Are stars with planets anomalous?

Mon. Not. R. Astron. Soc. 308, 447–458 (1999)

Are stars with planets anomalous?

Guillermo Gonzalezw

University of Washington, Astronomy Department, Box 351580, Seattle, WA 98195, USA

Accepted 1999 April 7. Received 1999 March 30; in original form 1998 December 7

A B S T R A C TThe chemical-dynamical properties of stars with giant planets are compared to those of anearby star sample within the framework of a stellar orbital diffusion model. The stars-with-planets sample includes recently discovered extrasolar planets and the Sun. We find that theplanet-bearing stars, 14 Her, r1 Cnc and t Boo, are much more metal-rich than stars ofsimilar age and this cannot be easily explained by orbital diffusion. We also confirmprevious claims that the motion of the Sun relative to the local standard of rest is very smallcompared to other G dwarfs of similar age, and we offer a possible explanation for thisapparent anomaly.

Key words: stars: abundances – stars: kinematics – planetary systems – Galaxy:abundances – solar neighbourhood.

1 I N T RO D U C T I O N

Spectroscopic studies of the solar-type parent stars of recentlydiscovered extrasolar planets (see Marcy & Butler 1998 for areview) have yielded accurate values for their physical parameters.In particular, Fuhrmann, Pfeiffer & Bernkopf (1997, 1998),Gonzalez (1997, hereafter G97), Gonzalez (1998, hereafter G98),Gonzalez & Vanture (1998, hereafter GV98) and Gonzalez,Wallerstein & Saar (1999, hereafter GWS99) have shown that thespectroscopically determined metallicities of stars with planetsare, on average, metal-rich compared to nearby F and G starsamples. This anomaly1 is likely an indication of a causal linkbetween high metallicity and the presence of planets, but thenature of the link is as yet unknown.

Recent studies of the metallicity distribution of nearby solar-type stars (Edvardsson et al. 1993, hereafter E93; Favata, Micela& Sciortino 1997, hereafter F97) and of the abundances of ‘zero-age’ objects (B stars and H ii regions) in the Milky Way (Smartt &Rolleston 1997; Afflerbach, Churchwell & Werner 1997; Estebanet al. 1998) have led some (Snow & Witt 1996; Wielen, Fuchs &Dettbarn 1996, hereafter W96; G97) to note that the Sun appearsto be anomalously metal-rich relative to both groups. Severaltheories have been put forward to try to account for the anomaloussolar metallicity, including stellar orbital diffusion (W96), alocalized metal enhancement by a nearby supernova (Snow & Witt1996), and self-enrichment as a result of the planet formationprocess (G97). Evidence cited in support of orbital diffusion in the

Milky Way includes the observed correlation between the dis-persion in metallicity and age for nearby stars (W96) and thesilicon isotope trends in presolar grains relative to the meteoriteratios (Clayton 1997). Evidence for the injection of supernovamaterial into the early Solar system has been discussed recently byCameron, Hoflich & Meyers (1995) and Amari, Zinner & Lewis(1995). The self-enrichment hypothesis has been proposed as apartial solution to the solar neutrino problem (Jeffery, Bailey &Chambers 1997 and references therein), but in G97 we proposed itto account for the high metallicities of the parent stars of the short-period extrasolar planetary systems and suggested that a similarmechanism also operated in the early Solar system; we presentedas positive evidence a correlation between the difference in solarphotospheric and meteoritic abundances and elemental condensa-tion temperature. A less well-known anomaly is the small velocityof the Sun relative to the local standard of rest (LSR), y lsr.Compared to other solar-type stars of similar age, the kinematicsof the Sun may be even more anomalous than its metallicity.

The primary goal of this study is to evaluate, within theframework of the stellar diffusion hypothesis of W96, the notionthat stars with planets are anomalous as compared to stars withoutplanets. We will do this by comparing the metallicities of theplanet-bearing stars to the metallicity distribution of nearby singlestars of similar spectral types. We employ a sample of nearby Fand G dwarfs and subgiants with well-determined metallicities,ages and kinematics. However, this comparison will not be perfectgiven that not all stars in the sample have been searched for thepresence of giant planets. Given the current rate of detection ofextrasolar giant planets (about 6 per cent, Marcy & Butler 1998),the number of stars with giant planets possibly contaminating oursample should be small. We begin with a description of the sampleselection, followed by an application of the diffusion model, andend with a discussion of the results.

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w E-mail: [email protected] In this study we define a quantity measured in a particular star asanomalous if it deviates significantly from the average of the same quantitymeasured in a group of otherwise similar stars. An anomaly may be due toa simple low-probability statistical fluctuation, or it may be an indicationof an unrecognized physical process or selection bias.

