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Astron. Astrophys. 334, 221-238 (1998)

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4. Discussion

4.1. Abundances

All our program stars are listed in the catalog of Cayrel de Strobel et al. (1997), which is a compilation of stellar spectroscopic [Fe/H] determinations from the published literature up through the end of 1995. They list seven estimates for HD 114762 ranging from -0.59 to -0.87. For the other stars the [Fe/H] estimates are as follows: [FORMULA] Cnc has four ranging from -0.15 to [FORMULA] 0.30; [FORMULA] CrB has four ranging from -0.26 to -0.14; 16 Cyg A has four ranging from 0.00 to 0.22, and 16 Cyg B has five ranging from 0.00 to 0.11; 51 Peg has three ranging from 0.06 to 0.12; 47 UMa has two, -0.02 and 0.01; 70 Vir has one at -0.11.

There are a few more recent spectroscopic studies that have included some of our program stars. Tomkin et al. (1997) have recently reanalyzed the "NaMgAl" stars, originally noted in the Edvardsson et al. (1993) study. Using higher quality spectra, they now conclude that this group was spurious. Included in this group was 51 Peg, for which they now derive [Fe/H] = 0.20 [FORMULA] 0.07. Feltzing & Gustafsson (1998) derive [Fe/H] = 0.06 for 16 Cyg B. Fuhrmann et al. (1997) derive [Fe/H] = 0.20 [FORMULA] 0.07 and 0.00 [FORMULA] 0.07 for 51 Peg and 47 UMa, respectively. All these determinations are very close to ours.

In his study of super metal-rich (SMR; defined as having [Fe/H] [FORMULA] 0.2 with [FORMULA] 95% confidence) stars, Taylor (1996) lists 29 luminosity class IV-V candidates (his Table 4). He includes [FORMULA] Cnc and 51 Peg in this list, for which he quotes photometric [Me/H] estimates of [FORMULA] and [FORMULA], respectively. Mean spectroscopic [Fe/H] values, based on published estimates and transformed to a uniform temperature and metallicity scale by him, are 0.41 [FORMULA] 0.10 and 0.17 [FORMULA] 0.05, respectively. While having two of our program stars appear in a list of 29 suspected SMR stars seems significant, it becomes less so when it is noted that 10 of the 120 stars analyzed by Marcy and Butler's group also appear on the list. More significant, however, is the fact that Taylor lists [FORMULA] Cnc as one of the 7 stars with a probability [FORMULA] 95% of being a SMR star; none of the other stars observed by Marcy & Butler's group is a member of this "magnificent seven." In Paper I we derived [Fe/H] values for [FORMULA] And and [FORMULA] Boo of 0.17 [FORMULA] 0.08 and 0.34 [FORMULA] 0.09, respectively. These results, combined with those of Boesgaard & Lavery (1986), compel us to add [FORMULA] Boo to this select group of nearby SMR stars.

More recently, Feltzing & Gustafsson (1998) have performed spectroscopic abundance analyses on 47 G and K stars with [Me/H] [FORMULA] 0.00. They sample a larger volume of space, going down to [FORMULA] = 9.15, and find seven stars with [Fe/H] [FORMULA] 0.30. One of these, HR 7373, is classified by Taylor as a SMR star. Castro et al. (1997) examined nine metal-rich dwarfs, with [FORMULA] as low as 11.3, and found that five have [Fe/H] [FORMULA] 0.30. Hence, while there are additional SMR stars than just those included Taylor's list, none of them are in the Bright Star Catalog, which is the source of Marcy and Butler's target list.

As an illustration of the unusual metallicity distribution of our program stars, we present in Fig. 5 the metallicity distribution of nearby G and K dwarfs from Favata et al. (1997) along with our spectroscopic [Fe/H] values; the peak of the distribution is -0.23. The mean metallicity of the parent stars of the nine planetary candidates is [FORMULA] 0.02. Excluding HD 114762 and 70 Vir, which have the most massive companions, the mean metallicity of the remaining seven systems is [FORMULA] 0.11. The mean metallicity of the four "51 Peg-like" systems is [FORMULA] 0.25. This comparison is meant as a qualitative illustration only. To determine if our sample stars really have a higher mean metallicity than the nearby field stars, it will be necessary to compare their metallicities to the metallicity distribution of Marcy and Butler's target list. We have not yet done this, as the metallicity estimates of K and M dwarfs cannot yet be reliably determined to within 0.1 dex (for a discussion of problems associated with spectroscopic analyses of cool dwarfs, see Felzing & Gustafsson 1998).

