Publications of the Astronomical Society of the Pacific. Vol May No The Prospects for Asteroseismology from Ground-Based Sites

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1 Publications of the Astronomical Society of the Pacific Vol May No. 723 Publications of the Astronomical Society of the Pacific 108: , 1996 May The Prospects for Asteroseismology from Ground-Based Sites J. N. Heasley Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, Hawaii Electronic mail: Kenneth Janes Department of Astronomy, Boston University, 725 Commonwealth Ave., Boston, Massachusetts Electronic mail: Barry LaBonte Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, Hawaii Electronic mail: David Guenther Department of Astronomy and Physics, St. Mary s University, Halifax, Nova Scotia, Canada Electronic mail: guenther@romana.stmarys.ca Donald Mickey Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, Hawaii Electronic mail: mickey@ifa.hawaii.edu Pierre Demarque Department of Astronomy, Yale University, P.O. Box , New Haven, Connecticut Electronic mail: demarque@astro.yale.edu Received November 16; accepted 1996 March 4 ABSTRACT. We reexamine the possibility of detecting p-mode oscillations in Sun-like stars with ground-based telescopes. Previous attempts to make such observations with photometric techniques have been limited to subgiant stars in M67 and have illustrated the great difficulties involved in performing ground-based asteroseismology. Substantial gains in observing efficiency can be realized from new diagnostic techniques and improvements in instrumentation, especially with new CCD camera systems. We show that for appropriately selected field stars observed with a network of telescopes or at a high-duty-cycle site, it will be possible to detect p-mode oscillations from the ground. An alternative to a network of telescopes for asteroseismology would be to develop a dedicated observatory for this purpose at a highduty-cycle site, i.e., the South Pole. We estimate the scintillation, the main noise source in asteroseismology, at the Pole by modeling the index of refraction structure parameter from meteorological data. The model results show that at the Pole the variance of the relative intensity fluctuations i.e., the scintillation should be a factor of 5 smaller than at Mauna Kea. Taking into account the improvements possible with target selection and instrumentation, the South Pole would be an excellent site for asteroseismological work on Sun-like stars. 1. INTRODUCTION The theory of stellar structure is widely regarded as one of the great success stories of twentieth century astronomy. Yet, until very recently, the only observational constraints on theoretical models of stellar interiors have been comparisons that measure or infer total luminosity and stellar radii, occa- sionally for stars of known mass. These quantities are integral properties derived from the cumulative effects of the physical variables, i.e., temperature, pressure, density, and composition profile, throughout the interior of the star. Now, for the first time, it is technologically possible to detect and analyze normal-mode pulsations (p modes) in stars, allowing us to examine directly the internal physical structure of stars Astronomical Society of the Pacific

2 386 HEASLEY ET AL. Fundamental, detailed testing of stellar evolution theory is now possible. The application of pulsation analysis techniques to the Sun, commonly known as helioseismology, is now quite developed and has yielded significant improvements in our understanding of the solar interior (see, e.g., the reviews by Libbrecht and Woodard 1991 and Gough and Toomre 1991). The approach is now being extended to probe the subsurface structure of sunspots (Penn and LaBonte 1993) and to search for variations of oscillations over the solar cycle (Issak et al. 1988; GONG 1990; Harvey et al. 1993; Ronan and LaBonte 1994a). The extension to stars other than the Sun, i.e., asteroseismology, is difficult because of the extremely small variations in intensity and velocity associated with the pulsation modes and the need to have adequate temporal coverage to resolve the modes of interest. Recent progress in the field has been reviewed by Brown (1991) and Brown and Gilliland (1994; hereafter BG). As noted in the latter review, the field is still, to a large extent, in the process of defining itself. Of special, interest to many astronomers is the application of asteroseismology to Sun-like stars. In this paper we will use the term Sun-like to refer to stars on or near the main sequence that have relatively shallow convection zones that might experience p-mode oscillations similar to those found in the Sun. Probing the internal structure of these stars should constrain our models of convection. A more challenging group of stars are the solar analogs those stars that are within say 10% of the solar mass and luminosity. Improving our knowledge of the internal structure of these objects will improve our understanding of the solar-stellar connection, and ultimately, of the solar-terrestrial connection as well. The reviews cited above describe the potential gains in our understanding of single and binary stars when asteroseismological information, in particular the large- and smallmode splittings A i^o and S ni, is added to the traditional observational data. More detailed studies of the potential of stellar seismology have been carried out for specific stars: e.g., Procyon (Guenther and Demarque 1993), a Centauri (Demarque et al. 1986; Edmonds et al. 1992; Brown et al. 1994) ; Eridani (Guenther and Demarque 1986; Guenther 1987), and the Sun as a star (Guenther 1991). In addition to providing strong tests of stellar-evolution models and probing the nature of convection and rotation inside stars, asteroseismology has the potential to allow the determination of stellar masses and ages for individual field stars. With the star s surface temperature, the seismology data, and reasonable constraints on the star s helium abundance, one can put strong constraints on the star s parallax (or, equivalently, luminosity) (Guenther and Demarque 1995). This would open the exciting possibility of directly determining the evolutionary history of the Galactic disk in the solar neighborhood. The astrophysical potentials of asteroseismology are great, but for the most common stars we have yet to realize the unambiguous detection of oscillation modes corresponding to those found in the Sun. The reason for this is quite simple the effects in integrated light in Sun-like stars, either in amplitude (several ppm) or velocity shifts (<1 m s -1 ), due to the oscillation modes are small. A further complication is that discriminating the modes in these stars requires a long (and continuous) time base for the measurements. To achieve these objectives, observing campaigns have been run at sites distributed in longitude to provide the necessary temporal coverage. The best time-series coverage obtained thus far is only 156 hours (Gilliland et al. 1993; hereafter G93). Recent attempts to determine oscillation