448 G. Gonzalez

2 S A M P L E S E L E C T I O N

We constructed our primary sample from E93, with several starsincluded from F97. E93 employed Stromgren indices to selecttheir sample according to certain specific criteria, which theydetail in their paper. We have adopted these same photometriccriteria along with Stromgren photometry from Hauck &Mermilliod (1998) to select a subsample from F97’s volume-limited spectroscopic survey of 91 G and K dwarfs. A few starsfrom E93 have been reanalysed by Tomkin et al. (1997) usingspectra of greater quality; in most cases the differences are notsignificant, so we have adopted the newer results only when thedifferences are significant. We have also eliminated from the E93and F97 subsamples known single-lined spectroscopic binaries.The mean difference �E93 2 F97� in [Fe/H] among the five starsin common to the two studies is 20:04 ^ 0:03 (s.d.), which is notsignificant. We should note that E93 put together their sample insuch a way as to achieve similar numbers of stars in eachmetallicity interval. This leads to an overestimate of metal-poorstars compared with a volume-limited sample (e.g., F97). Thisshould not be a problem for us, but such a sample is not suitablefor constructing an unbiased metallicity histogram distribution fornearby stars. We should also note that the cooler members of theF97 sample (with Teff , 5100 K) are metal-rich compared tothe hotter stars. This does not pose a problem for the present

study, since we restrict the primary sample to stars withTeff . 5600 K.

We have also prepared three samples containing the parent starsof planets: One contains stars from E93. Another contains starsfrom G97, G98, GV98 and GWS99 that are not in E93. The meandifference in [Fe/H] between stars common to E93 and the G97,G98, GV98, GWS99 studies is not significant. The third groupcontains only one star – the Sun. The typical uncertainties in the[Fe/H] estimates for the samples of parent stars are slightlysmaller than those for the primary sample of stars.

W96 made use of the E93 data set in their diffusion modelcalculations. However, since the E93 and W96 studies werepublished, Ng & Bertelli (1998) have produced an important newanalysis of this nearby star sample. They redetermined the ages forthe E93 stars using Hipparcos parallaxes (ESA 1997) andevolutionary tracks from Bertelli et al. (1994). We have adoptedtheir results in the present work and retained only those stars withthe highest-quality age estimates (n . 2 from tables 7 and 8 of Ng& Bertelli 1998). We used the same evolutionary tracks toestimate ages by visual inspection for our F97 subsample and forthe G97, G98, GV98 and GWS99 samples (except those starsnoted in the footnote to Table 1). A couple of stars from F97 tooclose to the zero-age main sequence (ZAMS) to derive accurateages were not included in the primary sample, even though theypassed all the other qualifications. We should note that these new

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Table 1. Data on the F97 and extrasolar planet samples.

HD HR [Fe/H] Ua V W Ageb Zmax

(km s21) (Gyr) (kpc)

F97 subsample:142 6 �0:04 258:3 236:8 212:8 4.8 0.082151 98 20:12 260:8 246:6 231:2 14 0.244597 – 20:39 �77:7 242:4 �40:4 6.0 0.6120010 963 20:35 237:0 �17:5 �32:3 5.4 0.4334721 1747 20:10 236:8 244:1 �20:6 7.2 0.3143587 2251 20:08 220:1 �15:0 29:0 12 0.0444120 2274 �0:06 �53:3 �8:1 212:3 6.0 0.1153705 2667 20:05 252:6 272:5 220:1 14 0.1567458 – 20:21 �60:9 26:0 �10:8 13 0.2078643 – 20:06 260:3 231:4 240:4 6.6 0.4088218 3992 20:20 253:3 249:3 223.8 14 0.1294444 – 20:65 261:2 226:2 227:6 15 0.21106116 – �0:15 2115:7 22:9 �28:4 6.4 0.54178428 7260 �0:10 �28:6 23:0 218:6 12 0.16216435 8700 �0:15 227:5 221:7 210:5 5.0 0.05

E93 extrasolar planets:9826 458 �0:09 �28:6 222:2 214:3 2.7 0.0895128 4277 �0:01 224:7 22:4 �1:9 6.3 0.07143761 5968 20:26 �54:5 235:6 �21:1 12.3 0.29217014 8729 �0:19 215:2 227:9 �14:5 6.0 0.19114762 – 20:68 282:7 269:6 �58:0 14 0.90

G97, G98, GV98, GWS99 extrasolar planets:75732 3522 �0:45 236:6 217.9 28:5 5 0.02117176 5072 20:03 �13:2 251:8 24:0 8 0.04120136 5185 �0:34 233:5 218:9 26:7 1 0.00145675 – �0:50 �25:9 26:9 210:1 6 0.04186427 7504 �0:06 �17:7 229:7 21:7 9 0.06187123 – �0:16 �2:4 215:9 243:5 5.5 0.45210277 – �0:24 �3:5 250:8 25:4 8.5 0.00

a The sign of the U velocity component employed here is opposite that of E93. Positive U isdirected towards the Galactic Centre. These velocities are relative to the Sun.b The age estimates for HD 114762 and HD 145675 are from G98 and GV98, respectively. Theage estimate for HR 8729 is from Ng & Bertelli (1998) corrected using the [Fe/H] estimate fromG98. The age estimate for HD 75732 is based on Ca ii observations.

Are stars with planets anomalous? 449

age estimates are a substantial improvement over those of E93 as aresult of the use of more accurate parallaxes and updated opacitytables for the stellar isochrones.

The space velocities have been calculated using the equations ofJohnson & Soderblom (1987). The radial velocity estimates arefrom the Simbad data base (most are listed in Duflot et al. 1995).

