Metallicities of Stars with Extrasolar Planets

Scientific Frontiers in Research on Extrasolar Planets ASP Conference Series, Vol. 294, 2003 D. Deming and S. Seager, eds.

Metallicities of Stars with Extrasolar Planets Debra A. Fischer University of California, Berkeley, Dept. of Astronomy, Berkeley, CA 94720 Jeff A. Valenti Space Telescope Science Institute, 3700 San Martin Dr., Baltimore, MD 21218 Abstract. We are carrying out spectral synthesis modeling for one thousand stars on the Lick, Keck and AAT planet search projects. Our analysis of the first five hundred stars confirms the metal-rich nature of stars with detected extrasolar planets. Of particular interest is the underlying mechanism for this metallicity correlation. We cannot identify any attributes of our data that provide evidence for enrichment of the convective zone by accretion as the primary source for the observed metallicity correlation. Specifically, we do not see a functional dependence of metallicity on convective zone depth in main sequence stars or the expected decrease in metallicity among planet-bearing subgiants with diluted convective zones.

1.

Introduction

In the past seven years, about 100 extrasolar planets have been discovered by Doppler surveys (for updates see http://exoplanets.org). The Doppler detection of an extrasolar planet requires velocity measurements over one full orbital period. A natural consequence of this requirement is that there is a gradual harvesting of planets from the closest to the widest orbital separations. Nearly all of the planets detected before 1999 reside in orbits with semi-major axes less than 1 AU. Except for planets closer than 0.05 AU (where tidal circularization is important), most of these close-in planets have moderately eccentric orbits. Because gas giant planets are expected to form outside of a 3 AU radius (where condensation of ice grains can occur and where there is more disk mass), the discovery of Jovian mass planets in eccentric orbits closer than 1 AU prompted a cascade of theories on orbital migration, planetplanet dynamical interactions and planetdisk tidal interactions (Goldreich & Tremaine 1980; Lin, Bodenheimer & Richardson 1996; Rasio & Ford 1996; Weidenschilling and Marzari 1996; Levison et al. 1998; Bryden et al. 1999; Murray & Holman 2001; Chiang et al. 2002; Malhotra 2002; Ford et al. 2003). Implicit in the concept of orbital migration is the expectation that not all migrating planets and planetesimals will park in stable orbits; some gas-depleted material will fall into the star and mix in the convective zone, possibly enriching the abundance of refrac117

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tory elements. Even in our own solar system, with a presumably gentler early dynamical history, the fossil record of a cratered surface on Mercury supports this concept of late stage accretion. In parallel with the discovery of the first few extrasolar planets and with the emerging theories of orbital migration, observations of super-solar metallicity in planet-bearing stars garnered immediate interest (Gonzalez 1997; Lin 1997; Laughlin & Adams 1997). The metallicity correlation for planet-bearing stars has persisted and it has become the subject of increasing debate (Laughlin 2000; Pinsonneault et al. 2001; Butler et al. 2000; Santos et al. 2000; Murray & Chaboyer 2002; Gonzalez and Laws 2003). At issue is the question of whether the metallicity correlation is primarily an initial condition, or a by-product of the accretion of gas-depleted material.

2.

Initial Conditions vs. Accretion

In support of the view that metallicity is an initial condition, high metallicity in a protoplanetary disk provides more raw materials: the grains that begin the process of planetesimal formation. Higher metallicity may also enhance cooling in the disk and hence condensation of gas which may facilitate grain formation and growth. The first generations of stars in our galaxy could not have developed planetary systems like our own because they lacked these planet building blocks. So, it seems clear that some threshold metallicity is required for planet formation, but it is not at all clear what that threshold might be. To test the importance of initial high metallicity, Gilliland et al. (2000) used HST to search for transits in the relatively metal-poor cluster, 47 Tuc ([Fe/H]= 0.7). If the stars in this cluster had hosted 51 Peg-like systems similar to those found orbiting main sequence field stars, then the 47 Tuc survey should have detected as many as 17 transits. However, no transits were observed in the sample of 34,000 stars. The explanation for this result remains somewhat ambiguous because the crowded stellar environment in 47 Tuc is so different from that of field stars on Doppler planet search projects. Perhaps there were more planet-destabilizing dynamical interactions in the cluster environment. Or perhaps photoionization of protostellar disks by rapidly evolving cluster stars retarded the formation of giant planets in 47 Tuc. If accretion is the dominant mechanism underlying the metallicity correlation then it seems reasonable to expect that there might be some fossil evidence. For example, the incremental increase in [Fe/H] abundance should sensitively depend on the mass of the convective zone, or equivalently, on the spectral type of the star. Under the assumption that gas-depleted material mixes in the convective zone, the late F-type stars with thin convective envelopes should show a higher [Fe/H] abundance than the G or Ktype stars (Pinsonneault et al. 2001). In addition to a higher [Fe/H] abundance, individual elemental abundances may be skewed. In particular, if volatile elements are expelled from the protoplanetary disk before significant accretion takes place, then the accreted disk material would be preferentially enriched in refractory elements. So, a high abundance ratio of refractory-to-volatile elements would be compelling evidence of accretion.

