© ESO, 2015

1. Introduction

That stars hosting a giant planet are, on average, more abundant in iron than stars in the solar neighborhood for which no planet has been detected (Santos et al. 2001, 2004; Fischer & Valenti 2005; Gonzalez 2006) is very accepted. Actually, it has been shown that this behavior is not exclusive to iron but is shared by several other metals (Bond et al. 2006; Gilli et al. 2006; Neves et al. 2009; Adibekyan et al. 2012b). Other studies also suggest that this kind of anomaly may involve not only the metal content of heavy elements but also some light elements such as carbon, nitrogen, and oxygen (Ecuvillon et al. 2004, 2006; Petigura & Marcy 2011).

Some authors have also been searching for differences in the abundance trends with metallicity for several elements in stars with and without planets. In other words, those works investigated whether the planetary formation affects the observed abundances in some way by comparing stars in the same metallicity range. Robinson et al. (2006) report that the [Si/Fe] and [Ni/Fe] abundance ratios in planet-host stars are systematically enhanced over their comparison sample of stars without planets of the same metallicity. Delgado Mena et al. (2010) derived the opposite behavior for Mg, and they find no differences regarding [C/Fe], [O/Fe], and [Si/Fe]. In any case, they state that their result for Mg disappears when only solar analogs are considered. Neves et al. (2009) also report no significant differences in [X/Fe] for 12 elements in stars with and without planets. Gonzalez & Laws (2007) derived lower [Al/Fe] and [Si/Fe] but higher [Ti/Fe] in stars with planets in the range of metal-rich stars. Brugamyer et al. (2011), on the other hand, confirm the [Si/Fe] enhancements in planet hosts, in spite of no [O/Fe] enhancements. Overabundances of several elements were also reported by Kang et al. (2011) and Adibekyan et al. (2012a), but only in the range of metal-poor stars, except for Mn. For this element, Kang et al. (2011) find an enhancement in the whole range of metallicity, a result that is not supported by Adibekyan et al. (2012a). The situation is, therefore, vast and varied, and also controversial for some elements.

In a previous paper (da Silva et al. 2011, from now on referred to as Paper I), we determined photospheric parameters and carbon abundances for a sample of 172 dwarf, subgiant, and giant stars (out of which 18 have planets) using spectra available in the ELODIE database (Moultaka et al. 2004). Our previous results did not point out, for instance, any significant difference between the carbon abundances of stars with and without planets, for the three substellar groups. However, the analyzed sample was too small to provide conclusive results, and it stimulated the inclusion of additional stars and other chemical elements.

In the current work we have 309 FGK stars (out of which 47 have detected planets) homogeneously analyzed to measure their photospheric parameters, masses, ages, and the abundances of volatile (C, N, and O) and refractory (Na, Mg, Si, Ca, Ti, V, Mn, Fe, Ni, Cu, and Ba) elements. The sample includes dwarf, subgiant, and giant stars, mostly belonging to the Galactic thin disk. We applied a set of statistical methods to the three subsamples, exploring their multivariate properties and, in particular, uncovering significant differences between dwarf stars with and without a known giant planet. In addition, we searched for relations involving the stellar parameters, the abundances, and the condensation temperature of the elements. This approach has very often been used to check whether any difference in the amount of refractory elements with respect to volatile ones has an influence on the formation of planetary systems (see, e.g., Smith et al. 2001; Meléndez et al. 2009; Ramirez et al. 2009; González Hernández et al. 2010, 2013a,b).

In Sect. 2 we describe the observations and the procedure of data reduction. In Sect. 3 we outline the methods used to derive the photospheric parameters and the chemical abundances. The determination of the evolutionary and the kinematic parameters is presented in Sect. 4. The results are presented and discussed in Sects. 5 and 6, in which we describe the statistical analysis. Finally, we present our final remarks and conclusions in Sect. 7.

2. Observation data and reduction

In this work, as a complement to our previous analysis of 172 stars published in Paper I, we have enlarged our stellar sample. Now we have 309 FGK stars from the solar neighborhood that include 140 dwarfs (31 of which have detected planets), 29 subgiants (4 with planets), and 140 giants (12 with planets).

The stars were observed with the ELODIE high-resolution spectrograph (Baranne et al. 1996) of the Haute Provence Observatory (France), and the data are publicly available in the online ELODIE database. The ELODIE spectrograph provides spectra with resolution R ~ 42 000 in the wavelength range 3895−6815 Å. The selection criteria are similar, but not equal, to those applied before since we have now considered a smaller inferior limit for the signal-to-noise ratio (S/N). Following this new criteria we selected:

• i)

  stars for which the averaged spectra have S/N ≥ 150: only individual spectra with a S/N ≥ 20 and with an image type classified as object fiber only (OBJO) were used;

• ii)

  stars within a distance ≤100 pc (parallax π ≥ 10 mas) and with spectral type between F8 and M1;

• iii)

  stars having no close-in binary companion that could contaminate the observed spectra: we used the information of the angular separation between components (rho) available in the Hipparcos catalog (ESA 1997), and we chose only those systems with rho> 10 arcsec; additionally, we searched in literature for any further information that could unveil a contaminant star in the observed field;

• iv)

  stars with (B − V) measured by Hipparcos and with cross-correlation parameters available in the ELODIE database: both (B − V) and the width of the spectral cross-correlation function are required to carry out a first estimate of the projected rotation velocity vsini of each star; and

• v)

  stars for which the determination of the photospheric parameters is reliable (see Sect. 3.1) and that passed the quality control of the spectral synthesis (see Sect. 3.2).

