LITHIUM ABUNDANCES IN CARBON-ENHANCED METAL-POOR STARS^*

By taking into account the veiling flux (F_BR²_B) of star B, the observed equivalent width EW^obs for star A can be expressed such that EW^obs_A × (F_AR²_A + F_BR²_B) = EW_A × F_AR²_A, where F_{λ, i} is the continuum flux at the wavelength λ of star i, EW_A is the computed equivalent width for star A, and R_i is the radius of star i. This formula can be then rearranged the following way:

$$\begin{eqnarray} \left (\frac{{\rm EW}_A}{{\rm EW}^{{\rm obs}}_A} - 1 \right) \times \frac{F_{\lambda,A}}{F_{\lambda,B}} & = & \left (\frac{R_B}{R_A}\right)^2 \end{eqnarray} \tag{ 1 }$$

(and reciprocally for component B).

While EW^obs_i can be directly measured on the spectrum (if the radial velocity shift between the two components is sufficiently large), F_{λ, i} and EW_i can be computed from synthetic spectra for any effective temperature, gravity, metallicity, and microturbulence. Note that using equivalent widths offers the advantage of being independent of the instrumental, macroturbulent, or rotation profile. These profiles can be derived by synthetic comparison once all the other parameters have been set.

Moreover, Equation (1) shows that the appropriate combination of these factors should be constant, as (R_B/R_A)² represents the radius ratio of the stars. This property can be used to derive the stellar parameters of the individual components of an SB2. In particular, (R_B/R_A)² must be independent of the excitation potential of the spectral lines. As is the case in the analysis of single-star spectra, the dependence of EW_A on excitation potential is mostly sensitive to changes in effective temperature. Thus, by requiring no trend of (R_B/R_A)² on excitation potential, we can constrain the effective temperature of each star.

In addition, the term F_{λ, A}/F_{λ, B} in Equation (1) is dependent on wavelength. Figure 2 illustrates how the contribution of the flux can vary over the spectrum, depending on its effective temperature. Hence, effective temperatures can be constrained by requiring no dependence of Equation (1) with wavelength instead of excitation potential. Because of the dependence of Equation (1) on excitation potential and wavelength and also on the continuum flux of the other component (i.e., its effective temperature), the temperature determination process must be iterated until convergence.

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However, there is no constraint in Equation (1) on the abundance. Consequently, the derived radius ratio from this equation is dependent on the metallicity, as illustrated in Figure 3. Assuming that the metallicity is identical for both components, the radius ratio and the metallicity of the system can then be immediately derived simultaneously by choosing the metallicity that gives the same radius ratio for both the primary and secondary EWs. Without this assumption, Equation (1) is completely degenerate between the ratio of the metallicities of each component and the radius ratio. In this case, additional constraints on the radius ratio may be set from their observed orbital motion, or constraints on metallicity may be derived from another element.

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Once the effective temperatures of the secondary and the primary, as well as the radius ratio, have been fixed, the veiling factor f_{λ, i} = EW_i/EW^obs_i can be computed for any set of lines. Hence, the respective EW_i of individual stars can be recovered and standard techniques applied. Thus, gravity can be determined from the ionization equilibrium, as is usually done. Similarly, microturbulence velocity can be set by comparing the abundances of strong and weak lines. Note that Equation (1) is also dependent on the microturbulence, thanks to EW_A, and the stellar parameter determination for the components has to be iterated until convergence.

In principle, this method should be applicable to any SB2 for which a spectrum with high resolution and a large wavelength range is available, with the minimum condition that the radial velocity shift is sufficiently large to permit the measurement of the equivalent widths of each component separately. In fact, this technique could even be extended to any SB2 spectrum, once constraints are known (or adopted) on the metallicity ratio or radius ratio of the components.

We have applied the above technique to our double-lined spectroscopic binary CS 22949-008, using a set of measured equivalent widths for the Fe i lines. The derived parameters are listed in Table 2, with errors derived from the line-to-line scatter (one standard deviation). It may be counterintuitive that the error on the effective temperature of the secondary is better constrained than that of the primary. However, as illustrated in Figure 2, a change of 250 K in the temperature of the secondary leads to a change of 5% in its flux contribution to the total flux. Since the S/N of our spectrum is typically 100, it follows that the precision of the flux is known as well as 1%. Hence, a precision of ≈50 K for the temperature of the secondary can be achieved, while the uncertainty of the temperature of the primary is similar to literature values, because it is essentially dominated by the uncertainty on the spectral line data.