Metallicities of Stars with Extrasolar Planets 3.

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Metallicity of Planet Search Stars

One concern regarding the reality of the claimed metallicity correlation is that the abundance analysis of planet-bearing stars has been carried out by different researchers using different spectral analysis techniques than the abundance analysis of the comparison field stars. Spectroscopic analysis is dominated by systematic errors that can be difficult to assess; systematic offsets of order 0.1 dex or more are common between different researchers using different techniques. In addition, it has not been demonstrated that the comparison field stars are necessarily representative of stars on planet search projects. The ideal approach to investigating this issue is a spectroscopic analysis of the hundreds of stars already on planet search surveys using a single, selfconsistent technique. While even this analysis will still suffer from systematic errors, the relative errors will be minimized and star-to-star comparisons will be on stronger footing. We have started spectroscopic analysis of 1000 stars on the Lick, Keck and AAT planet search projects. The Doppler analysis makes use of a high quality (S/N > 300), high resolution (R ∼ 70000), template spectrum without iodine to model instrumental broadening and to derive differential radial velocities (Butler et al. 1996). These template spectra, already in hand, are ideally suited for spectroscopic analysis. 3.1.

Spectral Synthesis Modeling with SME

The spectral synthesis analysis is being carried out with SME (Spectroscopy Made Easy), updated since a description by Valenti & Piskonov (1996). Some of the improvements in SME over the past few years include improved treatment of H− opacity, improved continuum placement and interpolation over 7000 Kurucz models with every iteration. In a given iteration, a Kurucz stellar model and a spectral line list are used to drive a radiative transfer code and create a synthetic spectrum. The radiative transfer code assumes LTE and molecular lines are not currently included, so at this time, we are restricting our analysis to F, G and early Ktype stars. The spectral line list used by the radiative transfer code contains information about the line identity, ionization state, excitation potential, gf value and van der Waals broadening coefficients. Before the first model spectrum is run, the atomic line data (gf values, van der Waals broadening and collisional broadening enhancement, drawn from the Vienna Atomic Line Data Base) are adjusted to match an SME synthetic spectrum to the R ∼ 600000 National Solar Observatory (NSO) spectrum (Wallace, Hinkle & Livingston 1998) for pre-selected wavelength segments. Once astrophysical atomic line data are in hand, a Marquardt minimization scheme is employed to fit synthetic spectrum to our observed spectra. The free parameters we have chosen to model include effective temperature, v sin i , [Fe/H] and several individual element abundances, namely, Si, C, Ca, Cr, Ti, V, Mn, Ni, Li. 3.2.

Fitting the Observed Solar Spectrum

We first ran SME on an observation of Vesta to verify that the solar solution used to model gf values would be recovered. The SME solution gave: Tef f = 5767, [Fe/H]= 0.007, v sin i = 1.87 and individual element abundances (C, Si, Ca, Ti,

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V, Cr, Mn, Fe, Ni) that were within 0.03 of solar. The formal assessment of the error in our abundances is determined by the RMS of the abundances from each spectral line. However, these formal internal errors are only of order ∼ 0.001 and overstate the true precision by at least a factor of twenty as can be seen from the solution for Vesta. The observed line depths for these elements are plotted against the SME model line depths for our observation of Vesta in Figure 2. Each subpanel in Figure 2 notes the RMS scatter in the (observed - model) line depth.

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Figure 1. Two of ten wavelength segments for Vesta (observed at Keck) are plotted with a solid line. The dashed line shows the SME model. The region near 5382˚ A is poorly fit because of missing or incorrect information regarding these spectral lines. 3.3.

Controlling Errors

Based on a preliminary run of 500 stars last year, we improved the wavelength dispersion solution for our spectra, the macroturbulent and microturbulent parameterization, the instrumental resolution, and the atomic line parameters. The real power of SME is that once systematic errors have been detected and controlled, the code runs through hundreds of spectra in batch mode. Each star currently requires 4 6 hours of cpu time on an Ultra 60. With batch jobs running around the clock on several computers, we analyze about 600 spectra in one month. One of the most serious concerns in the business of spectral synthesis modeling is cross-talk in the solution for various free parameters. A forced change

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Figure 2. The observed spectral line depths are plotted against the model line depths for Vesta. The subpanels for each individual element give the RMS scatter in the (observed - model) line depth. The dots refer to spectral lines that were used to constrain the solution and crosses mark lines that were masked out of our wavelength segments.

