LITHIUM ABUNDANCES IN A SAMPLE OF PLANET-HOSTING DWARFS^*

The formal uncertainties in the derived best-fit lithium abundances can be calculated by varying A(Li) around its best value and computing, for each lithium abundance tested, the quantity Δχ²_r = χ²_r − χ²_r,min. The difference between A(Li) and A(Li)_best that gives Δχ²_r = 1 is taken as the 1σ uncertainty. The derived lithium abundances and their formal uncertainties are presented in Column 3 of Table 1. The lithium abundances, however, are also sensitive to uncertainties in the effective temperature parameter: δT_eff = ±100 K introduces an uncertainty of ∼± 0.1 dex in the derived lithium abundances for most sample stars; for the cooler stars (T_eff∼ 5000 K) the sensitivity to T_eff is slightly larger (∼0.15 dex). The sensitivity of A(Li) to variations in the adopted log g's and microturbulent velocities is only marginal: a change in log g of ±0.5 dex changes the lithium abundance by 0.01–0.02 dex, with a slightly larger sensitivity of ∼0.05 dex for the coolest stars in our sample. A change in the microturbulent velocity by ±0.5 km s⁻¹ has virtually no effect on the derived A(Li). The total uncertainties in the derived lithium abundances are then calculated by the addition of all these uncertainties in quadrature, assuming that the errors are independent. The total estimated uncertainties in the derived Li abundances in this study are in Column 4 of Table 1.

Non-LTE effects have not been considered in this Li abundance analysis and these will contribute to the total error budget. Takeda & Kawanomoto (2005) calculated non-LTE Li abundances for their sample of stars with effective temperatures ranging between 5000 K and 7000 K and metallicities −1.0 <[Fe/H]< +0.40 dex. The non-LTE corrections in that study were found to range between −0.1 dex <Δ< +0.1 dex. Stars in restricted ranges in effective temperatures and metallicities, however, have similar non-LTE corrections. The stars with detected Li i lines in this study have effective temperatures roughly between 5700 K and 6200 K (as will be shown in Figure 6). For these hotter dwarfs, with A(Li) < 3.00, the non-LTE corrections are found to be small in the recent study of Lind et al. (2009).

As mentioned previously, interpreting lithium abundances can be a complex process because these abundances depend on a number of parameters, such as effective temperature, metallicity, mass, age, rotation, as well as the stellar activity level. The behavior of Li with T_eff can only be isolated if samples with similar metallicities, masses, ages, and activity levels are compared. The stars in the sample considered here are dwarfs, as shown in Figure 2; all targets lie on the main sequence.

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The metallicity distributions of the studied stars are shown in panel "a" of Figure 3 (same as Figure 9 of Paper I). As discussed in Paper I, there is a visible offset between the distributions of stars with and without planets; the average metallicity of stars hosting giant planets is 0.15 dex higher than that of the comparison stars. This metallicity offset, however, has a negligible effect on the Li abundances, as can be noted from panel "b" of Figure 3 where Li is shown versus [Fe/H]. The samples of stars with and without planets have considerable overlap with no significant trend of the lithium abundance with metallicity found over the roughly 1.0 dex change in [Fe/H] for the stars studied here. Also, the Sun does not exhibit any peculiarity in this plot.

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Panel "c" of Figure 3 presents the mass distributions for the two studied samples. The adopted values for the stellar masses correspond to the M_track values presented in Table 4 of Paper I (see that paper for details on the derived masses). The samples of stars hosting planets (represented by the red solid line histogram) and without planets (represented by the blue dashed line histogram) overlap closely in mass. The average masses for stars with and without planets are, respectively, 〈M〉 = 1.05 ± 0.16 and 1.02 ± 0.17 M_☉; there is a probability of 92%, based on a two-sample Kolmogorov–Smirnov (K-S) test that they are drawn from the same parent population of mass distributions. Panel "d" of Figure 3 reveals a tendency of higher Li abundances with increasing mass. This is expected (see, e.g., Lambert & Reddy 2004), as lower mass stars have deeper convective zones in which Li is destroyed more efficiently. The location of the Sun in this diagram (represented by the black star symbol) indicates it to be a normal star when compared to the samples of stars with and without planets.

The age distributions for the sample stars are shown in panel "a" of Figure 4. The stellar ages were taken from Table 4 of Paper I (see that paper for details). An inspection of the two histograms in this panel (red solid line representing stars with planets and blue dashed line representing stars without planets) indicates that overall there is not a significant difference between the age distributions of the two samples; the average values are: 〈Age〉_{P − Hstars} = 5.24 ± 2.48 Gyr and 〈Age〉_nonP-Hstars = 5.41 ± 2.86 Gyr. The probability that these two samples belong to the same parent population (from a K-S test) is 84%. In panel "b" of Figure 4, we observe an expected slight dependence of A(Li) upon age, with lower abundances being found for older stars. However, the behavior of stars with and without planets seems indistinguishable.