Table 2. CS 22949-008 Parameters

	Primary	Secondary
Teff(K)	6190+130− 150	5250+50− 50
log g	4.0 ± 0.2	4.7 ± 0.3
ξt (km s−1)	1.5 ± 0.3	1.3 ± 0.5
[Fe/H]	−2.14 ± 0.04
$\frac{R_{{\rm sec}}}{R_{{\rm prim}}}$	0.59 ± 0.07
$\frac{L_{{\rm sec}}}{L_{{\rm prim}}}$	0.18 ± 0.04

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Table 3 lists the systematic errors on the derived parameters of the SB2 due to uncertainties in the atmospheric parameters of each component. It is noticeable that changes in the stellar parameters of the primary do not impact on the determination of the parameters of the secondary. Indeed, the temperature of the secondary is strongly dependent on the wavelength, whereas a change in temperature of the primary acts as an almost constant change in the luminosity flux over wavelength; thus, it has little impact on the temperature determination. Overall, the technique we employ allows us to estimate the stellar parameters of CS 22949-008 fairly precisely. However, we emphasize that there is a relatively large contrast in effective temperature between the two components, such that Equation (1) is mostly sensitive to excitation potential in the case of the primary, whereas it is mostly sensitive to wavelength variation for the secondary. Hence, the derivation of stellar parameters for the two components is quite independent of one another. Indeed, the degeneracy that can be lifted in the analysis of our system, with a rather large contrast in temperature, is likely more robust than for systems with similar temperatures of the components.

Table 3. Error Budget for CS 22949-008

	Primary		Secondary
	Teff + 150 K	ξt+0.5	Teff + 150 K	ξt+0.5
$\Delta T_{{\rm eff\_prim}}$	+150	+0.5	+15	0
$\Delta T_{{\rm eff\_sec}}$	+16	0	+150	+0.5
Δ[Fe/H]	+0.11	−0.06	+0.02	−0.01
$\Delta \frac{R_{{\rm sec}}}{R_{{\rm prim}}}$	−0.053	+0.015	−0.007	−0.014
$\Delta \frac{L_{{\rm sec}}}{L_{{\rm prim}}}$	+0.02	−0.01	−0.02	+0.01

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Figure 4 presents examples of the Fe i line fits. The radial velocity shift between the two stars is 25 km s⁻¹. From this fit, convolution profiles have been set to 12 km s⁻¹ for the primary star and 6 km s⁻¹ for the secondary star.

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Because of the low temperature of the secondary, its spectral lines are often saturated, but not when their depth is above ∼90% of the continuum of the combined spectrum. For example, Figure 5 shows that the lines of the CH G-band are due exclusively to the primary, while the secondary acts only as a continuum offset. Hence, for our abundance analysis, a careful selection of lines has been performed, so that the chosen lines reach less than ∼90% of the continuum of the combined spectrum (e.g., Figure 5). In contrast, because the primary star is warmer, the CN (as well as C₂) bands appear mostly because of the secondary contribution to the spectrum (Figure 6). The Li line does not appear in either star's spectra. Therefore, we fix the upper limit to log(Li) < 1.0) (Figure 6).

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Using the previously determined radius ratio, we were able to compute synthetic colors for CS 22949-008 (Figure 7). Note that we had to compute specific atmosphere models and synthetic colors to properly take into account the effect of C on the photometry (see Masseron 2006). We see in Figure 7 that, although the secondary's temperature cannot be derived from this diagram, it contributes to the B − V and V − K colors and tends to "cool down" the apparent color compared to a single star by 200 K. Synthetic colors using the stellar parameters determined as described above agree fairly well with the observed colors, although a better match is obtained when the colors are not corrected for reddening. Indeed, we note in Masseron (2006) that the match between spectroscopic and photometric temperatures is generally better with the observed colors.

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For this system, the luminosity ratio determined via the spectroscopic technique does not exactly match the one predicted by standard evolutionary models (Figure 8). While log g for the secondary is in agreement with the theoretical value (log g = 4.7), the log g = 4.0 ± 0.2 for the primary is lower than the value of log g = 4.5 expected based on the isochrones. Although we carefully estimate errors in Tables 2 and 3, it should be stressed that effects such as NLTE can significantly impact estimates of surface gravity. Although we cannot evaluate quantitatively these effects at present, a reasonable change of ≈0.2 dex in gravity would lead to an agreement between the observed and theoretical luminosity ratio to within the uncertainties. We note that Thompson et al. (2008) found a similar problem in the other known C-rich metal-poor SB2 star, CS 22964-161, for which an orbital solution exists and a mass ratio could be derived. The resulting luminosity ratio in this system appeared to also be inconsistent with the gravity derived from spectroscopy (Figure 8).

