On the Nature of Stars with Planets

Table 1 lists basic photometric and parallax data for stars currently known to possess at least one planetary‐mass companion. We shall refer to those stars as ESP host stars. In compiling this list, we follow the Geneva convention² of setting an upper mass limit of M₂sin i = 17 M_J, where M_J is the mass of Jupiter. There are only four systems where M₂sin i exceeds 10 M_J. The parameters listed for the planetary systems are taken from the Extrasolar Planets Encyclopedia.³

Since we measure only M₂sin i for most of these systems, there is clearly potential for the inclusion of higher mass companions on low‐inclination orbits, either low‐mass stars or brown dwarfs. Indeed, there may well be an overlap between the upper mass range of planets and the lower mass range of brown dwarfs,⁴ leading to an inherent ambiguity in interpretation. Since those two classes of objects may have different intrinsic properties, it is important to consider the likely level of cross‐contamination.

The degree of contamination depends on the prevalence of brown dwarfs as close companions to solar‐type stars. Few unequivocal examples of such systems have been detected, leading to both the postulation of a "brown dwarf desert" at a<10 AU (Marcy & Butler 2000) and support for the hypothesis that the low‐mass (M₂sin i<10 M_J) companions that are detected are not a simple extension of the companion mass function at higher masses. On the other hand, there have been countersuggestions. Both Heacox (1999) and Stepinski & Black (2000) have pointed out the similarity between the orbital properties of planetary‐mass systems and stellar binaries, although that might reflect similar dynamical evolution rather than similar origins. More directly, Han, Black, & Gatewood (2000) and Gatewood, Han, & Black (2000) have analyzed radial velocity data in tandem with Hipparcos Intermediate Astrometric Data (IAD) and claim that in many cases the best‐fit orbits have low inclination and correspondingly high true masses in the brown dwarf or even the stellar regime.

The Han et al. result has been scrutinized intently and generally found wanting. Statistically, the scarcity of systems with M₂sin i>15 M_J demands a rather unlikely observational conspiracy, with orbital axes aligned within a few degrees of the line of sight. Under a random distribution of inclinations, one would expect several hundred systems with brown dwarf mass companions for each planetary‐mass system; not only are the latter systems not observed, but there are not sufficient G dwarfs in the solar neighborhood to meet the numerical requirements. The amplitudes of the derived astrometric orbits are comparable with the uncertainties in the Hipparcos IAD measurements, and Pourbaix (2001) has shown that the low inclinations found by Han et al. are largely an artifact of the fitting technique used. Pourbaix & Arenou (2001) conclude that ρ CrB is the only system where the data merit interpretation as a near face‐on orbit, but Hubble Space Telescope astrometry by McGrath et al. (2001) sets an upper limit on the semimajor axis at asin i<0.3 milliarcseconds (mas), corresponding to M₂<30 M_J, rather than the 1.5 mas and 0.14 ± 0.05 M_⊙ suggested by Gatewood et al. (2000).

Current estimates of the companion mass function are generally in good agreement, finding approximately equal numbers per decade in mass (dN/dM∝M^-1) for M<10 M_J, with a sharp drop at higher masses (Jorissen, Mayor, & Udry 2001; Zucker & Mazeh 2001; Tabachnik & Tremaine 2002). Indeed, astrometric observations have shown that many of the candidate brown dwarf companions are, in fact, low‐mass M dwarfs (Halbwachs et al. 2000), further enhancing the brown dwarf desert. Based on these results, we expect little contamination (less than 5%) in the ESP sample listed in Table 1. Nonetheless, one star deserves comment. As discussed later, HD 114762 is one of the most metal poor stars in the sample. The measured stellar rotational velocity suggests that the star is being viewed close to pole‐on, implying a low inclination for an equatorial orbit. In that case, the companion, detected by Latham et al. (1989), is a candidate for the first brown dwarf identification.

All of the ESP host stars except BD −10°3666 were observed by Hipparcos, and most have trigonometric parallaxes measured to an accuracy of better than 5%. The BV photometry listed in Table 1 is also taken from the Hipparcos Catalogue (ESA 1997), although we use the literature data cited therein in preference to Tycho photometry, given the systematic offset (and occasional large random errors) between the latter system and standard Johnson data (Bessell 2000). BD −10°3666 has UBV photometry by Ryan (1992) but no measured trigonometric parallax, and the absolute magnitude listed in Table 1 is based on an estimated photometric parallax. Since both this star and HD 4203 were selected for observation based on the known high metallicity, neither plays a role in the statistical comparison discussed in the following sections.

