Helioseismology on the Moon

Adv. SpaceRes.Vol. 14, No. 6, pp. (6)21--(6)31, 1994

Copyright © 1994 COSPAR Printed in Great Britain. All rights red,wed. 0273-1177/94 $6.00 + 0.00

Pergamon

HELIOSEISMOLOGY ON THE MOON E. J. R h o d e s , J r

Department of Physics and Astronomy, Universityof Southern California, Los Angeles, CA 90089-1342, U.S.A.; and Space Physics and Astrophysics Section, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, U.S.A.

ABSTRACT

The prospect of a future manned lunar base presents an interesting challenge for helioseismology-a field in which observations have been obtained from the Earth's surface, from near-earth satellites,and from interplanetary spacecraft. Similar observations from the Moon would possess several advantages over those from other sites. Advantages over the Earth would include the absence of the terrestrialatmosphere and the lower lunar surface gravity, both of which would allow for larger-aperture telescopes with which the highest-degree solar oscillations could be studied. Compared with the .99 A U halo orbit of the upcoming S O H O mission a lunar base would have less-restrictiveweight, power, and telemetry restrictions. An instrument there could also be repaired in-place and could be operated for at least one solar cycle. Disadvantages compared to SOHOzwould include interruptions from the lunar night and during lunar eclipses. Temporal sidelobes of frequency spacing comparable to that due to solar surface rotation would be introduced unless a network of lunar stations were operated. Finally, solar Doppler measurements made from the Moon would have to allow for the orbital velocity of the Moon around the Earth, but this should not pose a problem for such measurements. INTRODUCTION The possible establishment of a manned lunar base as part of America's Space Exploration Initiative(SEI) will pose a unique opportunity for the science of astronomy. With its low gravity, vacuum, and slow rotation rate, the Moon is an excellent site from which observations can be made of the heavens. The Moon provides a stable platform for the installation of sophisticated astronomical instruments which can be employed in the study of both distant stellar systems as well as our own Solar System. While much attention has been given to the advantages of a lunar observatory for nighttime astronomical studies, it is also important to note that a lunar observatory will also be an excellent location for conducting observations of our own nearest star -- the Sun. Chief among the benefits of a lunar observatory for solar studies axe: 1) the absence of the blurring effects of the Earth's atmosphere, 2) the low gravity which will facilitatethe construction and operation of solar telescopes having large-enough apertures to take advantage of such an unsmeared view of the Sun, 3) the opportunity of studying the Sun without interruption for over half of its rotational period from a single location, and 4) the future prospect of completely uninterrupted solar viewing from a lunar network of two or three solar telescopes. Other advantages of a lunar base over spacecraft for future solar studies include: 5) the availabilityof larger transmitting antennae which will allow relativelyhigh telemetry rates,especially when compared to those from interplanetary locations such as the inner Lagrangian point between the Earth and the Sun where the upcoming Solar and Heliospheric Observatory (SOHO) missin will be placed; 6) a much smaller systematic radial velocity toward and away from the Sun than is available with Earth-orbiting satellites;7) the opportunity of having the instruments repaired rather than abandoned after a relatively brief operational lifetime, and 8) much less restrictiveweight and power constraints. One of the branches of solar astronomy which can benefit from the installation of one or more relatively small (25cm aperture or less) solar telescopes on the Moon is the relatively new disdpline of helioseismology. Helioselsmology is the study of the unseen interior of the Sun using observations of the oscillatory motions of solar surface layers. While most of these past measurements have been made from the Earth's surface, a steadily increasing number of them have been made from earth-orbiting satellites and from interplanetary spacecraft. In the near future space-based helioseismology measurements will be undertaken with three different instruments which will be flown onboard the SOHO spacecraft. However, once the two-to six-year lifetime of these three instruments onboard SOHO has ended, there will still remain (6)21