Two velocities are from Marcy (private communication): HD187123, 217:5 km s21 and HD 210277, 220:9 km s21. Hisestimate for HD 187123 is the only one available, and weaveraged his estimate for HD 210277 with the Simbad value. Forthe other stars with no available published radial velocities, wederived them from the distances and space velocities given by

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Figure 1. (a) A plot of [Fe/H] against age for nearby stars. The dots are data from E93; the plus signs are the data from F97; the filled triangles are extrasolarplanet parent stars from G97, G98, GV98, GWS99 and not in E93; the empty triangles are extrasolar planet parent stars from E93; the empty circle is for theSun. The age estimates are based on Hipparcos parallaxes and the evolutionary tracks of Bertelli et al. (1994). (b) A plot of the average [Fe/H] against age forthe five age groups defined in the text from the primary sample. The averages for each group have been calculated using jW �W(j as the weight for eachstar; the error of the mean (m.e.) is shown for each age group. The dotted line is the least-squares fit to the five data points (equation 1).

450 G. Gonzalez

E93, who do not quote the radial velocity values for their stars.The proper motions are from the Hipparcos catalogue. Theadopted solar motion relative to the LSR is �U(; V(; W(� ��10; 6; 6� km s21:

The number of stars in our final subsamples from E93 and F97are 159 and 15, respectively, which are treated together as one dataset in the following analysis. It will be referred to as the primarysample. We list the basic data on the F97 and extrasolar planetparent star samples in Table 1, and plot the individual [Fe/H]values against age in Fig. 1(a). At the present time this is the best(with accurate metallicities and ages) nearby star sample that canbe assembled with fairly uniform selection criteria. While the E93subsample is biased in favour of metal-poor stars, the inclusion ofstars from F97 should mitigate this bias somewhat.

3 A P P LY I N G T H E D I F F U S I O N M O D E L

3.1 The primary sample

The primary sample data have been binned into five age groups asfollows (all ages are in Gyr):

(i) age , 3; N � 52;(ii) 3 # age , 6; N � 48;(iii) 6 < age , 9; N � 37;(iv) 9 < age , 12; N � 10;(v) 12 < age; N � 27;

where the number of stars in each bin is also indicated. The widthof each group was chosen to be slightly larger than 2s in age for a

typical star. They were also chosen to give similar numbers ofstars in each group. The recent reduction of the ages of globularclusters by about 20 per cent (Reid 1997) should have little effecton the analysis. In particular, stars comparable in age to the Sun oryounger should have reliable age estimates.

The kinematic orbit diffusion model was applied to the originalE93 sample by W96 in an attempt to explain the apparentlyanomalous metallicity of the Sun compared to nearby stars ofsimilar age and the present interstellar medium. We will repeatmost of W96’s analysis here with our primary sample.

We first determine the age–metallicity relation from theprimary sample. Following W96 the mean [Fe/H] value for eachgroup is calculated by weighting the individual [Fe/H] values byjW �W(j. This weighting scheme effectively gives a representa-tion of stars around the Sun in a cylinder with the long axisperpendicular to the Galactic plane. A least-squares fit through theweighted data yields the following relation:

�Fe=H� � �20:01 ^ 0:05�2 �0:035 ^ 0:005�t �1�

where t is the age in Gyr. We show the data points and least-squares fit in Fig. 1(b). W96 obtained �0:05 and 20:048 from theoriginal E93 sample for the intercept and slope, respectively.

The other key relation is that between [Fe/H] and the meanGalactocentric distance, Rm. We can derive this relation from ourprimary sample by excluding old stars, so that the change in [Fe/H]resulting from Galactic chemical evolution is negligible. Restrictingthe analysis to ages < 2 Gyr, we are left with 26 stars. Theindividual values of Rm were calculated from the V space velocity

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Figure 2. The [Fe/H] values for stars from the primary sample with ages less than or equal to 2 Gyr are shown. The dotted line is a least-squares fit to the data.Also shown as a triangle symbol is HR 5185, the youngest star in the extrasolar planet samples (it was not included in the least-squares fit). An error bar in[Fe/H] for the typical star in the figure is shown on the lower left.


component using equation (A2) of W96:

Rm � R0 � V=�22B� �2�

where V is relative to the LSR (unlike the velocities in Table 1,which are relative to the Sun), B is Oort’s constant and R0 is thepresent Galactocentric distance of the Sun (we adopt the samevalues as W96, B � 210 km s21 kpc21 and R0 � 8:5 kpc). The

resulting least-squares fit to these 26 stars is:

�Fe=H� � �20:02 ^ 0:02�2 �0:12 ^ 0:03��Rm 2 R0�: �3�We show the data in Fig. 2 along with the fit. The rms scatter ofthe data about the least-squares fit is 0.09 dex. Clearly, extra-polating this relation beyond the range of the data �7:5 , Rm ,9:5 kpc� is not justified – the predicted value of [Fe/H] at theGalactic Centre is 1.0!

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Figure 3. (a) The total velocity dispersion plotted against age for each of the five age groups in the primary sample. The dotted line is the least-squares fitusing equation (6). (b) The dispersion in [Fe/H] plotted against the dispersion in Galactocentric distance, calculated from equation (5). The dotted line is theleast-squares fit to the data using equation (4) with the initial dispersion in [Fe/H] set to zero. The dashed line is a least-squares fit with the initial dispersionset to 0.10 dex.

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However, the gradient given by equation (3) is not quite whatwe want. We really want the metallicity gradient with respect tothe initial Galactocentric distance, Ri. W96 noted that a nearbystar sample will be biased in favour of stars with their presentvalues of Rm very near R0. So, if a star has Ri , R0, it will be morelikely to be included in the sample if its present value of Rm islarger than Ri. To obtain a gradient appropriate for Ri, W96prescribe that we multiply the apparent gradient by 0.4. Doing so,the apparent gradient from equation (3) becomes a true gradient,a , of 20:05 ^ 0:01 dex kpc21.

