Is the Sun anomalous?

Transcription

1 The physical characteristics of the Sun are compared to those of nearby Sun-like stars, and it is argued that in several respects the Sun is not typical. A simple unifying explanation is offered to account for the apparent solar anomalies. Is the Sun anomalous? Guillermo Gonzalez ponders the Sun s place in the universe. Is the Sun typical or is it an oddball among nearby stars? This is an interesting question that is not answered uniformly by astronomers. Probably the most frequent response is that the Sun is indeed quite average. Is the Sun typical among nearby Sun-like stars?, is another related question. This question sounds circular, but it is a valid one, if one selects Sun-like stars according to spectral type and luminosity class and compares other characteristics unrelated to these selection criteria. In the following, I review those parameters of the Sun that appear to be anomalous with respect to nearby stars. I define a quantity measured in the Sun as anomalous if it appears to deviate significantly from the average of the same quantity measured in a group of otherwise similar stars. I begin by listing the apparently anomalous solar characteristics, followed by a brief evaluation of each. I then propose a simple unifying idea, which makes sense of these apparent solar anomalies. Comparing the Sun to nearby stars The most basic intrinsic global parameters of a star are its: luminosity, effective temperature, radius, mass, composition and rotation period. Of these, luminosity and effective temperature are the most easily determined. Not surprisingly, then, they are the two parameters plotted on the most important observational diagnostic in stellar astrophysics the Hertzsprung Russel (HR) diagram. The HR diagram is not uniformly populated. Among the known nearby stars within 1 parsecs, about 88% were less luminous than the Sun when they formed (Henry 1999) some of the originally more massive stars are now white dwarfs, and hence fainter than the Sun..1.1 rms variation (mags).1.1 rms variation (mags) long term short term log R HK log R HK 1: Photometric variability of Sun-like stars is shown for long-term (cyclical; left) and short-term (day-to-day; right) timescales plotted against the logarithm of the chromospheric emission index, R HK. The figures are adapted from Radick et al. (1998). Only stars that display variability are plotted. F to mid-g stars are shown as green squares; mid-g to K stars are shown as blue plus signs. The Sun is represented by two red triangles; the upper one represents the correction for the inclination effect. Least-squares fits to the data are shown as dashed lines. 5.25

2 [C/Fe]. [O/Fe] [Fe/H] [Fe/H] 2: [C/Fe] and [O/Fe] values for nearby single F and G dwarfs are shown in the left (73 stars) and right (5 stars) panels, respectively (data from Gustafsson et al. 1999). Known spectroscopic binaries have been removed from the samples, and each data point in the two plots has also been corrected for a weak correlation with galactocentric distance,.15 dex/kpc for [C/Fe] and.32 dex/kpc for [O/Fe] (these corrections were applied assuming a mean solar galactocentric distance of 8.8 kpc). Least-squares fits are shown as dashed lines. The Sun is shown as an open circle in both panels. The distribution according to spectral type can be found in Henry (1998). Since these are all main sequence stars (except the white dwarfs), the shape of the distribution will be similar for luminosity and for mass. However, it is not yet clear precisely where we should draw the boundary between stars and brown dwarfs. Magnetic activity cycles The typical Sun-like star does not have a constant luminosity. High-precision photometric observations at Lowell Observatory in Arizona have revealed that most F to K dwarfs vary at the millimagnitude level or greater (Radick et al. 1998). In addition to the well-established decline in chromospheric activity with age, the recent data also show that photometric variability declines with age. In fact, both the longterm (cyclic) variability and the short-term (day-to-day) variability correlate with the Ca II H&K emission index, R HK (figure 1) for a definition see Radick et al. and references therein. In both cases, the Sun s variability appears to be smaller than stars with a similar level of chromospheric activity. Gray (1999) gives a brief review of magnetic activity cycles in solar-type stars and compares them to the Sun. He notes that the variation in temperature lags behind the variation in the H&K emission index and appears to follow a simple trend, but that the