modes from variations of integrated stellar flux have received considerable attention. The observational task is to obtain highprecision time-resolved photometry of the star in question. This can be accomplished by imaging onto a CCD an area around the target star that includes an ensemble of stars to establish a well-defined mean magnitude against which the target star may be compared. Thus, the observational problem becomes one of high-precision relative photometry. The limitations of the technique have been discussed by Gilliland and Brown (1988), Honeycutt (1992), and Kjeldsen and Frandsen (1992). Attempts to apply the technique have been discussed by Gilliland et al. (1991), Gilliland and Brown (1992), and G93. The last of these studies, which made use of a global network that included several 4-m telescopes, showed that the method of CCD ensemble photometry is close to reaching the precision levels needed for asteroseismology, but as yet no definitive detections have been made. The situation with regard to detecting oscillations from Doppler shifts in integrated starlight also appears to be promising (BG). Thus far, observations in this area have been limited to three bright stars: Alpha Centauri A, Procyon, and Beta Hydri. Four groups have attempted observations of a Cen A with somewhat conflicting results, so that while some of the results are encouraging, no clear detection of oscillations in this star can be claimed. Brown et al. (1991) reported spectroscopy of Procyon that appears to be the best case to date for evidence of p modes on a star other than the Sun. Excess power was detected in the power spectrum of Procyon, but it was not resolved into distinct modes, probably because these data were all acquired at a single observing site over a six-night period. The theoretical study of Procyon, carried out by Guenther and Demarque (1993) to follow up on Brown et al. s observations, revealed that even with the latest stellar physics the mass of the star inferred from stellar evolution and its position in the H-R diagram is inconsistent with the mass determined from its orbit with its white-dwarf companion. In addition, the large frequency spacing suggested by Brown et al. s observations do not match the corresponding frequency spacing determined from Guenther and Demarque s stellar models of Procyon. The spectroscopic observations of Kjeldsen et al. (1995) for asteroseismology appear encouraging. Rather than detecting oscillations from Doppler shifts, they reported the detection of Sun-like oscillations in the GO IV star Eta Bootis based on a new spectroscopic technique that measures temperature fluctuations in the stellar atmosphere from lowresolution spectra of the Balmer lines. The claimed observations of p modes do match those predicted by stellar models of rj Boo (Christensen-Dalsgaard et al. 1995; Guenther and Demarque 1995). However, Noyes et al. (1995) report time

3 ASTEROSEISMOLOGY 387 series of radial-velocity observations of rj Boo that rule out the 13 frequencies reported by Kjeldsen et al. with typical amplitudes of 0.5 km s -1 or more, about a factor of 3 smaller than the amplitudes estimated from the analysis of temperature fluctuations in the equivalent widths. While this new technique appears promising, additional confirmation is needed. Because of the absence of a good model for convection, it is unclear exactly what levels of variation, either in intensity or velocity, one can expect in integrated starlight. Kjeldsen and Bedding (1995) have attempted to address this question by devising scaling relations for Sun-like stars. They conclude that for the Sun-like stars studied to date, observations have not yet reached adequate sensitivity to detect p-mode oscillations. However, for some F-type stars, notably Procyon and some of the members of M67, detection levels 30%-40% below the predicted amplitudes have already been obtained. They conclude that such stars must oscillate with amplitudes considerably smaller than previously assumed. The slow progress in asteroseismology, at least with regard to detecting p modes in solar analogs, has caused some to seek space-borne platforms for future observations, and BG point out several such missions that are planned or are in progress. There are certainly exciting prospects for asteroseismology from space, but spacecraft are very expensive. Regardless of whether one approaches the observational problem of asteroseismology from the ground or space, the fundamental problem remains the same, namely extracting from data a low-amplitude periodic signal that has higher random noise than the periodic signal one is attempting to detect. G93 not only demonstrated the great difficulties in performing asteroseismology with ground-based telescopes, they also report possible detections of oscillations (at about the 2a level) in half of their M67 ensemble. It is clear that to obtain definitive detections of pulsation modes that will allow us to derive meaningful information on stellar interiors is going to take considerably more telescope time than has heretofore been given to this type of work. In our opinion, the instrumental sensitivity necessary to perform meaningful asteroseismology from the ground is not out of reach with current technology. Given how large telescopes are currently scheduled, it is extremely unlikely that a network of existing large (4-m or larger) ground-based telescopes could ever be organized to detect oscillations in Sun-like stars (much less the solar analogs), but it is not impossible that a dedicated network of smaller telescopes, or a single telescope at the right site, could achieve this goal. In this paper we explore several aspects of the photometric approach to the asteroseismology problem, including some instrumental and site considerations relevant to raising the signal; site and instrumental possibilities for reducing scintillation, the primary noise term in performing asteroseismology; and a reexamination of the total error budget of such observations. 