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If the AGB mass-transfer model is correct, then both the large C abundances and the normal Li abundances need to be the result of transferred AGB material mixing with the material in the convective envelope of the CEMP star. Initially, before mass transfer took place, the star that is now observed as a CEMP star very likely had the same composition as any extremely metal-poor star, namely, no C-enhancement and normal Li abundance. As more and more AGB material is transferred and the ratio of mass in the convective envelope of the secondary component to transferred mass decreases, the C/H ratio on the surface of the CEMP star will increase. According to the yields we have adopted for this study, in most cases, the Li abundance in the AGB star is lower than the Spite plateau value. Consequently, the more AGB material is transferred, the more the Li/H ratio will drop. In a few specific cases depending on the model assumptions, the abundance of Li in the AGB star is higher than the Spite plateau value. In these cases, the more AGB material is transferred, the more the Li/H ratio will increase, along with C. In any case, the predicted C, N, and Li abundances of the CEMP star depends on the amount of dilution of the AGB material, the AGB yields, and the original abundances in the CEMP star.

To test if any observed combination of Li, C, and N can be explained by AGB mass transfer, we compare the measurements in the extended sample with different amounts of dilution of material having 2 M_☉ AGB yields for different models with different assumptions (Figure 10). We chose 2 M_☉ because this is the only value that permits comparison between all models available in the literature (the influence of the mass is discussed next). We define the dilution factor as the fraction of mass transferred from the AGB in the total mass of the convective envelope of the companion after the transfer. We plot [(C+N)/H], rather than [C/H], because the amount of C that is converted into N in AGB stars is currently not well understood (see, e.g., Johnson et al. 2007). We also choose to plot [(C+N)/H], rather than [(C+N)/Fe], because C is a primary element in AGB stars. There is not a strong dependence on metallicity for C production in AGB stars for the metallicity range we considered (e.g., the yields of a 3 M_☉ AGB of Karakas & Lattanzio (2007) give [(C+N)/H] = +0.97 for Z = 4 × 10⁻³ and [(C+N)/H] = +1.17 for Z = 10⁻⁴); thus, the comparison between CEMP stars of different metallicities and models of a single metallicity (Z = 10⁻⁴) is valid. Note that we ignored the effect of possible hydrogen injection episodes that are predicted to occur in stars with low metallicity (Campbell & Lattanzio 2008; Lau et al. 2009; Suda & Fujimoto 2010). The main results of H-ingestion episodes are large enhancements of C and N at the stellar surface.

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We computed dilution tracks using the relation

$$\begin{eqnarray} [{\rm (C+N)/H}] &=& \log ((A({\rm C})_{{\rm AGB}}+A({\rm N})_{{\rm AGB}}) \times d\nonumber\\ && + (A({\rm C})_{{\rm init}}+A({\rm N})_{{\rm init}})\times (1-d))\nonumber\\ && - \log (A(C_\odot)+A({\rm N}_\odot)) \end{eqnarray} \tag{ 2 }$$

$$\begin{equation} \log _\epsilon ({\rm Li}) = \log (10^{\log _\epsilon ({\rm Li})_{{\rm AGB}}} \times d + 10^{\log _\epsilon ({\rm Li})_{{\rm init}}} \times (1-d)), \end{equation} \tag{ 3 }$$

where d is the dilution factor, varying between 0 (no mass transfer) and 1 (convective envelope of the CEMP star composed entirely of AGB-transferred material). The initial C+N yields (log(C + N)_AGB) are taken from various models. We assume an almost Li-free accreted material (log(Li)_AGB = −1.0), as well as an initial Spite plateau Li (log(Li)_init = 2.2) and a [(C + N)/H]_init = −2.0, compatible with non-C-rich main-sequence metal-poor stars with [Fe/H] = −2.0 (e.g., Asplund et al. 2006).

Figure 10 shows that there is a regime where C remains high, while the Li abundance is almost identical to the Spite Li plateau. This corresponds to a dilution factor of ∼10%, similar to that found by Thompson et al. (2008).