Sun does not follow it. It should be noted, though, that Gray only presents data for four stars apart from the Sun. Stellar abundances Recent spectroscopic analyses of nearby Sunlike stars have produced high-quality data on their physical parameters (e.g. Edvardsson et al. 1993; Favata et al. 1997). In particular, the abundances of about 25 chemical elements can now be compared among F and G dwarfs ranging in age from less than 1 to about 14 Gyr. These new data have revealed that most of the metals are enriched in the Sun by.1 to.2 dex relative to F and G dwarfs of similar age and mean galactocentric distance (Edvardsson et al.; Rocha-Pinto and Maciel 1996; Favata et al.; Gonzalez 1999, hereafter G99). Recent studies of zero-age objects (B stars and H II regions) have demonstrated that the Sun is also O-rich relative to the nearby interstellar medium (see G99 and Gummersbach et al and references therein). Probably the least-biased determinations of the nearby star metallicity distribution are those of Rocha-Pinto and Maciel and Favata et al. Rocha-Pinto and Maciel applied a spectroscopically calibrated equation relating [Fe/H] to uvby photometry to 287 G dwarfs within 25 parsecs, obtaining a mean of.16±.23 dex. The mean [Fe/H] of single G dwarfs (62 stars) from the sample of Favata et al. is.12±.25 dex. Therefore the Sun appears to be moderately metal-rich relative to nearby G dwarfs. There are also deviations from mean stellar abundance trends among individual elements in the Sun s atmosphere, particularly the light elements. In a follow-up to their earlier study (Edvardsson et al.), Gustafsson et al. (1999) analysed the spectra of a subset (8 stars) of the original sample (189 stars) for the purpose of deriving accurate C abundances. The resulting [C/Fe] values display a tight correlation with [Fe/H], as do the [O/Fe] values from the Edvardsson et al. study (figure 2). These data show that the Sun is O-rich and C-poor relative to solar-like stars of the same galactocentric distance and hence has a relatively small C/O ratio. If we also remove the trends of [C/Fe] and [O/Fe] with [Fe/H], we can compare the distribution of [C/O] at [Fe/H] =. We have done this with the 5 stars with both [C/Fe] and [O/Fe] data and display the results in figure 3. Only three stars have [C/O] values (normalized to the same [Fe/H]) smaller than or equal to that of the Sun. The mean value of this distribution (not including the Sun) is.12±.8 dex. Gustafsson et al. quote a typical measurement uncertainty of.9 dex in [C/O]. Thus the intrinsic scatter in [C/O] among solar-like stars is likely even smaller than that implied by figure 3. The Li abundance is observed to range over two orders of magnitude among nearby field and open cluster F and G dwarfs (Pasquini et al. 1994; Jones et al. 1999). Pasquini et al. (1994) showed that among nearby early G dwarfs, the Li abundance correlates with temperature, chromospheric activity (which correlates with age), and metallicity; the Li abundance declines with increasing age, with cooler stars experiencing more rapid depletion. But even when these are accounted for, a significant scatter remains, especially among stars with low Li abundances. This scatter is also seen among single G dwarfs in the solar-age and solar-metallicity open cluster, M67. The Sun s Li abundance is low; about 5% of solartype stars of the Sun s age have comparable Li. Unfortunately, Li has only one measurable line in solar-type stars, and it is already quite weak in the Sun s spectrum. Space motion While not an intrinsic stellar property, the space velocity relative to the Local Standard of Rest, υ lsr, has been measured for thousands of nearby stars. It has been known for several decades that older stars have a larger υ lsr than younger stars (see figure 11 of Gaidos 1998 for 5.26

3 N 2 1 a recent dataset showing this). This is understood as the accumulation of perturbations to a star s trajectory due to close encounters with other stars and giant molecular clouds, which perturbs (or heats up ) its galactic orbit from an originally nearly circular motion in the plane. The trend of υ lsr with age can be seen in figure 4, which employs the stellar sample from G99. The typical uncertainty in a velocity estimate is only 1 to 2 km s 1, and the typical uncertainty in age is 1 to 2 Gyr. The Sun s υ lsr value is now well-determined, with three recent Hipparcos-based studies (Kovalevsky 1998; Dehnen and Binney 1998; Bienaymé 1999) yielding a mean value of 13.4±.4 km s 1. The mean value of υ lsr for the 37 stars with age estimates between 3 and 6 Gyr in the top panel of figure 