[FIGURE] Fig. 5. Histogram of the distribution of spectroscopic [Fe/H] estimates for nearby G dwarfs (with [FORMULA] K; 66 stars) from Favata et al. (1997). The average value of the distribution is indicated with a solid vertical line and our [Fe/H] estimates by dotted vertical lines (the two stars from Paper I are also included). Favata et al. have corrected their distribution for scale Galactic height inflation.

The lithium abundances have been estimated recently for 51 Peg and 16 Cyg A and B. François et al. (1996) find that 51 Peg has a solar lithium abundance, less than our estimate. We do confirm the findings of Friel et al. (1993) and King et al. (1997) that the lithium abundances of 16 Cyg A and B differ greatly; King et al. derive [FORMULA] = 1.27 [FORMULA] 0.05 and [FORMULA] for 16 Cyg A and B, respectively. The significance of these findings will be discussed in Sect. 4.5. A summary of published lithium estimates for the other stars in our program is given by King et al.

4.2. Ages, rotation periods, and masses

The [FORMULA] estimates, when combined with the rotation periods and masses of the program stars, can be used to set limits on the masses of their companions. The rotation periods can be measured directly in those stars that exhibit variations in the Ca II H and K flux (Baliunas et al. 1996). Given that both age and angular velocity correlate fairly well with the mean Ca II flux for G dwarfs (Donahue 1993; Dorren et al. 1994; Soderblom 1985), the mean Ca II flux can also be used to estimate the rotation period. In this section we will estimate the ages, rotation velocities, and masses of the program stars and their companions.

The most reliable method of estimating the mass and age of an isolated field main sequence or subgiant star involves comparing its observed physical parameters ([FORMULA], [FORMULA], [Fe/H]) to theoretical stellar evolutionary sequences. We make use of the Schaller et al. (1992) and Schaerer et al. (1993a, b) evolutionary stellar grids, to estimate their ages and masses. These theoretical tracks predict for the Sun a value of [FORMULA] too high by 50 K and [FORMULA] 5 too high by 0.08 mag. Therefore, in the following analysis we have added 50 K and 0.08 mag. to the measured [FORMULA] and [FORMULA] values of the program stars when comparing them to the theoretical tracks.

We calculated [FORMULA] for each star using the [FORMULA] parallaxes (ESA 1997); given the high precision of these parallaxes, the Lutz & Kelker (1973) correction was required only for HD 114762 (it is minor anyway). We list our age and mass estimates in Table 11. They were determined by visual inspection of the locations of the stars on the HR diagram relative to the isochrones with the appropriate metallicities. We employed the atmospheric parameters in Table 3 ([FORMULA] and [Fe/H]) and the adopted [FORMULA] values (the listed values are the unaltered ones). We have also included [FORMULA] And and [FORMULA] Boo in the table, but with updated [FORMULA] values compared to those quoted in Paper I, which are based on pre- [FORMULA] parallaxes.


[TABLE]

Table 11. Age and mass Estimates of the program stars derived from stellar evolutionary tracks


Ng & Bertelli (1998) have derived updated ages for the stars in the Edvardsson et al. (1993) sample with more recent stellar evolutionary tracks and with [FORMULA] values based on [FORMULA] parallaxes. They derived the ages and masses with a rigorous statistical methodology. We list in column 6 of Table 11 their age and mass estimates, which have typical uncertainties of 1 Gyr and 0.03 [FORMULA], respectively. The agreement between our estimates and those of Ng & Bertelli is quite good. Note, however, that they used the (incorrect) Edvardsson et al. (1993) value of [Fe/H] for 51 Peg; adopting [Fe/H] = 0.20 leads to a reduction in their age estimate for this star by 1.4 Gyr.