However, not all AGB stars have masses of 2 M_☉, and in Figure 11, we plot the dilution tracks for yields from AGB stars with a range of masses from Karakas (2010), including Li yields. Figures 10 and 11 also show that the observed abundances of Li-normal stars fall into this regime, suggesting that the Li abundances observed in these stars might not require any production by the AGB companion, in contrast to the conclusions of Norris et al. (1997a), Sivarani et al. (2006), and Thompson et al. (2008).

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We also see in this figure that it is the Li-depleted dwarfs with low [C/H] that cannot be reproduced by the dilution tracks. Even the lowest-mass AGB star shown in Figure 11 has a sufficiently high Li yield that it cannot reproduce the Li-depleted dwarfs. Figure 11 illustrates another prediction of the AGB models that makes the creation of Li-depleted dwarfs more difficult. The Li yields of the Karakas (2010) AGB models are not zero for stars of any mass, and for each mass, the dilution curves stop at the log(Li) abundance of pure AGB material. However, there are uncertainties of Li yields from the AGB models due to mass loss, for example. While taking the yields from an AGB model and then applying a dilution factor is a simple way to estimate the abundance of the companion, it does not exactly reproduce what the composition of the mass transferred in a real binary system. Once the mass transfer starts, the envelope of the AGB primary may be lost and the evolution truncated (Hurley et al. 2002; Izzard et al. 2009). Particularly for Li, it is very likely that the surface abundances of Li vary by more than one order of magnitude from early AGB until the end of evolution (Karakas 2003). Therefore, the Li abundance of the companion depends on when mass transfer starts and hence the period of the binary system. However, when comparing Figures 10 and 11, the dilution tracks do not much depend on the AGB Li yields. For instance, if more Li depletion is considered, the dilution tracks tends to extend toward lower Li values but still do not encompass the CEMP data. Therefore, within the assumption that [C+N] yields of a single AGB star are valid for CEMP binary systems, the presence of Li-depleted CEMP stars cannot be explained.

Comparison with Ba Abundances and ¹²C/¹³C Ratios. One alternative explanation for the results in the previous section is that current AGB models predict too high C+N yields. Stancliffe (2010) pointed out that, to fit the mild C abundances of the SB2 CS 22964-161, they need either to invoke some mixing process or to decrease the C yields of the former AGB companion. Additionally, Masseron et al. (2010) showed that the [Ba/C] measured in CEMP stars is too high compared to the predictions, highlighting a problem for the predictions of either the Ba or the C production. To explore this possibility, we checked whether the dilution models agree with other observations of CEMP stars, in particular the Ba abundances, which are sensitive to s-process production, and the ¹²C/¹³C isotope ratios, which are sensitive to proton-capture reactions that happen under the same physical conditions as the Cameron–Fowler mechanism.

Figure 12 shows the abundance of Li as a function of [Ba/Fe] compared with dilution tracks, similar to those obtained for C+N. In this case we use [Ba/Fe] = 0 as the secondary's initial Ba abundance. Here the dilution tracks also cannot reproduce the Li-normal and the Li-depleted stars based on a single set of models, as the full range is spanned only if we adopt different sets of models. However, this conclusion is less secure than for C+N because the available models cannot predict the abundances of Ba and other s-process elements in CEMP without requiring an ad hoc parametric mixing mechanism to form a ¹³C pocket and facilitate s-process production. Note that, while the observed data in the figure span a wide metallicity range, models shown have [Fe/H] = −2.3 only. However, Ba production in metal-poor AGB stars depends proportionately on the metallicity (Straniero et al. 1995; Goriely & Mowlavi 2000) and thus [Ba/Fe] is almost constant for a given AGB mass. This fact has been confirmed by Masseron et al. (2010), who noticed that [Ba/Fe] is strongly correlated to C in CEMP stars. For this reason, assuming a metallicity of [Fe/H] = −2.3 for all the models to represent the bulk of the CEMP-s stars is suitable for purposes since we are looking for global trends and not trying to fit abundance patterns of individual objects.