The photometry and astrometry listed in Table 1 allow a detailed assessment of the distribution of the ESP host stars in the H‐R diagram. Figure 1 makes that comparison, where the reference main sequence is provided by data for stars within 25 pc that have accurate photometry and trigonometric parallaxes measured to a precision of σ_π/π<10%. Almost all of the latter stars are members of the Galactic disk. Three features are immediately noticeable:

• 1.  
  G dwarfs contribute the majority of planet detections, with Gl 876 still the only M dwarf known to have planetary‐mass companions. To a large extent, the distribution likely reflects the continuing observational focus on solar‐type stars.
• 2.  
  The current sample includes a significant number of evolved stars. At least six stars lie at the base of the subgiant branch, while four have evolved a considerable distance from the main sequence. These stars are identified in Table 1.
• 3.  
  The ESP host stars are distributed throughout the full width of the main sequence. This is important since chemical abundance is the dominant factor that governs the location of single stars on the main sequence—at a given color, metal‐rich stars are more luminous than metal‐poor stars. Thus, the observed distribution points to a range of metallicity among stars with planets that is at least comparable to the abundance distribution among the underlying local disk (thin+thick) population.

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The last point is particularly pertinent given the recent emphasis laid on the high metal abundance measured for at least some of the ESP primaries (Gonzalez, Wallerstein, & Saar 1999; Gonzalez et al. 2001; Santos et al. 2001). Many of those abundances are significantly higher than the value usually taken as the median for the Galactic disk. Most previous studies, however, treat the metallicity distributions of the ESP hosts and of the disk as separate entities. The following section places the former in the context of the latter and considers how the high chemical abundances are reconciled with the distribution evident in Figure 1.

The metal content of stellar atmospheres can be measured using a wide variety of techniques. In general, the accuracy of the final measurement is at least inversely proportional to the difficulty of the observation. Analyses based on high‐resolution spectroscopy are usually more reliable than those that utilize broadband colors, but photometric data are obtained much more readily than echelle spectra. Thus, any statistical analysis requiring a data set of even modest dimensions must balance two factors—availability and accuracy.

As a further complication, comparative studies must ensure that data drawn from different analyses are tied to a consistent system. Different measurement techniques not only have different random uncertainties but can also exhibit systematic discrepancies in scale and/or zero point, as discussed in the context of globular cluster distance determination by Gratton et al. (1997) and Reid (1998). Apart from differences in the choice of standard stars, we note that the solar iron abundance was recalibrated relatively recently, revised downward from A(Fe) = 7.67 to A(Fe) = 7.54 (Biemont et al. 1991), where A(Fe) is the logarithmic abundance on a scale where A(H) = 12. While most abundances are measured differentially, this recalibration might lead to a systematic offset, depending on how and when the abundances of the standard stars were determined.

This issue is a concern since, while nearly all of the ESP host stars have recent high‐resolution spectroscopic abundance measurements, most estimates of the underlying field‐star metallicity distribution rest on lower resolution techniques. Santos et al. (2001) have addressed this problem to some extent by providing high‐resolution spectral analyses for 43 G dwarfs in 42 systems drawn from the volume‐limited sample of stars with (B−V)<1.1 and d<17 pc. That sample is scarcely sufficient in size, however, to provide an adequate mapping of the distribution of disk properties. We adopt an alternative strategy in this paper.

Strömgren uvby photometry provides a relatively simple means of determining abundances for F, G, and early K‐type stars (Strömgren 1966). Data are available for most solar‐type stars brighter than 10th magnitude. Indeed, both Giménez (2000) and Laughlin (2000) have applied those measurements to studying the ESP host stars. Metallicities are determined by measuring the differential line blanketing via the m₁ and c₁ indices, where

and

The latter index is also gravity sensitive, allowing discrimination between dwarfs and subgiants.

The literature contains several calibrations of the Strömgren indices against metallicity. Giménez adopts that given by Olsen (1984); we follow Laughlin in using the more recent calibrations derived by Schuster & Nissen (1989). They provide two calibrating relations,

for F stars (0.22≤(b - y)<0.375, 0.03≤m₁≤0.21, 0.17≤c₁≤0.58, and -3.5≤[Fe/H]≤0.2) and

for G stars (0.375≤(b - y)≤0.59, 0.03≤m₁≤0.57, 0.10≤c₁≤0.47, and -2.6≤[Fe/H]≤0.4).