A consistency check on our Fe-line analysis of Sect. 3.1.1 is provided by the [FORMULA] values derived from the evolutionary tracks (column 5 of Table 11). These [FORMULA] estimates are very close our spectroscopic estimates, except for HD 114762, which is smaller. Of course, these two methods of estimating [FORMULA] are not completely independent as both employ the same values of [FORMULA].

There are two stars for which we could not obtain self-consistent solutions: [FORMULA] Boo and [FORMULA] Cnc. Our [FORMULA] estimate for [FORMULA] Boo is too hot by about 200 K for the ZAMS corresponding to its metallicity. Conversely, our [FORMULA] estimate for [FORMULA] Cnc is too cool by about 200 K. The discrepancy for [FORMULA] Boo is not as serious, as our analysis of this star is less certain due to its broad lines. We do appear to have a problem with [FORMULA] Cnc, though, which we will address further in Sect. 4.4.

There are other indicators that can be used to further constrain the ages of single stars. One of these relates to the mean level of chromospheric activity. Baliunas et al. (1998) quote ages derived from the mean level of Ca II activity, which we list in Table 11. The typical uncertainty in these age estimates is about 2 Gyr (Donahue 1998). Another age indicator relates to the space motion in the Milky Way. As a star ages, chance encounters with molecular clouds perturb it away from a simple circular orbit in the plane of the disk. Therefore, the space velocity of a star generally increases with time. Of our sample, HD 114762 has the largest space velocity, as expected. Related to the level of chromospheric activity is the amplitude of the visual brightness variations; by the time a solar-type dwarf is about 3 Gyr old, the brightness variations drop below about 10 millimags (Dorren et al. 1994). High precision photometric monitoring of these stars by two groups (Guinan 1995; Henry et al. 1997) place upper limits of no more than a few millimags, indicating ages at least as great as the Sun's (even [FORMULA] Boo appears constant at the millimag level even though it is young according to our analysis). Additional monitoring will be required to determine if long-term variations exist.

Rotation periods have been estimated for these stars from Ca II observations, either with a mean Ca II activity-rotation period relation, or more directly by detecting a periodic modulation of the Ca II flux. The rotation periods are given in Table 12. The only star on our program not listed by Baliunas et al. (1998) is HD 114762. Using the Ca II activity-rotation period relation of Noyes et al. (1984), Henry et al. (1997) derive a rotation period of 12 [FORMULA] 2 days for HD 114762. This estimate is clearly incompatible with its great age; we will adopt a value of 54 [FORMULA] 12 days for this star (using Dorren et al.'s 1994 rotation-age relation). Also, 70 Vir is clearly evolved off the main sequence, so Noyes et al.'s relation will underestimate its rotation period. The value quoted by Baliunas et al. (1998), 36 days, has been increased by a factor of three, assuming simple conservation of angular momentum. A lower limit of 2 days was chosen for the uncertainties (except for [FORMULA] Boo, which has a very short rotation period) due to the presence of surface differential rotation in solar type stars, which leads to a modulation of the apparent rotation period on timescales of a decade (Donahue 1993).


[TABLE]

Table 12. Derived physical parameters of planetary systems


Using the adopted values of [FORMULA], rotation period, and radius for each star, we calculated [FORMULA] for each star. The value for 16 Cyg B is from Hale (1994). The estimates for 16 Cyg B and 51 Peg are problematic; both are greater than 1.0. If the rotation period listed in Table 12 for 51 Peg is correct, then most of the published [FORMULA] estimates for this star are too large; a value of 1.6 km s-1, which is consistent with our estimate and that of Soderblom (1982), would give a value of [FORMULA] near 1.0. Obviously, values of [FORMULA] [FORMULA] 1.0 are not acceptable. Taking this into account, we list the final [FORMULA] values in Table 12. One additional source of uncertainty needs to be included - the degree of misalignment between the orbital axis of the companion and rotational axis of the parent star, which we will represent as [FORMULA] = [FORMULA]. Hale (1994) estimated that [FORMULA] is about 10 degrees for solar-type binaries with semimajor axes less that 15 AU. Perhaps more relevant to the present analysis is the fact that the value of [FORMULA] for Jupiter is only about 6 degrees. Including an additional uncertainty of 8 degrees in the orbital inclination, the final values of the orbital inclinations of the companions are listed in column 5 of Table 12. The companion masses were calculated from the mass function estimates given in the respective discovery papers (listed in the Introduction) and our estimates of the inclinations. They are given in the final column of Table 12.

