THE ROTATION OF THE SUN

The sun turns once every 27 days, but some parts turn faster than others. Such variations are clues to interrelated phenomena from

the dense core outward to the solar wind that envelops the earth

by Robert Howard

hen Galileo turned his tele­ cause the gas that gives rise to them is sun's rotation. When sunspots are ob­ scope on the sun in 1610, he moving, and the amount of the shift is served with a small telescope, they ap­ Wdiscovered that there were proportional to the velOCity of the gas in pear simply as spots on the photosphere: dark spots on the solar disk. Observing the line of sight. Unfortunately for solar the bright surface of the sun that is seen the motion of the spots across the disk, observers each method has disadvan­ in ordinary white-light photographs. In he deduced that the sun rotated once in tages that limit its usefulness. larger telescopes they may appear as about 27 days. One of his contempo­ saucer-shaped depressions near the edge raries, Christoph Scheiner, undertook a iming a tracer as it crosses the disk of of the sun. Therefore it is hard to be systematic program of observing the the sun is a good technique for de­ sure that the same point in the sunspot is spots. From these observations Scheiner terminingT the solar rotation rate only if . being used for the purpose of measure­ found that the rotation period of the the tracer meets certain requirements. ment as the spot traverses the solar disk spots at higher solar latitudes was slight­ First, it must survive long enough un­ and is seen from a different angle each ly longer than that of the spots at lower changed in its appearance to be useful day. In order to avoid the problem, stu­ latitudes. In the middle of the 19th cen­ over some reasonable period of time. dents of the sun's rotation prefer to use tury R. C. Carrington, a wealthy English Second, it must have a clearly defined long-lived spots that cross the central brewer and amateur astronomer, deter­ structure, so that its position can be ac­ meridian of the sun more than once. The mined with good precision the amount curately determined. Third, it must be at central meridian is defined as the inter­ of the variation of the sun's rotation rate the same altitude in the sun's atmo­ section of the sun's visible surface with with latitude. sphere when it is seen at the center of the plane that passes through the sun's Scheiner's observations suggested that the solar disk and when it is seen at the axis of rotation and the earth; when a the sun does not rotate as a simple solid edge. Last, it must not wander around sunspot crosses the central meridian, the body. Since we now know that the sun the solar disk in some systematic way effect of its three-dimensional form is is a gas throughout, it does not surprise not directly related to the sun's rotation. minimized and its position can be most us that it does not rotate as a solid. One Although no features on the sun meet precisely measured. might have expected, however, that the all these requirements, sunspots are still Only a small fraction of sunspots live spots closer to the sun's equator would the easiest to observe, and they have long enough to cross the central merid­ move slower than the spots at the higher been studied more than any other trac­ ian more than once. The spots with the latitudes, just as the outer planets of the er. Thus they have probably provided longest lifetime are the ones found on solar system move slower in their orbits . the most accurate determinations of the the leading edge of groups of sunspots, than the inner ones. The fact that the equatorial regions rotate faster than the rest of the sun implies that an excess of angular momentum-the momentum of the sun's rotation-must be transferred SUN'S ROTATION can be monitored by noting the daily progress across the solar disk of from the higher solar latitudes to the a tracer such as a sunspot or a gaseous filament.Such features are associated with magnetic equatorial regions. This fact and its im­ fields, which can be detected directly by means of a solar magneto graph. The six magneto. plications yield information about the grams on the opposite page were made with the 150·foot tower telescop e at the Mount structure of the sun's interior and the Wilson Observatory. Tbe sequence reads from top to bottom and shows the magne tic activ­ nature of its activity. ity on the sun at intervals of every other day from May 30, 1974, through June 9, 1974. The There are two basic methods for pre­ contours on the magneto grams represent equal-strength areas in the magneti c fie lds. The strength in gauss of the fields at successive contour intervals is five,10, 20, 40 cisely determining the rotation of the and 80. (The strength of the earth's magnetic field is less than one gauss.) The solid contou rs rep. sun at a partkular latitude. The first is to resent positive magnetic fields; the broken contours represent negative fields. Th e life. time the passage of some tracer (such as times of the smallest magnetic features are less than Ii day, so that in general it is possible a sunspot) across the solar disk. The sec­ to trace the daily rotational movement of only the larger magnetic features. Strongest of ac· ond is to photograph the spectrum of the tive regions that are seen here are associated with sunspots; it is difficultto determine the sun; the spectral lines of the solar at­ exact location of spots, however, because angular resolution of magneto grams is low. Evo· mosphere will be Doppler-shifted be- lutionary changes within active regions somewbat alter their appearance from day to day.

