Helioseismology, a term coined by Douglas Gough, 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 (also coined by Gough), 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 realised that the oscillations propagated throughout the Sun and could allow scientists to study the Sun's deep interior. The modern field is separated into global helioseismology, which studies the Sun's resonant modes, and local helioseismology, which studies all the waves propagating at the Sun's surface.
Helioseismology has contributed to a number of scientific breakthroughs. The most notable was to show 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 (and higher-order) 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 a distinct entity.
Helioseismology benefits most from continuous monitoring of the Sun, which began first with uninterrupted observations from near the South Pole over the southern 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 (GONG) and the Birmingham Solar Oscillations Network (BiSON), which have been operating for over 20 years.
Solar oscillation modes are interpreted (to first order) as vibrations of a spherically symmetric self-gravitating fluid in hydrostatic equilibrium. Each mode is then characterised by three numbers:
The latter two correspond to the quantum numbers of the spherical harmonics. Under these assumptions, it can be shown that the oscillations are separated into two categories of interior oscillations and a third special category of surface modes.
Pressure modes are in essence standing sound waves. The dominant restoring force is the pressure (rather than buoyancy), 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. They span angular degrees from zero (purely radial motion) to several hundred.
Gravity modes are lower-frequency modes that are confined to the convectively-stable interior. The restoring force is buoyancy and thus indirectly gravity, from which they take their name. They are evanescent in the convection zone and therefore have tiny amplitudes at the surface. No individual g-modes have been detected but indirect detections have been claimed.
Surface gravity waves are analogous to waves on deep water. To good approximation, they follow the same dispersion law: , where is the angular frequency, is the surface gravity and is the horizontal wavenumber. Surface gravity modes observed on the Sun are all of very high degree ().
The chief tool for analysing data in global helioseismology 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. Resolved data is usually integrated over the desired spherical harmonic to obtain a single timeseries that can be Fourier transformed. In this way, helioseismologists combine a power spectrum for each spherical harmonic into a two-dimensional power spectrum.
The lower frequency range of the oscillations is dominated by the variations caused by granulation. This must first be filtered out before (or at the same time that) 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.
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. Given a reference model of the Sun, the differences in the mode frequencies are weighted averages of the differences between the structure of the reference model and the real Sun. The difference in the mode frequencies can then be used to infer the differences in the structures. The weighting functions of these averages are known as kernels.
The first inversions of the Sun's structure were made using Duvall's law and later using Duvall's law linearised about a reference solar model. These results were superseded by analyses that use the full set of equations describing the stellar oscillations and are now the standard way to compute inversions. The inversions demonstrated differences in solar models that were greatly reduced by implementing gravitational settling: the gradual separation of heavier elements towards the solar centre (and lighter elements to the surface to replace them).
If the Sun were perfectly spherical, the modes with different azimuthal orders m would have the same frequencies. Rotation, however, breaks this degeneracy, and the modes frequencies differ by rotational splittings that are weighted-averages of the rotation rate throughout the Sun. Different modes are sensitive to different parts of the Sun and, given enough data, these differences can be used to infer the rotation rate throughout the Sun. For example, if the Sun rotated with the same rotational frequency throughout, then all the modes would be split by the same amount. In reality, different layers of the Sun rotate at different speeds, as can be seen at the surface, where the equator rotates faster than the poles. The Sun rotates slowly enough that a spherical, non-rotating model serves as close enough to reality to derive the rotational kernels.
Helioseismology has shown that the Sun has a rotation profile with several features:
Helioseismology was born from analogy with geoseismology but several important differences remain. First, the Sun lacks a solid surface and therefore cannot support shear waves. 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.
Because the Sun is a star, helioseismology is closely related to the study of oscillations in other stars, known as asteroseismology. Helioseismology is most closely related to the study of stars whose oscillations are also driven and damped by their outer convection zones, known as solar-like oscillators, but the underlying theory is broadly the same for other classes of variable star.
The principal difference is that oscillations in distant stars cannot be resolved. Because the brighter and darker sectors of the spherical harmonic cancel out, this restricts asteroseismology almost entirely to the study of low degree modes (angular degree ). This makes inversion much more difficult but upper limits can still be achieved by making more restrictive assumptions.
Solar oscillations were first observed in the early 1960s as a quasi-periodic intensity and line-of-sight velocity variation with a period of about 5 minutes. Scientists gradually realised that the oscillations might be global modes of the Sun and predicted that the modes would form clear ridges in two-dimensional power spectra. The ridges were subsequently confirmed in observations in the mid 1970s although individual mode frequencies were not measured until several years later. 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.