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As shown by Masseron et al. (2010), CEMP stars exhibit a correlation between their ¹²C/¹³C ratios and C/N. This is clear evidence that CN cycling occurred in the AGB stars. Complete or partial CN cycling indicates that the envelope of the star has reached sufficiently high temperatures that Li can be easily destroyed. Naively, one might expect that the more complete the CN cycle is (hence the lowest ¹²C/¹³C ratios are reached), the more Li is destroyed. On the other hand, Masseron et al. (2010) demonstrated that extra mixing was at work below the convective envelope in the companions of CEMP stars. Li production by extra mixing may be possible (Domínguez et al. 2004; Stancliffe 2010) and is expected to also show a correlation with the ¹²C/¹³C ratio. In both scenarios, a correlation between Li abundances and C isotope ratios would be expected if the Li/H ratio was mainly determined by the Li/H ratio in the AGB gas. However, Figure 13 shows that both Li-normal CEMP stars with low ¹²C/¹³C ratios and Li-normal CEMP stars with high ¹²C/¹³C ratios exist. Li production or destruction is extremely sensitive to the adopted mixing parameters (Wasserburg et al. 1994). While continued investigation of the yields and the impact of extra mixing in AGB stars are important for this discussion, there is no conclusive evidence that they are uncertain enough to explain the broad dispersion of Li in CEMP stars. Actually, it is puzzling that CEMP stars with apparently similar companions (at least with identical extra mixing parameters leading to identical C isotopes and s-process enrichments) can exhibit such a broad variety of Li abundances (Figures 12 and 13). This may indicate that the carbon isotope ratios seen in the CEMP stars reflect the nucleosynthesis in the AGB stars, whereas the Li abundances reflect processing in the CEMP stars themselves.

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We have argued that the Li-normal CEMP stars can naturally appear in the AGB mass-transfer scenario. However, some AGB stars within a limited mass range are expected to produce Li in excess of the Spite plateau value and, if such an enriched gas is transferred to a companion, that companion should appear as a Li-rich star, unless in all cases processes in the CEMP star destroy the Li. We find no such Li-rich stars in our VLT sample, nor in the extended sample. We can test if the lack of Li-rich stars is expected in a sample of the size discussed in this paper, if AGB mass transfer is responsible for the creation of CEMP stars. As mentioned in the Introduction, the Li yields from AGB stars and the amount of mass transferred are uncertain, but we can calculate the statistics for several cases (see Table 8). In one case, we assume that the percentage of transferred mass compared to convective envelope mass is 10% (d = 0.1), similar to the ratio that Thompson et al. (2008) found for CS 22964-161. In another case, we assume that the dilution factor is so large (d = 1) that the abundances on the surface of the CEMP star reflect the yields of the AGB star for all elements. This case reflects the fact that Izzard et al. (2009) computed that as much as 0.1 M_☉ should be typically accreted onto the relatively small (i.e., a few 10⁻³ M_☉) convective envelope of the CEMP star. In contrast, we assume in the last case (d = 0.01) that the accreted material has been highly diluted into the CEMP star (possibly by thermohaline mixing; see Stancliffe et al. 2007).

Table 8. Predicted Distributions of Li Abundances

Primary Masses	Abundance Used	Dilution	% Li-rich	% Li-normal	% Li-poor
M☉		d	log (Li) >2.2	2.0 < log (Li) <2.2	log (Li) <2.0
		0.01	4	96	0
		0.10	4	96	0
0.83 M☉–8.0 M☉	K10	0.30	4	95	1
		0.50	4	73	23
		0.80	4	1	95
		1.00	4	0	96
		0.01	2	98	0
		0.10	2	98	0
0.83 M☉–3.0 M☉	K10	0.30	2	98	0
		0.50	2	76	22
		0.80	2	0	98
		1.00	2	0	98
		0.01	3	97	0
		0.10	3	97	0
1.0 M☉–3.0 M☉	K10	0.30	3	0	97
		0.50	3	0	97
		0.80	3	0	97
		1.00	3	0	97
		0.01	10	90	0
		0.10	10	90	0
1.5 M☉–3.0 M☉	K10	0.30	10	1	89
		0.50	10	1	89
		0.80	10	1	89
		1.00	10	1	89
		0.01	0	100	0
		0.10	0	100	0
1.0 M☉–3.0 M☉	log(Li) = −1	0.30	0	0	100
		0.50	0	0	100
		0.80	0	0	100
		1.00	0	0	100

Note. K10: Li AGB yields from Karakas (2010).

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We use the yields of Karakas (2010), performing a linear interpolation between the model yields to predict the Li yield for stars of any mass. For AGB stars with masses less than 1.0 M_☉ we adopt the ratios for a 1.0 M_☉ AGB star. We also need to assume the distribution of mass ratios (q) for binaries and the range of primary and secondary masses that will produce observable CEMP stars today.