A total of 1485 spectra of 309 stars were analyzed. The subsamples of dwarfs, subgiants, and giants are plotted in the Hertzsprung-Russell (HR) and color-distance diagrams of Fig. 1. As in Paper I, we chose to classify as subgiants those stars situated 1.5 mag above the lower limit of the main sequence and with M_v> 2.0 mag. The distance of dwarfs and subgiants is not limited to 100 pc, but to about 80 pc, which represents a selection effect of the ELODIE observation surveys. For comparison, in the righthand panel of this figure we plot the log g vs. T_eff diagram with the stellar parameters derived in the current work.

The spectra were reduced using IRAF¹ routines for order identification and extraction, background subtraction, flat-field correction, wavelength calibration, radial-velocity shift correction, and flux normalization (a global normalization first, and then a more careful one performed around regions containing molecular bands and atomic lines used in the spectral synthesis).

3. Spectroscopic analysis

3.1. Photospheric parameters and equivalent widths

In this work, as in Paper I, we performed a differential analysis relative to the Sun. The method requires a model atmosphere for each star, which in turn is computed using the so-called photospheric parameters: effective temperature T_eff, metallicity [Fe/H], surface gravity log g, and microturbulent velocity ξ. We computed these parameters through the excitation equilibrium of neutral iron and the ionization equilibrium between Fe i and Fe ii lines, using model atmospheres derived by interpolation in the grid of Kurucz (1993). As before, we used the MOOG LTE radiative code (Sneden 2002) and the same routine as developed by us to perform an automated calculation of the parameters and their uncertainties, allowing a fast and homogeneous approach.

To compute the solar model atmosphere, we adopted T_eff = 5777 K, log g = 4.44, ξ = 1.0 km s^-1, and the standard solar abundances of Anders & Grevesse (1989), but with log ϵ_⊙(Fe) = 7.47, to be consistent with the value adopted in Paper I. We also assumed the Unsöld approximation multiplied by 6.3 to account for the van der Waals line damping. This is useful for a better treatment of strong lines close to the spectral windows used in our spectral synthesis analysis.

Table 2 shows an excerpt of the atomic line parameters (wavelength, statistical weight of the lower level multiplied by the oscillator strength gf, and lower-level excitation potential χ) and equivalent width (EW) for our list of atomic lines. Table 3 contains an excerpt of the gf values for elements with important hyperfine structure (HFS). The complete tables for all the elements analyzed in the present work are available in electronic form at the CDS. These parameters were initially taken from the Vienna Atomic Line Database – VALD (Kupka et al. 2000, 1999; Piskunov et al. 1995; Ryabchikova et al. 1997) in the case of the elements without HFS, and from Steffen (1985) for those with significant HFS. The gf values were then revised in order to fit the equivalent widths measured in the spectrum of the Solar Flux Atlas (Kurucz et al. 1984) degraded to the ELODIE resolution. For the Sun and for all the other stars in our sample, the EWs were measured using the Automatic Routine for line Equivalent widths in stellar Spectra (ARES, Sousa et al. 2007).

The atomic lines of the elements Mg, V, Mn, and Cu have significant HFS that has to be taken into account. In the case of those elements with lines not listed in Steffen (1985), we adopted the values of neighboring multiplets. An exception is the Mg line at λ5785.29, for which no HSF information was available. Its gf value was obtained in the same way as those lines without HFS listed in Table 2. This line is not strong (EW< 60 mÅ), and the error induced in the Mg abundance determination is of second order. The HFS of Ba and also its isotopic splitting are of some significance but only for the line at λ6496.91, because they are negligible for the lines at λ5853.69 and λ6141.73 (see Korotin et al. 2011).

Table 4 shows an excerpt of the derive photospheric parameters for the 140 dwarf stars in our sample, along with their uncertainties. The complete tables, also for subdwarfs and giants, are available in electronic form at the CDS.

3.2. Abundance determination

The abundances of the refractory elements (Na, Mg, Si, Ca, Ti, V, Mn, Ni, Cu, and Ba), with respect to Fe, were determined based on the equivalent widths of a selection of spectral lines chosen as free from blends by inspection of the Solar Flux Atlas and the solar line identification catalog of Moore et al. (1966).

We used the abfind (in the case of elements without important HFS) and the blends (in the case of elements with HFS) drivers of the MOOG code to derive the abundances. These drivers require (i) the model atmospheres, which were previously computed using the photospheric parameters derived for each star; and (ii) a list of the selected lines, containing the respective wavelength (or the hyperfine structure), the atomic number, the lower-level excitation potential, the revised values of gf, and the measured equivalent widths. Again, using another routine for an automated calculation developed by us, we derived the abundances for each element in turn, excluding (by means of a sigma-clipping procedure) spectral lines that provided an incorrect abundance determination.

For the volatile elements (C, N, and O) and for Na as well, we used the spectral synthesis technique, also performed with the MOOG code, to reproduce the observed spectra in regions containing molecular lines of electronic-vibrational band heads of the C₂ Swan system (centered at λ5128 and λ5165), of the CN blue system (centered at λ4215), and to atomic lines of C (λ5380.34), O (λ6300.30), and Na (λ6154.23 and λ6160.75). Again, as in Paper I, we preferred not to use the C atomic line at λ5052.17 because it is blended with a strong Fe line, which may affect the abundance determination.

The synthetic spectra were computed in wavelength steps of 0.01 Å, also considering the continuum opacity contribution in ranges of 0.5 Å, line-broadening corrections (from velocity fields and instrumental broadening), and the limb darkening effect. Some parameters of atomic and molecular lines were taken from the VALD database and from Kurucz (1995). Additional molecules that contribute to the spectral line formation in the studied wavelength regions are MgH (at λ5128, λ5165, and for the C atomic line), CH (at λ4215), and CN (for the Na and O atomic lines), though their contributions are relatively small. The gf values of some atomic and molecular lines were revised to fit the solar spectrum, which was taken as a reference in our differential chemical analysis. The oxygen line at λ6300.30 is blended with a Ni line at λ6300.34 (log gf = −2.3098). Therefore, we derived the O abundances by taking the Ni abundance of each star into account when fitting the observed profile. Moreover, to account for the presence of telluric lines in this region, we adopted the telluric spectrum by Wallace et al. (2011) with the resolution degraded to match our spectra.