Apart from BD −10°1366 and Gl 876, where Strömgren data offer little useful information, only HD 177830 (HIP 93746) lacks uvby photometry. Table 2 lists (b−y), m₁, and c₁ color indices, taken from Hauck & Mermilliod's (1998) catalog, and the resulting [Fe/H]_uvby for the remaining stars, together with the metallicities derived from high‐resolution spectroscopy. As expected, there is a systematic offset to lower abundances in the Strömgren calibration. The results are compared in Figure 2, where the upper panels plot the full data set (see also Fig. 1 in Laughlin 2000). We note that residuals tend to increase among early type K stars, (b−y)>0.5, where both methods become more problematic.

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We have quantified the comparison using the data sets from Santos et al. (2001) and Gonzalez and collaborators, which provide two internally consistent data sets of moderate size. Based on the 22 ESP host stars observed by Santos et al. (2001), we derive

where the uncertainties quoted are the rms dispersion about the mean. The formal standard error of the mean, σ_μ, is 0.020 dex, and the median offset is −0.13 dex. The 22 stars in the Gonzalez data set give an almost identical result,

The median offset is −0.10 dex. Combining both data sets with 40 field stars from the Santos et al. reference sample gives

The median offset is −0.07 dex. This is in excellent agreement with Gratton et al.'s independent analysis of 152 stars spanning a much larger range of metallicity, where they derive

Given uncertainties of ±0.06 dex in the Santos et al. and Gonzalez spectroscopic measurements, the measured dispersion indicates that the Strömgren data have typical uncertainties of ±0.1 dex at near‐solar abundances, sufficient accuracy for present purposes.

Based on this comparison, we conclude that the Strömgren abundance scale is offset by −0.1 dex from the most recent calibrations. We note that the offset is intriguingly similar to the recalibration of the solar abundance, although that similarity may be coincidental. Rather than attempt to correct the metallicity measurements, we base our analysis on the uvby scale; in effect, we adopt the somewhat paradoxical definition

Since we are considering the comparative distributions of field star and ESP host star abundances, consistency is more important than the numerical value chosen for the fiducial zero point.

Defining a suitable reference sample is crucial to assessing how the properties of the ESP host stars map onto the overall field star distribution. Complete, volume‐limited data sets offer the most reliable comparison but have generally not been available to previous studies. Murray et al. (2001) have attempted to turn Hipparcos data to this end, with a reference sample defined by selecting HD stars with π>10 mas and σ_π/π<10%. However, the color‐magnitude diagram for this data set (Fig. 1 in Murray & Chaboyer 2002) is clearly biased strongly toward F‐type and early G‐type dwarfs, partly reflecting sampling in the Hipparcos Catalogue at V>9th magnitude and partly reflecting the fact that the HD catalog was selected from blue photographic plates. The resulting data set therefore provides a biased subset of nearby disk stars. Murray et al.'s metallicities are taken from the Cayrel de Strobel et al. (1997) catalog and therefore represent an amalgam of heterogeneous sources. Thus, this data set is not suitable as a local reference.

Several other analyses (e.g., Gonzalez 1999; Butler et al. 2000) have relied on the nearby‐star sample defined by Favata, Micela, & Sciortino (1997, hereafter F97) to represent the abundance distribution of local disk stars. That sample, however, is severely flawed in several important respects, as illustrated in Figure 3. The F97 abundances are derived from high‐resolution spectra, and a comparison with Strömgren abundances gives

somewhat less than the offsets derived in the previous section. The full sample of 90 stars includes both components of several binaries, giving those systems double weight in the abundance distribution, and spans a substantially larger color range than ESP host stars (excluding Gl 876). Finally, and most significantly, the sample is neither complete nor volume limited. Favata, Micela, & Sciortino (1996) constructed the original sample by taking a randomly selected subset of 200 stars with 0.5<(B−V)<1.4 from the second Catalogue of Nearby Stars (Gliese 1969; Gliese & Jahreiss 1979, hereafter CNS2). Ninety‐four of those stars were observed spectroscopically. Unfortunately, while the CNS2 has a nominal distance limit of 25 pc, subsequent Hipparcos astrometry has shown that a significant fraction of the stars lie at much larger distances. Figure 3 shows that at least 40% of the F97 data set lies beyond 25 pc. Our analysis demands a more reliable reference data set.

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Figure 4 shows the [M_V, (B−V)] color‐magnitude outlined by the 1549 stars in the Hipparcos Catalogue with formal trigonometric parallax measurements exceeding 40 mas [d≤25 pc, (m−M)≤1.99]. As in Figure 1, we use the literature BV photometry in the catalog in preference to Tycho data. We have not applied any cut based on parallax precision but use different symbols to identify the 1477 stars with parallaxes measured to a precision of better than 20%. Nearly all of the stars lying below the main sequence in this figure have inaccurate parallax measurements.

