Helioseismology
Helioseismology is the study of the structure and dynamics of the Sun through its oscillations. These are principally caused by sound waves that are continuously driven and damped by convection near the Sun's surface. It is similar to geoseismology, or asteroseismology, which are respectively the studies of the Earth or stars through their oscillations. While the Sun's oscillations were first detected in the early 1960s, it was only in the mid-1970s that it was realized that the oscillations propagated throughout the Sun and could allow scientists to study the Sun's deep interior. The term was coined by Douglas Gough in the 90s. The modern field is separated into global helioseismology, which studies the Sun's resonant modes directly, and local helioseismology, which studies the propagation of the component waves near the Sun's surface.
Helioseismology has contributed to a number of scientific breakthroughs. The most notable was to show that the anomaly in the predicted neutrino flux from the Sun could not be caused by flaws in stellar models and must instead be a problem of particle physics. The so-called solar neutrino problem was ultimately resolved by neutrino oscillations. The experimental discovery of neutrino oscillations was recognized by the 2015 Nobel Prize for Physics. Helioseismology also allowed accurate measurements of the quadrupole moments of the Sun's gravitational potential, which are consistent with General Relativity. The first helioseismic calculations of the Sun's internal rotation profile showed a rough separation into a rigidly-rotating core and differentially-rotating envelope. The boundary layer is now known as the tachocline and is thought to be a key component for the solar dynamo. Although it roughly coincides with the base of the solar convection zone — also inferred through helioseismology — it is conceptually distinct, being a boundary layer in which there is a meridional flow connected with the convection zone and driven by the interplay between baroclinicity and Maxwell stresses.
Helioseismology benefits most from continuous monitoring of the Sun, which began first with uninterrupted observations from near the South Pole over the austral summer. In addition, observations over multiple solar cycles have allowed helioseismologists to study changes in the Sun's structure over decades. These studies are made possible by global telescope networks like the Global Oscillations Network Group and the Birmingham Solar Oscillations Network, which have been operating for over several decades.
Types of solar oscillation
Solar oscillation modes are interpreted as resonant vibrations of a roughly spherically symmetric self-gravitating fluid in hydrostatic equilibrium. Each mode can then be represented approximately as the product of a function of radius and a spherical harmonic, and consequently can be characterized by the three quantum numbers which label:- the number of nodal shells in radius, known as the radial order ;
- the total number of nodal circles on each spherical shell, known as the angular degree ; and
- the number of those nodal circles that are longitudinal, known as the azimuthal order.
Pressure modes (p modes)
Pressure modes are in essence standing sound waves. The dominant restoring force is the pressure, hence the name. All the solar oscillations that are used for inferences about the interior are p modes, with frequencies between about 1 and 5 millihertz and angular degrees ranging from zero to order. Broadly speaking, their energy densities vary with radius inversely proportional to the sound speed, so their resonant frequencies are determined predominantly by the outer regions of the Sun. Consequently it is difficult to infer from them the structure of the solar core.Gravity modes (g modes)
Gravity modes are confined to convectively stable regions, either the radiative interior or the atmosphere. The restoring force is predominantly buoyancy, and thus indirectly gravity, from which they take their name. They are evanescent in the convection zone, and therefore interior modes have tiny amplitudes at the surface and are extremely difficult to detect and identify. It has long been recognized that measurement of even just a few g modes could substantially increase our knowledge of the deep interior of the Sun. However, no individual g mode has yet been unambiguously measured, although indirect detections have been both claimed and challenged. Additionally, there can be similar gravity modes confined to the convectively stable atmosphere.Surface gravity modes (f modes)
Surface gravity waves are analogous to waves in deep water, having the property that the Lagrangian pressure perturbation is essentially zero. They are of high degree, penetrating a characteristic distance, where is the solar radius. To good approximation, they obey the so-called deep-water-wave dispersion law:, irrespective of the stratification of the Sun, where is the angular frequency, is the surface gravity and is the horizontal wavenumber, and tend asymptotically to that relation as.What seismology can reveal
The oscillations that have been successfully utilized for seismology are essentially adiabatic. Their dynamics is therefore the action of pressure forces against matter with inertia density, which itself depends upon the relation between them under adiabatic change, usually quantified via the adiabatic exponent. The equilibrium values of the variables and are related by the constraint of hydrostatic support, which depends upon the total mass and radius of the Sun. Evidently, the oscillation frequencies depend only on the seismic variables,, and, or any independent set of functions of them. Consequently it is only about these variables that information can be derived directly. The square of the adiabatic sound speed,, is such commonly adopted function, because that is the quantity upon which acoustic propagation principally depends. Properties of other, non-seismic, quantities, such as helium abundance,, or main-sequence age, can be inferred only by supplementation with additional assumptions, which renders the outcome more uncertain.Data analysis
Global helioseismology
The chief tool for analysing the raw seismic data is the Fourier transform. To good approximation, each mode is a damped harmonic oscillator, for which the power as a function of frequency is a Lorentz function. Spatially resolved data are usually projected onto desired spherical harmonics to obtain time series which are then Fourier transformed. Helioseismologists typically combine the resulting one-dimensional power spectra into a two-dimensional spectrum.The lower frequency range of the oscillations is dominated by the variations caused by granulation. This must first be filtered out before the modes are analysed. Granular flows at the solar surface are mostly horizontal, from the centres of the rising granules to the narrow downdrafts between them. Relative to the oscillations, granulation produces a stronger signal in intensity than line-of-sight velocity, so the latter is preferred for helioseismic observatories.
Local helioseismology
Local helioseismology—a term coined by Charles Lindsey, Doug Braun and Stuart Jefferies in 1993—employs several different analysis methods to make inferences from the observational data.- The Fourier–Hankel spectral method was originally used to search for wave absorption by sunspots.
- Ring-diagram analysis, first introduced by Frank Hill, is used to infer the speed and direction of horizontal flows below the solar surface by observing the Doppler shifts of ambient acoustic waves from power spectra of solar oscillations computed over patches of the solar surface. Thus, ring-diagram analysis is a generalization of global helioseismology applied to local areas on the Sun. For example, the sound speed and adiabatic index can be compared within magnetically active and inactive regions.
- Time-distance helioseismology aims to measure and interpret the travel times of solar waves between any two locations on the solar surface. Inhomogeneities near the ray path connecting the two locations perturb the travel time between those two points. An inverse problem must then be solved to infer the local structure and dynamics of the solar interior.
- Helioseismic holography, introduced in detail by Charles Lindsey and Doug Braun for the purpose of far-side imaging, is a special case of phase-sensitive holography. The idea is to use the wavefield on the visible disk to learn about active regions on the far side of the Sun. The basic idea in helioseismic holography is that the wavefield, e.g., the line-of-sight Doppler velocity observed at the solar surface, can be used to make an estimate of the wavefield at any location in the solar interior at any instant in time. In this sense, holography is much like seismic migration, a technique in geophysics that has been in use since the 1940s. As another example, this technique has been used to give a seismic image of a solar flare.
- In direct modelling, the idea is to estimate subsurface flows from direct inversion of the frequency-wavenumber correlations seen in the wavefield in the Fourier domain. Woodard demonstrated the ability of the technique to recover near-surface flows the f modes.
Inversion