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Panel "c" of Figure 4 shows histograms comparing the chromospheric activity indices (log R'_HK) for the two samples studied here. The values of log R'_HK for the target stars were taken, whenever available, from Henry et al. (1996), Tinney et al. (2002), and Wright et al. (2004). An evaluation of possible systematic differences between the chromospheric activity indices in these studies follows. Tinney et al. (2002) find that the activity indices in their study are consistent with those from Henry et al. (1996). A comparison of indices for 13 stars in our sample which appear in both studies finds good agreement: the linear fit to the two data sets has a slope of 0.98 ± 0.12, a correlation coefficient R = 0.92, and a mean difference (in the sense "Tinney et al. − Henry et al.") of −0.01 dex. The works of Henry et al. (1996) and Wright et al. (2004) have 17 stars in common which are also present in our sample. A linear fit for these values reveals no significant trend, having a slope of 0.99 ± 0.04 and a correlation coefficient R = 0.99. There is just an offset in the averages of ∼0.04 dex, with the indices from Henry et al. (1996) being higher than those in Wright et al. (2004). Henry et al. (1996) derived an error of 0.052 for log R'_HK, while Wright et al. (2004) state that the uncertainties in log R'_HK are not larger than 13% (which would correspond to ∼0.057 for log R'_HK≃ −4.90). As the offset between the two studies is compatible with the errors in log R'_HK, no corrections in the indices were attempted in order to bring them to a consistent scale. In this study, whenever a star had more than one log R'_HK value, the average value was adopted.

Inspection of panel "c" of Figure 4 indicates that there is a visible offset between the distributions of log R'_HK for stars with and without planets, with a probability of 6.80 × 10⁻⁵ that they are drawn from the same population. This result is a consequence of the greater number of planet-hosting stars with low activity levels. We note that this fact may be related to a bias in the Doppler detection method, which is more accurate for inactive stars. In spite of this offset, the average chromospheric activity indices for planet-hosting and comparison stars are, respectively, 〈log R'_HK〉 = −4.94 ± 0.16 and −4.87 ± 0.17 dex. The overall global difference of 0.07 dex is interesting but cannot be considered as significant since it is roughly of the same order of the uncertainties discussed above. Panel "d" of Figure 4 shows that there is no clear correlation between Li abundances and log R'_HK and no visible difference in the behavior of stars with and without planets. Finally, the Sun (log R'_HK = −4.96; Wright et al. 2004) does not seem to be anomalous.

The comparisons of the various quantities discussed above show that the samples of planet host and comparison stars are similar in their mass and age distributions, although the metallicities do show a significant difference, with the planet-hosting stars being on average more metal rich (as discussed in Paper I). Small differences are found in their respective activity levels, but neither the metallicity nor the activity levels produce obvious trends with the lithium abundances.

Possible differences between Li abundances in stars with and without planets remains an active topic of discussion (Israelian et al. 2009; Sousa et al. 2010; Gonzalez et al. 2010; Baumann et al. 2010). In order to investigate such possible differences, we first examine the lithium abundance distributions for all stars in our sample, which are shown as the histograms in panel "a" of Figure 5. In this initial discussion, upper limits were included in the construction of this plot. An inspection of panel "a" reveals two interesting features. First, we can clearly see a bimodal distribution, with peaks located at A(Li) ∼0.5 and 2.4 dex. Second, the similarity in the distributions of stars with and without planets is evident, with a significant difference being visible only in the bin centered at A(Li) = 0.4 dex, which is dominated by upper limits; these facts become more evident if we analyze the cumulative distributions which are shown in panel "b" of Figure 5. The differences between the distributions are probably a result of the inclusion of those stars with only upper limits to the Li abundances. In fact, if only detected Li abundances are considered, the distributions become more similar, as can be seen in panels "c" (histogram) and "d" (cumulative distribution) of Figure 5. The average detected lithium abundances of stars with and without planets are 〈A(Li)〉 = 2.06 ± 0.63 and 2.06 ± 0.60 dex, respectively, and the probability that the two samples belong to the same parent population is 87% (K-S test). Therefore, this broad comparison of the entire sample does not seem to reveal any anomaly in the Li abundances of planet-hosting stars.