4 is 42±17 km s 1. Only one star in this sample has a smaller value of υ lsr than the Sun. The probability of finding ourselves at a given location in the Milky Way can be calculated from the space-distribution of stars. Our location is notable in two ways. First, we are presently only about 1 12 parsecs from the mid-plane (Reed 1997), but the Sun (and other old stars) spends most of its time at least 4 parsecs from it. So, if we could take a random snapshot of the Sun s location in the Milky Way at any time during its 4.5 Gyr history, finding it within 1 parsecs of the midplaneit would be rather unlikely. Secondly, we are very near the corotation circle (Mishurov and Zenina 1999). At the corotation radius in a spiral galaxy, the angular speeds of the spiral pattern and the stars are equal. Incompleteness and selection bias The datasets discussed above suffer from a number of incompleteness factors and selection biases that we cannot neglect. There may also..2.4 [C/O] 3: The linear trends with [Fe/H] have been removed from the [C/Fe] and [O/Fe] data in figure 2, and the resulting data used to produce a histogram for [C/O]. The mean value is indicated with a solid vertical bar, and the location where C/O =1 is shown with a dashed vertical bar. be some systematic errors. We will summarize these complications in the following and briefly note how they affect the interpretation of the apparently anomalous solar parameters. The nearby star surveys still suffer from incompleteness. Based on the number of known stellar systems within 5 parsecs, Henry et al. (1997) estimate that about 13 systems are missing from the 1 parsec sample. The vast majority of the missing stars are M dwarfs. Even the 5 parsec sample is still incomplete, though less severely. Considering this, the Sun is likely to be among the top ~9% of stars by mass in the solar neighborhood. Among the categories of solar anomalies listed in the previous section, perhaps the weakest case is the low photometric variability of the Sun. The number of nearby Sun-like stars with long-term high-precision photometry is still relatively small. More problematic, though, is the fact that the Sun is monitored with equipment very different from that used to observe other stars. Differential photometry through Strömgren filters is used to monitor bright stars in the night sky from the ground, while bolometers in space are used to monitor solar irradiance variations, which cover a much larger portion of the electromagnetic spectrum. So it is possible, for instance, that flux variations in the UV part of the Sun s spectrum partially compensate for the flux variations in the optical region, where the stellar observations are made. However, Radick et al. do make an attempt to correct the solar bolometric flux measurements to be consistent with optical observations we have certainly not heard the end of this story. Apart from this, there is very likely to be a bias in the solar data. We observe the Sun from a low angle relative to its equator, while nearby stars are observed at random orientations relative to their spin axes. This would not be a problem if there were no dependence of variability on heliographic latitude, but there is indeed reason to expect such a dependence (Schatten 1993; Radick et al.). The effect results from: 1) the fact that sunspots and faculae are confined to low heliographic latitudes, and 2) they have different angular irradiance dependencies on distance from the disk center. Radick et al. have modeled this inclination effect and determined that the Sun s long-term RMS variation needs to be increased by about 3% over the observed value (see figure 1). The short-term variations are not expected to suffer from this bias as strongly. Also not very convincing is Gray s (1999) discovery that the lack of a lag in the temperature variations relative to H&K index variations in the Sun is an anomaly. Five data points are simply not enough upon which to build a strong case. Selection bias is important for the [Fe/H] and υ lsr distributions. Both are affected by our particular location in the Milky Way a mere 1 to 12 parsecs above the disk mid-plane. As a result, stars with large velocities perpendicular to the galactic plane (the so-called W velocity), which spend most of their time far from the mid-plane, are under-represented in a sample that is restricted to a volume of space within 1 or 2 parsecs of the Sun. This means that the average value of υ lsr derived from the data in figure 4 is an underestimate making the Sun s small υ lsr value even more anomalous. Similarly, older stars typically have