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a need for continued acquisition of space-based helioseismic observations. Helioseismic observations from the Moon will provide the logical follow-up measurement opportunity. In this paper I will first describe briefly what helioseismology is and how it is carried out. I will then describe some of the currently-open questions about the solar interior which continued helioseismic measurements should help us address. I will then point out why helioseismologlsts are now going into space and then I will concentrate on the ways in which the Moon will provide a desireable platform for continuing such measurements. I will also mention some of the difficulties which a single solar-pointed telescope based on the Moon would encounter in helioseimic studies, and finally I will suggest how a modest network of three small telescopes on the lunar surface would provide an ideal long-term monitoring platform for future helioseismic studies. WHAT IS HELIOSEISMOLOGY? Helioseismology is a unique astronomical descipline which combines observations of the solar surface layers with computational techniques and theoretical tools which are very similar to thse employed by geophysicists in their studies of the Earth's interior in order to probe the otherwise unseen layers of the solar interior. Specifically, helioseismologists employ observations of the oscillatory motions and temperature fluctuations which appear to be always present in the solar surface layers to probe the thermodynamic structure and dynamical motions of the solar interior layers as functions of radial distance inward along the solar equatorial plane, of latitude above and below the equatorial plane, and of time. Helioseismology is made possible because the Sun - in contrast to the Earth which only vibrates for relatively short time intervals after the largest of earthquakes - is constantly vibrating or oscillating. These solar oscilllations were discovered in 1960 and 1961 at the Mount Wilson Observatory. Since the mid-1970s when observations confirmed the nature of these so-called "5-minute" oscillations as the surface manifestations of acoustic or sound waves which are trapped within the Sun, an ever-increasing number of observations have been made of them. HOW ARE HELIOSEISMIC MEASUREMENTS MADE? Five principal classes of measurements have been made of these solar oscillations. In two of these techniques the Sun has been observed as if it were a star. This is to say that the Sun has been seen as a single point source of light having no spatial extent. In instrumental terms the Sun has been observed as a single picture element, or pixel, in these two approaches. In one of them the solar irradiance has been measured, while in the other the inward and outward motions of the entire visible solar hemisphere have been integerated into single-point radial velocity measurments. The next two principal observational techniques employed in helioseismology have both made use of the proximity of the Sun to the Earth to obtain spatically-resolved measurements of the Earth-facing solar hemisphere. One of these techniques has studied the two-dimensional intensity fluctuations across the solar surface, while the other has measured the inward and outward velocity patterns instead of the intensity patterns. In the fifth technique measurements of the brightness near the extreme edges of the solar disk have been employed. All five of these measurement approaches are currently being employed in ground-based helioseismic studies. They will all also be employed in the cluster of three helioseismology instruments which will be flown onboard the SOHO spacecraft. An example of the type of image obtained with one of the spatially-resolved instrumental approaches is shown here in Figure 1. This image is a full-disk Dopplergram. In much the same way that a geophysicist employs a seismograph to tell him when, where, and by how much the Earth's surface is moving, this Dopplergram tells us how rapidly and in which direction each portion of the visible solar disk was moving at the moment that it was taken. In current ground-based observing programs which are operated from single mid-latitude observatories, such as Mount Wilson where the Dopplergram in Figure 1 was taken, similar Dopplergrams or in some cases intensity images are obtained at the rate of one per minute for up to 11 hours per day during as many as 220 days per year. The data tapes on which solar images such as the Dopplergram of Figure 1 are stored are then processed on massively-parallel supercomputers to provide helioseismologists with the spatial and temporal frequencies, the amplitudes, and the lifetimes of the large number of solar oscillations which were excited within the Sun when those observations were obtained. NATURE OF THE SOLAR OSCILLATIONS Oscillatory wave motions may be created within the solar interior in response to perturbations by the forces of gas pressure gradients and gravity. Gradients in the gas pressure give rise to acoustic or pressure waves, also known as p modes. The action of gravity gives rise to buoyancy effects that become manifest as convective motions in the solar convection zone or as gravity waves, called g modes, where the solar gas is locally stable against convection. To date only the p modes have been observed unambiguously, although numerous recent studies have claimed to observe the surface effects of low-degree internal g modes. In the gaseous interior of the Sun there are no solid boundaries in which its acoustic modes are confined. Nevertheless, the strong radial variations in the temperature and density of the solar gas allow acoustic cavities of many different effective lengths to be present simultaneously in the solar interior. Each of these cavities possesses both an inner and

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on the Moon

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Figure 1: Full-disk solar Dopplergram obtained at 07:07:00 P.S.T. on July 4, 1990, with a sodium Magneto-Optical Filter at the 60-Foot Solar Tower of the Mount Wilson Observatory. In this image the line-of-sight radial velocity of the entire visible solar disk is shown. The motions caused by the solar oscillations are superimposed upon the large-scale solar rotational velocity, which is responsible for the gradient from left to right across the image. an outer reflecting boundary at which the direction of travel of the waves is reversed. Just below the solar surface layers the gas density increases rapidly over a short ra~Ual distance. This rapid density increase reflects outward traveling sound waves back into the deeper layers of the solar interior. The reflected sound waves then are traveling toward the center of the Sun where the gas temperature and density are both much higher than they are near the surface. This inward increase in the gas temperature makes the speed of sound in the interior also increase toward the Sun's center. In the case of all of the nonradial oscillations modes, the acoustic wavefronts are inclined in such a way t h a t a part of each wave is located closer to the center of the Sun than is the rest of that wave. Because the sound speed is increasing inwardly, vthis innermost portion of the wavefront travels slightly faster than does the rest of the wavefront. This difference in speed causes the wavefront to be refracted away from its original inward direction. Eventually, the wavefront is refracted through an angle of 90 °. At this point the wave can travel no farther into the Sun. The wave begins traveling back outward toward the outer reflecting layer. The radial distance inside the Sun where an inward-moving wave is turned back outward is said to be the inner reflecting boundary of the acoustic cavity. The depth at which this inner reflecting boundary is located is different for different solar p modes. The depth of penetration of a given solar acoustic mode is related directly to its horizontal length scale at the solar surface. Because modes of vastly different horizontal scales are all present within the Sun at any given time, the Sun may be viewed as possessing acoustic cavities of many different lengths. Within the Sun the existence of both inward- and outward-propagating waves results in standing waves within the acoustic cavities. The frequencies of the standing waves depend in part upon the radial extent of the cavity in which they resonate. Therefore, the existence of acoustic cavities of various lengths within the Sun means that there are many different frequencies excited in the Sun at any one time. A single solar acoustic mode is illustrated schematically in Figure 2. In this computer-generated cutaway drawing of the Sun, both the surface structure and radial variations of this mode are illustrated. The motions or intensity fluctuations that would be visible at the solar surface are depicted as the alternating light and dark regions. In the case of instruments that measure the line-of-sight Doppler shifts of the surface layers, such as were illustrated in Figure 1, the light regions represent portions of the surface that were moving inward at that moment in time. The dark regions correspond to portions of the surface that were moving outward at the same moment. In another computer image made roughly 2 1/2 rain. after this one, the light regions would have turned dark and vice versa. After an additional 2 1/2 rain. the same pattern shown in Figure. 2 would have returned. In the case of instruments which are measuring the intensity of the solar surface the dark regions would correspond to regions which were cooler than their surroundings, while the light regions would be the places where the solar surface was hotter at that moment.