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© 1975 SCIENTIFIC AMERICAN, INC and so these are the ones that are most of their own later in their lifetime. A fur­ A second kind of tracer is the long commonly monitored. That is actually ther disadvantage of using sunspots as filaments of gas in or above the solar unfortunate, because the preceding and rotation tracers is that they are rarely chromosphere. The chromosphere is the following members of a sunspot group seen above a solar latitude of 35 degrees. transitional layer between the photo­ tend to separate early in the lifetime of Thus they can be used only for deter­ sphere, which has a temperature of the group. In addition the preceding mining the rotation of the sun at rather 6,000 degrees Kelvin, and the solar co­ spots tend to exhibit systematic motions low latitudes. rona, which paradoxically is much hot­ ter: about two million degrees K. The chromosphere can be observed only at the wavelengths of certain spectral lines, notably the line designated hydrogen alpha in the red region of the spectrum. Photographs of the chromosphere made in the light of the hydrogen-alpha line show an abundance of lovely detail. Al­ though most of these features are too short-lived or too ill-defined to be used for accurately determining the rotation rate of the chromosphere at various lati­ tudes, large dark filaments are fairly re­ liable tracers. The filaments are actually clouds above the chromosphere that ap­ pear dark when they are seen projected against its bright surface but appear bright when they are seen extending be­

CENTRAL MERIDIAN OF THE SUN as it is seen from .the earth is definedas the inter. yond the edge of the solar disk. They are section of the portion of the sun visible from the earth (colo r) with the plane (gray) de· not ideal tracers because their appear­ fined by the sun's axis of rotation and the earth. Longitudinal positions of the various ance changes too rapidly. Their lifetime markers that are monitored to study sun's rotation are referred to sun's central meridian. is not negligible, however, and they are present at higher solar latitudes than

N sunspots. For these reasons their rota­ tion characteristics have been studied in "/ detail. ( \ f the photosphere and the chromo- "-"" I sphere show rotation, what about the '" solar corona? This question is not easy " to answer. The corona is so faint com­ pared with the rest of the sun that it can be viewed only during a total eclipse of "- the sun or with the aid of the corona­ '\ graph: a telescope equipped with an oc­ I \ culting disk that blocks the light of the I \ photosphere as the moon does (although I \ not as effectively). In either case the E w exact connection between features of the \ solar disk and features of the corona is J hard to determine. Moreover, the coro­ / nal features are so poorly defined that it / is difficult to measure their size and po­ / sition. The rotation of the corona may therefore be measured accurately only / by correlating observations that extend / over at least several months. / Richard Hansen, S. F. Hansen and /" Harold C. Loomis have measured the //' rotation period of the corona with a spe ­ { cially designed instrument attached to a \ � corona graph on the mountain Haleakala on the Hawaiian island of Maui, and s they have found that the period varies somewhat from year to year. E. Anto­ SUN DOES NOT ROTATE AS A SOLID BODY but rotates differentially with latitude. nucci and Leif Svalgaard of Stanford The lines in color indicate position of tracers after one day (solid line) and 27 days (broken University have found that the rotation line) if the sun rotated as a solid body. The lines in black indicate their actual positions after one day (solid line) and 27 days (broken line) and illustrate the effects of the sun's rate of the corona varies with the age of differential rotation. In general the higher the latitude, the longer the rotation period. coronal features. The long-lived features'

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© 1975 SCIENTIFIC AMERICAN, INC BLUE