To compare the gradient of the young stars from the primarysample to recent estimates using zero-age objects (H ii regions andB stars), we need to determine the value of [O/Fe] for young starsnear the Sun. Six young stars from E93 with [O/H] and [Fe/H]estimates have Rm values near 8.5 kpc. The mean value of [O/Fe]for these stars is 20:1 ^ 0:02 (m.e.). Neglecting a possiblegradient in [O/Fe], we can convert the [O/H] values of the zero-age objects to [Fe/H]. The radial metallicity gradients from thevarious types of objects in the Milky Way will be compared inSection 4.1. It is sufficient to note for the present discussion thatthere is consensus that the radial metallicity gradient in the MilkyWay is 20:07 dex kpc21 (Gummersbach et al. 1998). This isconsistent with our determination from the young nearby starsample.

We can also derive an estimate of the metallicity gradientwithin the framework of the orbital diffusion hypothesis. Themethod is based on the assumption that the dispersion in [Fe/H] ata given age is proportional to the dispersion in R, or (repeatingequation 10 from W96 with the addition of the initial dispersion in[Fe/H]):

s�Fe=H��t� � �s2�Fe=H�0 � jaj

2k�DR�2�t�l�1=2; �4�where |a | is the absolute value of the true metallicity gradient, t isthe age, and the parameter k(DR)2(t )l is given by:

k�DR�2�t�l � 12 �1=k2 � 3=�2B�2�Dt; �5�

where D is the true diffusion coefficient and k is the epicyclicfrequency. We adopt the same value for k as W96(32.1 km s21 kpc21). The relation between D and the empiricaldiffusion coefficient, Cy , is D � Cy=2:95. We can determine thevalue of Cy from the primary sample by plotting the total velocitydispersion, sy , for each age group against age and fitting thefollowing equation to the data:

sy � �s2y;0 � Cyt�1=2; �6�

where sy ,0 is the initial velocity dispersion. The sy values werecalculated using the equations given by Wielen (1977). We presentthe data in Fig. 3(a) along with the least-squares fit from equation(6). The resulting values of the two constants are sy;0 � 12 ^

31 km s21 and Cy � 522 ^ 151 km2 s22 Gyr21. This correspondsto D � 1:8�^0:5� � 1027 km2 s22 yr21, which is only 10 per centsmaller than the estimate of Wielen (1977). Our estimate for theinitial velocity dispersion, while not well constrained, is inagreement with the velocity dispersion of Classical Cepheids(Wielen 1977).

Applying this value of D to equation (5), we have produced aplot of s [Fe/H] versus sDR (Fig. 3b). The values of s [Fe/H] havebeen weighted in the same manner as in Fig. 1(b). The least-squares fit with equation (4) [not including age group (v)] resultsin jaj � 0:098 ^ 0:016 dex kpc21 with s [Fe/H]0

set to zero. Whens [Fe/H]0

is set to 0.10 dex, the least-squares solution yields

jaj � 0:085 ^ 0:015 dex kpc21. While the initial dispersion in[Fe/H] is not well constrained with this technique, the range ofallowed values is consistent with dispersion in the residualsrelative to the least-squares fit in Fig. 2. The results shown in Fig. 3will be discussed further in Section 4.2.

In summary, the orbital diffusion model is able to account forthe full spread in [Fe/H] among the stars in the primary sample.The absolute value of the metallicity gradient is only slightlygreater than that derived from zero-age objects.

3.2 Stars-with-planets sample

We can use the results of the previous section to determine ifplanet-bearing stars are anomalous with respect to the diffusionmodel. We will assume in the following discussion that theappropriate value of the present true metallicity gradient to use is20:07 dex kpc21 (see Section 3.1). Therefore, we adopt thefollowing relation:

�Fe=H�ISM � 20:01 2 0:175�Rm 2 R0�2 0:035t �7�which is a combination of equation (1) and the radial gradientestimate from zero-age objects, converted to an apparent gradient�� 20:07=0:4 � 20:175�. In order to determine how well eachstar fits the diffusion model, we have calculated the differencebetween the observed value of [Fe/H] and value calculated withequation (7) from its present Rm value and t (Fig. 4a). We alsopresent the data in a different way: the measured value of [Fe/H] isequated to the right-hand side of equation (7) and the originalvalue of Rm is calculated and subtracted from the present value(Fig. 4b). Therefore, D[Fe/H] is a measure of the deviation of themetallicity of a star from that of the interstellar medium (ISM) atthe time and place of its birth, assuming no change in Rm.Contrariwise, DRm is the radial distance a star would have tomigrate from its birth place to be consistent with its measuredmetallicity.

As can be seen in both panels of Fig. 4, only one of the planet-bearing stars has large negative D values. The three planet-bearingstars with negative D values, in decreasing order, are r CrB, 70 Virand HD 114762. Two stars, r1 Cnc and 14 Her, have large positivedeviations. Also evident in Fig. 4 is the very small peculiarvelocity of the Sun and its positive D values. This point will beaddressed in Section 4.3.