2. SENSITIVITY REQUIREMENTS FOR ASTEROSEISMOLOGY The asteroseismology problem is simple to describe, but difficult to solve. Briefly, one is searching for a phenomenon with characteristic periodicities on the order of several minutes. There are, in principle, a huge number of possible modes in this general range of periods, but most or all of them are excited only to very low amplitudes most of the time. The fundamental assumptions are that there are discrete frequencies that are characteristic of the star in question and that the overall structure of the star does not change over the course of the observations, which in future investigations could last as long as several weeks. At any one time, the amplitudes of the stellar oscillations will be far smaller than any practical observational errors. Nevertheless, while the amplitude of the p-mode oscillations in solar analogs will be small, it is important to remember that it is not required that each single observation have a precision of parts per million in intensity or tens of cms 1 in velocity. It is well known that for a time series of observations the amplitude of a periodic signal can be determined with much greater precision than that of any individual measurement. The solution, then, is to get a continuous run of observations over a long period of time, to acquire huge numbers of samples of either the velocity or the luminosity. If the individual data samples are uncorrelated with one another, then eventually the noise will average out and the characteristic periods will begin to appear. The noise of any observational sample is assumed to originate in the atmosphere, the telescope, the instrument, or as Poisson noise in the original signal. Whatever the source may be, any instrumental or atmospheric effect with short characteristic time scales of the order of seconds or less will show up in the time-series data as an almost purely random process. The combined amplitude of all the short-period noise sources defines how many samples are needed to find the inherent periodicities in the signal itself. If the only noise sources are in the short-period regime, then the ultimate signal-to-noise ratio obtainable would be limited only by the observer s patience and the inherent stability of the source. At the other extreme, long-period effects such as clouds, most sources of instrumental drift, and so forth generally can be ignored in the time-series analysis. The quantity being measured is the difference from one sample to the next, so long-term effects will not ordinarily even be seen. Serious problems could occur at the intermediate periodicities, those similar to the ones being searched for with periods in the several-minutes range. These would of course mimic the real pulsational modes in the star. One could imagine, for example, a regular cycling of the cooling system that could be in the right period range. It will be necessary either to learn to measure them directly or at least be able to show that there is no inherent periodicity to all such sources. Clearly, adequate monitoring of the instrumental setup and observing conditions will be required to identify and compensate for such effects. For example, the laboratory tests by Buffington et al. (1990) showed that to attain high precision with CCD detectors it may be necessary to remove drifts due to temperature changes in the instrument. The camera-head temperature would be constantly monitored and its value recorded in the data headers for each image so that after-thefact tests for thermal drifts can be made and incorporated if necessary. In photometric observations, the atmospheric

4 388 HEASLEY ET AL. variations in transparency and color can be monitored directly from ensemble stars. Finally, small errors in the data that can be correlated with external parameters of the observations can be removed using the decorrelation technique described by Brown et al. (1991). The attempts made to date have not unambiguously led to the detection of p modes in Sun-like stars. If the required sensitivity levels are to be achieved from the ground, then additional improvements in instrumentation, observing techniques, and site selection are necessary. Broadly speaking, these fall into two categories: raising the signal levels and lowering the noise levels. The following sections discuss a series of improvements that can be made in both areas. When these are applied in a systematic program, they should make it possible to detect p modes in Sun-like stars. 3. RAISING SIGNAL LEVELS 3.1 Higher Duty-Cycle Detectors To date most experiments in asteroseismology have made use of general observatory facilities. Naturally in such circumstances the observers often end up using general purpose instrumentation, in particular the CCD cameras normally used at the site. With some attention to customization of the observing setup for asteroseismology, we believe it is often possible to pick up a factor of two or more in observing efficiency. The G93 campaign developed a standard set of photometric filters that were used at each site, albeit imaging onto a wide variety of CCD sensors. An excellent example of the gains to be realized in asteroseismology with customized instrumentation is seen in the spectroscopic work by Brown et al. (1991). An especially important advance in recent years, even since the campaign of G93, has been the improvement in CCD cameras. Better detectors with higher quantum efficiency and more stable electronics than those used in previous photometric studies in asteroseismology (e.g., G93) are now available. Faster read times mean a higher duty cycle (i.e., more time can be spent collecting photons and less reading out the CCD) and that very short exposures on relatively bright stars are practical, and can dramatically increase the number of independent samples per unit of time. The stability of modem camera electronics is illustrated by the laboratory tests of Robinson et al. (1995). Their results suggest that the camera electronics in a modem CCD are far from being a limiting factor for asteroseismology and that other sources of photometric errors (see, e.g., Young et al. 1991) dominate at the telescope. An important feature of current generations of CCD controllers is the ability to have a variable or adjustable gain. In most cases general-purpose CCD cameras are optimized to detect faint, fuzzy sources rather than to exploit the large dynamic range inherent in the large full wells of the sensors. By adjusting the camera gain to be large, but smaller than the shot noise in the observations, it is possible to exploit this large dynamic range. During the G93 campaign, this approach was adopted at several of the sites. The application of several well-known strategies can greatly improve the duty cycle of asteroseismology observa- tions. For imaging, one can use a camera designed around a CCD that employs an elongated format like the Loral 2048 X1024 sensor and has a physical mask over those pixels closest to the transfer registers. One can operate the camera in a shutterless mode using a rapid frame transfer to move the charge accumulated in the exposed portion of the chip into those pixels behind the mask. If the time required to read the masked segment of the device is shorter than the exposure time (which becomes practical with a CCD with a large full well), then one can attain essentially 100% efficiency with the camera. A procedure useful for spectroscopy would be to place the star on a short slit and clock the CCD continuously at some set rate so that the maximum signal on any portion of the spectrum during the effective exposure is below linear saturation. Each row of spectrum would then be an independent time sample of the star. Again, observing efficiencies of near 100% can be attained. 