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The box superposed on Figure 4 isolates 488 stars with 0.5≤(B−V)≤1.0 and 2.0≥M_V≥7.0, matching the color/magnitude range of the bulk of the ESP host stars. The limiting magnitude for completeness in the Hipparcos Catalogue is

so the 25 pc sample is effectively complete over the whole sky for M_V≤5.9 (dotted line in Fig. 4). The full catalog is ∼25% incomplete for stars with 8≤V<9 but should be significantly more complete for nearby stars, since all stars suspected of being within 25 pc were included in the input catalog—as emphasized by the large numbers of M dwarfs in Figure 4. Indeed, Jahreiss & Wielen (1997) argue that the Hipparcos Catalogue is essentially complete to M_V = 8.5 for stars within 25 pc of the Sun. Thus, the F, G, and K stars isolated in Figure 4 effectively represent a complete, volume‐limited sample. We identify these stars as the FGK25 Hipparcos data set. Note that the sample includes 20 known ESP hosts from Table 1.

As noted in the previous section, Strömgren photometry is now available for a substantial number of bright F, G, and K stars and is readily accessible through the catalog compiled by Hauck & Mermilliod (1998). We have cross‐referenced the FGK25 Hipparcos data set against that catalog and located photometry for 419 of the 486 stars (86% of the sample). Those stars are represented by filled squares in Figure 4. The sample includes members of binary systems, but only one star per system. It is clear that almost every star with (B−V)<0.8 has photometry, while the late G and K dwarfs that lack Strömgren measurements are distributed over the full width of the main sequence, interspersed with stars that have uvby photometry. We conclude that the abundance distribution deduced from these data is characteristic of the parent population(s) of the ESP host stars.

The overwhelming majority of the stars in the FGK25 sample are members of the Galactic disk. Five stars, however, lie significantly below the main sequence. These are HIP 57939, 62951, 67655, 79537, and 79979. Two of these stars, HIP 62951 and HIP 79979, are in binary systems where the companion has affected the parallax determination; Fabricius & Makarov (2000) have reanalyzed the Hipparcos data for HIP 62951 and find π = 2.4 mas. These are the only two stars in the FGK25 sample with σ_π/π>0.2 (there are only six other stars with σ_π/π>0.1), and we exclude both from our sample. The remaining three subluminous stars are bona fide metal‐poor subdwarfs. HIP 57939 is HD 103095, or Gmb 1830, the well‐known intermediate‐abundance ([Fe/H]_uvby = -1.4) subdwarf; HIP 67655, or HD 120559, has [Fe/H]_uvby = -0.94; and HIP 79537 is HD 145417, [Fe/H]_uvby = -1.25. The presence of three such stars in this volume‐limited sample suggests a somewhat higher density normalization (∼0.6% ± 0.35% relative to the disk population) than usually adopted for the local Galactic halo.⁵

Before comparing these results with other recent analyses, we should emphasize the limited nature of the present study. The question addressed here can be stated as follows:

Based on current statistics, and given a sample of stars drawn from the Galactic midplane near the Sun, what is the frequency of ESP systems as a function of metallicity?

Our goal in constructing the reference sample of field stars, therefore, is not an unbiased estimate of the present‐day metallicity distribution of the Galactic disk—a parameter used to constrain disk star formation histories. That undertaking requires limiting analysis to stars with main‐sequence lifetimes older than the age of the disk, avoiding possible bias through a disproportionate contribution from recent star formation episodes. Moreover, given a potential correlation between metallicity and velocity, one should weight each star's contribution by its W‐velocity to allow for the residence time in the midplane and convert volume density to surface density. The latter is not an option for the present sample, since over 25% of the stars lack radial velocities. Moreover, our (B−V) limits, modeled on the known ESP systems, include early type G and late F stars, whose main‐sequence lifetimes are shorter than 10 Gyr. Thus, our field star sample is tailored to provide a local snapshot of the present‐day abundance distribution in the midplane, rather than an integrated history of star formation in the disk.

We have compared the abundance distribution of the FGK25 data set against results from two other studies: the Favata et al. (1997) analysis, described above, and the recent study by Haywood (2001, hereafter H2001). In both cases, we consider volume‐limited samples (i.e., the distribution is not weighted by W velocity as in Fig. 3 of F97). Haywood's analysis is aimed at determining an unbiased estimate of the disk abundance distribution, so while his initial sample is selected to have M_V<8.5, (B−V)>0.25, and π>40 mas (based on Hipparcos data), the final analysis is limited to 328 stars with M_V>4.5, that is, main‐sequence dwarfs with lifetimes longer than the age of the disk. Abundances are derived primarily from Geneva photometry, supplemented by Strömgren data, with the metallicity scale effectively adjusted to the high‐resolution (Santos/Gonzalez) system.