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Differences between Li abundances in stars with and without planets have been reported in the effective temperature range 5600 K ≲T_eff≲ 5900 K (Israelian et al. 2009). In order to investigate this behavior in our samples, the lithium abundances derived in this study are plotted versus the effective temperatures of the target stars in Figure 6. This plot holds some interesting features. First, the detection limit of our method varies with T_eff roughly as 0.07 dex/100 K, increasing from ∼0.3 dex at ∼4800 K to ∼1.5 dex at ∼6500 K. Also, the well known decrease in lithium abundances with declining temperatures is recovered (see, e.g., Takeda & Kawanomoto 2005; Luck & Heiter 2006). This behavior is ultimately a reflection of the trend seen in panel "d" of Figure 3, as higher mass stars on the main sequence also have higher effective temperatures. As there are three clearly distinct Li regimes in Figure 6 (hotter stars with high A(Li); intermediate T_eff stars with A(Li) declining; and low T_eff stars with Li upper limits), in the following we discuss them separately (see Figure 7).

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For T_eff< 5600 K (upper most panel of Figure 7), almost all stars have very low Li abundances (≲0.7–0.8 dex) and only upper limits could be derived in most cases. With only upper limits, it is not possible to probe any possible differences in A(Li) in stars hosting planets compared to stars not known to host planets. The exceptions to upper limits are: HD 1237, HIP 14810, AB Pic, HD 69830, and HD 181433 (stars with planets); HD 17925, HD 36435, HD 118972, HD 128674, and HD 212291 (stars without planets). The two stars exhibiting extremely high Li abundances are AB Pic (A(Li) = 3.35 dex) and HD 17925 (A(Li) = 2.66 dex). As already noted by Takeda & Kawanomoto (2005), HD 17925 is a young star with high activity level (log R'_HK = −4.30; Henry et al. 1996). AB Pic is a young star identified as a member of the Tucana–Holorogium association (Song et al. 2003), which has an estimated age of ∼30 Myr. In Paper I, upper limits of 1 Gyr were derived for the ages of these two stars. The same age upper limit is derived in Paper I for HD 1237, which has A(Li) = 2.16 dex and is also a young, active star (age of 0.02 Gyr and log R'_HK = −4.27; Naef et al. 2001). The stars HD 36435 and HD 181433 have uncertain ages because they are located in crowded regions of their respective grids of isochrones. Based on its chromospheric activity level (log R'_HK = −4.44; Henry et al. 1996), HD 36435 is most likely young, which would explain its relatively high Li abundance (A(Li) = 1.49 dex). HD 181433, on the other hand, has log R'_HK = −5.11 (Bouchy et al. 2009) and does not seem to be young. Although consistent with the chromospheric activity level, its lithium abundance (A(Li) = 0.76 dex) is relatively high when compared to stars of the same temperature (difference of ∼0.35 dex). The lithium abundance of HD 212291 also seems to be higher (by ∼0.25 dex) than the typical value for stars with similar T_eff. Although its age is uncertain (the star is located in a crowded region of its grid of isochrones), its activity level (log R'_HK = −4.82; Wright et al. 2004) shows that it may be younger than the Sun, which could explain the value of the Li abundance. Finally, the four remaining stars (HIP 14810, HD 69830, HD 118972, and HD 128674) have Li abundances consistent with those of other stars within the same temperature range. In this lower temperature regime (T_eff< 5600 K), there are 41 and 34 stars with and without planets, respectively; this corresponds to the largest sample analyzed to date. If we do not consider the stars with high Li abundances (HD 1237 and AB Pic in the planet-hosting sample; HD 17925 and HD 36435 in the comparison sample), a general overlap of the two samples is clear. Taking the upper limits as real detections, we find that the average Li abundances of planet-hosting and comparison stars are, respectively, 〈A(Li)〉= 0.37 ± 0.25 and 0.35 ± 0.28 dex.

In the hotter main-sequence stars in this sample, where T_eff > 5900 K (bottom most panel of Figure 7), most have A(Li) ∼1.5–3.0. There are, however, a small number of stars with only upper limits, and we note that some of these stars (with low Li abundance and T_eff≳ 6300 K) may be in the Li dip (see Boesgaard & Tripicco 1986; Balachandran 1995). In this temperature interval, there are 34 and 54 planet-hosting and comparison stars, respectively, with considerable overlap. It is clear that the number of stars with planets diminishes with increasing temperature, reflecting the limitation of radial velocity surveys. Also, we notice that eight comparison stars belong to the low-Li group, while only one star with a planet has an upper limit on its Li abundance. Although this feature can also be seen in Takeda & Kawanomoto (2005) and Luck & Heiter (2006), we are not sure if this is related to any physical effect or selection bias. Considering only detected lithium abundances, we obtain 〈A(Li)〉 = 2.42 ± 0.31 and 2.44 ± 0.32 dex for stars with and without planets, respectively. Thus, we do not find the excess Li abundances for planet-hosting stars with T_eff∼ 6000 K discussed in Gonzalez (2008) and Gonzalez et al. (2010), and find no detectable differences in the Li abundances between stars with and without planets in the most massive stars of the sample (M ≳ 1.2 M_☉).

