Helioseismology

These are principally caused by sound waves that are continuously driven and damped by convection near the Sun's surface.

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.

[6] Helioseismology also allowed accurate measurements of the quadrupole (and higher-order) moments of the Sun's gravitational potential,[7][8][9] 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.

[11] 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.

[12] Helioseismology benefits most from continuous monitoring of the Sun, which began first with uninterrupted observations from near the South Pole over the austral summer.

[13][14] In addition, observations over multiple solar cycles have allowed helioseismologists to study changes in the Sun's structure over decades.

Solar oscillation modes are interpreted as resonant vibrations of a roughly spherically symmetric self-gravitating fluid in hydrostatic equilibrium.

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 (purely radial motion) 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.

Gravity modes are confined to convectively stable regions, either the radiative interior or the atmosphere.

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.

[17] 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.

Spatially resolved data are usually projected onto desired spherical harmonics to obtain time series which are then Fourier transformed.

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—a term coined by Charles Lindsey, Doug Braun and Stuart Jefferies in 1993[28]—employs several different analysis methods to make inferences from the observational data.

[2] The Sun's oscillation modes represent a discrete set of observations that are sensitive to its continuous structure.

This allows scientists to formulate inverse problems for the Sun's interior structure and dynamics.

[38] These results were subsequently supplemented by analyses that linearize the full set of equations describing the stellar oscillations about a theoretical reference model [18][39][40] and are now a standard way to invert frequency data.

From the data analysis perspective, global helioseismology differs from geoseismology by studying only normal modes.

Local helioseismology is thus somewhat closer in spirit to geoseismology in the sense that it studies the complete wavefield.

Solar oscillations were first observed in the early 1960s[48][49] as a quasi-periodic intensity and line-of-sight velocity variation with a period of about 5 minutes.

[13][54] At a similar time, Jørgen Christensen-Dalsgaard and Douglas Gough suggested the potential of using individual mode frequencies to infer the interior structure of the Sun.

[55] They calibrated solar models against the low-degree data[56] finding two similarly good fits, one with low

It was not until Tom Duvall and Jack Harvey[14] connected the two extreme data sets by measuring modes of intermediate degree to establish the quantum numbers associated with the earlier observations that the higher-

model was established, thereby suggesting at that early stage that the resolution of the neutrino problem must lie in nuclear or particle physics.

Towards the end of the decade, observations also began to show that the oscillation mode frequencies vary with the Sun's magnetic activity cycle.

[63] This coincided with the start of normal operations of the Solar and Heliospheric Observatory (SoHO), which began producing high-quality data for helioseismology.

[66] Though the results later shifted back towards the traditional values used in the 1990s,[67] the new abundances significantly worsened the agreement between the models and helioseismic inversions.

Illustration of a solar pressure mode (p mode) with radial order n=14, angular degree l=20 and azimuthal order m=16. The surface shows the corresponding spherical harmonic. The interior shows the radial displacement computed using a standard solar model. [ 15 ] Note that the increase in the speed of sound as waves approach the center of the Sun causes a corresponding increase in the acoustic wavelength.
A propagation diagram for a standard solar model [ 16 ] showing where oscillations have a g-mode character (blue) or where dipole modes have a p-mode character (orange). The dashed line shows the acoustic cut-off frequency, computed from more precise modelling, and above which modes are not trapped in the star, and roughly-speaking do not resonate.
Power spectrum of the Sun using data from instruments aboard the Solar and Heliospheric Observatory on double-logarithmic axes. The three passbands of the VIRGO/SPM instrument show nearly the same power spectrum. The line-of-sight velocity observations from GOLF are less sensitive to the red noise produced by granulation . All the datasets clearly show the oscillation modes around 3mHz.
Power spectrum of the Sun around where the modes have maximum power, using data from the GOLF and VIRGO/SPM instruments aboard the Solar and Heliospheric Observatory. The low-degree modes (l<4) show a clear comb-like pattern with a regular spacing.
Power spectrum of medium angular degree ( ) solar oscillations, computed for 144 days of data from the MDI instrument aboard SOHO . [ 27 ] The colour scale is logarithmic and saturated at one hundredth the maximum power in the signal, to make the modes more visible. The low-frequency region is dominated by the signal of granulation. As the angular degree increases, the individual mode frequencies converge onto clear ridges, each corresponding to a sequence of low-order modes.
The internal rotation profile of the Sun inferred using data from the Helioseismic and Magnetic Imager aboard the Solar Dynamics Observatory . The inner radius has been truncated where the measurements are less certain than 1%, which happens around 3/4 of the way to the core. The dashed line indicates the base of the solar convection zone, which happens to coincide with the boundary at which the rotation profile changes, known as the tachocline.