We consider several cases for the mass range of the primaries: the low-mass limit is between 0.83 M_☉ and 1.5 M_☉, while the high-mass limit is set to either 3 M_☉ or 8 M_☉. The 0.83 M_☉ limit for the AGB stars at the low-mass end comes from the fact that observations of the very low mass, low-gravity star CS 30322-023 are compatible with the theoretical expectation that it is a low-mass AGB that has dredged up C, N, and s-process elements (Masseron et al. 2006). On the other hand, this low-mass limit for third dredge-up is metallicity and model dependent (e.g., Karakas et al. 2002). Depending on the assumptions in models, stars with M < 1.5 M_☉ are not expected to produce enough C and s-process elements to make CEMP stars, so we adopt 1.5 M_☉ as another possible limit. At the high end, the 8 M_☉ limit comes from theoretical expectations of the highest mass an AGB star can have (see, for example, Ventura & D'Antona 2010). However, in AGB stars of very low metallicity (Z = 10⁻⁴ with M > 3 M_☉), hot bottom burning should have occurred, which will produce nitrogen-enhanced metal-poor (NEMP) stars rather than CEMP stars.

The limits for the secondaries are always between 0.71 M_☉ and 0.82 M_☉, which come from demanding that the secondary star have a luminosity where its Li is not expected to be depleted (see Figure 9). We converted between luminosity and mass using a 12 Gyr Padua isochrone with Z = 0.0001 (Girardi et al. 2002). For our mass ratios, we followed the lead of Izzard et al. (2009) and adopted a flat distribution of q values, because there is no estimate in the literature of q at low metallicity. The initial Li abundance of the CEMP gas was set to 2.2; thus, any secondary with a Li abundance higher than 2.2 is labeled Li-rich.

Examination of Table 8 reveals that, regardless of the assumptions, less than 10% of dwarfs should be Li-rich if CEMP stars are the result of AGB mass transfer. In the dwarf category, we have 12 stars with a useful Li measurement, none of which are Li-rich. Therefore, our approximate calculation of the number of Li-rich stars agrees with observations. We note that any subsequent mixing in the CEMP star that destroys Li will artificially decrease the number of detected Li-rich stars, which is another reason why it is not surprising that we have not found any. The adopted yields also play a role in the expected number of Li-rich stars. According to the Ventura & D'Antona (2010) yields, for example, Li is produced in excess of the Spite plateau value for AGB stars with M > 7 M_☉, which should produce substantial amounts of N and form NEMP stars rather than CEMP stars. We note that in the Galactic disk, the Li abundance in AGB stars that dredge it up from their interiors can reach very high values (log(Li) ≳ 4), but the majority of the AGB stars (∼90%) show no Li enrichment (Abia et al. 1993; Uttenthaler & Lebzelter 2010). The fact that we find no Li-rich CEMP stars may indicate that Li production during the AGB phase was rare at the metallicities of the CEMP stars, although a larger sample is necessary before any definite statement can be made.

The predicted relative numbers of Li-normal and Li-depleted stars in the absence of additional depletion in the CEMP stars depend much more on the amount of dilution than did the number of Li-rich stars. For the cases of ∼0%–20% dilution, the expected number of Li-depleted CEMP stars (i.e., log(Li) < 2.0) should be 0% and a majority of stars should be Li-normal (∼96%). The opposite is true in the case of very large dilution factors (Table 8), indicating the sensitivity of the Li abundance to details of the mass transfer rather than to AGB nucleosynthesis. We reiterate that Figures 10 and 11 show that large dilution factors should be accompanied by large C enhancements; therefore, at least some fraction of our sample of stars has likely experienced dilution factors of ∼0%–20%. More quantitatively, we can count 15 stars for which −1 < [C + N/H] < 0. This range of C+N approximately corresponds to a 10% dilution factor. Among these, 12 (∼80%) are Li-depleted. This is very far from <10% expected, based on dilution. Yet these stars are Li depleted, which must then happen during the lifetime of the CEMP star itself.

We have shown in Figures 10 and 11 that the low-C and low-Li stars are difficult to explain with just a dilution scenario. Therefore, some extra Li depletion should occur in the atmosphere of CEMP stars. For the case of the CEMP stars, two main physical mechanisms have been proposed in the literature that could be responsible for Li depletion: thermohaline mixing and rotation. In this section, we will examine whether either scenario is compatible with the observations of CEMP stars.