To account for spectral line broadening from velocity fields, as in Paper I, we adopted the same definition of V_broad (also listed in Table 4), which is a composite of velocity fields, such as rotation and macro-turbulent velocities. The instrumental broadening was estimated from the width of thorium lines, and the linear coefficient u of the stellar limb darkening was taken from Díaz-Cordovés (1995).

Figure 2 shows the spectral synthesis applied to three of the regions used for abundance determination, the C₂ (λ5165) and CN (λ4215) molecular band heads and the O atomic line at λ6300.30, for two dwarf stars with different spectral S/N. The synthetic spectra were resampled in steps of 0.05 Å to consistently match the wavelength scale of the observed spectra. For examples of spectral synthesis applied to other regions and to other stars, we refer the reader to Figs. 3 and 5 of Paper I.

For a comparison between the results provided by molecular- and atomic-line C abundances, Fig. 3 shows the differences plotted as a function of T_eff and of S/N for our subsamples of dwarfs, subgiants, and giants. Besides a slight underabundance (within errors, however) of molecular with respect to atomic C abundances for cool dwarfs, no systematic difference is observed in the whole range of T_eff or S/N.

We estimated the uncertainties in the same way as in Paper I, i.e., using our routine that includes the error propagation of the input parameters used by MOOG: the photospheric parameters T_eff, log g, [Fe/H], and ξ, and the broadening velocity V_broad. For each one in turn, the input parameters are iteratively changed by their errors, and new values of abundance are computed. The difference between new and best determination gives the error due to each parameter uncertainty, and σ([X/Fe]) is a quadratic sum of individual contributions. The error in V_broad was estimated to be of the order of 1 km s^-1 or smaller.

Table 4 shows an excerpt with the derived [Ti/Fe] abundance ratios for the 140 dwarf stars. The complete tables with abundances of all the other elements, also for subdwarfs and giants, are available in electronic form at the CDS. The parameters of atomic and molecular lines are listed in Tables 5 and 6, which are only available in electronic form at the CDS as well. Table 5 contains the wavelength of the spectral feature, the atomic and molecular line identification, the lower-level excitation potential, the gf values, and the dissociation energy D₀ (for molecular features alone). Table 6 (strong atomic lines) contains the same information as in Table 5, except the dissociation energy parameter.

4. Evolutionary and kinematic parameters

4.1. Stellar masses and ages

We derived masses and ages through interpolations in the grids of Yonsei-Yale (Y²) evolutionary tracks and isochrones (Yi et al. 2001; Kim et al. 2002) on the HR diagram. The determination of these parameters takes the metallicity of each star into account. The stars’ luminosities used in the diagrams were calculated with parallaxes taken from the new reduction of the Hipparcos data (van Leeuwen 2007), and bolometric corrections (BC) from Flower (1996), which were revised by Torres (2010). For the Sun, we adopt BC_⊙ = −0.07 and ${\mathit{M}}_{\mathrm{bol}}^{\mathrm{\odot }}\mathrm{=}\mathrm{4.75}$.

A few examples for different metallicities are illustrated in Fig. 4. To reproduce the Sun’s position in the HR diagrams, adopting T_eff = 5777 K and age = 4.53 Gy (Guenther & Demarque 1997), the evolutionary tracks and isochrones were displaced in log (T_eff) by 0.001628 (~22 K in T_eff) and in log (L/L_⊙) by 0.011. By doing so, we derived a mass M = 1.003 ± 0.004M_⊙ and an age = 4.37 ± 0.17 Gyr (see Fig. 4a) for the Sun. The figure also shows a metal-poor and young star (HD 106516, Fig. 4b); a metal-rich one (HD 12661, Fig. 4c); a young star that is outside the lower border of the models (HD 26767, Fig. 4d); a low-mass and old star (HD 208313, Fig. 4e); and another star outside the limits of the models, this time in the region of low-mass and old stars (HD 94518, Fig. 4f).

The star HD 26767 is known to be a member of the Hyades cluster with 625 Myr, and it has been studied in several works in recent decades. Other stars that are either very young or outside the lower border of the models have been identified as members of the Hyades, the Ursa Major (~500 Myr), or the Pleiades (20−150 Myr) moving groups, or even classified as possible subdwarfs. In the case of old stars outside the model limits, they are likely to be low-mass stars no older than the age of the Universe (13.8 Gyr, Komatsu et al. 2011).

Table 7 lists the derived masses and ages, along with the parameters used to compute the luminosities. The uncertainties were estimated taking the error propagation of the photospheric parameters and of the luminosity into account, using σ(π) from Hipparcos and adopting σ(V) = 0.01 and σ(BC) = 0.005. In view of the asymmetric distribution of the isochrones on the HR diagram, the table shows the lower and the upper uncertainties on age.

4.2. Kinematic properties

In the same way as in Paper I, we grouped our stars according to their main population membership by computing the probability that a given star belongs to the Galactic thin disk, thick disk, halo, or a population of transition. First, using equations of Johnson & Soderblom (1987), we computed the space-velocity components U_LSR, V_LSR, and W_LSRwith respect to the local standard of rest (LSR) using parallaxes and proper motions from the new reduction of Hipparcos and radial velocities from the ELODIE archive from the Simbad database and from Holmberg et al. (2007). For the Sun, we adopted U_LSR = 10.0, V_LSR = 5.3, and W_LSR = 7.2 km s^-1 (Dehnen & Binney 1998). Then, employing the equations of Reddy et al. (2006), we computed the probability that a star belongs to one of the three populations. A probability P_thin, P_thick, or P_halo greater than or equal to 70% classifies the star as a thin, a thick, or a halo member, respectively. If the probability is in between these, then the star is classified as belonging either to the thin/thick or to the thick/halo transition group.