3.2 More Numerous and Brighter Targets The stellar targets for photometric studies in asteroseismology have been limited to the moderately bright subgiant stars in the open cluster M67 (Gilliland et al. 1991; G93). That particular field was selected as the best choice for the winter season observing campaign. However, because the M67 stars are relatively faint, large (4-m class) telescopes were required for the observations. We will show here that by relaxing somewhat the requirement of a very small field that they imposed in their selection procedure, a substantial sample of bright field stars can be found that would be good targets for seismological studies and that could be observed with a smaller telescope. In the case of ensembles located in star clusters, one has the possibility of having a number of targets for asteroseismology measured simultaneously. With the field-star ensembles, however, we trade off the multiple targets for higher signal to noise in a single, brighter target star. The concept of ensemble photometry is to use all the stellar images on a CCD frame to define an instrumental mean magnitude for that frame and to measure the magnitudes of the individual stars relative to that mean. Obviously, the photon flux of the ensemble must be substantially greater than that of any individual stars, and the ensemble must cover a small enough area on the sky to minimize the differential effects of scintillation and transparency. Theoretical discussions (e.g., Roddier 1981) indicate that the isoplanatic patch of a meter-class telescope is only a few arcsec across. The isoplanatic patch is the angle over which there is instantaneous coherence of the speckle pattern in the images of objects. However, in the long exposure limit (times of the order of the telescope diameter divided by the wind speed, i.e., less than a few seconds) the averaged image shape is coherent over several arcmin (Cowie and Songaila 1988). This suggests that, correspondingly, it should be possible to at least partially correct for scintillation effects over similar fields. To investigate the feasibility of finding good ensembles of interesting stars, we searched the Michigan Spectral Catalog (Houk and Cowley 1975) for stars of spectral types F0 to K0

5 ASTEROSEISMOLOGY 389 Table 1 Potential Ensemble Fields South of -53 R (arcsec) N of luminosity classes V and IV, and with declinations south of -53. A total of 8918 stars match these criteria. We then examined stars on this list that also had SAO numbers (4991 stars) and cross-referenced them against the HST Guide Star Catalog (Lasker et al. 1990) to determine possible photometric ensembles. In calculating the ensemble flux, stars brighter than 20% of the target star were discounted to the 20% level to avoid the possibility that the ensemble flux would be dominated by one or two stars. Thus an acceptable ensemble has to have at least five moderately bright stars or a larger number of faint stars. We searched outward in distance from each target until ensemble flux was equal to that of the target star. In the area searched, HD , spectral type GO V, best fits the requirements for ensemble photometry within a small radius from the star. Within 2 arcmin of this V 8.5 star are 13 other stars whose ensemble flux (as defined above) is about equal to that of the target star; within 5 arcmin there are 41 stars with an ensemble flux of 2.8 times the target star. In Table 1 we summarize the search results for possible ensemble fields. If one can extend the ensemble radius out to 300 arcsec, a total of 290 possible candidates for asteroseismology are found. The median number of comparison stars for the sample is 17, while the smallest and largest ensembles contained 6 and 104 stars, respectively. Even taking a conservative radius of 200 arcsec, we find 23 possible targets for the photometric program. Our detailed search of the HST Guide Star Catalog was performed only for the southern-most region of the Michigan Spectral Catalog and for only half of the possible candidates in that region (i.e., those with positions in the SAO catalog). If we simply extrapolate our conservative results for this region to the remainder of the catalog (up to declination -12 ), we estimate there would be about 104 possible targets (in less than half the sky). If one factors in the Northern Hemisphere of the celestial sphere there would be many possible field-star candidates for photometric ensemble targets. 3.3 Higher Duty-Cycle Sites As discussed by G93, the noise goes down in proportion to the square root of the number of samples. Furthermore, systematic errors in the usual sense are not important for this problem unless they vary with time in some regular fashion. However, to split the fine spacing of p modes, which is between 0 and 30 / Hz for Sun-like stars, it is essential to have nearly uninterrupted runs of observations that are free of the 24-hour diurnal cycle. Thus, the detection of the p modes requires either a network of telescopes spaced in longitude around the Earth or the continuous observing window available at the South Pole. Either will increase the overall sampling while removing aliasing due to the Earth s 24-hour rotation period. The observed power spectrum of the data is the convolution of the true power spectrum of the star and the power spectrum of the window function. Deconvolution to remove the effects of the window function is possible in two cases. A simple Fourier deconvolution computes the true autocorrelation of the stellar oscillations from the ratio of the autocorrelations of the data and the window. This requires formally that the autocorrelation of the window function have no zeroes, that is, the duty cycle be larger than 50%. In practice, if the minimum of the window autocorrelation is small, amplification of the noise is objectionable. Experience suggests that a reasonable minimum is of order one-third, which requires a duty cycle greater than 60%. With allowance for interruptions by weather and instrument failure, the diurnal duty cycle must be higher still. Deconvolution is also possible if the signal-to-noise ratio of the power spectrum is high. Nonlinear deconvolution or modeling may be used to distinguish the true stellar oscillation power peaks from the window-generated aliases (cf., Libbrecht 1989; Ronan and LaBonte 1994b). There is no constraint on the mode properties, but the data quality must be high enough to easily identify the fundamental frequency spacing, requiring that an average mode be detected with a signal to noise much greater than 1. An alternative to developing a global network of telescopes for oscillation studies would be to locate a dedicated instrument for asteroseismology at the Amundsen-Scott South Pole Station. Even though the costs of developing a dedicated observatory for this purpose at the Pole will certainly be higher than those at a conventional observatory site, they would still be lower than developing a new network of telescopes specifically designed for asteroseismology. The major advantage gained by observing at the South Pole is the ability to obtain virtually continuous observations of the target stars, freeing the observer from the 24-hour periodic window. The possibility of asteroseismology at the South Pole was discussed by Linsky (1989), and solar-oscillation observations, which also require long time bases, have been undertaken at the South Pole on a regular basis since 1979 (Fossat et al. 1989; Harvey 1989). The South Pole has not been adequately characterized as a site for nighttime optical astronomy, i.e., the details of seeing, scintillation, and transparency, etc., there are not well known. During the nights there may be thin scattered clouds that are difficult to detect under moonless conditions, and aurora activity can become intense (Kay 1989). Nevertheless, there are powerful reasons for serious consideration of the South Pole as a site for asteroseismological study. The photometric approach to asteroseismology depends on high-precision relative photometry. Spectroscopic techniques for asteroseismology should not be seriously impacted by either the transparency variations or the aurora. A major uncertainty about the South Pole as a site for general-