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E.J. Rhodes, Jr

Figure 2: A computer-generated simulation of the three-dimensional structure of a single nonradial acoustic oscillation mode. The light colored regions on the surface and along the two panels of the cutaway portion of the Sun are places where the solar gas is momentarily moving inward, or toward the center of the Sun, while the dark colored regions are the places where the gas is moving outward at that same time. The convection zone is the stipled region beneath the surface t h a t is shown on the right hand panel of the cutaway. The radiative zone is beneath the convection zone and the energy generating core is at the very center. (Figure courtesy of John W. Harvey and John Leibacher, National Solar Observatory.) The surface pattern shown in Figure 2 is just one example of a mathematical surface called a spherical harmonic. Two quantities are enough to uniquely describe every spherical harmonic function that can possible exist on the Sun. These axe called the degree l and the azimuthal order m. The degree corresponds to the number of nodal lines in the pattern. That is, it represents the total number of circles in the surface at which the amplitude of the pattern is equal to zero. In the case of the radial modes the entire surface of the Sun will be moving with the same phase at any given moment of time Hence, there are no nodal circles on the solar surface and t = 0. All modes for which the degree is not equal to zero are referred to as nonradial modes. Low-degree modes axe those having few nodal circles and large horizontal scale lengths. The lowest degree modes are the most nearly radial of the nonradial modes. For high-degree modes there axe many, closely spaced nodal circles on the surface and the horizontal scale length of a given mode is small. The azimuthal order is equal to the number of nodal circles t h a t cross the solar equator. Nonradial modes for which m is 0 have no nodal circles t h a t intersect the equator. Their nodal circles run parallel to the equator. These modes axe referred to as zonal harmonics. When the degree and the aximnthal order are both equal, the nodal circles all lie at right angles to the equator. These modes axe called sectoral harmonics. All the other nonradial modes in the l ~ m are called tesseral harmonics. The tesseral pattern shown in Figure 2 represents a spatial standing wave. All such waves may also be thought of as a superposition of two oppositely directed traveling waves. In the case of the sectoral harmonics the two traveling waves of a given degree are moving in opposite directions around the solar equator. One mode is propagating in the direction of solar rotation and the second is traveling in the retrograde direction. In the case of tesseral harmonics such as that shown in Figure 2 the two modes of a given degree are propagating at oblique angles relative to the equator. The radial behavior of the particular mode shown in Figure 2 is shown on the left and bottom panels of the cutaway into the solar interior. These cutaway panels illustrate the additional nodal surfaces in the solar interior that have the shape of concentric spheres. These nodal surfaces represent radial points at which the amplitude of this harmonic mode is always quite close to zero. The number of nodes between the inner and outer reflecting boundaries for a given mode is called its radial order, or overtone number n. For each unique combination of t and m, such as the one shown

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Figure 3: Two-dimensional velocity power spectrum obtained from 93 consecutive observing days at the 60-Foot Tower beginning on July 14, 1990. The degree t, of the zonal (m=0) spherical harmonic patterns increases horizontally from 0 at the left axis to 600 at the right side. The temporal frequency axis increases upwardly, with the frequencies of the five-minute modes being located near 3.3 mHz where the observed power in the ridges is the strongest. These ridges of power have been shown to exist at far higher degrees in observations having finer spatial resolution. Solar internal gravity modes, if they become visible at the solar surface, will be found below the p mode ridges and will be concentrated at very low degrees (i.e. in the lower left corner). here, there is a series of modes each of which has a unique radial order. The lowest frequency is the fundamental mode and all of the overtone modes have higher frequencies. Each oscillating mode is then uniquely specified by the combination l, m and n. Each of these combinations of t, m and n corresponds to a unique frequency. The actual surface pattern that is observed at any moment in time is a superposition of many million different spherical harmonic modes, each oscillating with a unique frequency and spatial scale. An example of the dependence of the frequencies of the solar p modes upon the degree of the modes and upon their overtone number is shown in Figure 3. This is a two-dimensional power spectrum. Each different "ridge" of observed power corresponds to the set of zonal p modes of a given overtone number for degrees between 0 and 600. Because of the relationship between the horizontal scale length of a mode and the distance it will travel into the Sun before it is reflected, the lower-degree modes tend to penetrate more deeply into the Sun than do the higher-degree modes. For modes of a given degree the depth of the cavity increases with increasing radial order. By contrast, the radial modes penetrate all the way to the geometric center of the Sun. The internal g modes, are primarily confined to the deep solar interior where few of the p modes penetrate. Thus, should they be detected, these g modes will provide information about the solar interior that is complementary to that provided by the p modes. WHAT CAN BE LEARNED FROM HELIOSEISMOLOGY? One of the principal recent results from helloseismology is the realization that our best current "standard" solar models do not predict oscillation frequencies that match the observed frequencies to the accuracy of the observations. This discrepancy is. leading theoreticians to try many different refinements to the solar models. One such refinement has been a decrease in the central temperature of the models, which lowers their predicted solar neutrino fluxes. A second refinement has been the inclusion of so-called weakly interacting massive particles (or WIMPs) into the solar interior as a possible vehicle for such a lowered central temperature. Thus far, no single revised solar model has been able to "solve" the neutrino problem, include WIMPs, and match all of the observed oscillation frequencies. Other refinements currently being explored include changes to the equation of state of the solar gas, recalculations of the opacity of the solar gas, and changes in the treatment of convection in the computer-generated models of the outer portion of the solar interior. The second principal result has been the measurement of the Sun's internal angular velocity over the outer half of its JASR 14"6-C