Our sample of 309 stars contains 281 thin-disk (out of which 120 dwarfs, 25 subgiants, and 136 giants), and 16 thick-disk (10 dwarfs, 2 subgiants, and 4 giants) population members. None of them belongs to the halo, and 13 (10 dwarfs, 2 subgiants, and 1 giant) belong to a thin/thick transition population. The membership of each star is indicated in Table 7.

5. Results and discussion

5.1. Abundance trends with metallicity

The [X/Fe] abundance ratios as a function of metallicity are plotted in Figs. 5−7 for dwarfs, subgiants, and giants, respectively. Since most of our sample stars belong to the thin disk, for homogeneity, only these stars were used in the abundance analysis. They are all listed in the tables, but only thin-disk members are displayed in the figures. Besides iron, titanium is the only element in our study having spectral lines of both neutral and singly ionized atoms. We have found no significant difference between Ti i and Ti ii, so we adopted an average value of all lines together.

Despite the small number of metal-poor ([Fe/H] <−0.3 dex) or metal-rich ([Fe/H] > 0.3 dex) stars in this sample, the trends in the abundance ratios with metallicity are in good agreement with those published in the literature about the nucleosynthetic origin of the elements and the evolution of their abundances with time. Regarding the abundance trends for dwarfs, we recommend, for example, Adibekyan et al. (2012b) and Kang et al. (2011). For giant stars see, for example, Takeda et al. (2008). The abundance trends for subgiants are very similar to those for dwarfs for all the investigated elements. A few cases concerning the abundances of the three subsamples deserve particular attention, and we discuss them in the following paragraphs.

There are systematic differences in the abundance ratios of carbon, nitrogen, and sodium when the subsamples of dwarfs, subgiants, and giants are compared with each other: in the range of solar metallicity (from −0.1 to 0.1 dex) giant stars are underabundant in [C/Fe] by −0.17 ± 0.07 dex and overabundant in [N/Fe] by 0.31 ± 0.10 dex and in [Na/Fe] by 0.16 ± 0.08 dex. The abundance trends for these elements confirm our previous result for carbon discussed in Paper I and agree with the results of Takeda et al. (2008) for sodium and carbon. For oxygen, we found [O/Fe] = 0.07 ± 0.07 dex in the solar metallicity range. Therefore, we do not confirm the oxygen deficiency found by Takeda et al. (2008), who used the forbidden [O I] line at 5577 Å. Their oxygen abundances were in either case probably underestimated as affirmed by the authors. Our results also agree with those of Liu et al. (2010), who find that [C/Fe] is depleted by 0.13 dex, [Na/Fe] is overabundant by 0.1 dex, and [O/Fe] was not altered after the first dredge-up. From a theoretical point of view, changes in the surface abundances of evolved stars is expected for C and N, and unexpected for O according to quantitative predictions made by Iben (1991).

A commonly used explanation for such systematic differences is based on the effect of mixing processes that dredge up C-poor and N- and Na-rich material (produced by CN and NeNa cycles) to the surface of evolved stars. On the other hand, the use of spectral lines contaminated by blends is also a possibility. To test this, we derived the sodium abundances using the two techniques described in Sect. 3.2 from the equivalent widths and from spectral synthesis. The available Na lines in our spectral coverage are affected by C₂ and CN molecular bands. Performing spectral synthesis allows including the already derived C and N abundances and, therefore, accounting for the presence of such bands. However, in doing so, the [Na/Fe] overabundance in giants is only slightly reduced, so not enough to cancel out the larger systematic difference with respect to dwarfs, thereby favoring the mixing-process hypothesis. Another result that favors this hypothesis is that [C/Fe], [N/Fe], and [Na/Fe] have a trend with mass: a negative trend with increasing mass in the case of carbon and positive ones for nitrogen and sodium (see Fig. 8). More massive stars have evolved faster and, therefore, have become C-poorer and N- and Na-richer than stars with masses close to the solar value. The oxygen abundances remain constant and independent of mass, supporting the above discussion.

The nitrogen abundances of our giant stars show a clear dependence on the effective temperature (see Fig. 9, top right panel). One possibility is that this dependence is related to the continuum definition when using the CN molecular band. In this case, the reader would ask whether the trend in [N/Fe] vs. [Fe/H] is also related to this dependence on T_eff, owing to a bad continuum definition. However, if we limit the effective temperature within the almost flat region seen in the [N/Fe] vs. T_eff plane, from about 4600 to 5000 K, the trend in [N/Fe] with metallicity still remains. Moreover, the effective temperature of our sample of giants increases with increasing mass; that is, it seems that more evolved stars have higher temperatures. Therefore, we believe that the [N/Fe] dependence on T_eff is probably related to evolution effects instead of to a false continuum definition.

For the carbon abundances in dwarf stars, our result is in line with those of Delgado Mena et al. (2010) in the range of solar metallicities. They found, however, a steeper trend in [C/Fe] vs. [Fe/H] in the range of metal-poor stars, and practically a flat distribution of metal-rich dwarfs. On the other hand, González Hernández et al. (2010, 2013b) derived [C/Fe] ratios that continuously decrease with increasing [Fe/H] in the whole range of metallicities for their sample of dwarfs and solar analogs.