4 D I S C U S S I O N

4.1 The Galactic radial metallicity gradient

While not the primary goal of this study, the determination of theGalactic radial metallicity gradient for F and G dwarfs is anecessary step in the study of the chemical-dynamical propertiesof the parent stars of extrasolar planets. Gummersbach et al.(1998) give a brief review of recent estimates of the radialmetallicity gradient of the Milky Way. They range from 0 to20:11 dex kpc21, with the most common value being20:07 dex kpc21. Recent studies have derived the Galactic radialmetallicity gradient from H ii regions, B stars and open clusters.None of these types of objects is expected to display the effects oforbital diffusion – the H ii regions and B stars are too young, andopen clusters are too massive (Carraro & Chiosi 1994). Afflerbachet al. (1997) derived an O gradient of 20:064 ^ 0:009 dex kpc21

from 34 compact H ii regions. They estimate an intrinsic scatter ofO at a given value of Rm of s � 0:16 dex. Gummersbach et al.

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(1998) and Smartt & Rolleston (1997) derive O abundancegradients from B stars of 20:07 ^ 0:01 and 20:07 ^

0:02 dex kpc21; respectively (Fig. 5a). Carraro, Ng & Portinari(1998), using a sample of 18 open clusters with ages less than2 Gyr, derived a gradient of 20:07 ^ 0:02 dex kpc21; the rmsscatter about the linear metallicity–distance relation is 0.17 dex.Hence, all three types of objects give almost exactly the samegradient for either [Fe/H] or [O/H].

However, there are some significant differences among thesevarious relations. First, the zero-point of Smartt & Rolleston’s(1997) B star [O/H]–Rm fit is larger than that of the H ii region fitby 0.25 dex. Is this difference caused by a systematic error ineither the B star or the H ii region abundance analyses? The Orionnebula is the best-studied H ii region in the Milky Way. Recentstudies of the nebular emission lines and the associated B starshave resulted in a consistent picture. The carbon, nitrogen, oxygen

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Figure 4. (a) The difference between the measured value of [Fe/H] and the [Fe/H] value of the ISM as inferred from equation (7) and the age and Rm of eachstar. (b) The difference between the present value of Rm and the original one inferred from equation (7) using [Fe/H] and age for each star. The data areplotted against the velocity relative to the local standard of rest (y lsr).

454 G. Gonzalez

(CNO) gas� dust phase abundances in Orion determined byEsteban et al. (1998) are in very good agreement with the B starCNO abundances determined by Cunha & Lambert (1994).Esteban et al.’s gas� dust phase CNO abundances are about0.15 dex less than in the Sun, confirming previous studies. Theirabundance analysis is based on recombination line analysis, whichshould be less dependent on temperature variations in the nebulathan the more often used forbidden lines. This important resultgives us confidence that (1) modern methods used to derive O

abundances in H ii regions and B stars give consistent answers towithin about 0.1 dex, and (2) gas phase abundances can beproperly corrected for dust condensation. Interestingly, the B starFe abundances in the Orion nebula are solar. Being a zero-ageobject near the Sun, the Orion B star Fe abundance is, therefore,consistent with the prediction of our equation (7). The differencebetween the B star and H ii region zero-points in Fig. 5(a) mightinstead be the result of differences in the B star abundance ana-lysis methods of Smartt & Rolleston (1997) versus Gummersbach

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Figure 5. (a) The [O/H] values as a function of Rm for H ii regions (plus signs; data from Afflerbach et al. 1997) and B stars (empty squares; data from Smartt& Rolleston 1997) and the corresponding least-squares fits (solid line and dashed line, respectively). (b) The least-squares fits from (a) have been converted to[Fe/H] and replotted. The open cluster data (Carraro et al. 1998) are shown as empty circles. The least-squares fit from Fig. 2 is indicated with a dotted line,and the corrected gradient is shown with a short-dashed line.


et al. (1998) (the latter obtain an O abundance zero-point 0.2 dexless than the former), in particular, their different treatmentsof non-local thermodynamic equilibrium (NLTE) corrections(Gummersbach et al.’s study is probably more self-consistent). Ifwe take the Gummersbach et al. study as the more accurate oneand allow for a dust-correction offset to H ii region O abundancesnear 0.1 dex, then the differences between the H ii regions and Bstars can be accounted for.

The radial metallicity gradients of several other galaxies havebeen determined recently from studies of H ii regions (Garnettet al. 1997; van Zee et al. 1998) and even B stars (Monteverdeet al. 1997). The observed range of the oxygen abundance gradientfor non-barred spirals similar to the Milky Way is 20:04to 20:07 dex kpc21. Late-type spirals have gradients near20:15 dex kpc21:

4.2 The diffusion model

Our results are similar to those of W96 regarding the applicationof the diffusion model to nearby stars. The largest discrepancy inFigs 3(a) and (b) between theory and the observations is the datapoint corresponding to age group (v). This might be caused bycontamination of the group (v) stars by halo stars. Halo starsdisplay a large velocity dispersion and a relatively small spread in[Fe/H].

We offer a couple of suggestions concerning small deviations ofthe observations from the diffusion model. First, the presence ofthe Sun at or near the corotation radius, Rc (see next section for amore detailed discussion), could be relevant. The frequency ofspiral arm passages is greatly reduced near Rc, likely resulting in asubstantial modification of the star formation efficiency and otherGalactic parameters related to chemical evolution compared toregions outside the zone centred at Rc.