6 390 HEASLEY ET AL. purpose ground-based optical astronomy is the atmospheric seeing, which is thought to be poor during the winter because of a strong inversion layer located near the surface. Photometric programs require stable images but not necessarily good seeing. (Indeed, in making their photometric observations on Mauna Kea, Gilliland et al. found it necessary to defocus the stellar images on the detector to avoid saturating the device!) However, the upper atmosphere appears to be extremely stable (Gillingham 1992) and has led to proposals to take advantage of super-seeing that might exist above the surface inversion layer (Ford et al. 1993). The stability of the upper atmosphere above the Pole would also result in little scintillation, a key requirement for the asteroseismological observations. We return to this point later in the paper. The primary reason for proposing án asteroseismological observatory at the South Pole is to use the Antarctic night to obtain long periods of continuous observations. Ideally, the site should have a high percentage of time with clear weather, although previous work in asteroseismology indicates that cirrus, transparency variations, and moonlight will not seriously compromise the observing program (Gilliland and Brown 1988). Statistics on the number of clear days at the South Pole are available from Chen and his collaborators (Chen et al. 1987; Chen and Martins 1993). They find that over three Antarctic winters ( ) from April to August an average of 60% of the time is photometric. They report that during 1985 photometric conditions with aurora would have increased the possible observing time to 65%, while 68% of the total nights were considered to be spectroscopic. The recent success of SPIREX in observing the impact of comet Shoemaker-Levy/9 on Jupiter illustrates the utility of the South Pole for continuous observing campaigns. 3.4 New Diagnostic Techniques Recently developed and less traditional parameters of the oscillation spectrum to probe the interior of the star (Guenther and Demarque 1993) should allow observers to probe the structure of a target star in less observing time than the more traditional approaches to asteroseismology. Because the inner turning radius of the p modes depends on both / and n (equivalent to frequency), one can probe the interiors of stars with only low /-value p-mode frequencies. We note, for example, that for a given order /, the variations as a function of frequency (or degree n) of Ai> can be used to derive the depth of the convection zone. This effect may be more readily observed than Sv because it does not require the high resolution in frequency that determinations of Sv require. For example, one can reduce the observations for Ai> in two different frequency ranges and use the difference in the values of A v as a parameter to characterize the depth of the convection zone. Theory predicts a dip in Av in the phz frequency range. The precise location is a function of the convection zone depth, because the slope of the sound speed changes rapidly in the transition layer from convective to radiative equilibrium. The depth of the convection zone is an important parameter in stellar physics for problems of internal mixing, rotational braking, internal angular- momentum transfer, lithium depletion, and stellar activity. The efficiency of thermal diffusion in the stellar envelope can also be estimated from these observations. If the resolution of the observations is high enough to identify individual p modes, then surprisingly precise constraints can be applied to models of the star. For example, if the star has evolved off of the zero-age main sequence and has a core that is exhausted of hydrogen, then the enhanced mean molecular weight in the core alters the frequencies of individual modes. Rather than obtaining p modes that are evenly spaced in frequency, one finds that some of the mode frequencies are bumped to higher or lower values. The actual bumping is very sensitive to the precise nature of the core; hence it can be used to determine the age of the star very accurately (Guenther and Demarque 1995). The existence of the irregular spacing is easily observed, even at lowfrequency resolution, and would provide proof that a star is in a more advanced phase of evolution. It is possible that g modes could be observed from the South Pole. The long, uninterrupted and stable observing conditions should favor g-mode observations if indeed they are excited and have detectable amplitudes at the surface of stars like the Sun. The situation may be more favorable in stars similar to Procyon, which is believed to have a convective core and a thin convective envelope. The detection of g modes would provide a very sensitive opportunity to probe the innermost part of the star, much better than even the lowest (/) p modes. 4. LOWERING NOISE LEVELS 4.1 Photometric Programs Sites with Low Scintillation As discussed by BG, the fundamental limitation for ground-based asteroseismology remains atmospheric scintillation; as shown in Sec , it is possible to bring the other important noise sources down to levels below what can be expected from scintillation for any reasonable size of telescope and integration period. To take a worst-case situation, let us suppose that at least the scintillation is no larger than found at most continental sites. Then we can use an empirical formula for the scintillation developed by Young, as quoted in BG and rewritten in magnitude units: ÔI e=1.086y = D - 2/ lr 1-75 exp(-a/a 0 )/(2fJ 1/2 ) (1) where D is the telescope aperture in cm, X is the airmass, h is the height of the observatory, h 0 is the atmospheric scale height (quoted by BG as typically 8000 m), and t m is the integration time. In this relation, e is equivalent to the quantity C wn, the amplitude of the white-noise spectrum defined by Kjeldsen and Frandsen (1992), assuming that scintillation actually has a white-noise spectrum. Kjeldsen and Frandsen used time-series simulations to derive the S/N level required in the amplitude spectrum to detect peaks with a 95% confidence level (see their Fig. 4). Extrapolating beyond their diagram to the likely number of samples required for detection of single coherent modes suggests a target S/N=5.