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LINES IN SUN'S SPECTRUM ARE SHIFTED from their normal (right) on the eastern linib are shifted toward the blue region of position because of the Doppler effect if there is a relative motion the I spectrum (A) I andI the lines emitted by gas on theI western I limb along the line of sight between the source of the lines and the ob· are shifted toward the red end (B). If the slit of the spectroscope server. Since the sun rotates from east to west (left) the eastern is projected across the sun's equator, the lines on the spectrogram limb of the sun (A) is approaching observers on the earth and the will be tilted. (In illustration the magnitude of tilt is exaggerated.) western limb (B) is receding. Thus spectral lines emitted by gas Spectral line from gas on central meridian (C) will not be shifted.

rotate almost as though they were part seated magnetic framework of the sun. velocity along the line of sight of the of a rigid body, whereas the short-lived William Henze, Jr., and Andrea K. source with respect to the observer. If features rotate much as the sunspots do. Dupree of the Harvard College Ob­ the source and the observer are ap­ In 1908 George Ellery Hale of the servatory have measured the rotation proaching each other, all the wave­ Mount Wilson Observatory found that of the sun with an experiment aboard lengths will be shifted toward the blue sunspots are associated with strong mag­ 050-6 (the sixth Orbiting Solar Ob­ end of the spectrum; if they are receding netic fields. Only within the past two servatory). They observed the chromo­ from each other, all the wavelengths will decades, however, has it been possible sphere and the corona in the light of be shifted toward the red end. Thus a to reliably measure the weaker magnetic spectral lines in the extreme ultraviolet spectroscope aimed at a part of the sun fields that extend over large areas of the region of the spectrum. Such photo­ that is turning toward the observer will solar surface outside the sunspots. Some graphs are roughly similar in appearance detect lines that are shifted slightly years ago Vaclav Bumba of the Ondrej­ to the picture of the chromosphere made toward the blue, and an instrument ov Observatory in Czechoslovakia and in the light of the hydrogen-alpha line, aimed toward a part that is turning away I examined the large-scale patterns of but the ultraviolet emission originates at from the observer will detect lines that such fields. We found that although in­ higher elevations in the sun's atmosphere are shifted slightly toward the red. It is dividual magnetic features rotate at dif­ than the hydrogen-alpha emission. The these Doppler shifts that can in principle ferent rates depending on latitude in data from 050-6 have yielded rotation be used to measure the speed of rotation approximately the same way that sun­ rates that are somewhat slower than the of various regions of the sun. spots do, the rotation of the overall pat­ rates derived from the other features I The first Doppler-shift measurements tern of the fields does not change with have mentioned. Curiously these rates, of the sun's rotation were made by the latitude over long periods of time and at least at low latitudes, closely resem­ German astronomer Hermann Vogel in over a large range of latitudes. A few ble those derived from observations of 1871. Following on his work there were years later John M. Wilcox of Stanford the Doppler shift of spectral lines. numerous other determinations, all of and I confirmed these results and put them plagued by the fact that when a them on a more quantitative basis. We he wavelength at which a spectral spectroscope was aimed at the edge of found that the rigidly rotating patterns Tline is formed depends on a transition the sun, light was scattered into the in­ persist for many years. They are as­ between energy levels that is character­ strument from the sun's brighter central sociated with interplanetary magnetic istic of the emitting species of atom. The portion. The spectral lines of the scat­ fields that have been measured near the wavelength at which the line is ob­ tered light blended with the lines from earth, and they may represent a deep- served, however, depends further on the the region being observed and tended to

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© 1975 SCIENTIFIC AMERICAN, INC 15 I ited by the fact that parts of the corona I I also move randomly at substantial ve­ :::::::"., I 1 locities. , M The average rotation of the sun as a --..::::::�. ! I PHOTOSPHERICI AGNETIC FIELDS 14 function of latitude, derived from vari­ I ous studies, is shown in the illustration ---t----I '-.....� ./K-CORON l (INNER ORONA) at the left. In general the studies of the � � l e( SOLID BODY equatorial rotation velocity can be di­ � 13 w yided into two groups: the spectroscopic "­ -"""""'r-. "1" � I Cf) results and everything else. The sun­ l , w F LAMENTS I , w i spots, the filaments, the bright corona I a: I C) 1 streamers and the photospheric mag­ w � 12 I +' e. � I netic fields rotate approximately one dav , I w per rotation faster than the photosphere �a: does. These fast-moving features have z ' ----N one thing in common: they are all asso­ a 1 i=e( ciated with magnetic fieldsin the solar f­ a atmosphere. Sunspots have strong mag­ a: I� netic fields, filaments are known to lie DOPPLER SHIFT OF SPE TRAL L1Nl� � between magnetic regions of opposite 10 polarity and coronal streamers corre­ � spond to looping lines of magnetic force in the corona.