Secondly, the presence of a bar may alter some parameters. Acouple of barred spirals (NGC 1365 and 3359; Roy & Walsh1997) have been found to possess a break in the radial metallicitygradient with a steep gradient in the barred region and a flatgradient farther out in the disc. Martinet & Friedli (1997) arguethat a double gradient is present in a strong, young bar buteventually approached a single slope. So, while a bar can yield alocally different gradient, zero-age objects in the Milky Way showno evidence of a double gradient. However, the formation of atemporary bar in the past would have resulted in enhanced radialmixing for a short time.

There is independent empirical evidence that conditions in thedisc of the Milky Way at the location of the Sun are not typical.Olling & Merrifield (1998) show that the gradient of the H columndensity at the location of the Sun is quite large compared to themean (see their fig. 2). This necessarily leads to substantialdeviations of the Oort constants compared to extrapolations fromthe inner and outer disc values (see their fig. 3). Whether thesevariations in the Oort constants result from our being near Rc and/or from a Galactic bar remains to be determined.

Fuchs, Dettbarn & Wielen (1994) note that the Spitzer &Schwarzschild mechanism [involving the deflections of stellarorbits by giant molecular clouds (GMCs)] is more efficient atradial diffusion than the W96 diffusion model. This could accountfor the slightly high dispersions in [Fe/H] for the three youngestage groups in Fig. 3(b). For a brief summary of the possiblesources of the spread in [Fe/H] at a given age, the reader isreferred to Carraro et al. (1998).

4.3 Anthropic considerations

When comparing the properties of the Sun to other solar-type starswith planets, we must consider the fact that we, as observers in theSolar system, have a selection bias – the Solar system mustnecessarily possess properties which allow our existence.2 Hence,if the Sun appears anomalous in a particular property, this maysimply be an indication that it must have a value within a narrowparameter range to allow for our existence on the Earth. Forexample, the fact that the Sun ranks in the top ,10 per cent bymass among the nearest stars may be an indication that a parentstar with a mass near that of the Sun is a requirement for ourexistence. Certainly, reasonable reasons can be given why Gdwarfs should be favoured over K and M dwarfs for habitability.We should note, though, that while the WAP removes the surpriseof our discovery that we are living near one of the most massivestars in the solar neighbourhood, it does not explain why massivestars are rare to begin with. Thus, while the WAP can removesome of the apparent anomaly of a particular observation, it hasonly limited explanatory power.

The anomalously small y lsr value of the Sun may be anotherexample of an observer selection bias. Shown in Fig. 6 is the y lsr

value of the Sun along with those of all the other stars studied inthe present work.3 The general trend of increasing y lsr with age isevident, as is the very small solar y lsr. Only one star in the figurehas a significantly smaller value of y lsr. The anomalously smally lsr value of the Sun can also be seen in Gaidos’ (1998) discussionof the kinematics of solar analogues. The position of the Sun onthe V–U and V–W diagrams is much more consistent with theyoung solar analogues (age less than , 1 Gyr) than it is with theold solar analogues (see Gaidos’ fig. 11, but note that he adopts asolar y lsr value of 16:2 km s21 from an old study).

To first order, y lsr can be decomposed into two parametersdescribing the orbit of a star in the Milky Way: the pseudo-eccentricity, e, and the maximum height reached relative to themid-plane, Zmax. Hence, a small value of y lsr necessarily requiressmall values of both e and Zmax. Since these two parametersdescribe orthogonal components of a star’s motion in the plane ofthe Milky Way, it is possible that they relate to habitability indifferent ways. For this reason, below we will discuss mechanismsthat affect habitability via their relation to e and Zmax. There aretwo broad groups of astrophysical phenomena that may relate to theanomalously small value of y lsr of the Sun via their effects onhabitability: radiation damage to the ozone layer from extraterrestrialradiation sources and comet impacts. We will discuss each in turn.

Ruderman (1974) was the first to estimate the effects ofradiation (both high-energy ionizing photons and cosmic rays)from supernova (SN) explosions on the Earth’s biosphere. Heconcluded that the primary effect of such an event on thebiosphere is damage to the ozone layer via NOx production. Morerecent calculations have concentrated on the effects of cosmic raysin a supernova remnant (SNR) bubble with the Sun located insideit. Whitten et al. (1976) applied a more refined atmospheric modelto the problem, and found that ozone reductions of 20 to 50

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2 This statement is called the weak anthropic principle (WAP). A moreformal definition can be found in Barrow & Tipler (1986).3 The value of y lsr of the Sun adopted here is 13.1 km s21. This is slightlysmaller than, but consistent with, the mean of the recent Hipparcos-derivedvalues of 14:1 ^ 1:4 km s21 (Kovalevsky 1998), 13.4^0.8 km s21 (Dehnen& Binney 1998) and 12:9 ^ 1:1 km s21 (Bienayme 1999).

456 G. Gonzalez

per cent lasting about 104 yr would result from cosmic rays from aSN 5 to 10 pc from the Sun. Reid, McAfee & Crutzen (1978),employing yet another treatment of the atmosphere, derived totalozone depletions of 64 to 89 per cent for the same SN distances;they also noted that the production of NO2 by the ionizingradiation would lead to a several per cent increase of absorption ofblue to green solar radiation, thus further reducing photosynthesis.