Now that we have estimates of the masses of the planetary companions, their true nature can be constrained, assuming, of course, that the radial velocity variations are not intrinsic to the stars' photospheres. The results in Table 12 indicate that 70 Vir b and HD 114762 b are brown dwarfs or possibly even very low mass M dwarfs (for a contrary view, see Lin & Ida 1997 and Weidenschilling & Marzari 1996). The companions of [FORMULA] Boo, [FORMULA] CrB, and 47 UMa are also quite massive and might be brown dwarfs. Those companions most securely in the giant planet mass regime are 16 Cyg B b, 51 Peg b, and [FORMULA] And b ([FORMULA] Cnc is an anomaly at this time).

Of relevance to 51 Peg is the fact that tidally locked close binaries (orbital periods of a few days) have lithium abundances larger than their single star counterparts (Soderblom et al. 1990; Balachandran et al. 1993). If, contrary to our findings, the 51 Peg system has a very small orbital inclination and its companion is of stellar mass, then its lithium abundance would likely have been larger than we measured. This argument is less relevant to the other 51 Peg-like systems because: 1) [FORMULA] And and [FORMULA] Boo are young and hence expected to have larger lithium abundances, 2) [FORMULA] Cnc's orbital period is longer, making tidal effects less important. Also, the rotation period of 51 Peg does not allow the possibility that this is a tidally locked system (Mayor & Queloz pointed out that the lack of synchronization on Gyr timescales is a strong argument against a stellar mass companion for 51 Peg).

4.3. Possible sources of high [Fe/H]

The high [Fe/H] values of 51 Peg and [FORMULA] Cnc (also [FORMULA] And and [FORMULA] Boo) require explanation. It is too much to ascribe to coincidence the presence of two SMR stars and two stars very near the SMR limit in our small sample of planetary system candidates. In Paper I we suggested that the original photospheric compositions of the "51 Peg-like" systems had been altered by the same processes that lead to the creation of these unusual planetary systems.

Lin et al. (1996) have proposed that 51 Peg b, if it is indeed a gas giant, was formed at about 5 AU from the star and, at early times (within a few million years of its formation), migrated inward as a result of interactions with the circumstellar disk. The disk material (and presumably protoplanets) inside the orbit of 51 Peg b would likely have fallen into the star. Since much of it would have been inside the so-called "ice-boundary", much of the solid-state material would have consisted of refractory elements (essentially everything except H and He). This accreted material would have been mixed throughout the convective envelope of the parent star.

Using the Solar System as a model, we can estimate the effect on its photospheric abundances had the Sun ingested the equivalent of Mercury, Venus, Earth, and Mars in its early history. Sackmann et al. (1993) calculate that at an age of about 30 Myrs the convective region of the Sun contained about 0.03 [FORMULA]. Assuming a composition similar to the C1 chondrites (Anders & Grevesse 1989), the addition of the terrestrial planets at this time would have dumped 2.18 x [FORMULA] g of Fe into the convection zone, leading to an increase of [Fe/H] in the photosphere of 0.01 dex. The addition of 20 [FORMULA], which is still only 0.06 [FORMULA], would have resulted in an increase of 0.11 dex, a detectable change. The timing of the accretion is critical, as the stellar convection zone rapidly shrank in size during the first few million years of the Sun's existence - add the material too early, and it is diluted throughout a large volume; the timescale for the evolution of the protostellar disk is about 5 Myr (Strom et al. 1993).

What would have happened to the photospheric abundances of the early Sun if Jupiter were thrown into the convective envelope? The answer to this question depends on the bulk composition of Jupiter. If it is the same as the Sun's photosphere, then there will be no change in the Sun's metallicity. Estimates of the bulk composition of Jupiter indicate that it is enhanced in metals by about a factor of two relative to the Sun (Hubbard 1989); this is equivalent to about 10 [FORMULA] of chondritic material mixed with 308 [FORMULA] of H and He. Given this, adding Jupiter would increase the Sun's photospheric metallicity by about 0.05 dex. Adding two Jupiters would increase it by 0.08 dex.