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E.J. Rhodes, Jr

radius. The picture that is emerging is that the Sun maintains the latitudinaldifferentialrotation that is seen at its surface (in which its equator rotates faster than the higher latitudes)throughout its convection zone, but then appears to be rotating more like a solid sphere in its radiativeinteriorbeneath the convection zone. Such a rotational profile, ifverified,will place severe constraints on models of the dynamo that is thought to be driving the solar activitycycle. The third principal result is that the frequencies of the low- and intermediate-degree p mode oscillationshave been discovered to be changing in phase with the solar activitycycle. The discovery of these frequency shiftshas opened up the prospect that we may be able to learn more about the shallow sub-surface magnetic fieldswhich are most likelyto be more prevalent at the times of m a x i m u m solar activityfrom their possible influence on the oscillationfrequencies. The discovery of these frequency shiftshas also suggested that the amplitudes and lifetimesof the oscillationsshould be studied as functions of the changing levelsof solar activity. A fourth exciting result to come from helioseismology is the prospect of being able to probe the sub-surface structure of sunspots and other regions of solar activity. This prosect has come about through pioneering studies in what has become known as "acoustic tomography." This area of research may ultimately enable solar physicists to predict the locations of future sunspots before they become visible. A n additional topic of much current research concerns the method of excitation of p modes. Although the earliest theoretical work indicated that these modes might be due to the same radiativeprocess that drives the large nonradial oscillationsseen in high-amplitude variable stars,more recent theoreticaland observational work has concentrated on the possibilitythat individual modes are stochasticallyexcited by the motion of convective eddies within the convection zone. Yet another possible area of "big physics" that helioseismology may be able to make a contribution to is the determination of the initial solar helium abundance. An important prediction of all cosmological models is the proportionate amount of helium produced at the formation of the universe. The distribution of helium within the current Sun can be inferred from the frequencies of the global modes of oscillation, thereby permitting detailed estimates of the abundance of helium in the protosolar state. This may yield the most reliable estimates of helium abundance in the early universe, thereby impacting both theories of cosmology and stellar evolution. NATURE OF THE DATA REQUIRED FOR HELIOSEISMOLOGY INVESTIGATIONS Solar oscillation data must meet a number of specific requirements if we are to obtain information on the scientific topics discussed in this article with the precision that helioseismology is capable of yielding. Broadly speaking, the requirements are as follows: 1) individual modes or groups of modes must be accurately identifiable with specific values of l, n and m, 2) the frequencies of the modes must be measured precisely enough to permit the deduction of interior properties, 3) nonsolar noise must be at a low enough level that the frequencies of the solar oscillations are distinct and unaltered, and 4) for the study of dynamics, the data to be inverted must be acquired within a time interval shorter than the lifetime of the phenomenon under study. The difficulty of meeting each of these requirements depends on the particular set of modes employed, which in turn is dictated by the specific scientific goal involved. For example, requirement 3) is easily satisfied for modes in the 5minute band because these modes have large amplitudes. However, for modes with longer periods, this requirement is more difficult to satisfy because the amplitude of the oscillations is very much less for periods away from the 5-minute band. In order to obtain an adequate set of data to study the entire solar interior, oscillation modes with many different spatial structures must be combined. Specifically, to determine the details of the structure or dynamics within a desired region of the solar interior, such as the convective envelope or the deep interior, we must construct combinations of a large number of modes whose raclial variations are concentrated within the particular region and which tend to cancel outside that region. An overall model of the Sun will require information from many such groups of modes. To address the usefulness of various oscillation modes in the deduction of the properties of the solar interior, it is useful to divide the modes illustrated in Figure 3 into several different groupings in terms of their modal frequencies and degrees. The principal division of the observed solar modes is by their degree. This results in the so-called low-degree (0 ~ t ~ 3), intermediate-degree (4 < l < 150), and high-degree (150 < t < 4000) portions of the t - v plane. (In the near future I suspect that the high-degree portion will be further sub-divided into high-degree (150 < l < 600), very-high-degree (600 < t < 1500) and extremely-high-degree (1500 < t < 4000) sub-groupings.) The low-degree modes are further divided into the low-frequency (those having periods longer than 10 minutes), intermediate-frequency (modes having periods between 10 and 4 minutes), and high-frequency (modes having periods less than 4 minutes) sub-groups. For the intermediate- and high-degree groups there are only the intermediate- and high-frequency sub-groups. I will now discuss the difficultiesposed by ground-based observations for all of the above seven sub-groupings of solar oscillations. For example, the low-frequency part of the low-degree portion of the spectrum is very important for