For the nitrogen abundances of dwarf stars, we derived a slope of 0.31 ± 0.06 in the [N/Fe] vs. [Fe/H] plane for dwarfs with and without planets fitted together. This is much steeper than the one derived by Ecuvillon et al. (2004) for their sample of solar type stars with and without planets (0.10 ± 0.05) based on the NH band at 3360 Å. We checked whether our [N/Fe] correlates with the effective temperature or the surface gravity, and no significant trend is observed in either case. However, it seems that our dwarf stars with temperatures higher than the solar value either have [N/Fe] close to zero or are slightly overabundant, whereas those cooler than the Sun are slightly underabundant (see Fig. 9, top left panel). By performing the same fit in the [N/Fe] vs. [Fe/H] plane, but only to stars with T_eff< 5800 K, we derive a slope of 0.28 ± 0.06, a number that is less steep but is still a significantly high value.

The decreasing [O/Fe] with increasing metallicity observed for our sample of dwarfs agrees with the trends derived by Delgado Mena et al. (2010) and by González Hernández et al. (2010, 2013b), and also with the recent results by Bertran de Lis et al. (2015) for the O abundances based on the O i λ6158.17 and [O i] λ6300.30 atomic lines.

The distributions of [X/H] are shifted toward higher abundances (see Fig. 13) owing to the metal-rich nature of stars hosting giant planets, as already known and discussed in the literature (see, e.g., Neves et al. 2009; Adibekyan et al. 2012b). The exceptions in the current study are oxygen and barium, whose [X/H] abundances show no clear enrichment in giant planet hosts (see discussion in Sect. 6). In other words, most of these elements follow the same behavior of iron and are, for some reason, also linked to the planetary formation process. It is worth noting that only stars with giant planets (mass ≳50 Earth masses) were considered and compared with only stars for which no giant planet has been detected. We conducted an exhaustive search in the literature in order to classify each star and create these two subsamples. They are identified in the remarks column of Table 7, together with the respective reference. In addition, we note that we performed this comparison only for dwarf stars of the thin disk population. Evolved stars are normally not included in the surveys of planet search, because they are well known for their intrinsic radial-velocity variation due to pulsation and/or jitter (distortion in the observed signal caused by stellar magnetic activity). Subgiant stars could be added to the subsample of dwarfs, but we preferred to keep the homogeneity.

To quantify the observed trends with metallicity, we fitted linear regressions in the range of stars that are metal-poorer or metal-richer than the Sun, or in the whole range of metallicity, depending on which one provides a higher correlation. The abundance ratios were then subtracted by the predictions of these linear fits trying to remove (or at least minimize) the effects of the chemical evolution of the Galaxy’s thin disk. The abundances corrected from such effects are used and discussed in Sect. 5.3, where we derive the abundance trends with the condensation temperature of the elements.

5.1.1. Chemically peculiar stars

Most of the dwarf and subgiant stars plotted in Figs. 5 and 6 follow the abundance trends with metallicity. A particular exception seems to be the vanadium abundance ratios for some of them. Such stars have [V/Fe] higher than what is expected for their metallicity. By plotting the abundance ratios of the elements as a function of the other stellar parameters, we noticed that there is a systematic positive trend in [V/Fe] as a function of the effective temperature for T_eff≳ 6000 K for our sample of dwarfs (see Fig. 9, bottom left panel). For this reason, in the following sections we discuss the results obtained by including or excluding the vanadium abundances of stars with temperature higher than this limit. No clear trend in the abundance ratios as a function of temperature is observed for the other elements, or as a function of other stellar parameters (except age) either. This is the case at least for dwarfs and subgiants, because the elemental abundances in giants may have been affected by stellar evolution (see discussion in Sect. 5.1).

Concerning the chemical peculiarity of giant stars, two of our sample stars deserve special given their position in the [Ba/Fe] vs. [Fe/H] diagram of Fig. 7. Both HD 104979 and HD 202109 appear enriched in barium compared to other giants with the same metallicity. Williams (1971) derived a [Ba/Fe] = 1.1 dex for HD 104979 and first suggested it to be a Ba ii star². More recent works have confirmed the barium overabundance for this star, namely [Ba/Fe] = 0.93 ± 0.10 dex (Zǎcs 1994) and [Ba/Fe] = 0.54 ± 0.31 dex (Smiljanic et al. 2007), both in agreement with our determination of [Ba/Fe] = 0.77 ± 0.06 dex. The barium star nature of HD 202109 was first suggested by Chromey et al. (1969), who measured [Ba/Fe] = 0.8 ± 0.3 dex, and was afterward classified as mild (marginal enriched) barium stars: [Ba/Fe] = 0.41 ± 0.13 dex by Zǎcs (1994) and [Ba/Fe] = 0.31 ± 0.26 dex by Smiljanic et al. (2007). We derived [Ba/Fe] = 0.40 ± 0.09 dex, which is a result that agrees with the mild barium star classification.

5.2. Abundance trends with age

Figure 10 shows the [X/Fe] abundance ratios as a function of age for the subsample of dwarf stars in the thin disk population. Similar to what is described in Sect. 5.1 in the case of the metallicity, we also quantified the observed trends with age by fitting linear regressions in the range of stars younger or older than the Sun, or in the whole range of age, depending on which one provides a higher correlation. Again, the abundance ratios were subtracted by the predictions of these linear fits in order to remove (or at least minimize) the effects of the chemical evolution of the Galaxy, using another approach,. The abundances corrected from such effects are used and discussed in Sect. 5.3, where we derive the trends with the condensation temperature of the elements.

Depending on the position of the star in the HR diagram, the errors in age may be quite high, and the age determination is thus less reliable. By means of the distribution of the uncertainties on this parameter, we set a 2σ confidence limit up to which about 95% of the stars are found to have errors smaller than that limit, namely ~4 Gyr. Only stars with σ(age) < 4 Gyr were therefore considered in the analysis.