A more complicated behavior of the Li abundance occurs in the transition region between high and low Li, within the temperature interval 5600 K ⩽T_eff⩽ 5900 K (middle panel of Figure 7). In this temperature regime, there are 42 and 57 stars with and without planets, respectively, in our sample. The overlap is considerable, except in the narrow range of T_eff∼ 5700–5800 K. Over the entire temperature range shown in this panel (T_eff = 5600–5900 K), 26 planet-hosting stars (or 62%) have detected Li abundances, with an average value of 〈A(Li)〉 = 1.68 ± 0.53 dex. For the comparison stars, the average lithium abundance for 37 stars (65%) with detections is 〈A(Li)〉 = 1.69 ± 0.54 dex. Treating the upper limits as actual detections, we derive 〈A(Li)〉 = 0.58 ±  0.11 and 0.62 ±  0.17 dex for stars with and without planets, respectively. Finally, it is interesting to note that the Sun does not exhibit an excessive Li depletion; actually, it looks like a "normal" main-sequence star.

Within this complex temperature transition region for Li, if we now follow the analysis of Israelian et al. (2009) and keep only stars within the very narrow range of T_eff = 5777 ± 80 K, the sample here is left with 21 planet-hosting and 27 comparison stars. For the sample of stars with planets, the average is 〈A(Li)〉 = 1.50 ± 0.44 dex for the 16 detections (76%) and 〈A(Li)〉 = 0.65 ±  0.08 dex for the 5 upper limits. For the control sample, the average is 〈A(Li)〉 = 1.76 ± 0.48 dex for the 19 detections (70%) and 〈A(Li)〉 = 0.64 ±  0.11 dex for the 8 upper limits. Following the analysis of Gonzalez et al. (2010), on the other hand, we have 20 and 30 planet-hosting and comparison stars, respectively, in the temperature interval 5650–5800 K. For the former group, we obtain 〈A(Li)〉 = 1.30 ± 0.26 dex for the 13 detections (65%) and 〈A(Li)〉 = 0.63 ± 0.08 dex for the 7 upper limits. For the control sample, we derive 〈A(Li)〉 = 1.45 ± 0.47 dex for the 16 detections (53%) and 〈A(Li)〉 = 0.64 ± 0.11 dex for the 14 upper limits. These comparisons between Li abundances in planet-hosting stars and comparison stars using the different T_eff boundaries as defined by Israelian et al. (2009) and Gonzalez et al. (2010) are intriguing, with averages differences of +0.26 dex and +0.15 dex, respectively. Note, however, that in the latter case, in particular, the average lithium abundances in the two samples overlap within our estimated uncertainties.

It is interesting to investigate in more detail the Li abundances derived here for stars falling in the narrow T_eff range centered on the solar effective temperature as used by Israelian et al. (2009), since this temperature interval resulted here in the larger difference of +0.26 dex. The Israelian et al. sample in this T_eff interval contains more stars than analyzed here, with 23 planet-hosting stars and 60 comparison stars, compared to 21 and 27 stars here. The Li abundance distribution from Israelian et al. (2009) is heavily influenced by non-detections of Li i and thus, upper limits to A(Li), with 17 and 28 upper limits for planet-hosting stars and comparison stars, respectively. Taking the remaining Li i detections from Israelian et al., which span values of A(Li) ∼ 1.0–3.0, and examining the cumulative fraction of A(Li) reveals a shift toward larger Li abundances in the stars without planets, as discussed in Israelian et al. (2009). This same procedure is carried out for the samples of stars here, where there are only 5 upper limits in planet-hosting stars and 8 upper limits in comparison stars. The cumulative fractions of A(Li) in the two sets of stars also show that the comparison stars are shifted toward somewhat larger values of A(Li), but not as large a shift as found by Israelian et al. (2009). Taken together, we find the same effect as found by Israelian et al., however the difference in the samples here is not as large. It is worthwhile to probe for other differences between planet-hosting and comparison stars that might pertain to these possibly real differences in Li abundances between the two sets of stars.