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improving our knowledge of inner portion of the solar interior, yet this is the most difficult portion of the spectrum to be observed from ground-based measurements. The main difficulty in making these low-v measurements in integrated solar light (i.e. when observing the Sun as a star) is the photometric variability of the terrestrial atmosphere. Hence for integrated-light intensity measurements of low-frequency low-degree modes it has been mandatory to go to space. Two such experiments have been the ACRIM experiment on the Solar Maximum Mission (and now on the UARS spacecraft) and the IPHIR experiment on the USSR Phobos spacecraft. Second, all ground-based observations of the solar oscillations are affected by turbulence in the Earth's atmosphere. This produces the phenomenon of "atmospheric seeing" that consists of image motion, blurring, and distortion across the field of view. Atmospheric seeing smears out the velocity field, reducing the measured power for spatial scales comparable to the smearing function. It also shifts the measured power into incorrect temporal frequencies and horizontal wave numbers, reducing the power where the signal is large and introducing spurious broadband power at other wave numbers and frequencies. These effects are particularly important for modes of high degree. Third, all ground-based observations of the solar oscillations which are made from a single observatory will be affected by the periodic interruptions of the data which are introduced by the daily setting of the Sun. These interruptions introduce several sets of temporal sidelobes which surround every solar oscillation peak in a power spectrum such as that shown in Figure 3. The two principal sidelobes are spaced at ± 1/24 hours, or ± 11.57 #Hz, on either side of each true oscillation peak. The appearance of these temporal sidelobes causes sufficient confusion in the identification and measurement of the true solar oscillation modes that great effort is currently being expended by the U.S. National Solar Observatory in the construction and installation of a network of six coordinated ground-based solar oscillation observing stations so that the temporal sidelobes can be effectively eliminated. This network, which is known as the Global Oscillation Network Group (GONG) project, is supported by the U.S. National Science Foundation. While the G O N G network will make major improvements in eliminating the confusion from the diurnal sidelobes, it will only do so for the low-and intermediate-degree modes groups. The G O N G network is not designed to obtain measurements of the high-degree oscillationmodes. Hence, even after the G O N G network has started operations in 1994 observations of the high-degree modes will stillbe affected by both atmospheric blurring and by the dirunal sidelobes. Both of these difficultieshave led to the realization that the best place for studying high-degree solar oscillationsis from above the Earth's atmosphere and from one (or more) instruments which are constantly viewing the Sun. FUTURE

SPACECRAFT

HELIOSEISMOLOGY

EXPERIMENTS

The above difficulties have led the European Space Agency and the National Aeronautics and Space Administration to include a group of three helioseismology instruments as part of their jointly-planned SOHO mission. These three helioseismology investigations primarily aim at studies of those two portions of the power spectrum shown in Figure 3 which cannot adequately be studied from the Earth's surface. These two regions are the low-frequency, low-degree portion and the high-degree portion. The required sensitivity for observing the low-frequency, low-degree modes is difficult to achieve from the ground because of the remaining level of noise that is introduced by the Earth's daily rotation even when a network such as the GONG's is utilized. Also, as was pointed out above, the transparency fluctions of the Earth's atmosphere effectively require that studies of low-frequency low-degree oscillation modes which employ measurements of the integrated intensity of the solar disk be carried out from above that atmosphere. Similarly, the high-degree modes are difficult to study completely from the ground both because of the transparency variations and the blurring caused by the terrestrial atmosphere, and because of the diurnal data gaps. T w o of the three S O H O helioseismology instruments, the G O L F (Global Oscillationsat Low Frequencies) and V I R G O (Variability of Irrarlianceand Gravity Oscillations)investigationsare aimed primarily at the study of the solar core. Consequently, they will be concentrating on the low-frequency, low-degree region of Figure 3. The third instrument MDI/SOI (which stands for Michelson Doppler Imager/Solar Oscillations Investigation) will attempt to study the entire oscillationspectrum; however, it is being designed to concentrate on the high-degree portion of Figure 3. The MDI/SOI experiment will be concentrating on the short-term temporal variations in these modes in the hopes of learning about possible temporal variations in the sub-surface flow patterns in the solar convection zone. The GOLF experiment will obtain uninterrupted velocity oscillation measurements of the Sun seen as a star through the use of a sodium-filled resonance cell which will employ resonant-scattering techniques as opposed to the spatiallyresolved resonant transmission techniques employed in the Magneto-Optical Filter (MOF) which was utilized to obtain Figure 1. VIRGO, on the other hand, will study the variability in the solar irradiance. VIRGO will include two active cavity radiometers and sunphotometers. VIRGO will also include a low spatial resolution detector containing 16 separate elements. This part of VIRGO is known as the luminosity oscillation imager, or LOI. The M D I instrument will use two solid Michelson interferometers as the finalelements of a tunable narrow-bandpass filter. The prefilteringwill be accomplished with a blocking filterand a Lyot filter. The tuning of the Michelson interferometers will be done by moving halfwaveplates. Full-disk intensity filtertgram and Dopplergrams, and some