9 It thus appears that the magnetic o 10 20 30 40 50 60 70 80 90 fields rotate somewhat faster than the NORTH AND SOUTH LATITUDE (DEGREES) bulk of the photospheric gas does by about one day per rotation, or about 75 ROTATION RATES OF MARKERS DIFFER from the rotation rate of the gas of the sun's photosphere, or visible surface, as well as differing with latitude. Since all the tracers are meters per second. (The rotation speed associated with magnetic fields, this fact is interpreted to mean that the sun's magnetic of the photospheric gas at the equatorial field rotates slightly faster than the gaseous body of the sun itself. The rate of rotation for latitudes of the sun is about two kilo­ each marker is given in degrees per day of longitude on the sun. A curve showing what the meters per second.) It is possible, al­ rotation rate of the sun would be if it behaved as a solid body is given for comparison. though it is by no means universally be­ lieved by solar physicists, that the mag­ netic fields rotate more rapidly than the make the measured rotational velocities ronal green line, which originates with photospheric gas does because they are too low. iron atoms that have been stripped of connected to certain interior layers of In 1966, however, measurements many of their electrons by the corona's the sun whose rotation rate is also fast. were undertaken with the solar magne­ high temperature. These measurements The magnetic fields, which are generally to graph on Mount Wilson, a photo­ showed little evidence that the corona's confined to tightly packed lines of force electric scanning spectrometer. Actually rate of rotation varies with latitude, al­ occupying only a small fraction of the measuring the rotation of the sun with though their accuracy is somewhat lim- surface area of the sun, can move this instrument was a by-product of an effort to monitor the magnetic fields of

the sun. The solar magneto graph is so 16.38 sensitive that it can detect a difference in 16.02 velocity along the line of sight as small as 10 meters per second (a figurethat 15.66 � e( 15.30 happens to be equivalent to the top a speed of a human sprinter). \Vith such a: w 14.94 sensitivity it is now possible to measure "- Cf) 14.58 IV\ w the rotation of the sun close to the center w 1\ a: 14.22 � -"" of the solar disk, where the scattered­ C) \ w I v \ V 1"1 \ 13.86 v �--- light problem is not as severe as it is at e. f'V \/ w 1\ VV\! the disk's edge. Since 1966 the rotation f- 13.50 '-J" v e( v ',,= of the sun has been monitored daily at a: ,.,J I \ 13.14 z Mount Wilson, and these observations a 12.78 constitute the bulk of the spectroscopic i=e( f- r rotation data now available. a 12.42 a: /\ 12.06 uring the total solar eclipses of 1970 !' IV \ 11.70 and 1973 John W. Har\'c�', "'illiam \l D 11.34 C. Livingston and L. Doe of the Kitt 1967 1968 Peak National Observatory measured the rotation of the corona with spectro­ ROTATION RATE OF THE SUN VARIES with time as well as with latitude. That varia­ scopic techniques. They studied the co- tion is shown by this illustration of the sun's equatorial rotation rate monitored over a