Figure 5 compares the abundance distributions derived in those studies with our own results. For consistency, we have adjusted all of the metallicity scales to match [Fe/H]_uvby. All three distributions peak at values close to the solar abundance, with a substantial fraction of the sample (45% in the FGK25 data set) having supersolar metallicities. As discussed by Haywood, this represents a significant revision of previous analyses and may reflect a bias against metal‐rich stars in samples selected based on spectral type rather than distance/color. We note that only a small fraction of the local disk have abundances of less than 1/3 solar: only 25 stars (6%) in the FGK25 sample. If ≈10% of the local stars are members of the thick disk, as suggested by kinematic analyses (Reid, Hawley, & Gizis 1995), then the mean abundance of that subpopulation lies much closer to the solar metallicity than the value of [Fe/H ] = -0.6 adopted in some Galactic models.

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Both the F97 and H2001 samples show a more extended distribution toward higher abundances than the FGK25 data set. This is somewhat surprising, since the latter sample, extending to stars brighter than M_V = 4, should include a higher proportion of younger stars, which are likely to be more metal‐rich. The discrepancy may originate from the abundance calibrations. Figure 6 shows the metallicity distribution as a function of (B−V) color for the H2001 and FGK25 data sets. The former shows a clear trend of increasing metallicity at redder colors, suggesting a possible systematic bias in the abundance calibration of Geneva photometry. Further observations are required to verify this hypothesis.

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For our present purposes, the most significant point is that the metallicities discussed here for both field stars and ESP host stars are derived from a single source—Strömgren photometry, as calibrated by Schuster & Nissen (1989). Thus, the comparison between the two abundance distributions described in the following section is internally fully self‐consistent.

Before comparing metallicities, Figure 7 matches the [m₁, (b−y)] and [c₁, (b−y)] distributions of the ESP host stars and the FGK25 Hipparcos sample. We have distinguished between main‐sequence stars and potential subgiants in the former sample. As previously noted by Giménez (2000), a significant fraction of the ESP host stars have high c₁ values, suggesting low gravities and a mildly evolved status. In some cases, however, the colors reflect high metallicity rather than low gravity; thus, both HIP 43587 (55 Cnc) and HIP 79248 (HD 145675) lie well above the [(b−y), c₁] sequence at (b−y)∼0.42, but their location in the [M_V, (B−V)] plane demands that both be main‐sequence dwarfs. Spectroscopy indicates that both are super–metal‐rich (Table 2). Nonetheless, the fraction of subgiants among known ESP hosts (∼15%) is at least a factor of 3 higher than that in the volume‐limited sample. This may reflect an observational selection effect, since evolved stars are intrinsically more luminous and therefore more likely to be included in the radial velocity monitoring programs.

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The reddest star in the sample is the K2 subgiant, HD 27442 (HIP 19921). This lies beyond the formal limits of the Schuster & Nissen (1989) abundance calibration, at (b−y) = 0.65; however, the derived metallicity, [Fe/H]_uvby = 0.26, is not inconsistent with the spectroscopic determination of [Fe/H] = +0.22, so we have retained the star in the sample. We have excluded both BD −10°1366 and HD 4203 from the statistical comparison. As noted above, those stars were added to the Keck/Lick radial velocity program because they were known to be extremely metal rich. The M dwarf, Gl 876, is also excluded, but we include HD 177830, adjusting its abundance from [Fe/H] = 0.36 to [Fe/H]_uvby = 0.26.

The sample of ESP host stars is not volume limited, partly reflecting the fact that the original target list was constructed before the availability of Hipparcos data, and is therefore subject to the type of distance errors illustrated in Figure 3. There may therefore be underlying biases reflecting the initial selection of which stars to monitor for radial velocity variations. Those effects can be quantified once the full data set is available. Nonetheless, it is not unreasonable to hope that the current catalog of ESP host stars provides a representative subset of stars with currently detectable planetary systems, that is, stars with relatively massive (super‐Jovian) companions on relatively short period (less than a few years) orbits.

Figure 8 plots the abundance distribution of both the ESP host stars and the reference FGK25 Hipparcos data set. The subgiant contribution to the former distribution is shown as the shaded histogram and is consistent with the overall distribution. As emphasized in § 3.1, these data are all on the Strömgren system, [Fe/H]_uvby, placing the Sun as −0.1 dex, at the mode of the local abundance distribution.