7 ASTEROSEISMOLOGY 391 is For such a 5<x detection, the number of samples required JV obs =25(e/A coh ) 2, (2) where A œh is the amplitude (in magnitudes) of a coherent oscillation mode. These two relations can be combined to get the total length of time needed to extract a 5 a signal from the scintillation noise: T=N obs t m = > _4/3 Z 3 5 exp( 2/i//î 0 )A h- (3) We now use this result to consider the possibilities at an asteroseismology observatory located at the South Pole. For an object at the zenith, measured at the South Pole (A =2740 m) with a telescope of aperture D = 130 cm, a continuous 118-day period would be required to get a 5 a detection of oscillations on Sun-like stars (A œh =3 micromagnitudes). For comparison, BG used as an example the detection of pulsations in Sun-like stars with a 4-m telescope at an elevation of h =2000 m and integrated the airmass over a 9-hour window, presumably for an object at intermediate declination (e.g., M67) and an observatory at mid-latitudes (e.g., Kitt Peak) to get a 4a signal in 111 days. (A 5a detection would require 173 days at Kitt Peak.) In fact, it should be possible to do considerably better than 118 days. First, at the South Pole in winter, the atmospheric pressure is equivalent to almost 4000 m at the Equator. Furthermore, by the use of a comb response (Kjeldsen et al. 1995) to pick out the mode spacings, it may be possible to derive useful information even with a lower S/N. Finally, as we show in the following paragraphs, the scintillation may be considerably smaller at the South Pole than the predictions of the Young model. For the following discussion, we have assumed that in approximately 50 days of measurements at the South Pole, the scintillation noise can be reduced to levels to permit detection of oscillations in Sun-like stars. The Young model for scintillation used by BG in their analysis of the errors intrinsic to ground-based asteroseismology is based on typical conditions at mid-latitudes in the Northern Hemisphere, and we have assumed that the conditions at the South Pole are no worse. In fact, we show there is good reason to believe that the conditions could be much better. There is a deep inversion layer over the South Pole that extends approximately 0.5 km above the surface (Chamberlain, private communication). Below an inversion the seeing is generally mediocre. However, the effects of scintillation are produced primarily at altitudes of 2-4 km (Roddier 1981), and there has been speculation (see, e.g., the POST proposal by Ford et al. 1993) that at the South Pole, there could be what has been called super seeing, above the local inversion layer. Thus there are reasons to suspect that at the Pole, stellar images will be fuzzy but steady. At the South Pole in winter, the atmospheric scale height is substantially smaller than at the equator (the pressure is equivalent to that at almost 4000 m near the equator), and the tropopause is only a few km above the surface. Furthermore, the Pole is at the center of a permanent anticyclone, and the winds are very light at all elevations, right through to the top of the stratosphere. Above the local inversion layer, the atmosphere appears to be very steady (Gillingham 1992). While we are not aware of any direct measurements of scintillation at the South Pole, we show here using theoretical modeling that the site should be an excellent choice for ground-based asteroseismology. Even if the Pole were no worse than that at other telescope sites used in the multitelescope campaigns for asteroseismology, it would be a good site for such observations, but we show here that the scintillation is likely to be greatly reduced at the Pole. For monochromatic light with wavelength X, the scintillation can be characterized by a 2, the variance of the relative intensity fluctuations, which is given by a- / 2=A 1 \ 7/6 [sec(w)] 11/6 Zm z 5/6 C 2 n(z)dz, (4) Jz t where A! is a constant, œ is the zenith angle, and C\ is the index of refraction structure parameter (Coulman 1985). The vertical profile of C 2 n can be measured directly by Doppler radar or estimated from radiosonde profiles using a theoretical model (or inferred from measurements of scintillation). We have used VanZandt s theoretical model (VanZandt et al. 1978) for deriving C 2 n with radiosonde data for 146 nights covering the period of 1992 April to August (Chamberlain, private communication) to deduce the refraction-structure parameter above the South Pole. This theoretical model allows the calculation of C 2 n from radiosonde profiles of wind, temperature, and humidity; the model predictions agree well with measurements of C\ as deduced from radar observations (VanZandt et al. 1978). While more sophisticated models of this type are available, we chose to use the original formulation of the VanZandt model so we may compare it directly with a similar calculation by Bely (1987) for Mauna Kea, now recognized as one of the premier astronomical sites in the world. While this type of model provides only an estimate of the general shape of C\ with height, using it in a differential comparison between the South Pole and a known high-quality observing site should illustrate the likely differences in scintillation between the two sites. Our modeling with the radiosonde data indicates that at a given wavelength and zenith distance the scintillation index at the South Pole is a factor of 5.3 smaller than for the same telescope located on Mauna Kea. (Bely s comparison C\ for Mauna Kea with mean C 2 n profiles for several European sites suggests that Mauna Kea is likely to be better than typical continental observatory sites in terms of scintillation, cf., his Fig. 17.) As the scintillation is the dominant noise term in asteroseismology, we would gain more than a factor of 2 in S/N (hence sensitivity to oscillations) in a given integration time with a telescope located at the South Pole The Photometric Error Budget We turn now to an examination of the error budget in asteroseismology if we combine the various factors presented in the previous sections. The arguments would be applicable to a dedicated asteroseismology telescope of