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© 1975 SCIENTIFIC AMERICAN, INC through the solar atmosphere like the or months the equatorial rotation rate sun. �Iost of the mass is concentrated in periscopes of a Reet of submarines plow­ may vary from the average by as much the sun's dense, hot core, where thermo­ ing through the ocean. as 5 percent. These variations could be nuclear reactions release the energy that The rates of rotation of the visible fea­ correlated with short-term variations in is ultimately radiated from the photo­ tures of the sun not only differ from the some aspect of solar activity, such as the sphere. The energy is transmitted from rate of the photosphere but also differ number of sunspots, the mean strength the core up to the convective zone by slightly from one another, depending on of the magnetic fieldsor the frequency means of radiative processes, that is, their latitude. Such differences are puz­ of solar Rares. The first attempts to atoms within the sun absorb radiation zling and for the present have no ex­ demonstrate such associations , however, and then reemit it. In the outer 20 per­ planation. The uncertainties in the mea­ have yielded no positive results. Over cent of the sun's radius, however, the gas surements of most of these rates increase the past few years the spectroscopic data becomes unstable. Convective motions at higher latitudes, and it is possible that from Mount Wilson have shown a gen­ result, and almost all the energy in this at least some of the discrepancies are eral tendency for the rotation rate to in­ region is transported by convection: hot­ caused by systematic errors. By the same crease as solar activity has declined from ter gases rise and cooler gases sink. token slight differences in the spectro­ the most recent maximum of the II-year scopically measured rotation rate of the solar cycle in 1969. The increase has hen we observe the sun, of course, photosphere in the northern and south­ been only a few percent, and under the Wwe see only the layers of the photo­ ern hemispheres of the sun are near the circumstances it is premature to con­ sphere above the convective zone. All limit of detectability, and for now they clude that there is a firm relation be­ that we know about the structure of the too must be set aside as possibly result­ tween the sun's rotational velocity and solar interior is inferred from the sun's ing from systematic errors. the phase of the solar cycle. N everthe­ mass, its surface temperature, its chemi­ less, there is a strong possibility that cal composition and our theoretical SpectroscopiC observers early in this such a connection exists, and solar ob­ knowledge of nuclear processes and the century generally agreed that the servers will be examining the rotation physical behavior of gases. We have no gases at higher altitudes in the solar rate with great care as the next maxi­ means of directly observing the rotation atmosphere rotated significantly faster mum of the solar cycle approaches. of the solar interior. Robert H. Dicke than those lower down. This view has As yet there is no generally accepted and his collaborators at Princeton Uni­ since been discredited, not only because theory as to why the sun's rotation versity have nonetheless advanced a hy­ it seems highly unlikely but also because should vary with latitude. The differen­ pothesis about this rotation on the basis Livingston and Robert W. Milkey at Kitt tial rotation, or any other large-scale of their careful measurements of the Peak have recently made accurate ob­ phenomenon on the sun's surface, must sun's oblateness. servations that show it is untrue. They be intimately related to the sun's inter­ From the observed fact that the sun attribute the erroneous earlier results to nal structure and to the dynamics of the rotates once every 27 days one would the fact that in the spectra some of the convective zone in its interior. The con­ predict that its poles would be Rattened absorption lines in the solar atmosphere vective zone has a thickness equal to by about .01 second of arc out of the blended with weak lines due to mole­ about 20 percent of the solar radius, and sun's apparent radius of 15 minutes of cules in the earth's atmosphere, distort­ its upper boundary lies just below the arc, corresponding to seven kilometers ing the measurements. layer of the photosphere where most of out of the sun's average radius of 700,- Spectroscopic determinations of the the spectral lines we see are formed. The 000 kilometers. Such a minute quantity rate of the sun's rotation have shown gas in the convective zone comprises less is very difficult to measure accurately that it changes frequently. Over weeks than 1 percent of the total mass of the because it is at least 100 times smaller

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period of six years. The rate is plotted in degrees of longitude on resents the average equatorial rotation rate over this period. Some­ the sun per day. The horizontal line at 13.86 degrees per day rep· times the rate varies suddenly for reasons that are not fully known.