Estimates of the probability of a SN occurring within 5 to 10 pcfrom the Sun vary. The calculation is complicated by the fact thatType II SNe concentrate in the spiral arms. Clark, McCrea &Stephenson (1977) estimated that the interval between Type IISNe within 10 pc is about equal to the interval between spiral armcrossings, which they claimed to be about 108 yr (they assumed aGalactic mean interval between Type II SNe of 100 yr). However,Tammann, Loffler & Schroder (1994) have estimated a GalacticType II SN interval of about 50 yr (with a total SN interval of40 ^ 10 yr), which results in a halving of Clark et al. nearbyType II SN interval. Whitten et al. (1976), neglecting theconcentration of SNe within spiral arms, but taking into accountClark & Caswell’s (1976) observations that SNRs at the solarcircle have a volume density about a quarter as great as in theinner regions of the Milky Way, estimated a nearby SN intervalnear 1010 yr (they assumed a Galactic total SN interval of 50 yr).

These estimates of the threat from SNe can be improved with theinclusion of additional details, such as the distribution of SNR sizesat a given age and the theoretical evolution of the SNe rate. Even ifthe threat from ‘killer SNe’ (see van den Bergh 1994) is found to benegligible, less lethal SNe resulting in relatively short-term, moderatereductions in ozone may still satisfy the WAP requirements. This is

so, because the WAP applies to humans (and related advancedlife), which are much more sensitive to environmental catastrophe.

Relating all this to the Galactic orbit of the Sun, we note thatincreasing its eccentricity in the plane, e, while maintaining aconstant Galactocentric distance, will lead to a reduction inperigalactic distance. With e � 0:11 and R0 � 7:1 kpc,4 the Sun’sperigalactic distance is about 6.3 kpc. According to fig. 8 of Clark& Caswell (1976) (and rescaling it from R0 � 10 to 7.1 kpc), thesurface number density of SNRs in the Galactic plane jumpsabruptly by over a factor of 4 for R & 5:7 kpc, which correspondsto e . 0:20. A larger value of Rm with a perigalactic distanceequal to the Sun’s present value of R would also avoid the SNthreat. However, a larger Rm combined with the negative Galacticmetallicity gradient would have resulted in a smaller initialendowment of metals for the Solar system. This, in turn, wouldlikely reduce the probability of planet formation in the Solarsystem (see G97; G98).

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Figure 6. The total space velocity relative to the LSR, y lsr, is plotted against age for the primary and extrasolar planet samples.

4 Although we adopt R0 � 8:5 kpc in our calculations, recent studiesappear to be converging on a value between 7 and 7.5 kpc. Reid (1993)obtains R0 � 7:2 ^ 0:7 kpc from H2O masers, Olling & Merrifield (1998),who take into account the radial surface density distribution of the ISM,obtain R0 � 7:1 ^ 0:4 kpc, Dambis, Mel’nik & Rastorguev (1995) obtainR0 � 7:1 ^ 0:5 kpc from Classical Cepheids, and Metzger, Caldwell &Schechter (1998) obtain R0 � 7:7 ^ 0:3 kpc also from Classical Cepheids,but with the inclusion of a weak ellipticity in the disc orbits. A smallerMilky Way leads to an increase in the estimated surface number density ofSNRs in the disc.


Although it is still somewhat controversial, the precise locationof the Sun relative to the corotation circle might be an importantGalactic-scale constraint on habitability (Marochnik 1983).Amaral & Lepine (1997), using mostly open cluster data, deriveDRc�; R0 2 Rc� � 1:1 kpc. Using Classical Cepheid radial velo-cities and distances, Mishurov et al. (1997) calculated DRc �0:3 ^ 1:3 kpc: More recently, Mishurov & Zenina (1999) haverepeated the analysis with Hipparcos proper motion data added;they now derive DRc � 0:1�0:3

20:03 kpc (note, a more appropriatemeasure is Rm;( 2 Rc, which is about 0.4 kpc). In an axisymmetricmodel, a star located precisely at Rc with e � 0 orbits at the sameangular speed as the spiral arm pattern. Hence, such a star wouldnever cross a spiral arm after its birth. The farther a star is locatedfrom the corotation circle, the more frequently it crosses the spiralarms. Hence, the Type II SNe threat is minimized for low-e orbitsat Rc. The presence of the Sun very near the corotation circle alsopresents us with a possible explanation for its very small y lsr.According to Jenkins (1992) most of the heating of disc stars isaccomplished via spiral wave passages and scattering by GMCs.Both types of perturbations will be less common for stars withnearly circular orbits located near the corotation circle.

While SNe probably pose the greatest threat on a Galactic scale,there is another potential danger: active galactic nucleus AGNoutbursts. Clarke (1981) briefly discusses the possible threat froma Seyfert-type outburst in the Milky Way. He argues, assuming thecosmic rays from the outburst are evenly distributed in the disc ofthe Galaxy, that such an event would increase background cosmicrays to levels comparable to that of a nearby SN; the X-ray fluxwould not pose a threat at our present distance from the GalacticCentre. More likely, there would exist a radial gradient in thecosmic ray number density, resulting in a greater radiation threatinside the solar circle.