5.3. Abundance trends with condensation temperature

During the past few years, several works have investigated the relation between the stellar chemical abundances and the condensation temperature (T_C) of the elements in stars with and without planets. Aiming to minimize systematic errors, the abundance difference between the Sun and other stars, Δ[X/Fe], has been used, where the solar abundances are derived from a Moon’s spectrum, for example.

On the one hand, it has been suggested that the observed trends of Δ[X/Fe] as a function of T_C may have some relation with the planetary formation, in particular, with the formation of terrestrial planets (see the review performed by Ramirez et al. 2010). On the other hand, other authors argue that this kind of relation practically vanishes after removing the Galactic chemical evolution effects (see González Hernández et al. 2013b, and references therein). Indeed, positive slopes in these diagrams may be the result of having higher abundances of less refractory elements, such as Na and Cu, with respect to more refractory ones, such as Ti and Ca. In Fig. 5, both [Ti/Fe] and [Ca/Fe] have a slight decrease with increasing metallicity, whereas [Na/Fe] and [Cu/Fe] clearly increase for higher metallicities.

In particular, some of the studies discussed in the papers above consider only solar twins (T_eff = 5777 ± 100 K, [Fe/H] = 0.0 ± 0.1 dex, log g = 4.44 ± 0.10 dex) or solar analogs (T_eff = 5777 ± 200 K, [Fe/H] = 0.0 ± 0.2 dex, log g = 4.44 ± 0.20 dex) in their analysis. Recently, Adibekyan et al. (2014) have published the results of their study in which they searched for correlations of the Δ[X/Fe] vs. T_C trends with some stellar and orbital parameters. After correcting the abundances from the Galactic chemical evolution effects, they found that the observed trends correlate with age and anticorrelate with the surface gravity, and possibly with the mean Galactocentric distance, and that the correlations (or anticorrelations) are even steeper and more evident if only solar analogs are plotted.

Here we also investigate the relations involving Δ[X/Fe] as a function of the condensation temperature of the elements. To compute [X/Fe]_Sun, we used the solar abundances derived from the spectrum of the sunlight reflected by the Moon. First, we fit linear regressions for elements with T_C> 900 K, a limit normally used to distinguish refractory from volatiles. Values of T_C were taken from Lodders et al. (2009). To account for any effects that the Galactic chemical evolution may have on the observed trends, we applied the corrections based on both metallicity and age, as described previously. Figure 11 shows a few examples. Table 8, which is available in electronic form at the CDS, lists the slopes of the linear regressions and the respective standard deviations for thin disk dwarfs. Only dwarf stars were used in this analysis because their abundances are normally not affected by stellar evolution. The table contains the slopes and their uncertainties, the correlation coefficients, and the standard deviations of the regressions before and after applying the corrections for the Galactic chemical evolution effects based on age and on metallicity.

We then plot (Fig. 12) the respective slopes as a function of the stellar parameters T_eff, [Fe/H], log g, ξ, mass, and age. In this figure, solar analogs are distinguished from non-solar analogs and stars with planets from those without planets. Regarding the sample of solar analogs, the figure shows: i) a marginal correlation with metallicity (in the sense that metal-richer stars have more positive slopes) and with mass after removing the effects of chemical evolution based on age; however, these correlations completely disappear if the correction is based on metallicity; ii) a clear anticorrelation with the surface gravity in both scenarios of Galactic chemical evolution correction; iii) a marginal correlation with age, slightly steeper after applying the correction based on metallicity. The directions of these correlations agree with those reported by Adibekyan et al. (2014). We cannot check the T_C trends with Galactocentric distance because we only have solar neighborhood stars (distance to the Sun <100 pc). Concerning the relation with the presence of planets, the small number of planet hosts in our sample of solar analogs prevents us from any conclusions.

By excluding the vanadium abundances of stars with T_eff≳ 6000 K from the analysis, the correlations and anticorrelations obtained above are still the same, specially because this limit is already imposed when only solar analogs are used.

6. Statistical analysis

We have used a number of statistical methods (see Breiman et al. 1984) to explore the multivariate properties of our sample. We are interested in uncovering significant differences in the stellar properties for stars with and without a known giant planet. Hereafter we use the indices 1 and 0 to distinguish these two samples, respectively. Moreover, the sample of dwarf stars is prefixed by the letter “d”. Thus, samples d1 and d0 stand for dwarfs with and without a known giant planet, respectively. The analysis and the following discussion are restricted to the dwarfs because their sample is thought to be less affected by an observation bias.

6.1. Abundance distributions

We compare the abundance distributions between the samples d0 (red) and d1 (blue) in Fig. 13. The boxes and whiskers summarize percentiles of these abundance distributions graphically. Particularly, the middle line inside each box indicates the median for that distribution, whereas the upper and lower edges of the box indicate the interquartile range. We applied a 2σ clipping in the abundance data of each single element in order to get rid of outliers in the abundance space. Panel (a) shows the comparison for all dwarf stars after applying the sigma clipping, while panel (b) restricts the comparison to those stars having −0.25 ≤ [ Fe / H ] < + 0.35 (a range in common between the subsamples of stars with and without planets). Both comparisons depict that dwarf stars with giants planets (d1) have generally larger abundances in nearly all elements compared to dwarfs without giant planets (d0). We note that vanadium seems to be exceptionally abundant in d1 stars, whereas no significant difference is seen between d1 and d0 for the oxygen and barium abundances. Concerning vanadium, the overabundance of d1 with respect to d0 does not change if only stars with T_eff≲ 6000 K are used.