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© 1975 SCIENTIFIC AMERICAN, INC than the blurring effects of the turbu­ group have failed to confirm his results. velope and tend to decrease the differ­ lence of the earth's atmosphere on the If the core of the sun is rotating rapid­ ence in the two rotation rates. image of the sun. It is also smaller than ly, it cannot be tightly coupled to the errors introduced by imperfections in­ convective zone. Ionized atoms are elec­ ithin the convective zone itself an- herent in the optical systems used to trically charged particles that "feel" a Wgular momentum is transferred eas­ study the sun. In spite of these obstacles magnetic field, and in a highly ionized ily and quickly in the radial direction by Dicke, working with an instrument of in­ gas such as the one that makes up the the continual convective motions. More­ genious design, has measured the sun's sun the lines of magnetic force can be over, the "wind" of solar particles that is shape and has concluded that its oblate­ considered to be mechanically coupled constantly streaming away into space ness is five times as large as one would to the constituent atoms. Therefore if along the lines of force in the sun's mag­ predict, namely about .05 second of arc. the lines of magnetic force are moving as netic field exerts a dragging effect that is This relatively large oblateness, he ex­ the sun rotates, they will drag the ion­ strong enough to stop the rotation of the plains, is due to the rapid rotation of the ized gas along with them. And ifthe convective zone inonly one million central core of the sun: about one turn lines of magnetic force thread their way years. A million years is a short time on per day. Such a rapidly rotating core from the sun's core through the convec­ the scale of cosmic events, and we know will itself be oblate and will slightly al­ tive zone, the two zones cannot maintain the sun's surface layers cannot be de­ ter the gravitational field at the surface very different rotation rates for very celerating that rapidly. If they were, and of the sun, so that the surface too will be long. In addition any exchange of ma­ if the deceleration rate had remained slightly oblate. Dicke's work has stimu­ terial between a rapidly rotating core constant for some time, only a few hun­ lated a controversy that has not yet been and a slowly rotating outer envelope will dred million years ago the sun would resolved. Recent attempts by another transfer momentum to the outer en- have been rotating so fast that it would

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MAGNETIC FIELD LINES (blac k) at the surface of the sun (col. the surface. The small arrows at the base of the field lines show or) are confinedto sunspots and to small hundles of lines outside that they rotate about 75 meters per second faster than most of the spots. They are always closed loops, originating at the side of the photospheric gas; the gas not directly connected with a magnetic sun with positive polarity and looping over a narrow neutral region feature simply allows the lines to pass through. TII·defined region (broken line) intoan area of negative polarity. The long field lines centered on the field lines between sunspots is a coronal enhance· extend far out into interplanetary space before they loop back to ment; above it streamers of the corona are particularly prominent.

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© 1975 SCIENTIFIC AMERICAN, INC have thrown off an appreciable fraction of its mass by centrifugal force. Since the dragging force of the solar wind is not strongly slowing the rotation of the convective layer, much of the force must be expended in slowing the denser mat­ ter below the convective layer, although not necessarily the matter in the core. In this general picture the lines of force in the sun's magnetic field are firm­ ly connected to deeper layers of the sun where the rotation rate is higher than it is at the surface. The lines of force are RAPIDLY ROTATING dragged through the photosphere by CORE? their roots, although the depth of these E roots has not been established. An al­ temative explanation for the difference between the rotation rates of the mag ­ netic fields and the rotation rate of the photosphere is that there is a large-scale pattei'll of