Solar geodesy

Solar geodesy is the study of the size and shape of the Sun. In attempts to measure the shape of the Sun precisely, astronomers accidentally discovered solar oscillations, complex rhythmic pulsations involving both the deep interior and the atmosphere of the Sun.

Overview

Geodesy is the mathematical study of the size and shape of the Earth, and how these affect the precise location of points on the Earth’s surface. Solar geodesy is the application of this discipline to the Sun, especially the study of the size and shape of the Sun. The main impetus for such studies up to the mid-1900s was twofold: (1) to see if the Sun is oblate due to its rotation and (2) to find out if the Sun is slowly shrinking. Although not conclusively settled, it appears neither of these is actually the case. However, detailed measurements revealed something unexpected: the Sun undergoes complex oscillations, or as one researcher put it, “The Sun rings like a bell.” This discovery led to a new branch of solar studies called solar seismology, or helioseismology, which uses these oscillations as probes of the Sun’s interior, analogous to the way geologists use seismic waves as probes of the Earth’s interior. The Sun’s vibrations are geometrically complex, and solar physicists can infer the physical nature of the solar interior by analyzing the timing and amplitudes of the many vibration patterns observed on the Sun’s surface. Hence, solar geodesy is focused largely on helioseismology.

In 1960, Robert Leighton of the California Institute of Technology observed that small regions on the Sun’s surface were oscillating or pulsating with a period of approximately five minutes. He detected this oscillation by using the Doppler effect, a shifting of the wavelengths or frequencies of electromagnetic radiation. The motion of the source toward the observer causes a “blueshift,” a shift to shorter wavelengths. Motion of the source away from the observer causes a “redshift,” a shift to longer wavelengths. The amount of the shift is in proportion to the speed of the source toward or away from the observer. Leighton wondered whether the pulsations he observed were occurring only in small regions on the Sun, perhaps a few thousand kilometers in extent, or over a more extended region, possibly even the entire Sun. Although his discovery was noted and subsequently confirmed by many other observers at many observatories, these confirming observations could indicate only that the oscillations were localized. The data would not permit any conclusion regarding coherent motion (connected or related motion over a wide region) on the Sun.

In the early 1960s, a group of researchers at Princeton University led by Robert H. Dicke claimed that they had measured an oblateness (a distortion of a sphere resulting from compression along the polar axis and stretching around the equator) in the shape of the Sun. Using a highly specialized telescope of their own construction, they made measurements of the solar equatorial and polar diameters. They claimed the equatorial diameter to be slightly greater than the polar diameter.

They made these measurements to test Albert Einstein’s general theory of relativity against an alternative, the Brans-Dicke scalar-tensor theory, developed by Dicke and Carl Brans. Both theories predicted, among other things, that the orbit of the planet Mercury around the Sun should precess, meaning that Mercury’s elliptical orbit itself should slowly rotate around the focus occupied by the Sun. According to the theory of general relativity, this would be due to the warpage of space-time by the Sun’s mass. According to the Brans-Dicke theory, however, a small oblateness in the shape of the Sun would cause the same thing. Thus, the oblateness measurements were crucial in distinguishing between general relativity and the Brans-Dicke scalar-tensor theory.

In the mid-1960s, Henry Hill at the University of Arizona designed and built another specialized telescope for detecting distortions in the Sun’s surface. Hill’s preliminary measurements, however, could not confirm the measurements of the Princeton group. By the late 1960s, other astronomers had shown that the Princeton results probably were due to solar activity that was producing increases in brightness in the Sun’s equatorial regions. The increased brightness was caused by plages—bright, patchy regions on the Sun produced by magnetic activity. The plages are usually found near sunspots or centers of magnetic activity, which tend to concentrate within about 30° to 40° north and south of the Sun’s equator. Measurements of the solar equatorial diameter are highly influenced by plages. There is a tendency to overestimate the edge of the Sun, or its limb, because of the bright glow of these plages near the solar equator.

In 1975, Hill and Robin Stebbins concluded that the Sun was not oblate but apparently fluctuated or oscillated rhythmically over a large region, possibly its entire surface. Further research verified that the observed phenomena were genuinely solar, not introduced by Earth’s atmosphere or telescopic effects. Delicate instruments always have random fluctuations, or “noise,” associated with their measurements, but researchers showed convincingly that the observed oscillations were real and not simply the misinterpretation of observational noise.

It came to be accepted that the Sun shakes or vibrates in a range of spectacular ways, like a ringing bell. In this process, the Sun’s shape undergoes tiny, patterned distortions of a rhythmic nature. These distortions are, in effect, three-dimensional waves that pass from the deep interior of the Sun to the surface and also move about the Sun’s circumference. The periods of these measured oscillations range from about three minutes to 160 minutes and perhaps longer.

These oscillation patterns carry information about the deep solar interior, which cannot be observed directly since the Sun’s interior is opaque. The waves or disturbances producing these oscillations originate at different levels within the Sun, some just beneath the surface and others farther within the interior. The observed properties of the oscillations—their timing and the extent of their displacement—depend upon the environment through which they pass on their way to the surface, where solar physicists detect them spectroscopically using the Doppler effect. Just as geophysicists study seismic waves traveling through Earth as a result of earthquakes, solar physicists study solar oscillations traveling through the Sun to study the solar interior.

Why does the Sun shake? What in the solar interior sets the oscillations in motion, and how do they move through the Sun? All physical bodies, whether they be solid or fluid (fluids include gases and liquids), can oscillate or shake with a variety of frequencies or periods. Virtually any disturbance or natural internal motion can start the oscillations. Convection (the process whereby heat is transferred in the outer regions of the solar interior) is one such stimulus. Solar convection involves the ascent of hot, lower-density bubbles of gas. These bubbles are heated in the deeper, hotter interior; with lower density, they rise buoyantly upward and convey the heat to higher, cooler layers. The motion of the bubbles disturbs the surrounding gases and starts them oscillating, and the oscillations move throughout the Sun. Just as the length of an organ pipe determines the note played, certain fractions of that length produce overtones or harmonics. The Sun’s spherical shape, interior density, and temperature determine both the frequency and the length of the waves that are set in motion, regardless of the process that caused those waves.