Thermohaline Mixing. Because CEMP stars have accreted large amounts of material from their companions, there are probably changes in their stellar structures that result. Whether thermohaline mixing, caused by the addition of material with a higher molecular weight on top of a material with lower molecular weight, is sufficient to explain abundance correlations in stars is still the subject of debate (Charbonnel & Zahn 2007; Eggleton et al. 2008; Denissenkov 2010; Palmerini et al. 2011), as it is dependent on the free parameter that is supposed to represent the thermohaline "finger" length. Note that while Masseron et al. (2010) did not find strong evidence for deep thermohaline mixing in CEMP stars, they could not rule it out. If it occurs, thermohaline mixing will affect other abundances besides Li. Stancliffe et al. (2009) predicted that thermohaline mixing will affect the C isotope ratios in the material transferred from the AGB star. Because of mixing in the CEMP star, the original AGB composition is not preserved, and there should be a change in the ¹²C/¹³C ratio as a function of the CEMP luminosity when the stars evolve from dwarfs to giants. If we advance the hypothesis that the observed Li-depletion spread is related to different thermohaline mixing efficiency, we would expect that the ¹²C/¹³C ratios would reflect the same efficiency. Figures 13 and 14 show no evidence to corroborate this idea. However, Stancliffe & Glebbeek (2008) noted that gravitational settling could weaken the thermohaline process. Also, Li burns at 2.5 × 10⁶ K, while CN cycling starts only at 90 × 10⁶ K, so there is still some room for Li to be destroyed in the CEMP star while ¹²C/¹³C remains unchanged from the AGB yields. Another test is that the thermohaline strength should be correlated with the amount of accreted material, i.e., the more C is accreted on the surface of the CEMP stars, the deeper the mixing under the atmosphere of the star, and the larger the Li depletion. However, the more efficient the thermohaline mixing is, the more the accreted material is diluted. Hence, it is difficult to confidently predict an anti-correlation between C+N and Li.

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Nevertheless, we stress that Stancliffe (2009) shows that thermohaline mixing inevitably leads to Li depletion, and thus the presence of Li-normal stars along Li-depleted stars with the same C+N abundances requires Li production in the AGB companion, which is uncertain (see Section 3.3.1). Although the μ-gradient established by the transfer of material should initiate thermohaline mixing in the CEMP stars' atmospheres, its efficiency and therefore its impact are difficult to detect, and it might not be the major source of the Li depletion.

Rotation. An alternative explanation for Li depletion is rotation, where the additional meridional circulation and shear turbulence drag down some Li to hotter temperatures and partially destroy it. Lithium depletion in dwarfs is not only seen in CEMP stars. Norris et al. (1997b) found three non-C-rich metal-poor stars with depleted Li. They argued that these stars were likely in binary systems that somehow caused their Li depletion. Ryan et al. (2001) and Ryan et al. (2002) further analyzed some of these Li-depleted main-sequence halo stars and presented evidence that rotation has indeed played a role in the Li destruction. Most CEMP stars are demonstrated to be old binary systems (Lucatello et al. 2005b). Indeed, increased rotational velocities of CEMP stars are all the more likely.

Figure 15 shows the Li abundances as a function of line broadening profile for the CEMP dwarfs. Broadening profiles have been derived by setting a Gaussian profile of synthetic Fe lines to match the observations. For stars that do not belong to our sample, the synthesis has been made according to the published stellar parameters and the observations have been obtained from available archives. By using this technique, the resulting broadening profile represents either the macroturbulence velocities in the atmosphere of the star, its rotation, or both (note that the broadening due to the instrument should not be a limiting factor in our case because the spectra have a resolving power high enough to resolve the intrinsic line profiles). Concerning macroturbulence broadening, 3D modeling predicts a broadening of typically 3 km s⁻¹ for metal-poor stars (e.g., Asplund et al. 2006; Steffen et al. 2009), which is negligible compared to the broadening profiles displayed in Figure 15.

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Finally, a large fraction of stars have a broadening profile >8 km s⁻¹, which cannot be consistent with the slow rotational velocity expected for the old population of dwarfs (typically 2 km s⁻¹; Skumanich 1972; Lucatello & Gratton 2003). Therefore, we assume that the derived velocities are mainly due to the rotation of the star, in particular for the highest values. It is notable that the largest broadening profile obtained corresponds to HE 0024-2523 (Lucatello et al. 2003), the shortest period binary known among CEMP stars, hence possibly the fastest rotating star we have considered.