Stellar rotation would be an obvious candidate on which to focus more closely in trying to understand why there might be differences in A(Li) between the planet-hosting and comparison star samples, however such a study is not feasible at the spectral resolution of the observed spectra studied here given the considerable degeneracy between macroturbulence and vsin i.

Another observational variable to investigate is the stellar activity level in the different types of stars studied here for lithium. The index of stellar activity discussed in Section 4.1 is log R'_HK and this index is plotted in Figure 8 versus T_eff over the limited range 5700–5850 K. Within this narrow temperature range, which was the focus of the discussion in Israelian et al. (2009), it is clear that the planet-hosting stars tend to fall toward lower values of log R'_HK relative to the comparison stars.

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The point noted above about differences in stellar activity levels is made clearer by the respective frequency distributions and cumulative fractions of log R'_HK shown in the top and bottom panels of Figure 9, respectively. The comparison stars are shifted significantly toward larger levels of stellar activity when compared to planet-hosting stars. Within a sample of stars which have a restricted range in mass and effective temperature, such as the small subset of stars being discussed here, the value of log R'_HK is likely related to both rotational velocity and age, with both the rotational velocities and chromospheric activity decreasing with increasing age. As noted above, all of the stars studied here within this range of T_eff = 5700–5850 K are slow rotators, thus it is not possible to directly disentangle differences in rotation between stars with and without planets. The other main parameter associated with chromospheric activity and rotation is age; a detailed comparison of derived ages from Paper I between the planet-hosting and comparison stars reveals no significant difference in the age distributions, however it must be noted that the age estimates come with large uncertainties of typically ±2–3 Gyr.

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Takeda et al. (2010) has already noted the difference in chromospheric activity levels between stars with and without planets and argue that the differences in activity levels are rooted in differences in the underlying rotational velocities. The picture put forth in Takeda et al. (2010) is that the stars with planets tend to rotate more slowly (with less stellar activity) due to the influence of giant planets or massive protoplanetary disks slowing down stellar rotation early in the evolution of the parent star.

Sousa et al. (2010) have also investigated the behavior of the Li abundance in stars with and without planets across the 5700–5850 K range in T_eff and find differences in the behavior of A(Li), with the stars with planets having smaller abundances of Li. They investigate the stellar parameters age and mass and conclude that neither the age distributions nor the mass distributions are different for stars with and without planets and thus suggest that the observed difference in lithium abundances is likely due to some process related to the formation of planetary systems (as also concluded by Takeda et al. 2010).

Most recently, Baumann et al. (2010), in a study of 117 solar-like stars, find strong correlations of a decrease in the lithium abundance with stellar age but do not find any differences in the behavior of Li in planet-hosting stars compared to stars without known planets when rather restricted ranges in stellar masses and metallicities are enforced. They suggest that the previously identified differences were due to systematic biases caused by combinations of age and metallicity in the samples.

We investigate the conclusions from Baumann et al. (2010) by restricting the metallicity and mass of the sample of stars studied here and comparing the A(Li)—stellar age relations for stars with planets and those stars without. Using a similar procedure as that in Baumann et al. (2010), we isolate a subset of stars from the already restricted range in effective temperature (T_eff = 5700–5850 K) with [Fe/H] = 0.00 to +0.20 (or +0.10 ± 0.10). Within this parameter range, there are 12 stars without planets having measured Li abundances (and an additional 3 with upper limits) and 6 planet-hosting stars. The parameters of these two sets are closely matched, with the means and standard deviations of stars with planets and stars without planets being, respectively, [Fe/H] = +0.12 ± 0.05 and +0.10 ± 0.03; M = 1.12 ± 0.05 and 1.09 ± 0.06 M_☉; and age = 6.1 ± 1.5 and 5.4 ± 2.0 Gyr. The values of A(Li) versus stellar age are plotted in Figure 10 for the planet-hosting stars and stars without known planets. In this case, there is no significant difference in the behavior of A(Li) with stellar age between the two stellar samples. As noted by Baumann et al. (2010), when the stellar parameters which are known to influence Li abundances over time are restricted, the behaviors of A(Li) in stars with and without planets appear very similar.

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Given that there remains some uncertainty in the detailed behavior of A(Li) and the underlying processes that shape this behavior, the observation noted here that stars with planets tend to exhibit lower stellar activity levels remains. However, at this point, this signature cannot be separated from observational biases which are present in planet detection from radial velocity measurements. Lower values of stellar activity may result in smaller intrinsic radial velocity variations, making the chromospherically quiet stars targets around which planets producing small RV amplitudes can still be detected.