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Visual comparison clearly confirms previous suggestions that the abundance distribution of the ESP host stars is weighted more heavily toward supersolar metallicity than the field distribution. To quantify that comparison we have combined the distributions by scaling the upper distribution to match the observed fraction of ESP hosts among the volume‐complete sample. As noted above, 20 of the 486 stars in the FGK25 sample, or 4.1%, are known to have planetary‐mass companions. This fraction is broadly consistent with previous estimates (e.g., Marcy & Butler 2000). We have used this factor to scale the metallicity distribution in the uppermost panel of Figure 8, and the two lowest panels in Figure 8 show the fraction of ESP host stars,

as a function of metallicity. There is an obvious trend with abundance, with f_ESP rising to near unity at the highest abundances; both of the stars in the highest metallicity bin of the FGK25 sample are known to have planetary‐mass companions. However, even at an abundance of 2/5 solar, ∼1% of F, G, and early K stars are predicted to have Jovian‐mass planetary companions. HD 114762b, the likely brown dwarf, contributes the spike at [Fe/H]_uvby = -0.7 dex.

Finally, we have compared the properties of the individual planetary systems against the abundances derived from the Strömgren data. Figure 9 shows the results, where we identify separately systems with multiple components (including the Sun, represented by Jupiter and Saturn). There is no obvious correlation between [Fe/H]_uvby and any of the observed characteristics.

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Is the correlation with metallicity evident in Figure 8 a selection effect? Metal‐rich stars are more luminous than their metal‐poor counterparts and therefore, like subgiants, might be expected to be better represented in a target list that is partly magnitude limited. However, it seems unlikely that this type of bias could account for the smooth trend evident in the observations, particularly given the identification of planetary companions to BD −10°1366 and HD 4203, stars specifically added to the Keck program because they were known to be super–metal‐rich. Thus, the simplest interpretation of Figure 8 is that the correlation represents a real physical phenomenon. The explanation for this phenomenon is somewhat less clear.

Perhaps appropriately, the two mechanisms proposed to account for the observed correlation mirror the classic nature versus nurture debates of biological behavioral sciences. Under the first hypothesis, planetary systems (at least those with giant planets) form more readily in the dustier environment likely to be present in high‐metallicity circumstellar disks. Under the alternative hypothesis, gas giants migrate inward because of dynamical friction with residual disk material and are absorbed into the stellar envelope. The enhanced metal content of the planet (solar system giants are likely to have Z>0.1) enriches the metallicity of the outer convective envelope, leading to a higher measured chemical abundance.

One question mark hanging over the planetary pollution hypothesis centers on the details of the enhanced metal content of Jovian planets. In astronomical terms, "metals" encompass all elements except hydrogen and helium, but not all metals are created equal. Metallicity measurements for F, G, and early K‐type stars are primarily measuring blanketing due to heavy elements, notably iron. The giant planets are known to have noncosmic interelement abundance ratios, but if the additional "metals" are ices (C, N, O) rather than minerals (Fe, Si, Ni), as suggested by the possible absence of a rocky core in Jupiter (Guillot 1999), then planetary pollution will have little effect on the apparent metallicity of the stellar envelope.

These two competing scenarios are discussed extensively by, among others, Gonzalez (1997, 1999), Laughlin (2000), Murray et al. (2001), and Santos et al. (2001). A major prediction of the pollution hypothesis is that the degree of metallicity enhancement should increase with increasing mass of the parent star. This follows from the corresponding decrease in mass of the convective envelope; adding high‐Z material gives a proportionately larger increase in metallicity. Both Laughlin and Murray & Chaboyer (2002) have argued that this effect is present, although the latter authors note that a similar trend is present in their reference sample, and both analyses are based on a subset of the current catalog of ESP hosts. Santos et al. (2001), in contrast, arrive at the opposite conclusion based on an analysis of more than 60 systems. In their analysis, they rightly place more emphasis on the location of the upper envelope of the abundance distribution as a function of mass, rather than the mean metallicity.

All three of these analyses use theoretical tracks to deduce masses for individual ESP host stars. Figure 10 shows an alternative, more empirical approach. We have separated the current sample into main‐sequence stars and subgiants based on location in Figure 1 and plot the spectroscopic abundance measurements as a function of (b−y). For the main‐sequence sample, (b−y) effectively traces mass, and the absence of any strong trend in the location of the high‐metallicity boundary, in particular, a decrease in [Fe/H]_max at redder (b−y) colors, supports the conclusion reached by Santos et al. Moreover, the latter authors point out that as stars evolve onto the subgiant branch, the convective envelope increases in size, diluting the effect of any planetary pollution. It is clear from Figure 10 that the evolved stars can be as metal‐rich as the main‐sequence dwarfs; indeed, the K2 subgiant HD 24427 (HIP 19921) is among the most metal‐rich stars in the sample. Thus, these results suggest that planetary systems are born metal‐rich, rather than having high metallicity thrust upon them.