8 392 HEASLEY ET AL. 1.3-m aperture located at the South Pole (the largest telescope it would be possible to transport with the current support aircraft servicing the site). A typical CCD with pixel size of 15 /mm will be well matched to a telescope of 10 m in focal length, that is an //7.7 system, with an image scale of 20.6 arcsec per mm or 0.31 arcsec per pixel. Recent measurements with the SPIREX telescope located at the pole (Chamberlain, private communication) indicate that the seeing (i.e., image size as opposed to scintillation, or changes in the image brightness) is probably in the range of 2-3 arcsec. This means that a star image will be spread over many pixels, permitting the observation of bright stars. To detect oscillations in Sun-like stars, a relative precision of the order of one part in 10 6 is needed; a total of at least photons would have to be detected to reduce the Poisson error to the level of the scintillation error. Taking a target of 50 days for an observing campaign (see Sec ) and assuming an effective time resolution of 90 s per sample to permit clear resolution of the 5-min oscillations, some 48,000 samples would be required, each with 2.1 X10 6 electrons, corresponding to a detected flux of 233,000e s -1. G93 quoted a measured flux on a CCD detector of approximately 8X10 5 e s' 1 for a star of 11.5 at a 4-m telescope using a filter with FWHM of 1665 Â centered at 4720 Â. These figures are consistent with our experience at the KPNO 0.9-m telescope, and imply a 1.3-m telescope limiting magnitude of almost = 10.5 to yield the 233,000e s -1 flux limit at which the Poisson errors and the scintillation errors are equal. The practical magnitude limit would need to be somewhat brighter, to ensure that the Poisson errors would be insignificant compared to the irreducible scintillation errors. Previous measurements with 1-m telescopes on stars in this magnitude range, (e.g., G93; Kjeldsen and Frandsen 1992; Janes 1996), have shown that measured photometric errors on the order of mag or better can be obtained even through thin clouds and with variable seeing over the integration times of the order of one minute. Taking into account the 4000-m pressure height at the Pole, it should be possible to achieve a precision of 7.5 X10 4 mag or better on bright stars with 5-s sample times. Thus for stars somewhat brighter than the above Poisson limit of m v = 10.5, it should be possible to detect oscillations in the 50-day continuous observing campaign. Furthermore, in a future system, the CCD detector would likely have about a 30% improvement in quantum efficiency over the systems used by G93, and further gains can be realized by using a somewhat broader bandpass. Finally, there could be almost a 100% duty cycle. These more favorable circumstances will permit a shorter cycle of exposures, so that many more independent samples can be collected per unit time, adding an additional margin of safety in the above estimates. A 50-day period is a long time for a continuous run of observing, even at the Pole, and it is unlikely that the skies will remain continuously clear for such long time. The 50- day period represents a total integration time, and some interruptions will be permissible, as long as there is no regular pattern to them, such as the 24-hour diurnal pattern. At the South Pole, that diurnal pattern is missing completely. The essential requirements are to minimize the random effects, keeping them well below the scintillation value, eliminate as far as possible any periodic effects, and monitor carefully all the instrumental characteristics, such as voltages, instrument temperature, etc., and keep track of the minute-by-minute weather conditions. This auxiliary data would be subjected to the same sort of analysis as the photometric or spectroscopic data to test for false periodicities. 4.2 Advantages of Spectrophotometry The recent work by Kjeldsen et al. (1995), in which lowresolution spectra of Balmer lines are used in an attempt to detect pulsational modes in the subgiant r/ Boo, has raised considerable interest in the asteroseismological community. Bedding et al. (1996) have synthetic spectra to explore the sensitivity of other features for measuring temperature fluctuations in stellar atmospheres. If it is indeed possible to detect p-mode oscillations with low-resolution spectroscopy, the number of potential targets for asteroseismology, even with a telescope of modest aperture, is greatly increased. While there is still some question as to the certainty of the detection reported by Kjeldsen et al. (see Noyes et al. 1995), both Christensen-Dalsgaard et al. (1995) and Guenther and Demarque (1995) show that the reported oscillation spectra are consistent with theoretical predictions for a star of r/ Boo s evolutionary state. On the Sun, the Balmer lines are poor choices for observing resonant oscillations. The Ha line formation is split, with large contributions in the chromosphere and the low photosphere, and no contribution near the temperature minimum in the solar atmosphere (Schoolman 1972). The temperature contrast of the resonant oscillations grows with height up to the temperature minimum; therefore the Balmer lines are insensitive to the signal. Chromospheric oscillations and dynamics are uncorrelated with the resonant oscillations; therefore the Balmer lines are highly sensitive to noise (Harvey et al. 1993). A study of the spectral behavior of the solar resonant oscillations was made by Ronan et al. (1991). They confirmed that the oscillation amplitude in the Balmer lines is greatly reduced compared with the continuum, and the contrast of the oscillations, relative to the temporal mean, is low in the Balmer lines compared with metal lines that are formed in the mid to upper photosphere. The highest contrast oscillations are seen in the Ca II H and K line cores and the CN bandhead, all formed at the temperature minimum. They did not measure the Ca II infrared triplet lines, but we would expect those lines to behave similarly. The measurements made by Kjeldsen et al. assumed that the continuum was invariant and the Balmer lines oscillated; just the opposite occurs in the Sun. In either case an oscillation of the line equivalent width would result. The reality of the stellar result must be judged by the agreement of the absolute amplitudes and frequencies in the data with the rough estimates available from theory, in the absence of confirming observations.