In Figure 15, all stars with large rotational velocities show depleted Li. Additionally, all Li-normal stars have low rotational velocities. This indicates that rotation is responsible for depletion in some CEMP stars (at least for the fastest rotators). For this explanation to work, the degree of mixing caused by rotation needs to be large enough to destroy Li without affecting CN or carbon isotopes, because we see no correlation between [C/N] and C isotopes and rotation. However, unlike thermohaline mixing models, models of rotational mixing, at least for Sun-like stars, suggest that it destroys Li without affecting C or N until the subgiant/giant branch (Pinsonneault et al. 1989)

We note also that Li-depleted CEMP stars with low rotational velocities exist as well. Nevertheless, due to the unknown projection angle of the rotation axis of the stars, it is impossible to conclude for these stars whether the rotation is actually low in these stars or another mechanism is at work to deplete the Li. It is therefore difficult, with the current data, to exclude thermohaline mixing as the driver for Li depletion in CEMP stars. Charbonnel & Lagarde (2010) studied the complex interplay between rotation and thermohaline mixing and found that rotation favors the occurrence of thermohaline mixing in low-mass solar metallicity RGB stars. Furthermore, Stancliffe & Glebbeek (2008) show that, beyond rotation and thermohaline mixing, other mechanisms such as gravitational settling may play some role in dwarf CEMP stars and subsequently affect the observed Li abundances. In the end, the various contributions of all these physical processes may explain the observed Li abundance scatter.

In view of the ongoing debate about whether the different CEMP subclasses are the result of the same basic phenomenon, it is interesting to compare the behavior of Li in CEMP-s, CEMP-rs, and CEMP-no stars. The last column of Table 4 reports the stellar classification as CEMP-s, CEMP-rs, or CEMP-no, for the stars of our sample based on the Ba and Eu abundances, as defined in Masseron et al. (2010). The classification for the stars mentioned in Table 7 can be found in Masseron et al. (2010). Figure 16 shows the distribution of Li abundances for stars in each subclass. There are Li-normal and Li-depleted stars in both the CEMP-s and CEMP-rs subclasses, which suggests either that the carbon for each subclass comes from a similar source or that effects in the CEMP star, such as extra mixing, dominate over the Li signature of the polluting material. All of the CEMP-no stars in the extended sample are Li depleted. The origin of CEMP-no stars is still uncertain—their peculiar abundances come either from a non-s-process-element producing AGB mass transfer or from C-rich gas coming from a previous generation of massive stars (see, e.g., Masseron et al. 2010, for more details). If the C comes from pollution by the winds of rapidly rotating massive stars, it is not clear if the Li abundances can discriminate between the scenarios, because the yields given by Meynet et al. (2006) are compatible with AGB yields down to the point that "almost no distinction could be made" (Meynet et al. 2006). Figure 10 shows that with high dilution factors (∼50%), the wind models can explain some Li-depleted CEMP-no stars with moderate carbon enhancements. The lack of Li-normal stars among the CEMP-no stars may also be the result of the combination of their metallicities and our definition of "Li-normal." Aoki et al. (2007) and Masseron et al. (2010) noted that CEMP-no stars are on average more metal-poor ([Fe/H] ≲ −2.7) than CEMP stars in other subclasses. Bonifacio et al. (2007), Aoki et al. (2009), and Sbordone et al. (2010) found that non-C-rich metal-poor stars with [Fe/H] <−3.0 appear to exhibit a decrease in Li abundance compared to the Spite plateau. Hence, the fact that we do not see Li-normal stars among CEMP-no stars might also be affected by our conservative definition of Li-normal stars, which does not encompass stars with log(Li) < 2.0. However, in the end, our sample of the CEMP-no stars is small; more Li data for this category could reveal Li-normal stars here as well.

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The presence of Li-normal stars among CEMP-rs stars is informative for another reason. As observed by Masseron et al. (2010), some CEMP stars, mostly in the CEMP-rs subclass, lie off the standard evolutionary tracks and are more luminous or bluer than expected from isochrones of the appropriate metallicities. It is not yet clear why these stars show such properties, but some of the scenarios for forming field blue stragglers imply mass transfer of material, as is the case for CEMP-rs stars. CEMP-rs stars show the highest enhancements of C and neutron-capture elements in their atmospheres. This could drive efficient thermohaline mixing, which drags the C-enriched material down to the core and boosts the luminosity of the stars through the CNO cycle (Stancliffe et al. 2007). In any possible scenarios, Li should have been heavily destroyed. However, the upper panel of Figure 16 shows that there are Li-normal stars in the CEMP-rs class. Therefore, the reason why some CEMP-rs stars are not located on the regular track of the H-R diagram remains unsolved.