Alexander (1967) suggested that the injestion of a planet by a giant star can result in a large increase in its photospheric lithium abundance. Brown et al. (1989) resurrected this mechanism to try to account for the anomously high lithium abundances they measured in a few field giants. The present solar photospheric abundance of lithium is just over two dex less than the meteoritic abundance. This is commonly interpreted in terms of a gradual depletion of lithium in the envelope of the Sun on a billion year timescale. The addition of Jupiter to the present Sun would boost the lithium abundance by about 1.5 dex, while a very early ingestion would have boosted the lithium abundance by only 0.05 dex. The addition of the terrestrial planets to the present Sun would increase the lithium abundance by about 0.8 dex. Since lithium depletion in a solar-type star is probably not linear in time, the degree of its enhancement due to the addition of a planet depends sensitively on the timing of the injestion. Hence, the lithium abundances we have estimated for the parent stars of the planetary candidates are not easy to interpret, given the uncertainty of the age estimates and given the as yet incompletely understood mechanisms of lithium depletion. It is interesting to note, however, that [FORMULA] CrB, 51 Peg, and 47 UMa, which appear to be older than the Sun, have significantly higher lithium abundances. Particularly valuable is the case of 16 Cyg A and B, which have significantly different lithium abundances (to be discussed in Sect. 4.5).

The next logical question to ask is, Why did the Solar System and the 51 Peg-like systems evolve differently? The metallicities of the parent stars appear to be the most significant differences. If 51 Peg was originally slightly more metal-rich than the Sun, then this would have resulted in the formation of a protoplanetary disk more abundant in refractory elements, which might have led to the more rapid formation of protoplanets. A slightly more massive disk also might have led to greater transfer of mass into the parent star (Laughlin & Bodenheimer 1994). Hence, according to this scenario, a more metal-rich star is more likely to alter its surface composition during the protostellar disk evolution phase than a similar but less metal-rich one. This is consistent with the similarity of the Solar System to the 47 UMa system, which has a solar metallicity parent star. The companion of 47 UMa orbits at about 2 AU in a low eccentricity orbit (Butler & Marcy 1996), apparently having avoided the orbital decay phenomenon proposed to have been experienced by 51 Peg's planet. However, [FORMULA] CrB is more metal-poor than 47 UMa, and its companion orbits closer to its parent star. Clearly, the diversity of the extrasolar systems shows that such a simple model is unlikely to fully account for the observed correlations between planets and the metallicities of their parent stars.

One additional piece of circumstantial evidence in favor of the self-enrichment scenario, noted in Paper I, is the scarcity of metal-rich giant stars. If the envelope of a 51 Peg-like system is metal-rich, then as it ascends the giant branch, the metallicity of its photosphere will decrease as the deepening convection zone is diluted with deeper more metal-poor layers. However, Taylor's (1996) claim that there are no definite SMR K giants needs to be revised; Castro et al. (1996) have performed a detailed abundance analysis of µ Leo finding that [Fe/H] = 0.46 [FORMULA] 0.14. Hence, there are at least eight SMR dwarfs and one SMR giant in The Bright Star Catalogue.

If the photospheres of the parent stars of the 51 Peg-like systems are metal-rich relative to their interiors, then the evolutionary ages derived above are not correct. The metallicity affects not only the effective temperature and radius but also the luminosity. A reduced interior metallicity leads to a larger core mass and hence a greater luminosity (Jeffery et al. 1997).

Finally, we need to address the possibility that the high metallicities of the 51 Peg-like systems are primordial. Certainly, there is a spread in the metallicities (or oxygen abundances) of young stars and nebulae at the Sun's galactocentric distance (see Smartt & Rolleston 1997 for a summary of the observational evidence). The Sun itself is near the upper envelope of the metallicity distribution. One traditional explanation for this is that the Solar System formed in a metal-rich clump in the (inhomogeneous) ISM. In Paper I we suggested that the Sun might have been self-enriched during the planet formation process. However, the [FORMULA] Cen system, which is about the same age, is even more metal-rich than the Sun. Tripicco et al. (1995) derive an age and [Fe/H] value of the open cluster NGC 6791 of about 10 Gyr and [Fe/H] [FORMULA] 0.3, respectively. Hence, clusters like NGC 6791, although very rare, might account for the existence of the 51 Peg-like stars.