smaller [Fe/H] and larger W, so a local sample overestimates [Fe/H]. This bias against metal-poor stars is partly the cause of the asymmetry of the [Fe/H] distribution. Rocha-Pinto and Maciel applied a scale-height correction factor to their nearby G dwarf sample, obtaining a mean [Fe/H] of.19±.27, which is only.3 dex smaller than the raw mean. The Li abundances and [C/O] distribution are not likely to suffer from significant systematic errors or selection biases. The Li, C and O abundances have been determined in differential spectroscopic analyses calibrated with the solar spectrum. Larger samples would be worthwhile, though. Anthropic considerations Certainly these anomalies could just be due to chance. But just chance is not a very satisfying answer. In the following we propose to unify the apparent solar anomalies within a single, simple hypothesis. To a significant degree, we can remove the anomalous label from the solar parameter values if we consider them within the framework of the Weak Anthropic Principle (WAP). Briefly, the WAP is the recognition that the particular values that 5.27

4 solar-age stars υ lsr (km s 1 ) 1 5 N υ lsr (km s 1 ) age (Gyr) 4: Velocity with respect to the Local Standard of Rest (υ lsr ) is plotted against age for 179 F and G dwarfs in the left panel; the Sun is represented by an open circle. The data are from Gonzalez (1999) and references therein. The histogram of υ lsr values for 38 Sun-age (3.5 6 Gyr) stars from this dataset is shown in the right panel. The mean of this subsample is indicated with a solid vertical bar, and the Sun s υ lsr value is indicated with a dashed vertical bar. we observe in our physical environment must be consistent with our existence. This implies that we, as observers, are relevant to the proper interpretation of our observations. Thus the WAP is just a type of observer selection bias. To take a simple example, we should not be surprised to find that we are living on a planetary body with oxygen in its atmosphere, because we require it for our survival. The apparent anomaly of our living on the only planet in the solar system with a high abundance of oxygen in its atmosphere is thus solved, but the more fundamental question of the source of the Earth s high oxygen abundance is not addressed. Thus, while the WAP can remove some of the apparent anomaly of a particular observation, it has only limited explanatory power. While the arguments presented here are necessarily speculative at this stage, we believe there are reasonable physical mechanisms that relate each solar anomaly to our existence. Before we begin, though, we should note that the requirements for habitability we are considering refer specifically to observers (i.e. humans who can observe and write) and advanced life (i.e. mammals), not to simple life. We begin with the most obvious anomaly the Sun s high mass relative to the average nearby star. There are several reasons to prefer an early G dwarf to a K or M dwarf as our parent star: 1) the habitable zone (HZ) is located sufficiently far from a G dwarf such that tidal locking does not occur in 4.5 Gyr (Whitmire and Reynolds 1996); 2) a G dwarf produces more blue light, which is important for photosynthesis; 3) stellar flares are a greater threat around K and M dwarfs, given that the HZ is closer to the parent star; and 4) Wetherill (1996) has argued that the formation of terrestrial planets around a star is insensitive to its mass and that their distribution peaks near 1 AU; since the location of the HZ is highly sensitive to stellar mass, then the probability of forming a terrestrial planet in the HZ is greatest for stars near one solar mass. The habitable zone A brief note concerning the HZ concept is in order. The most-often quoted estimate for the size of the HZ in the solar system is that of Kasting et al. (1993). Its extent is determined by the requirement that liquid water exist on the surface of an Earth-like planet. The inner edge is bounded by runaway greenhouse, and the outer edge is set by formation of CO 2 clouds, which increase albedo, and hence produces cooling. However, this standard definition is not sufficiently restrictive for our application of the WAP. Advanced land life can only tolerate a relative narrow range of mean surface temperature and atmospheric composition; towards the outer edge of the HZ, the CO 2 content of the atmosphere must be very high in order to maintain warm surface temperatures. One can make a strong case on physiological grounds that advanced mobile life requires high O 2 and low CO 2 abundances in the atmosphere. Given the increasing