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The age distribution of the ESP host stars is clearly an important parameter for understanding the Galactic origins of these systems. Two techniques have been used to estimate ages for individual stars: isochrone fitting; and the level of chromospheric activity, as measured through emission at the Ca ii H and K lines. Both methods can be applied to individuals, but both have limitations. Isochrone fitting provides reliable ages for F and early G stars but becomes less accurate for longer lived, later type stars. Chromospheric ages, quantified using the R^'_HK index (Soderblom, Duncan, & Johnson 1991), are more readily derived but are also less reliable since there is a considerable dispersion in activity among individual stars with similar ages (see Fig. 10 in Soderblom et al.). Moreover, variability is an issue; as Henry et al. (1996) point out, the Sun's age could be estimated as anywhere between 2.2 and 8 Gyr depending on when the observations are taken during the solar cycle. Finally, both of these techniques become significantly less reliable at ages exceeding ∼2 Gyr (as evidenced by continuing uncertainties in the Galactic star formation history).

Nonetheless, both of these methods provide useful insight into the age distribution, and both have been applied by Gonzalez and coworkers (Gonzalez & Laws 2000; Gonzalez 1999; Gonzalez et al. 2001) to estimate ages for 33 of the systems listed in Table 1. A comparison between the different estimates emphasizes the inherent uncertainties, most dramatically for HD 217107 and HD 222582, where both have chromospheric age estimates of 5.6 Gyr but isochrone estimates of 1.2 and 11 Gyr, respectively. Averaging the results for all 33 stars, we derive a mean age of 5.6 Gyr (σ = 3.6 Gyr).

Space motions cannot be used to provide age estimates for individual stars. However, stellar kinematics offer an alternative means of comparing the average properties of diverse groups of stars. Velocity dispersion increases with age, probably through the mechanisms of orbital diffusion (Wielen 1977) and scattering due to molecular clouds (Spitzer & Schwarzschild 1953). A comparison between the velocity distributions of the ESP host stars and the local disk can test whether there is a significant difference in the mean age of the two samples.

We have calculated space motions for the ESP hosts using astrometric data from the Hipparcos Catalogue and the available radial velocity measurements. Table 3 lists those data and the resulting (U, V, W) motions, where U is positive toward the Galactic center, V positive in the direction of rotation, and W directed toward the north Galactic pole (NGP).

All of the FGK25 stars have accurate proper motions and parallaxes from Hipparcos, but only 60% have published radial velocities, rendering the sample unsuitable as a reference. However, the volume‐complete M dwarf sample from the Palomar/Michigan State University (PMSU) survey of nearby stars (Reid et al. 1995, hereafter PMSU1) gives a ready alternative, providing an unbiased representation of the kinematics of local disk stars. Reid, Hawley, & Gizis (2002, hereafter PMSU4) have revised the original data set to incorporate more recent astrometric data, notably from Hipparcos, besides including higher accuracy radial velocities from echelle observations summarized by Gizis, Reid, & Hawley (2002, hereafter PMSU3). The final sample is comparable in size to the FGK25 data set, with 436 systems lying within M_V‐dependent distance limits ranging from 10 to 20 pc.

Figure 11 compares the velocity distributions of the two data sets. The left‐hand panels plot the two‐component velocity distributions; the right‐hand panels show probability plots of the (U, V, W) distributions. As originally discussed by Lutz & Upgren (1980), these diagrams plot the cumulative distribution of a sample, C(x), against the difference with respect to the mean value, x, in units of the standard deviation. A normal distribution, f(x) = [1/(2πσ)^1/2]e^{-(x - x)2/σ2}, gives a straight line with slope σ in this plane. Figure 11 plots three empirical velocity distributions: data for the ESP host stars; for the full PMSU M dwarf sample; and for the PMSU dMe dwarfs, with Hα emission exceeding 1 Å equivalent width. As discussed by Hawley, Gizis, & Reid (1996, hereafter PMSU2), chromospheric emission is an age‐dependent phenomenon, so the last data set is characteristic of a moderately young stellar population, 〈τ〉 ≈ 1–2 Gyr.