4.4. p1 Cnc

A number of our results concerning [FORMULA] Cnc seem inconsistent. For instance, in Sect. 3.2 we derived a value of [FORMULA] from equation 1, which is much smaller than we measured directly on its spectrum and also smaller than the value predicted by Eq. 2; however, Eq. 2 gives a similar value to the measured value. Its [FORMULA] and [FORMULA] parameters place it in the subgiant region of the HR diagram, implying an age much greater than the currently accepted range for the age of the universe. Cayrel de Strobel (1987), in her review of 30 SMR dwarfs and subgiants (at that time defined as being more metal-rich than the Hyades), also derived an extremely high age for [FORMULA] Cnc (one other star in the sample, HD 190248, also appeared to have an extreme age). The low surface gravity we derived from our spectroscopic analysis ([FORMULA]) appears to confirm its subgiant status; the surface gravity for G dwarfs ranges from about 4.4 to 4.5. Neuforge-Verheecke & Magain (1997) derived [FORMULA] for [FORMULA] Cen B, a metal-rich K1V dwarf. Baliunas et al. (1997) also note that their spectrum of [FORMULA] Cnc is a better match to a subgiant than it is to a dwarf (see their paper for a discussion of previous studies bearing on this subject).

We have derived additional temperature estimates for [FORMULA] Cnc from Johnson [FORMULA] and [FORMULA] photometry given by Gliese & Jahreiss (1991). The equations relating [FORMULA], [FORMULA], and [Fe/H] to [FORMULA] and [FORMULA] were derived from the synthetic colors given by Buser & Kurucz (1992). Corrections were then applied to the equations to give the correct value of [FORMULA] for [FORMULA] Cen B (using the results of the spectroscopic analysis of Neuforge-Verheecke & Magain 1997) from its observed colors. The resulting values of [FORMULA] for [FORMULA] Cnc from its [FORMULA] and [FORMULA] colors are 5195 and 5460 K, respectively (this compares with [FORMULA] = 5150 [FORMULA] 75 K from our spectroscopic analysis). The corresponding values for the K0IV star [FORMULA] Eri are 4895 and 5035 K, respectively; Morell et al. (1992) derived [FORMULA] = 4800 K for this star. The corresponding values for the G8V star HR 509 are 5385 and 5429 K, respectively; Morell et al. (1992) derived [FORMULA] = 5300 K for this star. Note, if our spectroscopic [FORMULA] estimate for [FORMULA] Cnc is too low, then its true [Fe/H] value is even higher than than our estimate of 0.29, which is already unusually high. Arribas & Martinez Roger (1989) derived [FORMULA] = 5100 [FORMULA] 150 K and [FORMULA] = 0.736 [FORMULA] 0.043 mas for [FORMULA] Cnc by applying the infrared flux method to its optical and infrared colors. This angular size corresponds to a physical size similar to that of the Sun, which is too large for a late G or early K dwarf.

The [FORMULA] Cnc system is part of a common proper-motion pair with an M3.5 dwarf. This allows the possibility of comparing the metallicities of the two components. We have approached the problem in the following way: an equation relating [FORMULA], [FORMULA], and [Fe/H] was derived from a small sample of M dwarfs that are members of nearby common proper motion pairs (the sample is from the listing of Poveda et al. 1994); the metallicity of each M dwarf was equated to that of its brighter F or G dwarf companion; the relation was applied to [FORMULA] Cnc's companion in order to determine [Fe/H]. The result is [Fe/H] = -0.15 [FORMULA] 0.31, where the uncertainty was calculated from the residuals of the calibrating stars. A similar equation was derived for G and K dwarfs and applied to [FORMULA] Cnc. Our result is [Fe/H] = 0.32 [FORMULA] 0.08, nearly identical to our spectroscopic estimate. This is only a preliminary analysis. A larger sample of M dwarfs will be required to reduce the uncertainty in this method to a level that may give us a definitive answer. This might best be accomplished with observations of a nearby solar-age open cluster with well-determined parameters.

