Trapped Sounds

tte Sun is playing a secret melody, which produces a widespread throbbing motion of its surface, tte sounds are coursing through the Sun's interior, causing the entire globe, or parts of it, to move in and out, slowly and rhythmically like the regular rise and fall of tides in a bay or of a beating heart (Fig. 4.1). Such radial oscillations are imperceptible to the naked eye; the surface moves a hundred-thousandth (0.000 01) of the solar radius.

tte Sun's tiny periodic motions have nevertheless been observed as subtle changes in the wavelength of absorption lines that are formed in the solar gas. When part of the Sun heaves up toward us, the wavelength of the line formed in that region is shortened, introducing a small blueshift in its spectrum; if the region moves away from us, back toward the solar interior, the wavelength is lengthened, introducing a redshift in the spectrum.

ttese motions are inferred by subtracting an image of the Sun taken in the long-wavelength side of a stationary, or non-moving, absorption line from an image taken in the short-wavelength side of the line. In such a "Dopplergram", an outward motion of a region results in an increase in brightness at that place in the subtracted image, while an inward motion darkens it. tte Dopplergrams show that bouncing regions move in and out all over the Sun (Fig. 4.2).

tte American astrophysicist Robert B. Leighton (1919-1997) and his students, Robert W. Noyes (1934- ) and George W. Simon (1934- ), were the first to employ such techniques, ttey used subtracted images to show that the local vertical motions are not random in their time variation, but instead oscillate with a period of about five minutes. As Leighton announced, at an international conference in 1960, a sequence of Dopplergrams indicated that:

"ttese vertical motions show a strong oscillatory character, with a period of 296 ± 3

seconds [about five minutes].19

tte observed five-minute oscillations had a velocity amplitude of about half a kilometer per second, and covered roughly a third of the visible disk at any given time, localized within numerous patches a few thousand kilometers across. Moreover, the repetitive, vertical oscillations did not seem to be continuous, apparently lasting only a few periods before disappearing.

But the Sun does not resonate with a single pure note, tte observed oscillations turned out to be due to the combined effect of millions of sound waves traveling in all directions and with a large range of sizes. And it is not just the visible part of the Sun, but the interior as well that is oscillating.

Some of these oscillations can last several weeks to months, and they are not confined to localized regions on the Sun. Careful observations showed that the five-minute oscillations are a global phenomenon, coherent across the entire Sun. Eventually, other solar astronomers demonstrated that the entire Sun is ringing like a bell, with sound waves that resonate within its interior and penetrate to its very core.

In 1961 Franz Daniel "F. D." Kahn (1926-1998) showed that sound waves could be trapped near the visible solar disk, essentially because the temperature increases both

FIG. 4.1 Internal contortions The Sun exhibits over a million shapes produced by its oscillations. Two of these shapes are illustrated here with exaggerated amplitude. (Courtesy of Arthur N. Cox and Randall J. Bos, Los Alamos National Laboratory.)

above and below it. tte hotter material acts as a kind of mirror, reflecting sound waves back into the regions they come from. So, the Sun's throbbing motions could be caused by sound waves trapped inside the Sun; on striking the visible disk and rebounding back down, the sound waves cause the gases there to move up and down.

Building upon this result, Leighton and his colleagues concluded in 1962 that:

"tte atmosphere may therefore act as a wave guide for laterally moving [acoustic] waves, and the observed oscillation may correspond to the lower "cutoff" frequency of the waveguide.20

In an extensive observational study of the five-minute oscillations, Edward N. Frazier (1939- ), at the University of California, Berkeley, showed, in 1968, that the oscillatory power is concentrated at specific combinations of size and duration, suggesting to him that they are not being pushed in and out by the motion of granules seen on the Sun. Instead, the five-minute oscillations were attributed to sound waves generated by the same convection that produces the up and down granular motion. In his own words:

"tte well-known five-minute oscillations are primarily standing resonant acoustic

[sound] waves____["ttey] are not formed directly from the "piston action" of a con-

vective cell impinging on the stable photosphere, but rather are formed within the convection zone itself.21

According to this interpretation, a sound wave resonates within the convective zone, like the plucked string of a guitar or the beat of a drum, effectively standing in one place and growing in power, ttis resonance effect is somewhat analogous to repeated pushes on a swing. If the pushes occur at the same point in each swing, they can increase the energy of the motion. In the absence of such a resonance, the perturbations would be haphazard and the effect would eventually fade away. When you regularly move water

Photosphere

FIG. 4.2 The pulsating Sun Sound waves inside the Sun cause the visible solar disk to move in and out. This heaving motion can be described as the superposition of literally millions of oscillations, including the one shown here for regions pulsing inward (red regions) and outward (blue regions). The sound waves, whose paths are represented here by black lines inside the cutaway section, resonate through the Sun. They are produced by hot gas churning in the convective zone, which lies above the radiative zone and the Sun's core. (Courtesy of John W. Harvey, National Optical Astronomy Observatories, except cutaway.)

in a bathtub, the waves similarly grow in size, but when you swish it randomly, the water develops a choppy confusion of small waves.

As suggested in 1970 by Roger Ulrich (1942- ) at the University of California, Los Angeles, and independently in 1971 by John Leibacher (1941-), then at the Harvard College Observatory, and Robert F. Stein (1935-), then at Brandeis University, the convective zone acts as a resonant cavity, or spherical shell, tte sound waves are trapped inside this circular waveguide, and can't get out. ttey therefore go around and around, bouncing repeatedly against the photosphere like a hamster caught in an exercise wheel, reverberating between the cavityboundaries and driving oscillations in the overlying material.