evidence for a link between solar irradiance variations and the global terrestrial climate (see Lean and Bind 1998 for an up-to-date review), it is likely that the habitability of the Earth is not independent of the Sun s rapid (compared to its evolutionary timescale) changes. Therefore, advanced life may only be able to tolerate a relatively low level of variability of its parent star. This also has implications for the timing of our appearance, given that the photometric variability amplitude of Sun-like stars steadily declines with age. Gray (1999) speculates that the unusually stable terrestrial climate of the past 1 years may be a result of the Sun going through a superstable state. However, irradiance variations may not be the only Sun climate link; interactions between the geomagnetic and interplanetary magnetic field and the solar wind might also be important (Baranyi and Ludmany 1994). There must be a strong correlation between the metallicity of a star and the habitability of its environment for the simple reason that terrestrial planets are composed primarily of metals (i.e. elements heavier than H and He). This point was made recently by Trimble (1997) and Whittet (1997). While the functional dependence of the mass of the largest terrestrial planet in a planetary system on the metallicity of the parent star is not yet known, there is little doubt that Earth-like planets do not exist around metal-poor stars (such as in a globular cluster). There is now empirical evidence that at least giant planets favour metal-rich stars (see Gonzalez et al and references therein). This finding relates to habitability in two ways: 1) Wetherill (1994) has shown that the gas giants in the solar system act to shield the inner planets from frequent cometary impacts; with fewer or with less massive giant planets, the shielding effect is weakened, and 2) if the number of massive gas giants depends on metallicity, then the probability of large gravitational perturbations among them is increased (Weidenschilling and Marzari 1996). A high metallicity will also likely result in a large number of debris (asteroids and comets) left over from the 5.28

5 formation of planets around a star, thus enhancing the probability of impacts. A high metallicity may also make it more likely for giant planet migration to occur (Murray et al. 1998). If these speculations are correct, then habitability is optimized within a narrow range in [Fe/H]. The possible connections between [C/O] and habitability are less obvious. However, there should be little doubt that the C/O ratio is an important factor in determining the final state of a terrestrial planet. Oxygen is the most abundant element (by number) in the Earth (Kargel and Lewis 1993), forming many oxides with heavier elements. Carbon is present in trace quantities, but its role as a climate regulator via CO 2 and CH 4 greenhouse gases is extremely important for habitability; had there been significantly more C in the Earth, perhaps too much CO 2 would have been produced. One could argue that self-regulation processes can modify an atmosphere hospitable to advanced life, but they can only go so far. In addition, the C/O ratio may have been an important factor in the earliest stages of the formation of the proto-solar nebula. Interstellar chemistry is very sensitive to the C/O ratio (Watt 1985; Pratap et al. 1997). Most of the C and O atoms go into CO, and the more abundant species forms additional molecules, mostly with H. Thus a low C/O ratio results in a high abundance of O-rich molecules, OH and H 2 O, and a high C/O ratio results in C-rich molecules, CH n. The dividing line between C- and O-rich molecules occurs at C/O =1, but even small departures from the solar ratio can result in large changes in the abundances of some species (C, O 2, H 2 CO, and CH 4 ; Watt). The four elements H, C, N, and O are responsible for most of the ices in interstellar space. Thus, since the C/O ratio is so central to light-element astrochemistry, it is likely to have a bearing on the condensation of ices. However, the C/O ratio will have differing effects over the wide range in temperature and pressure of the early solar nebula. Why a low C/O ratio should be preferred overall is not clear. Implications of space motion The large deviation of the solar υ lsr value from the mean of nearby solar-age stars implies that this parameter may be strongly related to habitability. Solutions to this problem should be sought among those phenomena that can threaten advanced life on the Earth and that relate to the Sun s galactic orbit. In this regard, it is