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Figure 4: SOHO insertion and orbit projections in two orthogonal planes. magnetograms will be taken. The MDI instrument will use a 12 cm aperture refracting telescope and a re-imaging lens to project the solar image onto a CCD array which will contain a grid of 1024x1024 pixels. In this mode of operation each pixel of the MDI will cover an area 2 arcseconds on a side, for a spatial resolution of four arseconds. The MDI will also contain magnifying optics which will form a 600 arcsecond square image of a portion of the solar disk on the 1024x1024 pixel detector for a spatial resolution of 1.2 arcseconds. The MDI will be comprised of two separate boxes: an optical package and an electronics package. The combined mass of both portions of the MDI is estimated to be 58 kilograms, while the combined power consumption is expected to be 57 watts. The telemetry data rate will be 5 kilobits per second for 16 hours per day and 165 kilobits per second for the remaining 8 hours per day. During one two-month interval in each of the two scheduled operational years of the SOHO spacecraft the 165 kilobyte per second data rate will be provided on a continuous basis. The SOHO spacecraft will be three-axis stabilized and will be kept pointing at the Sun. The SOHO spacecraft is scheduled to be launched in July 1995 and is designed for an on-orbit lifetime of two years. It will, however, carry enough on-board consumables to last for an additional four years. The orbit in which the SOHO spacecraft will be placed has both advantages and disadvantages for the MDI experiment in comparison to ground-based imaging helioseismology instruments. In particular the spacecraft will be placed in a halo orbit around the L1 Sun-Earth Inner Lagrangian point. This orbit is shown to scale along with the orbit of the Moon around the Earth in Figure 4. The L1 point is located between the Earth and the Sun at a distance of roughly 0.01 astronomical units, or 1.5 x l0 s kin, from the Earth. The halo orbit about this L1 point will have a period of about 180 days and an amplitude of about 500,000-600,000 km in the direction of the Sun. One of the advantages of this halo orbit is that it will provide a relatively smooth Sun-spacecraft velocity change during each circuit. It will also be permanently in view of the Sun in contrast to the once per orbit solar eclipses which occur in low-inclination Earth orbits. The current design specifications call for the Sun-spacecraft velocity to be measured with an accuracy better than 2 cm per second. A second advantage of the SOHO orbit is that the maximum value which the SOHO-Sun velocity will attain will be on the order of 0.1 km/sec. This is almost 100 times smaller than are the spacecraft-Sun velocities available from Earth-orbiting spacecraft. It is also about ten times smaller than is the Moon-Sun velocity due to the Moon's orbital motion around the Earth. Since the L1 inner Lagrangian point is a point of unstable equilibrium in the Earth-Sun-SOHO restricted three-body problem the orbit of the L1 point around the Sun also possesses the same eccentricity as the orbit of the Earth around the Sun. Hence, during each year the size of the solar image as seen by the MDI will change in exactly the same way that the image size changes at ground-based observatories. Additional information about all three SOHO helioseismology experiments, about the SOHO spacecraft, and about its orbit can be found i n / 1 / . WHY GO TO THE MOON FOR HELIOSEISMOLOGY? While the three SOHO helioselsmology instruments have the advantages over ground-based instruments of being above the Earth's atmosphere, of continuous solar viewing, and of a relatively well-known and smoothly-varying instrumentSun velocity, there are also several the limitations that the SOHO mission envelope places on each of them. A principal limitation which all three instruments will share is two-year nominal mission lifetime. Given the variability of at least one of the principal helioseismic parameters with varying levels of solar activity and the ll-year length of an average