Marcy & Butler (1998) have noted the presence of a long-term trend in the velocity residuals of [FORMULA] Cnc after subtracting the main 14.6 day variation. They attribute the residuals to the presence of a companion with a minimum mass of 10 [FORMULA] and an orbital period of about 20 years. Assuming a total system mass of [FORMULA] 1 [FORMULA], the mean apparent separation should be about 0.60 arcseconds. McAlister et al. (1993) reported on the absence of a visual companion to [FORMULA] Cnc from a single speckle observation. They would have been able to detect a companion with a separation from the primary between 0.038 and 2 arcseconds and no more than 3 magnitudes difference in brightness. Hence, it is unlikely that this object is contaminating the optical colors of the primary. A search with an infrared imager may prove fruitful, though.

At this time, then, the observations are inadequate to determine the true nature of [FORMULA] Cnc. Three possible explanations of the data are: 1) our spectroscopic analysis is in error more than we claim, 2) the [FORMULA] Cnc system is actually a nearly pole-on stellar spectroscopic binary (as opposed to a star-planet binary), 3) [FORMULA] Cnc really is a subgiant. While we believe the first case to be unlikely, verification of our results for this star would be welcomed. The second case could be tested by searching for variations in the line profile shapes. A system of two different stars viewed almost exactly pole-on will be seen as a very small amplitude single-lined spectroscopic binary with line profile variations that correlate with the mean wavelength shift of the lines, and a spectroscopic analysis will give the wrong answer for what is assumed to be a single star. The third possibility requires an explanation as to why [FORMULA] Cnc prematurely evolved into a subgiant.

4.5. 16 Cyg A and B

The 16 Cyg system is particularly valuable as a test case of the self-enrichment scenario, because, presumably, both stars formed simultaneously from the same interstellar cloud. We confirm previous claims that both stars have the same metallicities to within about 0.1 dex and yet very different lithium abundances. Cochran et al. (1997) were not able to detect any significant modulation in the velocity data for 16 Cyg A, which they monitored over the same time interval as 16 Cyg B, implying, but not proving, that it does not have a companion. Another unusual feature of the system is the very high orbital eccentricity, 0.63, of 16 Cyg B b. They pointed out that among the substellar companions there exists a sharp boundary in a plot of orbital eccentricity versus M [FORMULA] at about 10 [FORMULA], where the less massive companions all have small eccentricities, except 16 Cyg B b.

The unusual characteristics of the 16 Cyg system led Mazeh et al. (1997) to propose that the orbit of 16 Cyg B b had been altered from an orginally more nearly circular configuration by the gravitational perturbations of 16 Cyg A. The current separation between the two stars is about 840 AU. Mazeh et al. (arbitrarily) set the semi-major axis of the stellar binary at 1100 AU, and ran simulations with eccentricities of 0.60 and 0.85 (also arbitrarily chosen). The closest separation for the [FORMULA] case is 165 AU. If, however, e is nearer to unity, then the two stars approach within a few AU of each other. At such a close range, assuming each star started with a gas giant with a semi-major axis [FORMULA] 2 AU, planet-planet interactions are possible at some periastron passages and could result in severe perturbations of the planetary orbits. One planet could be ingested by its parent star as a result of a close planet-planet encounter, leaving the other in an eccentric orbit. In summary, in this scenario star-planet perturbations would gradually pump-up the eccentricity of each planet until they were able to get sufficiently close to each other for planet-planet perturbations to become significant. Unfortunately, as admitted by Mazeh et al., there are too many free parameters in the 16 Cyg system to definitively test any given dynamical scenario. Other possible perturbations not addressed by them are those due to nearby star encounters and the Milky Way gravitational tidal force.