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It is clear from Figure 11 that the velocity distribution of the ESP host stars is more closely matched to the full M dwarf sample than to the dMe sample. Quantitatively, linear fits to the central regions of the probability plots (-1.9<rms<1.9) give

where σ_tot is the overall velocity dispersion. Applying the same technique to the M dwarf samples gives

for the emission‐line dwarfs and

for the full sample.

Based on this comparison, we conclude that the current sample of F‐, G‐, and K‐type ESP hosts is younger, on average, than the overall disk population but includes stars significantly older than typical of the dMe sample. Quantitatively, if we assume diffusion with σ∝τ^1/2, then

suggesting an average age of 3–4 Gyr for ESP host stars for an approximately uniform star formation rate in a 10 Gyr old disk. This younger mean age is not unexpected, given the higher proportion of metal‐rich stars among the ESP sample. The average metal abundance of the Galactic disk is expected to increase with time, as successive generations of star formation contribute additional nucleosynthetic debris to the interstellar medium, so a sample biased toward high metallicities is also likely to be biased toward stars that are younger than average.

The previous section considered the overall distribution of velocities of the ESP host stars. We can also look for correlations using velocities for the individual stars, correcting the observed heliocentric data for the solar motion with respect to the local standard of rest (LSR). For the latter parameter, we use the values derived by Dehnen & Binney (1998),

where these values give the motion of the Sun with respect to the LSR. Thus, the Sun is moving toward the Galactic center, toward the direction of rotation, and toward the NGP, and the observed velocities must be corrected accordingly. We denote the corrected velocities as (U', V', W').

Figure 12 plots velocities for the ESP host stars as a function of abundance. We also indicate the location of the Sun on these diagrams. There is no obvious correlation between metallicity and either the (U', V', W') component velocities or the total motion with respect to the LSR, V_tot. The highest metallicity stars in the sample span essentially the same range of velocities as the solar‐abundance and subsolar‐abundance ESP host stars.

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Several previous studies have commented on the relatively low velocity (∼13 km s⁻¹) of the Sun with respect to the LSR. Gonzalez (1999), in particular, has invoked the weak anthropic principle (WAP; Barrow & Tipler 1988) in conjunction with this property, arguing that the small offset from corotation minimizes excursions into the potentially dangerous environment (supernovae, gravitational interactions) of spiral arms, therefore providing the long‐term quiescence that may be necessary for advanced life forms to develop. We can make two points in this context:

• 1.  
  First, it is clear from Figure 12 that ∼10% of the known ESP host stars have velocities V_tot within a few km s⁻¹ of that of the Sun. Indeed, the transiting system, HD 209458, has a space motion with respect to the LSR that is almost identical to that of the Sun, while HD 114783 has a relative motion of only 6.2 km s⁻¹. Gonzalez et al. (2001) derive age estimates of 3 Gyr (isochrones) and 4.3 Gyr (activity) for the former star. HD 114783 is too red to allow a reliable isochrone‐based age estimate, but Vogt et al. (2002a) note that HD 114783 is chromospherically inactive, log R^'_HK = -4.96, or ∼4.8 Gyr for the Donahue (1993) calibration. Both stars are therefore likely to have ages similar to that of the Sun.
• 2.  
  Second, the WAP can be expressed in two ways: as a positive concept, in that the planetary environment must permit the development of advanced life forms; or as a less restrictive, negative concept, in that the environment should not be inimical to the development of advanced life forms. Whether one chooses to express the WAP as a positive or a negative concept depends on other issues, notably belief in the likelihood of life developing elsewhere in the universe. In either case, with a current sample of one known inhabited planet, the WAP should be given the same scientific weight as its converse, the Copernican principle ("we're not special"). Both are interesting philosophical concepts, which may have explanatory power; neither carries any evidentiary weight in the present context.

Finally, we have compared the distribution of properties of the extrasolar planetary systems against the systemic velocities to search for possible trends or correlations. The only potentially significant result is shown in the uppermost panel of Figure 13, plotting M₂sin i against velocity perpendicular to the Galactic plane. The data suggest that, with the exception of HD 114762, higher mass companions tend to be found in systems with low W velocities. The result is statistically marginal but might indicate a correlation with the mass of the parent circumstellar disk. Clearly, more data are required to confirm whether this effect is real.

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I would like to thank Bruce Twarog and Barbara Anthony‐Twarog for providing prepublication access to their analysis of the Schuster & Nissen abundance calibration, Geoff Marcy for providing radial velocity measurements for several stars in advance of publication, David Trilling for useful comments, and David Koerner for interesting discussion and sparking my initial interest in this topic. The research for this paper made extensive use of the SIMBAD database, maintained by Strasbourg Observatory, and of Jean Schneider's Extrasolar Planets Encyclopedia.