helpful to decompose the Sun s galactic orbit into two orthogonal components: motion in the plane (characterized by an eccentricity, e) and motion perpendicular to the plane (characterized by a maximum distance above the plane, Z max ). A small value of υ lsr requires that both e and Z max must be small. Two oft-discussed threats are nearby supernovae and perturbations of the Oort comet cloud leading to comet impacts. Both are sensitive to the particular galactic orbit of the Sun. Furthermore, the Sun s galactic orbit is very close to the corotation circle. A star with a circular orbit near the corotation radius will cross the spiral arms infrequently. The observed surface density of supernova remnants in the Milky Way rises steeply inside the solar circle (Clark and Caswell 1976); supernovae in nearby galaxies are also observed to be centrally concentrated (van den Bergh 1997). If the Sun s e were greater, its perigalacticon distance would be smaller and the probability of spiral arm crossings would be greater, hence increasing the threat from nearby supernovae. In a similar way, excursions of the Sun into the inner disk of the Milky Way increase the probability of perturbations to the Oort cloud comets due to nearby star and molecular cloud encounters and the changing galactic tide One obvious application of our proposal is the calculation of the probability of ETI. (Matese et al. 1995; Matese and Whitmire 1996). Since a star located near the corotation circle will encounter spiral arms infrequently, dynamical heating of its orbit will be small. So it could be that our proximity to the corotation circle is the key galactic-scale requirement for habitability low e and Z max values may simply be natural by-products of this configuration. The reader is referred to Gonzalez (1999), where this is discussed in greater detail. One obvious application of our proposal is the calculation of the probability of ETI. Once we are confident that a given solar parameter value is relevant to habitability, we can add it to a Drake-like equation, as an additional constraint. A crude estimate of the degree of finetuning required for the constraint can be had from the deviation of the solar value from the mean among nearby stars. So, for example, since the Sun is among the 9% most massive stars in the solar neighbourhood, we can infer that about 9% of nearby stars have the required minimum mass for habitability. However, this should be considered only as a first-order approximation, since we have to allow the possibility that a given parameter must lie within a range in a probability distribution (as opposed to a simple inequality). A more refined estimate must make use of theoretical arguments. Therefore, we can argue that significantly more massive stars than the Sun are less favourable for habitability for a number of reasons relating to luminosity evolution, mass loss, UV light luminosity, etc. Taking these other factors into account, then, probably less than 9% of nearby stars have a mass in the range required for habitability of advanced life. Summary We have argued (admittedly, at a rather speculative level) that the apparently anomalous solar parameter values are clues about the habitability of the Earth. We have offered some possible links between them and habitability, but much more can be said about this topic. We close with a simple suggestion. The approach outlined here can serve as a guide to direct astrobiology research programmes looking to determine the basic requirements for advanced life on a terrestrial planet. We especially encourage research on a careful comparison of the Sun s chemical abundance pattern to those other nearby G dwarfs. Guillermo Gonzalez is research assistant professor of astronomy at the University of Washington. He studies the chemical abundance patterns of stars. References Baranyi T and Ludmany A 1994 Solar Phys Bienaymé O 1999 A&A Clark D H and Caswell J L 1976 MNRAS Dehnen W and Binney J J 1998 MNRAS Edvardsson B et al A&A Favata F et al A&A Gaidos E J 1998 PASP Gonzalez G 1999 MNRAS in press. Gonzalez G et al ApJ 511 L111. Gray D F 1999 Stars and Sun; Treasures and Threats in Tenth Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun ed. Donahue R A, Bookbinder J A, in press. Gummersbach C A et al A&A Gustafsson B et al A&A Henry T J 1997 AJ Henry T J 1998 Suspicious Characters Lurking in the Solar Neighborhood in Brown Dwarfs and Extrasolar Planets ed. Rebolo R, Martin E L, Osorio M R Z, ASP Vol. 134, Book Crafters, San Francisco, p28. Henry T J 1999 private communication. 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