Schwartz & James (1984) noted that the protection offeredagainst soft X-rays by neutral hydrogen in the plane of the Galaxyis a strong function of the height of the Sun above the plane. Theycited three sources of radiation as possibly relevant to habitabilitywith respect to interstellar matter: SNRs, the diffuse X-raybackground, and the Galactic Centre. However, none of thesesources are likely to have a significant impact on the ozone layeras the Sun oscillates relative to the plane for two reasons. First, thespectral indices of SNRs and the diffuse X-ray background are tooshallow; the flux of X-rays above 2 keV, where interstellarextinction is negligible, dominates the total high-energy outputfrom these sources. Hence, reducing the amount of interstellarextinction towards a hard X-ray source has little effect on the totalflux of ionizing radiation received at the top of the Earth’satmosphere. Interstellar extinction does have a large effect on thereceived flux from a so-called super-soft X-ray source, for whichthe energy spectrum peaks near 0.1 keV. However, the brightestsuch sources typically have LX < 1038 erg s21, and they arerelatively rare in the Milky Way. Secondly, the soft X-rayluminosity from AGN outbursts and nuclear starburst is not goingto have a significant effect at our current distance from thenucleus. Orbits within a few kpc of the nucleus are at greater riskbecause of the closer proximity to the ionizing radiation and thesmaller protection offered by the neutral hydrogen (the scaleheightof neutral hydrogen is much smaller in the inner disc).

The second category of possible threats to life on Earth includestemporary increases in the Oort comet impact rate resulting fromperturbations from sources outside the Solar system. The primaryperturber is considered to be the Galactic radial and z tides(Heisler & Tremaine 1986; Matese et al. 1995; Matese &

Whitmire 1996); impulses from GMCs, and nearby stellarencounters are secondary in importance at our location in theGalaxy. Excursions to smaller Rm would increase the probabilityof nearby stellar and GMC encounters as well as increase theradial Galactic tide. If Matese et al. are correct in predicting thatthe z Galactic tide dominates and that we are in for a cometshower in ,1 Myr, then this may be an example of an observerselection effect in the temporal domain, in that the biosphere hasbeen relatively free of large impacts for a prolonged period (thelast large impacts on Earth occurred about 35 Ma), hence settingthe stage for our appearance. This selection effect would alsoexplain the apparent spatial domain coincidence of the very smallheight of the Sun above the Galactic plane (about 10 to 12 pc;Reed 1997), since comet showers are predicted to occur shortlyafter a plane crossing.5

Fuchs & Wielen (1987), using the original and present temporalboundary conditions on the kinematic parameters of the Sun, havecalculated the most probable history of the solar peculiar velocitywithin the framework of the diffusion model. They find that, sinceits birth, the Sun has likely maintained larger y lsr than the presentvalue; only within the last Gyr has it come within a factor of 2 ofits present value (see their fig. 14). If true, then spiral armcrossings and large perturbations to the Oort comet cloud werelikely more common prior to 0.5–1 Ga. This tends to confirm theWAP, since it is during this same time interval that advanced lifefirst appeared on the land. Note that the WAP does not remove thesurprise that any old star has a small y lsr, but rather that we shouldbe orbiting one. But the calculations of Fuchs & Wielen (1987)assume that the dynamical history of the Sun is not ‘special’ inany way. Perhaps the Sun experienced an atypical dynamicalhistory that allowed life to flourish. So, for instance, if the Sun’sproximity to Rc reduces the probability of dynamical heating of itsorbit, then the low y lsr of the Sun could be long-lived.Unfortunately, with only the present kinematic parameters to goby, we can only speak in terms of the probable dynamical historyof the Sun, not the actual one.

The anomalously small solar y lsr value was noted also by W96.They offered a link between habitability and Galactic kinematics;they suggested that the predicted birthplace of the Sun, accordingto the diffusion model, at a smaller Rm would have presentedgreater threats from nearby SNe and molecular cloud passages.This implies that a certain amount of migration in the Galacticdisc was required before we could exist.

In summary, there are some plausible reasons related to theWAP for removal of the Sun from the list of apparently anomalousstars. Which threat to habitability dominates is not clear, but goodarguments can be given for both SNe and comets.

5 C O N C L U S I O N S

Stars with planets are indeed anomalous with regard to theirmetallicities; 14 Her, r1 Cnc and t Boo are especially anomalousrelative to nearby stars. The diffusion model is not able to accountfor their high metallicities. The Sun, while only moderately metal-rich relative to nearby stars of similar age, has an unusually smallpeculiar velocity. The anomalous label can be removed from thesolar kinematics if it can be shown that a nearly circular orbit in

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5 This is a remarkable coincidence given that the Sun spends most of itstime near the apex of its z oscillation. The plane crossing occurred about1.5 Ma.

458 G. Gonzalez

the plane of the Milky Way is essential for our existence. We haveoffered some reasons to believe that indeed such an orbit offersgreater protection than the typical one. Certainly, we encourageothers to repeat our analysis with a larger nearby star sample,when additional high-quality data become available, and a morerealistic model of Galactic kinematics (i.e., barred models andvariable Oort constants).

AC K N OW L E D G M E N T S

We thank Scott Anderson, Derek Richardson and GeorgeWallerstein for helpful comments and discussions. The referee,Burkhard Fuchs, is gratefully acknowledged for valuable adviceon the diffusion model. We are also thankful to Geoff Marcy forproviding radial velocity estimates for two planet-bearing stars.This research has made use of the Simbad data base, operated atCDS, Strasbourg, France. The research was supported in part bythe Kennilworth Fund of the New York Community Trust.

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Are stars with planets anomalous?

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