Helioseismology developed rapidly in the 1980s. A major breakthrough was made when observations from Antarctica linked the frequencies for modes of low and intermediate angular degree, from which the radial orders of the modes could be identified. In addition, new methods of inversion developed, allowing researchers to infer the sound speed profile of the Sun. Towards the end of the decade, observations also began to show that the oscillation mode frequencies vary with the Sun's magnetic activity cycle.
To overcome the problem of not being able to observe the Sun at night, several groups had begun to assemble networks of telescopes (e.g. the Birmingham Solar Oscillations Network, or BiSON, and the Global Oscillation Network Group) from which the Sun would always be visible to at least one node. Long, uninterrupted observations brought the field to maturity, and the state of the field was summarized in a 1996 special issue of Science magazine. This coincided with the start of normal operations of the Solar and Heliospheric Observatory (SoHO), which began producing high-quality data for helioseismology.
The subsequent years saw the resolution of the solar neutrino problem and the long observations began to allow analysis of multiple solar activity cycles. The agreement between standard solar models and helioseismic inversions was disrupted by new measurements of the heavy element content of the solar photosphere based on detailed three-dimensional models. Though the results later shifted back towards the traditional values used in the 1990s, the new abundances significantly worsened the agreement between the models and helioseismic inversions. The cause of the discrepancy remains unsolved and is known as the solar abundance problem.
Space-based observations by SoHO have continued and SoHO was joined in 2010 by the Solar Dynamics Observatory (SDO), which has also been monitoring the Sun continuously since its operations began. In addition, ground-based networks (notably BiSON and GONG) continue to operate, providing nearly continuous data from the ground too.
The 160-minute solar cycle was an apparent periodic oscillation in the solar surface which was observed in a number of early sets of data collected for helioseismology.
The presence of a 160 minute cycle in the Sun is not substantiated by contemporary solar observations, and the historical signal is considered by mainstream scientists to occur as the redistribution of power from the diurnal cycle as a result of the observation window and atmospheric extinction.Amil Kumar Das
Amil Kumar Das (1902 – February 18, 1961) was an Indian astronomer.
During the International Geophysical Year, observatories in Madrid, India, and Manila were responsible for monitoring solar effects. The Kodaikanal Solar Observatory in South India performed this monitoring using their recently built solar tunnel telescope. Dr. Das was the director of the Kodaikanal observatory at this time. In 1960 he was responsible for installing a tower/tunnel telescope at the facility that would be used to perform some of the first ever helioseismology investigations.
The crater Das on the far side of the Moon is named after him.Asteroseismology
Asteroseismology or astroseismology is the study of oscillations in stars. Because a star's different oscillation modes are sensitive to different parts of the star, they inform astronomers about the internal structure of the star, which is otherwise not directly possible from overall properties like brightness and surface temperature. Asteroseismology is closely related to helioseismology, the study of stellar oscillations specifically in the Sun. Though both are based on the same underlying physics, more and qualitatively different information is available for the Sun because its surface can be resolved.Birmingham Solar Oscillations Network
The Birmingham Solar Oscillations Network (BiSON) consists of a network of six remote solar observatories monitoring low-degree solar oscillation modes. It is operated by the High Resolution Optical Spectroscopy group of the School of Physics and Astronomy at the University of Birmingham, UK, in collaboration with Sheffield Hallam University, UK. They are funded by the Science and Technology Facilities Council (STFC).The BiSON has been collecting data continuously on solar oscillations since 1976, making it the longest running helioseismology network with data covering three solar cycles.Bright giant
The luminosity class II in the Yerkes spectral classification is given to bright giants. These are stars which straddle the boundary between ordinary giants and supergiants, based on the appearance of their spectra.Convection zone
A convection zone, convective zone or convective region of a star is a layer which is unstable to convection. Energy is primarily or partially transported by convection in such a region. In a radiation zone, energy is transported by radiation and conduction.
Stellar convection consists of mass movement of plasma within the star which usually forms a circular convection current with the heated plasma ascending and the cooled plasma descending.
The Schwarzschild criterion expresses the conditions under which a region of a star is unstable to convection. A parcel of gas that rises slightly will find itself in an environment of lower pressure than the one it came from. As a result, the parcel will expand and cool. If the rising parcel cools to a lower temperature than its new surroundings, so that it has a higher density than the surrounding gas, then its lack of buoyancy will cause it to sink back to where it came from. However, if the temperature gradient is steep enough (i. e. the temperature changes rapidly with distance from the center of the star), or if the gas has a very high heat capacity (i. e. its temperature changes relatively slowly as it expands) then the rising parcel of gas will remain warmer and less dense than its new surroundings even after expanding and cooling. Its buoyancy will then cause it to continue to rise. The region of the star in which this happens is the convection zone.Free-fall time
The free-fall time is the characteristic time that would take a body to collapse under its own gravitational attraction, if no other forces existed to oppose the collapse. As such, it plays a fundamental role in setting the timescale for a wide variety of astrophysical processes—from star formation to helioseismology to supernovae—in which gravity plays a dominant role.Global Oscillations Network Group
The Global Oscillation Network Group (GONG) is a community-based program to study solar internal structure and dynamics using helioseismology.