in log g can result in a compensating change in Tef f which may in turn drive an adjustment in [Fe/H]. Or, a change in v sin i can yield the same χ2 fit if vmac is left free to adjust the line-broadening. For N free parameters with correlated errors, the best fit solution from spectral modeling is free to slide about in an N dimensional ellipsoid of nearly constant χ2 . To constrain this error ellipsoid, we have expended considerable effort to identify physically reasonable constraints that allow us to fix parameters and break degeneracies. For example, in order to resolve the competing effects of Tef f and [Fe/H], several hundred spectral lines with different ionization states and different excitation potentials are analyzed. In Figure 3 the χ2 degeneracy has been mapped out between log g and Tef f by stepping through fixed values for log g and running SME with Tef f as the only free parameter. This test shows a valley of constant, minimum χ2 from 4.4 < log g < 4.6. It also shows that Tef f is quite well determined - the error ellipsoid is narrow along the Tef f dimension. However in a more realistic test where other parameters (v sin i and elemental abundances) are also allowed to float, the error along the Tef f dimension would grow to about 50 K. The parallax measurements from Hipparcos provide excellent absolute magnitudes. Together with an assumed mass-radius relation and a derived Tef f , a physically

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Figure 3. The χ2 Degeneracy between log g and Tef f shows that these parameters cannot actually be resolved by synthesis modeling. Here, a constraint on log g was made using Hipparcos-based MV and our solution for Tef f . reasonable value for log g was identified (indicated by delineation on the grid of χ2 values in Figure 3) to restrict the χ2 degeneracy. 3.4.

Distinguishing Contributions from Line Broadening Parameters

The instrumental profile (IP), v sin i and vmac all produce Gaussian broadening in spectral lines. The IP for each spectrograph was independently determined by fitting observations of Thorium-Argon and Iodine lines. To determine vmac , we used our pre-determined soluton for the IP and fixed v sin i equal to zero. We then let vmac serve as the only free line-broadening parameter and matched synthetic models to observations for a few hundred stars. Of course, each solution for vmac now includes a contribution from v sin i . However, there is a floor in the values of vmac as a function of Tef f defined by those stars with an unmeasurable, low v sin i . The floor delineates empirical values of vmac over our range of Tef f : vmac = (-5.3 + Tef f / 650.0) With this approach, we have fixed values for the instrumental profile and fixed values for vmac (that are updated with each iteration of modeled Tef f ). Thus, we are able to leave v sin i as the only free line broadening parameter.

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Figure 4. SME-derived metallicities for 550 stars on the Lick and Keck planet search projects. The small dots indicate stars without detected planets and the filled squares indicate planet-hosting stars.

4.

SME Metallicities

With the described improvements in the code and physical parameters, we ran a recent batch job on ∼ 550 stars. The stars were simply selected in order of ascending HD number and happened to include 33 stars with known planets. We compared our values with all available published values for stars in common, compiled by Cayrel de Strobel (2001). We find an RMS scatter between the published and SME results of 80 K for Tef f and 0.08 dex for [Fe/H]. The SME metallicities are plotted as a function of Tef f in Figure 4. The bold squares represent stars with known planets and the dots represent stars without detected planets. These same data are represented in a histogram in Figure 5. Both the Wilcoxon Rank-Sum and Kolmogorov-Smirnov statistical tests yield probabilities of less than 0.05% that the metallicity distribution of these two populations is drawn from the same parent distribution. This supports previous findings that stars with Doppler-detected extrasolar planets appear to be more metal-rich than other stars. Based on our results, we note that:

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• The metallicity distribution for stars with detected planets is nested within the overall metallicity distribution of our sample stars. Stars with known planets do not have metallicities that exceed those of stars without detected planets. • The fraction of stars with planets increases with increasing metallicity. [Fe/H]< 0.0: fewer than 5% of the stars have Doppler-detected planets. [Fe/H]∼ 0.1: about 10% of the stars have extrasolar planets [Fe/H]> 0.1: about 25% (albeit, of only 40) metal-rich stars have known planets.

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5. 5.1.

Interpretation and Speculation Accretion

Enrichment by accretion implies enrichment of the convective zone only, not the entire star. If accretion is the dominant underlying mechanism for the observed metallicity correlation, then one might expect that:


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• there should be higher metallicity among stars that have experienced latestage accretion • the metallicity distribution should have a functional dependence on spectral type (i.e., the depth of the convective zone) The upper envelope of the distribution might show an upward slope with increasing Tef f or the mean metallicity of stars with planets could be higher among the Ftype stars than among the G or Ktype stars. However, neither of these trends are observed. Another accretion signature would be an observation of 6 Li in stars with planets. Since this element is destroyed before stars reach the main sequence, accretion of rocky material could result in a detectable 6 Li line. However, far from being prevalent among planet-bearing stars, a 6 Li detection has only been claimed for one star, HD 82943 (Israelian et al. 2001) and this claim has recently been disputed (Reddy et al. 2002; Gonzalez 2003). The first extrasolar planets that were discovered in close-in, eccentric orbits triggered interest in the metallicity of host stars because these stars seemed to be the most likely cases where a significant amount of late-stage accretion took place. However the metallicity trends presented here simply do not provide any evidence that accretion is the source of the observed metallicity correlation. Is lack of evidence for accretion, evidence that accretion did not take place? We concede that late-stage accretion must have taken place in stars with and without detected planets. But the lack of an accretion signature suggests that accretion may not be the dominant underlying physical mechanism for the observed metallicity correlation. 5.2.