circulation in the sun that somehow (it is not clear exactly how) moves the field lines preferentially in one direction. On a small scale of per­ haps 1,000 kilometers there is a circula­ tion pattei'll on the solar surface called granulation, and on a slightly larger scale of about 30,000 kilometers there is a pattei'll called supergranulation. George W. Simon of the Sacramento s Peak Observatory has suggested that there might be an analogous pattei'll On INTERIOR OF THE SUN in this cutaway view shows the convective zone and the hy­ a scale of about the radius of the sun. pothesized rapidly rotating core. The sun's energy is generated by thermonuclear reactions Observational evidence for such a giant in the core and is transported toward the surface by means of radiative processes: atoms of the gas absorb, reemit and scatter the radiation. At a point about 20 percent of the circulation pattei'll is skimpy, but per­ radius from the surface the gas becomes unstable to motions along the radius and the en­ haps that is not surprising, because the ergy is transported by convection: hot gases rise and cool gases fall. The roots of the mag­ velocity of the flows in such a patte i'll is netic field lines extend through the convective zone, although the depth to which they expected to be quite low-only a few reach is not known. The lines that extend into interplanetary space carry with them a meters per second. steady flow of ionized gas: the solar wind. Entire pattern of the magnetic fieldsrotates with There are several theoretical models the sun, and the effect of the solar wind is to exert a drag on rotation of outer layers of sun. that attempt to explain why the angular velocity of the sun varies with latitude. None of these models, however, is based convective circulation pattems result in cause of the way in which the waves are on exact solutions of all the physical a net transport of angular momentum slanted [see illustration on next page]. equations involved. Solar physics suffers toward the solar equator because the gas The waves moving toward the equator from the lack of a definitive theory of moving radially toward the equator car­ carry more angular momentum than the turbulent convection in a compressible ries more angular momentum than the waves moving toward the poles, and gas. The models I shall discuss are for gas moving radially toward the poles. thus the waves moving toward the equa­ the most part ingenious combinations of Hence the energy maintaining the high tor support the faster equatorial motion. solutions for large-scale motions in sim­ equatorial rotation rate comes from the Here one considerable problem remains: plified physical cases and assumptions convective motions. One disadvantage to explain why the waves exist and how about the large-scale effectsof small­ of this model is that it requires the inner they are maintained. One suggestion is scale processes. layers of the sun to rotate slower than that they are maintained by a tempera­ the outer layers, whereas the evidence ture gradient on the sun: the poles are dwig Biermann of the Max Planck from the rotation of the magnetic tracers hotter than the equator. Such a tempera­ � Institute for Physics and Astrophys­ points to the opposite conclusion. ture gradient has not been observed. Re­ ics in Munich has suggested that if the A second model, firstsuggested by cently, however, a wave pattern similar viscosity of the convective gas in the sun Fred W. Ward of the Air Force Cam­ to the one required for this model has is not the same in all directions, the re­ bridge Research Laboratories, posits been detected by R. G. Hendl of the sult can be differential rotation. Bier­ that there are surface circulation pat­ Massachusetts Institute of Technology mann's colleagues have extended this terns in the solar atmosphere that are on the basis of the observations made at notion into a more refined model. If the analogous to pattems in the earth's at­ Mount Wilson, lending support to the viscosity of the solar gas in the radial di­ mosphere known as Rossby waves. Such Rossby-wave hypothesis. rection is less than that in the plane per­ patterns would transport angular mo­ A third model relies on the notion of pendicular to the radial direction, the mentum toward the solar equator be- the giant convection cells. According to