We used the Welsch’s t-test to quantitatively assess whether the means of these distributions are significantly different from one another. Table 1 gives the test statistics for stars having −0.25 ≤ [Fe/H] < +0.35, after applying 2σ clipping. Some p-values are very low (<0.001), reinforcing the visual comparison provided by Fig. 13. The mean of the abundance distribution of all elements, but O and Ba, are higher in d1 stars, compared to d0 stars. Oxygen abundances are not represented very well in our sample, and only 32 d0 and 4 d1 stars have measured O abundance; this could be one of the reasons for the t-test giving a high p-value for the O abundance distribution comparison. Notwithstanding, it is highly interesting, although not clear, why Ba is not particularly more abundant in d1 stars.

The t-tests described above can only be applied to the abundance distribution of a single element at a time. They can pinpoint elements that are particularly more or less abundant in one of the tested distributions. To use the information encoded in the whole abundance space, we also applied a multivariate analysis of variance (MANOVA) to assess the significance of differences in the multivariate means (that is, the location of samples 0 and 1 in abundance space). According to this MANOVA, we can reject the null hypothesis that the d0 and d1 samples have similar locations in abundance space (p = 0.006).

6.2. Abundance difference per metallicity bin

We have also considered a different approach to disentangling the effects of the chemical evolution of the Galaxy from the metallicity–giant planet connection. We defined a crude abundance quantity = [Mg/H] + [Si/H] + [Ca/H] + [Ti/H] + [V/H] + [Mn/H] + [Ni/H] + [Cu/H] + [Ba/H]. The symbol does not have an exact physical meaning, on account of the sum of unscaled log abundances, but it can serve as an enrichment index for the purpose of this analysis. For instance, it is clear that and [Fe/H] should be correlated as a result of the Galactic chemical evolution. This index could only be defined for those stars having a complete set of abundances of the elements Mg to Ba, including Fe. CNO and Na abundances were not included in the definition because this would substantially lower the final number of stars having a complete set of abundance measurements.

The index was used in a linear model of the type $\mathrm{𝒵}\mathrm{=}\mathit{\beta ̂}\mathrm{0}\mathrm{+}\mathit{\beta ̂}\mathrm{1}\mathrm{[}\mathrm{Fe}\mathit{/}\mathrm{H}\mathrm{]}\mathrm{+}\mathit{ϵ,}$(1)fit by least squares to the d0 stars. The residuals of the fit are given by ϵ for each star. Following this, we calculated the residuals of the d1 stars with respect to the same linear model fit to the d0 stars. A Welch’s t-test applied to these residual distributions indicates that the difference in their means are significant (a p-value p = 0.0023), with . That is, for a given [Fe/H], d1 stars have generally larger indices than do d0 stars. If we can consider the d0 stars as a “null hypothesis” population, for which the elemental abundances only reflect the Galactic chemical evolution, the residuals of for the d1 stars using the linear model in Eq. (1) should have no chemical evolution bias. Again, if we calculate excluding [V/H], this result practically does not change (the new p-value would be p = 0.0026). On the other hand, if is calculated excluding the [Ba/H] abundance ratios, we obtain p = 0.0005 and ; i.e., the difference between the d0 and d1 populations is even greater.

We defined by mixing elements with different nucleosynthetic origins, which might veil the real difference in abundance between stars with and without planets. However, the mean [X/H] distributions for α (Mg, Si, Ca, Ti) and for iron-peak (V, Cr, Mn, Co, Ni) elements in stars hosting giant planets are very similar, as reported by Mata Sánchez et al. (2014). Indeed, if we calculate for α elements alone, we obtain , whereas for only our iron-peak elements (V, Mn, Ni), we have . For stars without planets, the [X/H] distributions are also very similar, having a maximum abundance at ~−0.1 for most species (Mata Sánchez et al. 2014). Therefore, we conclude that the mix of elements when calculating is not a bad approach, especially because the differences that we are comparing become more significant when the abundances of all these elements are added together.

6.3. Classification trees

Assuming the general connection between chemical abundance and the presence of a giant planet, we can extend the reasoning in using the iron abundance as an indicator of the plausibility that the star harbors a planet. To do this, we applied a classification tree to a complete set of [X/H] abundances for the dwarfs in our sample. Classification trees give the optimal splitting of observations coming from different classes (or populations). In our problem, we consider two classes: stars with and without giant planets. The tree is built through recursive partitioning of the abundance space into nested groups, aiming at terminal groups having the highest purity (that is, having most, if not all, of its members coming from a single class). Each classification tree has nodes, branches, and terminal leaves (or group). The nodes are annotated with some property (or variable) and a splitting rule that points to one branch or the other. The leaves are usually labeled with the statistics of the partitioned group.

As previously explained, on account of the requirement of having a complete set of abundances, CNO and Na measurements were not used in this analysis. No sigma clipping to the abundances was used before applying the classification trees. We show in Fig. 14 four classification trees. The leaves are marked (and color-coded, for easy identification) with the most likely class of its members: 0 (red) if the star is not likely to harbor a giant planet, and 1 (blue) if the opposite holds. Two numbers are annotated below each terminal leaf, showing the fraction of d1 stars in the group (stars harboring a giant planet) and the percentage of all dwarfs stars that were classified in that leaf. Thus, the numbers 0.42 9% can be read as 9% of all dwarfs that were classified in that group and 42% of them that harbor a giant planet. The upper lefthand panel gives the classification tree when we consider all elements from Mg to Ba. Although this abundance space is formed by the measurements of ten chemical species, only two of them are needed for an optimal partition: Cu and V. Copper abundances seem to be the best single indicator of the presence of a giant planet: only 8% of the stars having [Cu/H] < 0.15 dex harbor a giant planet. Vanadium comes second in refining this: 78% of stars having [Cu/H] ≥ 0.15 dex and [V/H] ≥ 0.33 dex harbors a giant planet. The three other classification trees in Fig. 14 show the partition model when Cu, V, or both variables are not used. If vanadium is taken out of the independent variable set, the whole ten-dimensional abundance space could still be partitioned using the Cu abundances alone. The purity is somewhat lower: 73% of the stars having 0.15 ≤ [ Cu / H ] ≤ 0.24 harbor a giant planet. If, on the other hand, we take Cu from the set of independent variables, V takes the lead as the most relevant element, followed by two more splittings using Ti and Ca. The two more meaningful (extreme) leaves give: i) 5% of stars having [V/H] < 0.19 dex harbor a giant planet; and ii) 71% of stars having simultaneously [ V / H ] ≥ 0.19, [ Ti / H ] ≥ 0.14 and [ Ca / H ] ≥ 0.15 dex harbor a giant planet. Taking both Cu and V out of the set of independent variables yields a classification tree based on Ti and Ca abundances that is an exact subtree from the third case (with no Cu abundances).