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solar cycle, it is clear that a two-year mission for the SOHO spacecraft will leave many of the scientific goals of helioseismology only partially fulfilled. Even the possibility of an additional four years of operation for SOHO will still be significantly less than one sunspot cycle. The second disadvantage which all three SOHO helselsmology instruments will share is the risk of premature instrument failure. In contrast to the Solar Maximum Mission there will he no possibility of an astronaut repair mission should any one of the three instruments fail during either the two-year design mission or the six-year extended mission. The location of the SOHO orbit places an extremely high premium on the reliability of each of the helioseismology instruments. It is important to note in this context none of these three instruments has ever been flown before in space and therefore none of them has a well-established track record from a spacecraft reliability standpoint. Clearly, the prospect of the subsequent repair of a malfunctioning instrument would be very desirable. The remaining limitations of the SOHO mission envelope primarily impact the MDI/SOI experiment more than they do the GOLF and VIRGO instruments. These are: 1) the restricted telemetry rate of 165 kilobits per second, 2) the lack of continuous telemetry coverage of the SOHO spacecraft by NASA's Deep Space Network (DSN), 3) the restricted weight, and 4) the restricted mass available onboard the SOHO spacecraft. The telemetry rate restriction means that the MDI instrument will not be able to send back to the Earth either as many images per minute as would be desirable nor will each of the images that is sent back have as many pixels as would be employed if the telemetry rate were higher. Since the MDI instrument is primarily designed to study the high-degree oscillation modes and since the location of the instrument will allow the optics to be diffraction-limited, an array size of 2048x2048 pixels for the CCD detector would allow each pixel to cover one arc-second on a side instead of the currently-designed two in the full-disk mode. This would allow the instrument to resolve oscillation modes to twice the limiting degree of the currently-planned full-disk mode of operation. Similarly, such a large detector array would make it possible to image a larger portion of the solar disk than will currently be possible during the time the high spatial resolution mode of the instrument is in operation. Such large CCD arrays are now available and are being designed into other astronomical instruments. Unfortunately, the restricted telemetry rate available to SOHO precludes their use in the MDI. The lack of continuous tracking coverage of the SOHO spacecraft, coupled with the lack of a large-enough tape recorder and the restricted telemetry rate described above, means that except for the two planned two-month intervals of 100% tracking coverage, the 1024x1024 pixel images which the MDI is designed to acquire will only be available for eight hours per day. Since these images are expected to be employed in the study of sub-surface dynamical flows within the solar interior, this limitation will mean that these moderately high resolution images will not be available on most days of the SOHO mission for as many hours per day as comparable size images are now available from ground-based observatories. In our current ground-based studies having such images available for even 11 hours per day has still posed major difficulties in our abilities to learn about changes in the sub-surface flow patterns. Perhaps the two twomonth intervals will be enough, but it is likely to expect that we will still be desiring longer intervals of continuous, high-resolution, full-disk images when the MDI experiment has finished transmitting its last image back to the Earth. The weight and power restrictions available to the MDI, along with the need to keep its design as simplified as possible in order to minimize the possibility of a premature failure, have resulted in an instrument which is more restrictive than an ideal high-resolution imaging instrument would be. The MDI's original capability of making measurements in more than a single spectral line is no longer part of its baseline design. Similarly, the in-flight calibration system which was originally proposed for the MDI is no longer part of the design. Also, its ability of obtaining vector magnetograms was eliminated. Clearly, an observing location which would not impose such severe constraints on an MDI-type of helioseismology instrument yet one which would still be above the telluric atmosphere and which could view the Sun continuously would be highly desirable for future helioseismic studies in the post-SOHO era. Can the Moon provide such a location? If not, could a network of stations suitably emplaced on the Moon provide such a facility? The answer to the first question is most likely "no", while the answer to the second is definitely "yes". Clearly, any single observing site that would be located anywhere on the Moon except possibly at the top of a tower which would in turn be located on top of a mountain near either of the lunar poles would not be able to see the Sun continuously. At most of the single sites where future lunar astronauts could be expected to emplace a small, 25-cm aperture solar telescope with an advanced version of the MDI experiment attached to the back end, the Sun would only be visible for roughly half of a solar rotation and then it would be below the lunar horizon for roughly the other half. Since the Sun would return to about the same location in the sky once every synodic month, or once every 29.53 days, it would be visible for roughly 14.77 days and would then be unobservable for 14.77 days. Solar observations made with such a window function would have temporal sidelobes spaced not at the ~11.57pHz which currently is available at a single location such as Mount Wilson, but rather at ~0.392pHz. As viewed from the Earth the Sun's surface layers rotate once every 27 days in the solar equator plane. Hence, the motion of solar active regions across the visible solar disk during a time series of oscillation measurements can introduce a frequency sphtting of about 0.430 pHz into integrated-light solar measurements. The similarity between 0.392 and 0.430 ftHz suggests that some solar features in the resulting power spectra might be confused with the temporal sidelobes introduced by the setting of the Sun as viewed from a single lunar observing station. Furthermore, the presence of the two sidelobes separated by a total of 0.784 pHz around each solar peak in a spectrum could interfere