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© 1975 SCIENTIFIC AMERICAN, INC N Some Matters of Matter and Energy

GENERAL CHEMISTRY Readings from SCIENTI FIC AMERICAN With I ntroductions by E w JAMES B. IFFT, University of Redlands, and JOHN E.HEARST, University of California, Berkeley "I will certainly recommend this for my freshman general chemistry students .... The selection of articles and introductory material is excellent-a good blend of theoretical and applied information. Ifft and Hearst should be congratulated." -Fred Decker, University of Connecticut 1974,434 pp., 404 ill us., cloth $12.00, paper$6.50

CHEMICAL THERMODYNAMICS A Course of Study FREDERICK T. WALL, Rice University Ari Answer Book is available. s This is the latest edition of a standard text for advanced undergraduate and first-year ROSSBY WAVES is one model proposed for explaining why the sun rotates differentially. graduate courses in thermodynamics and The curved arrows of the Rosshy waves (gray) are streamlines, representing the motion statistical mechanics.Many new and of the gas on the sun's surface. Because of the shape of the streamlines the motion of the thought-provoking problems have been gas toward the equator (arrows in color) carries more angular momentum (momentum of added and the notation has been updated rotation) toward the equator than toward the poles. The net effectis to transfer momentum. in accordance with current international practice. A new chapter shows how the statistical mechanical distribution laws "can be derived without recourse to the theoretical calculations made by B. R. from the deceleration of the regions at methods of variational calculus, Lagrangi­ Durney and Peter A. Gilman at the higher latitudes. He argues that the an multipliers, and Stirling's approxima­ National Center for Atmospheric Re­ lines of magnetic force extending into tion." search, the sun is likely to generate interplanetary space originate preferen­ Third Edition, pp., iIIus., 1974,493 44 large-scale convective circulation in long tially at the high latitudes, so that the $14.95 rollers that move predominantly from dragging effect of the solar wind will A SEARCH FOR ORDER east to west near the surface. The rollers slow those regions more. Hence it is not IN THE PHYSICAL UNIVERSE can transport momentum to the equator necessary to transfer angular momentum CLIFFORD E. SWARTZ iftheir motions are not exactly east to to the equator because it is automatical­ and THEODORE D. GOLDFARB, State west. This model has had some success ly extracted from the high latitudes. University of New York at Stony Brook in reproducing some of the character­ This collaboration of physicist and chem­ jstics of the sun's differential rotation. It N..the moment it is not possible to say ist is designed to give the non-scientist a contemporary perspective on the physical suffers, however, from the disadvantage which, ifany, of these models gives sciences.The traditional survey of diverse that it too calls for a lower rotation rate the correct explanation. The fertile topics has been abandoned in favor of "a below the surface than at the surface. minds of theoreticians seem able to de ­ study of interactions and a search for con­ An additional disadvantage is that a vise many mechanisms to explain the served quantities, particularly energy." sizable How from north to south is also differential rotation of the sun. When The mathematical level has been confined needed to make the model work. Al­ the explanation is known, it will greatly to high school algebra.Many easy-to-per­ though some observers, notably H. H. assist our understanding of the structure form and inexpensive experiments are de­ Plaskett of the University of Oxford, and rotation of the solar interior and, scribed in the book. have reported detecting such motions, through the connecting medium of the 1974,315 pp., 172 illus., $10.50 sensitive observations made at Mount magnetic fields, our understanding of Wilson do not confirm their existence. solar activity. Moreover, since the sun is K. H. Schatten of the Victoria Uni­ a Rosetta stone for learning about the I. versity of Wellington in New Zealand billions of other stars in the universe, the has suggested that the differential rota­ explanation will also aid investigations W. H. FREEMAN AND CO MPANY tion of the sun results not from the ac­ into the nature of stars and into the evo­ 660 Market St., San Francisco, Ca 94104 celeration of the equatorial region but lution of the galaxy.

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© 1975 SCIENTIFIC AMERICAN, INC Not too long ago, computers were practical only PRICES: Altair Computer Kit with complete assembly when it came to handling large quantities of data. instructions $439.00 Assembled Altair Computer In more recent times. computers have been engi­ $621.00 neered to be smaller and less expensive without loss 1,000 word static memory cards $176.00 kit of power or speed. Computer uses have multiplied. And & $254.00 assembled. most importantly. computers have become easier to 4,000 word dynamic memory card 5264.00 kit understand and to use. & $338.00 assembled. The engineers who designed the Altair Computer MITS/6328 Linn, NE, Albuquerque, New Mexico 87108 understood this trend perhaps better than anyone else in the computer industry. They designed the Altair to be NOTE: Altair Computers come with complete documentation and operat­ ' ' ing instructions. Altair customers receive software and general computer a powerful. general purpose computer that sells for information through free membership to the Altair User 5 Club. Software $439.00 in kit form and $621.00 assembled. now available includes a resident assembler. system monitor and text editor. Basic language soon to be available They did it without sacrificing performance or quality. Prices and specifications subject to change without notice. warranty 78 basic machine instructions. a cycle time of 2 micro­ 90 days on parts for kits and 90 days on parts and labor tor assembled units. seconds. and buss orientation make the Altair Computer ideal for thousands of existing and new applications. I------�ILT�ISCO�ON�ODAY_;_------10 Enclosed i s check for $ i I The Altair Computer can directly address up to 10 BankAmerlcard II 0 or Master Charge II I 65.000 words of memory and 256 input/output devices. Credit Card Expiration Date ' I 0 I 8800 It can be connected to a growing number of Altair Com­ 0 A LTAIR 0 Kit 0 Assembled I puter Options such as memory boards. parallel and 1 Options I list on separate sheetl 10 S8.00 I serial interface boards. floppy disc storage. audio tape Include for postage and handling. 0 PLEASE SEND FREE ALTAIR SYSTEM CATALOGUE I interface. alpha-numeric displays and keyboards. com­ I I puter terminals. line-printers. etc. I Name I i You can order the Altair Computer by simply filling I ADDRESS I out the coupon in this Ad or by calling us at 505! I I 265-7553. Or you can ask for free technical consultation I CITY STATE & ZIP I or for one of our free Altair System Catalogues. TS/6 L n b r N 8 0 5 � . _____ �':... � �� � ���=- � !!� ":' '::� �::? J

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© 1975 SCIENTIFIC AMERICAN, INC