Initial Conditions

If high metallicity is an initial condition, then that high metallicity applies to the entire star, not just the convective zone. If planet-bearing stars are metal-rich because they were born from metal-rich clouds, then true to the observations, no functional dependence on Tef f or spectral type should be observed. Another way to distinguish between metal enrichment in the convective zone only (accretion) vs. high metallicity throughout the star (an initial condition) is to examine the metallicity of subgiant stars with and without planets. High metallicity should not persist in evolving subgiants with a deeper, diluted convective zone if the metallicity was merely accreted onto the surface of the star. However if the star is metal-rich throughout, then evolution will not affect that metallicity. There are five subgiants with detected extrasolar planets: HD 38592 ([Fe/H]= +0.32), HD 177830 ([Fe/H]= 0.0), HD 10697 ([Fe/H]= +0.15), 70 Vir ([Fe/H]= 0.03), HD 16141 ([Fe/H]= +0.22). These subgiants show metallicities comparable to their planet-bearing, main-sequence counterparts. This lends important support to the interpretation of high metallicity as an initial condition. 6.

Conclusions

Our data do not reveal any of the traits that might be associated with accretion as the underlying mechanism for metallicity enhancement in planet-bearing

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stars. By default, rejection of accretion as the source of high metallicity leaves initial high metallicity as the alternative interpretation for the observed metallicity correlation. Extrasolar planetary systems detected with Doppler observations are complex. More than half of the systems appear to have additional, detectable planets and mean motion and secular resonances are important in some of these cases (GJ 876, Upsilon Andromedae, 55 Cancri, HD 82943). Our own solar system is dynamically filled with planets and in the case of Upsilon Andromedae, numerical simulations show that the inner 8 AU of this triple-planet system is dynamically full (Rivera & Lissauer 2000) there are only a few narrow windows along the semi-major axis where a low mass planet might find a gravitationally stable niche. These features suggest that planet formation in these systems did not proceed from a tenuous disk with only a few planetesimals. Rather, planet formation has been a robust and efficient process in a disk rich with raw materials. This in turn suggests that the formation efficiency of planets is sensitive to the initial metallicity of the protostellar cloud and disk. But, how or why a metal-rich disk evolves differently than a metal-poor disk is not understood in any detail. The Doppler detections suggest that stars with super-solar metallicity form planets that migrate or scatter inward. Is planet formation in these systems so efficient as to be destructive for solar systems like our own? Does low metallicity retard planet formation? How does metallicity of the protoplanetary disk affect planet formation rates, dynamical evolution of the disk, and the planet mass function? Perhaps the next few years of extrasolar planet detections, with gas giant planets in jupiterlike orbits, will help answer some of these questions. Acknowledgments. We thank Geoff Marcy, Paul Butler and Steve Vogt for the use of their Keck template spectra and for helpful discussions. We thank Greg Laughlin, Doug Lin, Norm Murray, Robert Noyes and Dimitar Sasselov for stimulating conversations. References Bryden, G., Chen, X., Lin, D. N. C., Nelson, R. P., & Papaloizou, J. C. B. 1999, ApJ, 514, 344 Butler, R. P., Marcy, G. W., Williams, E., McCarthy, C., Dosanjh, P., & Vogt, S. S. 1996, PASP, 108, 500 Butler, R. P., Vogt, S. S., Marcy, G. W., Fischer, D. A., Henry, G. W., & Apps, K. 2000, ApJ, 545, 504 Cayrel de Strobel, G., Soubiran, C., & Ralite, N. 2001, A&A, 373, 159 Chiang, E. I., Fischer, D. A., & Thommes, E. 2002, ApJ, 564, L105 Ford, E. B., Havlickova, M., Rasio, F. A., & Yu, K. 2003, Chaotic Interactions Among Multiple Planet Systems to appear in Planetary Systems and Planets in Systems, Space Sciences Series of ISSI, Vol. 19, and Space Sciences Reviews eds. Udry, S., Benz, W., & von Steiger, R. Gilliland, R. L., Brown, T. M., Guhathakurta, P., Sarajedini, A., Milone, E. F., Albrow, M. D., Baliber, N. R., Bruntt, H., Burrows, A.,


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Debra Fischer