In a structure such as the Sun, the oscillations can be of two types, depending on the nature of the force that maintains the oscillation. Either gravity or pressure can supply the restoring force (the mechanism that brings the displaced fluid back to its original position, thus maintaining the motion necessary to produce the pulsations or waves). Small pressure fluctuations give rise to acoustic or soundlike waves, alternate compressions, and rarefactions that move through the fluid at the speed of sound. Waves of this type are referred to as “p modes.” Just below the visible solar surface, the convection produces a deafening roar, similar to that produced by a jet or rocket engine.

Gravity waves are created when an element or small volume of fluid is displaced and subsequently returned to its position by gravity. This type of wave can occur only when the density or compactness of the material varies with depth. On Earth, water waves larger than small ripples are of this type. The wave moves toward the shore, and its vertical displacement is restored by gravity, causing the wave to move along the surface of the water. (These gravity waves are not to be confused with the gravitational waves predicted by Einstein’s theory of relativity, which are of a completely different nature.)

Any movement or perturbation in the interior of the Sun can start the quivering process and produce an oscillation. Individual oscillations can be manifested in many ways, with a variety of wavelengths and nodes (regions or points free of oscillations; in a vibrating string, the node would be the tied-down point not undergoing vibration). Because of the three-dimensional, spherical structure of the Sun, a virtually endless variety of modes or patterns can occur in it. Some modes encompass the Sun’s entire structure, while others take place in localized regions.

The quivering waves generated by these oscillations reflect from the surface layers of the Sun and speed back toward the deep interior, where, in turn, they are refracted or bent back toward the surface. The layer of refraction depends on the speed of the waves. In many cases, the speed is the local speed of sound for the solar interior gas, which, in turn, depends on the temperature of the gas at that location. The reflection from the surface is caused by a rapid decrease in density since the surface represents an abrupt boundary between the solar gas and space. Since sound cannot travel through a vacuum, the waves are reflected at the boundary back into the Sun. Such a process can occur again and again, resulting in waves moving along curved paths and bouncing and refracting their way completely around the interior of the Sun.

Knowledge Gained

The Sun oscillates like a giant, spherical bell. This discovery was first made by Robert Leighton in 1960. The observed oscillations were about five minutes in duration. It was not known at that time whether the oscillatory motion involved small, localized regions on the Sun or much larger regions. Hill’s 1975 observations found oscillations of relatively short duration, with periods of a few minutes. A considerable effort went into showing that these oscillations were real and not the result of distortions caused by Earth’s atmosphere or by instrumental effects. By 1980, however, similar oscillations had been observed at other observatories, and some had been shown to have periods between two and three hours long.

These oscillations were found to be of two types: (1) pressure waves and (2) gravity waves, based on the natural force that maintains the oscillations. In the case of short-period waves, those lasting a few to several minutes, the wave is essentially a sound wave traveling through the solar interior. Such waves are known as pressure waves since alternate compression and rarefaction of local gas produce the oscillations. Long-period waves, with oscillation periods as long as two or three hours, have gravity as the driving, restoring force. A single oscillation can be set up in an almost infinite number of geometric shapes or modes. Many of these patterns have striking geometrical beauty and symmetry.

Observations of solar oscillations have revealed many new things about the nature of the Sun’s interior and have confirmed other things. For example, at the surface, the Sun’s equatorial zone is observed to rotate somewhat faster than do regions north or south of the equator; this phenomenon is known as differential rotation. The rotation of the Sun’s interior cannot be directly observed, but observations of surface waves generated in the deep and shallow solar interior indicate a complex rotation pattern, with “flowing rivers” and “zones” and layers rotating at different and sometimes varying rates. Other studies find oscillation patterns that are consistent with the Sun’s deep interior temperature being about fifteen million kelvins, a value derived from computer models of the Sun’s interior.

Early theories of stellar evolution and energy generation held that stars should slowly contract gravitationally as they age, so solar geodesy was once concerned especially with measuring such shrinkage in the Sun. Solar eclipses provided much of the raw data. If the Sun were shrinking, annular eclipses would have been more common, and the duration of totality during total eclipses would have been shorter in the past. Although some early studies claimed to have found these effects, they have not been substantiated by more recent work that better accounts for instrumental errors.

Context

Later studies concentrated on measuring solar oblateness, but claims that the Sun is slightly oblate have not been confirmed. Instead, solar observers have discovered that the Sun oscillates in complex patterns. By observing oscillations visible on the Sun’s surface, astronomers are assembling a detailed picture of the solar interior in much the same way that geologists and geophysicists gain knowledge of Earth’s interior by the study of waves produced in earthquakes. The most extensive series of observations of solar oscillations have been made by the Global Oscillations Network Group (GONG), an array of small telescopes around the world that provide continuous monitoring of solar oscillations over many years. The data gathered by GONG are enabling astronomers to differentiate real solar oscillations (together with their amplitudes and periods) from noise produced by instrumentation or Earth’s rotation. An average value for the diameter of the Sun is 1,392,000 kilometers, or the equivalent of 110 Earths lined up side by side. In the twenty-first century study into solar oscillations continued. Analyzing ten years of data from NASA’s Solar Dynamics Observatory, in 2021, scientists reported newly-discovered long-range solar oscillations that provided new insights into the Sun’s interior structure and dynamics.

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