6.4. Linear discriminant analysis

A similar, but more sophisticated, approach can be taken using a linear discriminant analysis (LDA), which finds the linear combination of observed properties (in our case, abundances) which best separates two or more classes of objects. The result is an index, or system of indices, that may act as a linear classifier. The difference from the classification tree is that this one uses a hierarchical recursive splitting of single properties, which aims at classes with the highest purity possible, while the LDA searches for rotations of the original multiparametric space that leads to the best categorization of the classes in the entire space.

We applied the LDA to the complete abundance set of Mg to Ba for dwarfs, looking for the linear combination of abundances that could differentiate the d0 from d1 samples better. The resulting linear discriminant is given in the last column of Table 1 and in Fig. 15. As explained, the LDA finds the best linear combination of the original abundances that discriminates among the tested classes. The numbers in the table are the coefficients of this linear discriminant. An index formed by − 0.87 [ Fe / H ] −5.43 [ Mg / H ] + ... + 0.99 [ Cu / H ] −2.01 [ Ba / H ] can thus be used to differentiate d0 from d1 stars. If our sample can be taken as unbiased and representative of the stellar abundances of stars with and without giant planets, we can use this discriminant index in a predictive way, when the giant planet-harboring status of the star is unknown a priori. As pointed out before, the concept is similar to using a classification tree, although now we use all abundances to build a single optimizer classifier. The power of this classifier can be seen in Fig. 15, where we show the histogram of the discriminant index.

We explored all possible combinations of abundance ratios involving the elements from Mg to Ba, using the Welch test to assess interesting pairs. After considering all possibilities, we have found that [V/Ca] seems to be a good abundance ratio for distinguishing dwarfs with planets: the average difference in [V/Ca] between the d0 and d1 groups amounts to 0.07 dex, leading to the rejection of the null hypothesis with p = 0.005.

Kernel probability density functions for the relevant abundance ratio that allows distinguishing dwarfs with and without giant planets are shown in Fig. 16. The color code is similar to the one used before: blue and red for stars with and without planets, respectively. The figure shows the [V/Ca] among dwarf stars. Although there is considerable intersection between the red and blue curves, it is both remarkable and puzzling that this abundance ratio seems to distinguish stars according to their planet-harboring status.

7. Conclusions

Including more stars, with and without detected planets, and more elements in the current study aimed to improve the work presented in Paper I. A summary of our new results and conclusions follows:

• i)

  The systematic differences in the abundance ratios of C, N, and Na among dwarfs, subgiants, and giants seem to confirm that mixing processes, together with cycles of nucleosynthetic reactions, do modify the abundances in the surface of evolved stars.

• ii)

  Such mixing processes indeed seem to alter the Na photospheric abundances in giant stars, considering that, even when taking the influence of C₂ and CN molecular features into account, a Na overabundance is still observed.

• iii)

  The slopes in the Δ[X/Fe] vs. T_C diagrams show a correlation with age and an anticorrelation with the surface gravity, even after accounting for the effects of the Galactic chemical evolution. These results appear only when the sample is restricted to solar-analog stars; in other words, as also pointed out by Adibekyan et al. (2014), older and more evolved stars are in same way connected to a lower number of refractory elements available for the star formation. No significant correlation with other stellar parameters and no relation with the presence of planets are observed.

• iv)

  Our statistical analysis has provided the following results.

  • a)

    The overabundance of other elements in dwarf stars hostinggiant planets confirms the previous statement that not only is ironlinked to the planetary formation process, but also C, N, Na, Mg,Si, Ca, Ti, V, Mn, Ni, and Cu.

  • b)

    For O and Ba there are no significant differences between the samples of dwarfs with and without giant planets. oxygen is not very well represented in our analysis, but the result for barium is intriguing and deserves further investigation.

  • c)

    Vanadium is the element with the most significant abundance difference between giant planet hosts and single dwarfs, and this difference is still significant if only stars with T_eff≲ 6000 K are used.

  • d)

    By combining the elements from Mg to Cu according to Eq. (1), we found a significant overabundance, for the same metallicity, in giant planet hosts in comparison with our sample of single dwarfs.

  • e)

    Based on the classification tree analysis we have found that abundances of copper and calcium are special discriminators of dwarfs with and without giant planets (over the [X/H] scale).

  • f)

    By means of a linear discriminant analysis, we have found that [V/Ca] seems to be a good abundance ratio for distinguishing dwarfs with giant planets.

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Acknowledgments

R. da Silva thanks the Instituto Nacional de Pesquisas Espaciais (INPE) for its financial support in the form of a grant (PCI-DA 300.422/2011-3, MCTI/INPE/CNPq). We thank Jorge Meléndez for critically reading the manuscript. This research made use of the SIMBAD database, operated at the CDS, Strasbourg, France.

References

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