Our scenario might be tested, instead, by comparing the compositions of 16 Cyg A and B. The addition of a 2 [FORMULA] gas giant to a solar type star several billion years after its formation will increase the surface lithium abundance by about 1.7 dex. Currently, the lithium abundance of 16 Cyg A is about 0.8 dex greater than that of 16 Cyg B. Hence, within the self-enrichment scenario, 16 Cyg A swallowed its planetary companion at some intermediate age. Also important is the prediction that the iron abundance would increase by only a small amount if a gas giant is ingested (about 0.08 dex for a 2 [FORMULA] gas giant). Averaging our [Fe/H] estimates of 16 Cyg A and B with those of Friel et al. (1993), we obtain [Fe/H] = 0.08 [FORMULA] 0.04 and 0.04 [FORMULA] 0.04 for A and B, respectively. Thus, A and B have the same metallicities to within the quoted uncertainties, but it is notable that both studies 6 obtain a slightly higher [Fe/H] value for A (the older studies listed by Cayrel de Strobel 1997 also obtain a higher [Fe/H] for 16 Cyg A).

Self-enrichment is not the only explanation consistent with the 16 Cyg A and B system. Cochran et al. (1997) propose a scenario whereby the different lithium abundances in 16 Cyg A and B are the result of different initial rotation rates, which were, in turn, the result of different circumstellar environments early on. In this picture, 16 Cyg A would have lacked a massive proto-planetary disk, which would have provided rotational braking to the star. With rotational breaking, angular momentum is redistributed in a low mass star's interior, leading to enhanced lithium depletion at the base of the convection zone. One weakness with the Cochran et al. model is that it does not explain why 16 Cyg B was formed with a massive proto-planetary disk, while 16 Cyg A was not. Unfortunately, the rotation periods of 16 Cyg A and B are not known from direct measurement; Hale (1994) quotes rotation periods of 26.9 and 29.1 days for 16 Cyg A and B, respectively, based on the mean Ca II flux.

Is it possible that differences in the lithium abundances between 16 Cyg A and B can be due to different rates of lithium depletion on long timescales? For example, Deliyannis & Ryan (1997) present evidence that the lithium abundances in the atmospheres of the metal-poor common proper pair HD 134439 and HD 134440 differ by over 1 dex. These are cool dwarfs [FORMULA] and differ in temperature by only about 200 K. This large difference in the lithium abundances is interpreted by Deliyannis & Ryan as the result of a strong temperature dependence on lithium depletion, which is seen to occur in dwarfs with [FORMULA]. The large observed difference in the lithium abundances between [FORMULA] Cen A and B (King et al. 1997) also fits this trend. However, given that 16 Cyg A and B differ in temperature by no more than 50 K and that they are above the 5500 K limit, it is unlikely that significant gradual differential lithium depletion is occurring in this pair.

4.6. Testing planet formation models

The observed metallicity distribution of the parent stars of extrasolar planetary systems should eventually (when the number statistics are better) help to choose between the two most popular planet formation mechanisms: core instability-accretion (CIA; reviewed by Podolak et al. 1993) and gravitational instability (GI; Boss 1997). In the formation of a gas giant, the CIA model requires first the buildup of a 10-15 [FORMULA] rocky core via planetesimal accretion before a protoplanetary nebula loses most of its H and He inventory. Once its core is sufficiently massive to accrete and retain H and He, a gas giant will grow in mass very quickly. Hence, in this model, the formation of a gas giant should have a strong dependence on the metallicity of the parent cloud from which it formed. The GI model has gas giants forming through the breaking-up of a disk into clumps through its self-gravity. This model is essentially the reverse of CIA in that core formation is not the trigger of planet formation but rather a by-product. The GI model should have a much weaker dependence on the metallicity of the parent cloud. Note, that the formation of terrestrial planets is strongly dependent on metallicity since they consistent almost entirely of metals.

While both models are still in an immature state with regard to specific predictions, it should be possible to make predictions about the metallicity dependence of giant planet formation (possibly also including correlations with planet mass). Particularly valuable would be an examination of parameter space near the Brown dwarf boundary ([FORMULA]). Current high-precision radial velocity searches are uncovering companions over a large mass range, [FORMULA] (Mayor et al. 1998). It should be very illuminating to compare the metallicity distributions of the parent stars of the Jupiter-mass companions with those of the Brown dwarf companions. Mayor et al. suggest that the discontinuities observed in the companion mass-function histogram and the companion mass-eccentricity plot are evidence of different formation mechanisms for objects below [FORMULA] and above 5 [FORMULA].

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© European Southern Observatory (ESO) 1998

Online publication: May 12, 1998

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