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with the measurments of the intrinsicwidths of the low-frequency oscillationmodes, since they have widths near one pHz. O n the other hand, this confusion would likely be limited primarily to the low-degree modes which could be observed by GOLF-like or VIRGO-like integrated light instruments emplaced on the Moon. Since the intrinsicwidths of the high-degree modes which a follow-on M D I instrument would primarily be observing are much broader than one /~Hz the 4-0.392pHz lunar sidelobes would have only a minor impact on the determination of those modal widths and frequencies. In this context, it is interesting to note that Heiken, Vaniman, and French / 2 / h a v e pointed out that "...there may be elevated 'mountains of perpetual light' at the (lunar) poles, which could serve as sites for continuous solar power collection." However, these same authors went on to point out that "the combination of rough terrain plus the slight, but not insignificant, inclination of the moon's spin axis makes such features unlikely." Other astronomers have speculated on the possible existence of permanent polar water ice in the shadows of some of the polar mountains where the sunlight never is seen, so it is possible that the lunar polar regions might be explored as part of future lunar explorations. In any event, it is more likely that a series of non-polar bases will be established sooner on the Moon. Since as we have pointed out earlier much interesting helioseismology could be accomplished with a 25-cm aperature (or even smaller) solar telescope, it is not inconceivable to envision a lunar network of two or three such small telescopes which could then provide nearly continuous solar viewing. Such a simple network would reduce the lunar sidelobes to complete insignificance. Even with a simple lunar network of small solar telescopes the Sun could not be viewed continuously. This is because of what lunar experts refer to as "Earth shadows," or what we more commonly refer to as lunar eclipses. Such eclipses repeat with a cycle of roughly four years. The first two years of each cycle contain four total lunar eclipses separated by intervals of roughly six months, while the third and fourth years of each cycle contain five additional eclipses which are either partial or penumbral in nature. Since even penumbral lunar eclipses will affect helioseismic observations of the Sun, such measurements would be interrupted a total of nine times every four years. Beginning with the year 2003, which is the earliest possible manned return to the Moon mentioned in America at the Threshold, the Report of the Synthesis Group on America's Space Exploration Initiative/3/ and ending in the year 2020 the Fifty Year Canon of Lunar Eclipses: 1986-2035/4/fists a total of 42 lunar eclipses, of which 17 will be total, 9 partial, and 16 penumbral. However, because lunar eclipses last no more than about four hours from the time the Moon enters the penumbra of the Earth until it exits, and in many cases are significantly shorter, solar observations from a network of lunar locations would have duty cycles in excess of 99.9%, or greatly superior to the best performance expected from the six-station GONG network here on the earth. Similar duty cycles would hold for the other 17 years of possible manned lunar bases. Clearly, the "Earth shadow" events will have negligible impact on possible lunar-based solar observations. Will a lunar base provide adequate telemetry resources? According to America at the Threshold single lunar-based instruments having telemetry rates of up to 10 Mbps are envisioned/5/. A follow-on instrument to the MDI which might employ a 2048x2048 pixel CCD array and which would send back four images every minute would need only 1.2 Mbps if each of the images were compressed to six bits per pixel and the pixels in the roughly 20% of each square frame outside the solar image were not transmitted back to Earth. Even if a 4096x4096 pixel array was used to give 0.5 arcsecond pixels over the entire visible solar hemisphere, a telemetry rate of 4.8 Mbps would be needed. While such rates are unthinkable for spacecraft such as SOHO, they appear to be emminently feasible from a single lunar base. Even in the case of a network of three solar telescopes, only one would be in operation most of the time, and so the maximum telemetry rate from such a network would still be feasible. The low lunar gravity would make the installation of 25-cm solar pointed telescopes very easy for future lunar astronants. In the Analysis of the Synthesis Group's Science Emphasis for the Moon and Mars Architecture a much larger solar telescope is envisioned for lunar emplacement in 2008 by Cooke, Weary, and W e a v e r / 6 / . In fact, such a solar telescope is estimated to weigh 200 Kg, to occupy 9.4 m 3, and to require 500 watts of power. Clearly, the much smaller helioseismic instruments could be deployed as "targets of opportunity" by lunar astronauts at earlier phases in the future manned missions due to their smaller size, weight, and volume. Installation of one small helioseismology telescope per year for the years 2003 through 2005, for example, would provide for nearly continuous solar coverage for an entire solar cycle by the year 2015. The emplacement of these helioseismology telescopes near the manned lunar bases would allow each of them to be repaired by the astronuats should they malfunction. The inherent redundancy of a small network of telescopes would mean that some solar data would be available at all times unless all three instruments failed simultaneously, which would be very unlikely. This would be much better than the SOHO situation where the failure of any of the three instruments will be permanent. Finally, it is important to investigate the systematic velocity which a lunar base would introduce into helioseismic observations. The maximum orbital velocity of the Moon in its orbit around the Earth is about 1.05 km/s. While this is larger than the 0.1 km/s Sunward velocity of the SOHO spacecraft, it is only two and one-half times larger than the 0.4 km/s velocity which existing ground-based observations have had to deal with on a daily basis due to the Earth's own rotation. Also, this velocity will vary 27.3 times more slowly than does the velocity component due to the Earth's

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spin. This 1.05 km/s velocity component is also much smaller than that available on low-inclinationEarth-orbiting satellites, which can be as large as 8 km/s. Current instrumental techniques can adequately compensate for the 0.65 km/s difference between the orbital velocity of the Moon and the rotation of the Earth. The velocity component introduced by the Moon's rotation about its own axis as it orbits the Earth is only 4.6 m/s. This velocity is very small, but it will also be well-known as soon as the selenographic co-ordinates of the solar telescopes are available. Lastly, it is important to note that the measurements of solar intensity will not be affected at all by the Moon-Sun velocity component.

CONCLUSIONS The need and prospects for future helioseismic obserwtions from the lunar surface have been investigated. The scientific return concerning the solar interior in the post-SOHO era has been shown to warrant continued helioseismic observations. The advantages and disadvantages of lunar observations compared to Earth-based observatories, to Earth-orbiting satellites, and to the SOHO mission have been carefully explored. In summary, the advantages of even a single small solar telescope looking at the Sun for 14.7 days out of every 29.5 days outweigh any possible disadvantages. A better arrangement would be a network of two such instruments placed in opposite hemispheres of the lunar surface. The best possible situation would be a network of three such instruments emplaced over a three-year interval which would continue to study the Sun for one complete solar cycle. By analogy with the current NSF-supported GONG project, we might refer to such a lunar network as the LONG (or Lunar Oscillation.Network Group). Perhaps some currently-working helioselsmologlsts will not yet be retired when it is placed into operation. REFERENCES

1. V. Domingo, The SOHO Mission, Scientific and Technical Aspects of the Instruments, esa SP-1104, European Space Agency, Paris, France (November 1988). 2. Heiken, Vaniman, and B. French, Lunar Sourcebook, Cambridge, 1991, p.40. 3. T. P. Stafford, America at the Threshold: Report of the Synthesis Group on America's Space Ezploration Initiative, Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 (May 1991), page 40. 4. F. Espanek, Fifty Year Canon of Lunar Eclipses: 1986-~035, NASA Ref. Publication 1216, Sky Publishing Corp., Cambridge, Massachusetts, 1989. 5. T. P. Stafford, America at the Threshold: Report of the Synthesis Group on America's Space Exploration Initiative, Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 (May 1991), page A-26. 6. D.I~. Cooke, D.P. Weary, and D.B. Weaver, Analysis of the Synthesis Group's Science Emphasis for the Moon and Mars Architecture, ExPO Document XE-92-003, NASA (March 1992), pages B-2, B-3, and C-11.