude of the solar cycle but also the timing of the activity maximum. In this review, we focus on different prediction methods and compare their outcome for previous cycles with an emphasis on cycle 24. We further analyze and compare various predictions for solar cycle 25 and beyond.


The figures above and below illustrate the variation of the meridional flow.


reference 11,12 helioseismic detection of supergranulation
We present measurements of the Sun’s sub-surface convective flows and provide evidence that the pattern of supergranulation is driven at the surface. The pattern subsequently descends slowly throughout the near-surface shear layer in a manner that is inconsistent with a 3D cellular structure. The flow measurements are obtained through the application of a new helioseismic technique based on traditional ring analysis. We measure the flow field over the course of eleven days and perform a correlation analysis between all possible pairs of depths and temporal separations. In congruence with previous studies, we find that the supergranulation pattern remains coherent at the surface for slightly less than two days and the instantaneous surface pattern is imprinted to a depth of 7 Mm. However, these correlation times and depths are deceptive. When we admit a potential time lag in the correlation, we find that peak correlation in the convective flows descends at a rate of 10-40 m s-1 (or equivalently 1-3 Mm per day). Furthermore, the correlation extends throughout all depths of the near-surface shear layer. This pattern-propagation rate is well matched by estimates of the speed of downflows obtained through the anelastic approximation. Direct integration of the measured speed indicates that the supergranulation pattern that first appears at the surface eventually reaches the bottom of the near-surface shear layer a month later. Thus, the downflows have a Rossby radius of deformation equal to the depth of the shear layer and we suggest that this equality may not be coincidental.

We present measurements of the Sun's sub-surface convective flows and provide evidence that the pattern of supergranulation is driven at the surface. The pattern subsequently descends slowly throughout the near-surface shear layer in a manner that is inconsistent with a 3-D cellular structure. The flow measurements are obtained through the application of a new helioseismic technique based on traditional ring analysis. We measure the flow field over the course of eleven days and perform a correlation analysis between all possible pairs of depths and temporal separations. In congruence with previous studies, we find that the supergranulation pattern remains coherent at the surface for slightly less than two days and the instantaneous surface pattern is imprinted to a depth of 7 Mm. However, these correlation times and depths are deceptive. When we admit a potential time lag in the correlation, we find that peak correlation in the convective flows descends at a rate of 10 - 30 m s-1 (or equivalently 1 - 3 Mm per day). Furthermore, the correlation extends throughout all depths of the near-surface shear layer. This pattern-propagation rate is well matched by estimates of the speed of down flows obtained through the anelastic approximation. Direct integration of the measured speed indicates that the supergranulation pattern that first appears at the surface eventually reaches the bottom of the near-surface shear layer a month later. Thus, the transit time is roughly equal to a solar rotation period and we suggest this equality may not be coincidental. 

References

  1. Helioseismology
  2. Lecture notes on stellar oscillations
  3. Introduction to helioseismology
  4. Leibacher, A New Description of the Solar Five-Minute Oscillation
  5. Ulrich, The Five-Minute Oscillations on the Solar Surface
  6. Junior introduction to Helioseismology 
  7. Deubner, F.-L., Acoustic waves and the geometric scale in the solar atmosphere  see also Some properties of velocity fields in the solar photosphere. V - Spatio-temporal analysis of high resolution spectra
  8. Lopes, The Sun as a probe of Fundamental Physics and Cosmology
  9. Tripathy, Predictions of solar cycle
  10. Jain K, Tripathy, Hill, Solar Activity in Cycle 24 - What do Acoustic Oscillations tell us? 
  11. Greer, Hindman and Toomre, Helioseismic Imaging of Supergranulation throughout the Sun’s Near-Surface Shear Layer 
  12. Hindman, Greer, Toomre, Helioseismic Imaging of Supergranulation throughout the Sun's Near-Surface Shear Layer 
  13. Solar wave theory blog: helioseismology 
  14. Solar wave theory blog: solar global oscillations 
  15. A Comparison Between Global Proxies of the Sun's Magnetic Activity Cycle: Inferences from Helioseismology