9 ASTEROSEISMOLOGY 393 A more important result of the Ronan et al. (1991) study was the demonstration that the phase of the intensity oscillation varies with line depth. They could measure the oscillation amplitude and phase at each wavelength because their observations were brief and the sky conditions good, so that only slow trends in the intensity were present as a background. In the case of stellar observations, the time series are long and the spectra must be self-referenced. Then we can measure only the vector (amplitude and phase) difference of the line and continuum oscillations. However, if we simultaneously use ensemble average photometry to measure the continuum oscillation directly, then we can determine the continuum and the line oscillation vectors separately. The test for the reality of the detection of stellar oscillations would then include the relative amplitudes and phases of the line and continuum oscillations in addition to the match of frequencies and absolute amplitudes. This diagnostic is an important reason for conducting simultaneous photometric and spectroscopic observations of stellar oscillations on individual stars. Finally, the spectroscopic approach used by Kjeldsen et al. (1995) suggests a means by which the noise due to scintillation can be eliminated, at least to first order, in a photometric approach. Rather than using spectral diagnostics that are sensitive to temperature, the key would be to examine the color changes of an individual star as a function of time. Based on the temperature fluctuations inferred by Kjeldsen et al., we estimate that the variation in a broad-band color (e.g., V I) would be on the order of several parts per million. While this is at the same level of difficulty as measuring the intensity fluctuations themselves, by any number of suitable optical arrangements one could simultaneously record both broad-band channels simultaneously after the star s light has passed through the atmosphere, i.e., both channels would have experienced the same scintillation. This selfdifferential approach would allow us to work on even the brightest field stars that are not located in fields rich enough to perform ensemble photometry. This would open to photometric observations bright field stars like a Cen A, which are too bright for ensemble photometry but are difficult targets for Doppler measurements even with large telescopes. Previous experiments in helioseismology and future work in that area suggest a spectrophotometric approach to detecting oscillations from color fluctuations hold promise. Transparency fluctuations in the Earth s atmosphere in the 5-minute band are several orders of magnitude larger than the expected amplitude of resonant solar oscillations observed in integrated sunlight (cf., Hill et al. 1994). However, the long coherence time of the oscillations increases the detectability of the individual power peaks in long time series, as the incoherent transparency noise cancels. A few attempts to observe the solar oscillations with simultaneous multicolor photometry have been made (Fröhlich 1984; Jimenez et al. 1987; Andersen and Domingo 1988). Only Fröhlich formed the ratios of the intensities observed in the different bands; his data were only a few hours of balloon observations, and he could only conclude that color of the oscillations was consistent with pressure-driven waves in the photosphere. Andersen and Domingo used scaled differences of the power spectra of the separate filter signals to combine 15 days of data. By folding the difference spectra at the known 135 phz fundamental frequency, they detected the existence of the solar modes and were then able to isolate a series of the individual peaks. The Solar and Heliospheric Observatory (SOHO) spacecraft, scheduled for launch this year, carries a set of three filter photometers that will give precise oscillation colors (Domingo 1994). 5. SUMMARY We conclude that it is premature to dismiss the possibility of performing asteroseismology on Sun-like stars from the ground, even with telescopes as small as 1 m. Both improvements in instrumental sensitivity and efficiency, combined with the advantages of a site like the South Pole, where the diurnal observing window can be removed, would allow us to achieve a detection of p-mode oscillations within reasonable observing periods. Further, at the South Pole the scintillation, which is the primary source of photometric error in asteroseismology, may be considerably less than at conventional observatory sites. The selection of moderately bright field stars as targets for such studies offers an adequate number of targets even for a telescope of modest aperture at the South Pole, or a networked observing program. We would like to thank Dr. François Roddier for helpful discussions regarding scintillation, and Dr. Duane Stevens of the Department of Meteorology of the University of Hawaii for his assistance in developing the numerical code for deriving the atmospheric index of refraction-structure parameter. Finally, we would like to thank Dr. Ron Gilliland, who refereed this paper, for his many helpful comments about the original manuscript. REFERENCES Andersen, B. N., and Domingo, V. 1988, in Advances in Helio- and Asteroseismology, IAU Symp. 123, ed. J. Christensen- Dalsgaard and S. Frandsen, p. 67 Bedding, T. 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