A real breakthrough came in 1975, when the German astronomer Franz-Ludwig Deubner (1934- ) showed that the oscillating power is concentrated into narrow ridges in a spatial-temporal display of horizontal wavelength and period, which meant that they are due to the standing acoustic waves that had been predicted, ttat is, the vertical motions vary in space and time across the Sun, but only at specific sizes and periods, creating a regular pattern in the apparently random oscillations. For a given size, only certain periods will give a cavity that has the proper depth for a resonant superposition, ttis pattern is described in terms of narrow bands, or ridges, of enhanced oscillation power when decomposed into a two-dimensional display of size and period, or horizontal wavelength and frequency (Fig. 4.3).

Many of the sound waves eventually fade away without contributing much to the observed motions. Other sound waves are amplified by repeated reflection, like a swing

FIG. 4.3 Oscillation period and size Sound waves resonate deep within the Sun, producing oscillations of the photosphere with periods near five minutes, or frequencies near 3 milliHertz, abbreviated 3 mHz and equal to 0.003 cycles per second. Only waves with specific combinations of period or frequency (left axis) and size, wavelength, or angular degree (bottom axis) resonate within the Sun, producing the fine-tuned "ridges" in the oscillation power shown in this image, obtained from 2 months of

Deg lv data from the Michelson Dop-pler Imager, abbreviated MDI, instrument aboard the SOlar and Heliospheric Observatory, or SOHO for short. The angular degree is the inverse of the size or spatial wavelength, and an angular degree of 150 corresponds to waves about 27,000 kilometers in size. The oscillation power is contained within specific combinations of frequency and degree, demonstrating that the oscillations detected in the photosphere are due to internal standing waves confined within resonant cavities. (Courtesy of the SOHO MDI/SOI consortium. SOHO is a project of international cooperation between ESA and NASA.)

that is pumped at regular intervals. Such a standing wave rises in the same location, over and over again, pushing the visible solar disk in and out at the same places every time it circulates around the Sun. A sound wave's path inside the Sun then forms a regular sequence ofloops, like the lace filigree on a napkin or the hoops in a round rug (Fig. 4.4).

When a sound wave angles up to the visible solar gases, it strikes them with a glancing blow, turning around and traveling back into the Sun, like light reflected from a mirror,

FIG. 4.4 Sound paths The trajectories of sound waves are shown in a cross section of the solar interior. The rays are bent inside the Sun, like light within the lens of an eye, and circle the solar interior in spherical shells or resonant cavities. Each shell is bounded at the top by a large, rapid density drop near the photosphere and bounded at the bottom at the inner turning point (dotted circles), where the bending rays undergo total internal refraction, owing to the increase in sound speed with depth inside the Sun. How deep a wave penetrates and how far around the Sun it goes before it hits the photosphere depends on the harmonic degree, I. The white curve is for I = 0, the blue one for I = 2, green for I = 20, yellow for I = 25 and red for I = 75. (Courtesy of J0rgen Christensen-Dalsgaard and Philip H. Scherrer.)

FIG. 4.4 Sound paths The trajectories of sound waves are shown in a cross section of the solar interior. The rays are bent inside the Sun, like light within the lens of an eye, and circle the solar interior in spherical shells or resonant cavities. Each shell is bounded at the top by a large, rapid density drop near the photosphere and bounded at the bottom at the inner turning point (dotted circles), where the bending rays undergo total internal refraction, owing to the increase in sound speed with depth inside the Sun. How deep a wave penetrates and how far around the Sun it goes before it hits the photosphere depends on the harmonic degree, I. The white curve is for I = 0, the blue one for I = 2, green for I = 20, yellow for I = 25 and red for I = 75. (Courtesy of J0rgen Christensen-Dalsgaard and Philip H. Scherrer.)

and causing the gas to rise and fall in a ponderous rhythm. Above this level, which is the same for all waves, the sound waves are evanescent and cannot propagate.

tte inner turning point, or cavity bottom, depends on the increase of sound speed, or wave velocity, with depth. Because the speed of sound is greater in a hotter gas, it increases in the deeper, hotter layers of the Sun. tte deeper part of a wave front traveling obliquely into the Sun moves faster than the shallower part and pulls ahead of it. Gradually the advancing wave is once again headed back up. Sound is similarly refracted down into the cool air above a mountain lake; the hotter, higher air bends the sound downward permitting it to travel great distances across the lake's surface.

So, the increase in sound speed with depth eventuallybends a downward-moving sound wave back up, and this inner turning point depends upon the period of the wave. Long-wavelength sound waves penetrate deep into the Sun before they return, while short waves travel through shallower and cooler layers and bounce off the visible solar disk more often, tte turn-around depth also depends on physical conditions within the Sun's interior and can be used to determine their radial variation within the Sun.

Each note of the vibrating Sun is similar to the sound wave produced when you tap a crystal glass or strike a doorbell's chime; an outside force makes each sound, which lasts only a short time. Something must therefore ring the solar bell, and set the oscillations in motion. And because any oscillation must eventually lose energy and disappear, the solar oscillations must be continually excited.

tte sound, or acoustic, waves that produce the five-minute oscillations are probably generated by vigorous turbulence in the convective zone, where motions at near-sonic speed are expected to be a strong source of acoustic waves. It's somewhat like the deafening roar of a jet aircraft or the loud hissing noise of a boiling pot of water. As the hot convective bubbles rise in the Sun, their motion disturbs the gas they flow through and starts it oscillating. And the violent, turbulent convective motions occur continuously and randomly, so the visible solar disk is always oscillating in tune with its internal sounds.

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