Six solar observatories are involved, with the intention of achieving almost unbroken observation of the Sun. The six observatories are the Teide Observatory (Canary Islands), the Learmonth Solar Observatory (Western Australia), the Big Bear Solar Observatory (California), the Mauna Loa Solar Observatory (Hawaii), the Udaipur Solar Observatory (India) and the Cerro Tololo Inter-American Observatory (Chile). In 2001, the original GONG detectors were upgraded to 1000 x 1000 pixels and continuous magnetograms were implemented, and the new system is known as GONG++. More recently (c. 2010), improvements to GONG observatory instrumentation have been made to enable imaging of
the Hα ("H-alpha") spectral line of hydrogen in the solar atmosphere.
The GONG Program is managed by the National Solar Observatory, which is operated by AURA, Inc. under a cooperative agreement with the National Science FoundationHarvey Summit
Harvey Summit (78°18′52″S 162°18′9″E) is a peak 2,644 metres (8,675 ft) high at the head of McDermott Glacier in the Royal Society Range of Victoria Land, Antarctica. It was named after John W. Harvey of the National Solar Observatory who, along with Thomas L. Duvall, Jr. and Martin Pomerantz, conducted research in helioseismology at the South Pole for some years from 1980 onwards.Jørgen Christensen-Dalsgaard
Jørgen Christensen-Dalsgaard (born 6 October 1950) is a Danish astronomer at Aarhus University in Denmark. He specializes in asteroseismology and helioseismology. He has made significant contributions to both fields, including predicting the oscillation of Sun-like stars in 1983. He is the head of "Rumudvalget" (the committee of space of the Danish Ministry of Science, Technology and Innovation) and the Stellar Astrophysics Centre (SAC) supported by the Danish National Research Foundation. He is co-investigator on the Kepler mission and, with Hans Kjeldsen in Aarhus, leads the 500+ researchers in the Kepler Asteroseismic Science Consortium (KASC). KASC is responsible for the asteroseismology component of the Kepler mission. Christensen-Dalsgaard has published several papers on this subject. He was also previously the president of Commission 27 of the International Astronomical Union.He has been featured on Danish television and radio several times and has given many free public lectures on astronomy and asteroseismology.Christensen-Dalsgaard obtained his PhD from the University of Cambridge in 1978, under the supervision of Douglas Gough.Lead star
A lead star is a low-metallicity star with an overabundance of lead and bismuth as compared to other products of the S-process.Mount Duvall
Mount Duvall (78°22′S 162°31′E) is an ice-covered mountain, 2,149 metres (7,050 ft) high, standing close west of Fisher Bastion on the north side of Solomon Glacier, in the Royal Society Range, Victoria Land. It was named by the Advisory Committee on Antarctic Names (1994) after Thomas L. Duvall Jr., who conducted research, along with John W. Harvey and Martin Pomerantz, in helioseismology at the South Pole Station from 1980.Peter Goldreich
Peter Goldreich (born July 14, 1939) is an American astrophysicist whose research focuses on celestial mechanics, planetary rings, helioseismology and neutron stars. He is currently the Lee DuBridge Professor of Astrophysics and Planetary Physics at California Institute of Technology. Since 2005 he has also been a professor at the Institute for Advanced Study in Princeton, New Jersey. Asteroid 3805 Goldreich is named after him.Philip R. Goode
Philip R. Goode is an American theoretical physicist also working in observational astronomy and its instrumentation. He is a Distinguished Research Professor of Physics at New Jersey Institute of Technology (NJIT). His career divides into five overlapping periods as follows.
His earliest work in theoretical nuclear physics, 1967-1982.
Pioneering research in helioseismology (1981-2005).
He created, developed and directed (1995-2014) NJIT’s Center for Solar-Terrestrial Research (CSTR), which made NJIT one of the most important universities in the U.S. for observational solar physics, heliophysics, and solar-terrestrial physics.
The construction of, and scientific results from, the world’s most powerful solar telescope (2002–present) in Big Bear Solar Observatory (BBSO). In 2017, this ground-based telescope was renamed the Goode Solar Telescope (GST). Goode was director of BBSO from 1997, when the observatory was transferred from Caltech to NJIT, until 2013.
Sustained earthshine studies of Earth’s reflectance (1998–present).Picard (satellite)
PICARD is a satellite dedicated to the simultaneous measurement of the absolute total and spectral solar irradiance, the diameter and solar shape, and to the Sun's interior probing by the helioseismology method. These measurements obtained throughout the mission allow study of their variations as a function of solar activity. It launched, along with the Prisma spacecraft, on 15 June 2010 on a Dnepr launcher from Dombarovskiy Cosmodrome, near Yasny, Russia. The mission, originally planned for two years, ended on 4 April 2014.Solar tower (astronomy)
A solar tower, in the context of astronomy, is a structure used to support equipment for studying the sun, and is typically part of solar telescope designs. Generically, the term solar tower has many more uses especially for a type of power production using Earth's Sun. Solar tower observatories are also called vacuum tower telescopes.
Solar towers are used to raise the observation equipment above the atmospheric disturbances caused by solar heating of the ground and the radiation of the heat into the atmosphere. Traditional observatories do not have to be placed high above ground level, as they do most of their observation at night, when ground radiation is at a minimum.
The horizontal Snow solar observatory was built on Mount Wilson in 1904. It was soon found that heat radiation was disrupting observations. Almost as soon as the Snow Observatory opened, plans were started for a 60-foot-tall (18 m) tower that opened in 1908 followed by a 150-foot (46 m) tower in 1912. The 60-foot (18 m) tower is currently used to study helioseismology, while the 150-foot (46 m) tower is active in UCLA's Solar Cycle Program.
The term has also been used to refer to other structures used for experimental purposes, such as the Solar Tower Atmospheric Cherenkov Effect Experiment (STACEE), which is being used to study Cherenkov radiation, and the Weizmann Institute solar power tower.Standard solar model
The standard solar model (SSM) is a mathematical treatment of the Sun as a spherical ball of gas (in varying states of ionisation, with the hydrogen in the deep interior being a completely ionised plasma). This model, technically the spherically symmetric quasi-static model of a star, has stellar structure described by several differential equations derived from basic physical principles. The model is constrained by boundary conditions, namely the luminosity, radius, age and composition of the Sun, which are well determined. The age of the Sun cannot be measured directly; one way to estimate it is from the age of the oldest meteorites, and models of the evolution of the Solar System. The composition in the photosphere of the modern-day Sun, by mass, is 74.9% hydrogen and 23.8% helium. All heavier elements, called metals in astronomy, account for less than 2 percent of the mass. The SSM is used to test the validity of stellar evolution theory. In fact, the only way to determine the two free parameters of the stellar evolution model, the helium abundance and the mixing length parameter (used to model convection in the Sun), are to adjust the SSM to "fit" the observed Sun.Tachocline
The tachocline is the transition region of Stars of more than 0.3 Solar masses, between the radiative interior and the differentially rotating outer convective zone. It is in the outer third of the Sun (by radius). This causes the region to have a very large shear as the rotation rate changes very rapidly. The convective exterior rotates as a normal fluid with differential rotation with the poles rotating slowly and the equator rotating quickly. The radiative interior exhibits solid-body rotation, possibly due to a fossil field. The rotation rate through the interior is roughly equal to the rotation rate at mid-latitudes, i.e. in-between the rate at the slow poles and the fast equator. Recent results from helioseismology indicate that the tachocline is located at a radius of at most 0.70 times the Solar radius (measured from the core, i.e., the surface is at 1 solar radius), with a thickness of 0.04 times the solar radius. This would mean the area has a very large shear profile that is one way that large scale magnetic fields can be formed.
The geometry and width of the tachocline are thought to play an important role in models of the stellar dynamos by winding up the weaker poloidal field to create a much stronger toroidal field. Recent radio observations of cooler stars and brown dwarfs, which do not have a radiative core and only have a convective zone, demonstrate that they maintain large-scale, solar-strength magnetic fields and display solar-like activity despite the absence of tachoclines. This suggests that the convective zone alone may be responsible for the function of the solar dynamo.The term tachocline was coined in a paper by Edward Spiegel and Jean-Paul Zahn in 1992 by analogy to the oceanic thermocline.Yvonne Elsworth
Yvonne Elsworth FRS FInstP FRAS is an Irish physicist, Professor of Helioseismology and Poynting Professor of Physics in the School of Physics and Astronomy at the University of Birmingham. Elsworth is also the Head of the Birmingham Solar Oscillations Network (BiSON), the longest running helioseismology network with data covering three solar cycles.