Li i AND K i SCATTER IN COOL PLEIADES DWARFS^*

It is expected that surface magnetic activity (spots and plages) could alter Li i line strengths. Spatially resolved solar observations show variations by factors of ∼2 and 10 in the Li i equivalent width in spot and plage regions, respectively (Giampapa 1984). Patterer et al. (1993) have found Li i line strength variations in weak-lined T Tau stars that are not correlated with chromospheric emission variations, but are consistent in size with those expected from the simple spot/plage model of Giampapa (1984). Jeffries et al. (1994) find rotational modulation of the λ6707 (and/or nearby blended features) in the young Local Association K6 dwarf BD+22 4409.

One might think that the stark difference between the factor of ∼2 scatter in λ6707 Li i line strengths for 0.7 ⩽ (B − V)₀ ⩽ 0.8 versus the absence of scatter in λ7699 K i over this same range is a powerful argument against spots as a source of Li scatter in our stars. Surprisingly, this is not necessarily the case. The influence of various analytic spot models on the location of Pleiades in the K, Li line strength versus color plane can be seen in Figures 3 and 6 of Barrado y Navascues et al. (2001). The models with the two lowest photosphere-spot temperature contrasts (their models 2a and 2b) and 80% spot coverage are able to displace stars redward and to higher Li i equivalent width into the 0.7 ⩽ (B − V)₀ ⩽ 0.8 color range in such a way as to introduce a near factor of 2 scatter in Li line strength, but move stars nearly parallel to the intrinsic K i line strength versus color locus; i.e., the analytic spot models can, in fact, produce the Li i scatter we observe while not introducing substantial scatter in the K line strengths.

As seen in Figure 2 of Barrado y Navascues et al. (2001), these models also move the Pleiades roughly parallel to the main-sequence in the H–R diagram such that significant photometric scatter, ΔV ⩾ 0.1 mag, is not introduced either; such scatter is not evinced by our stars (Figure 3). Barrado y Navascues et al.'s (2001) larger photosphere-spot temperature contrast models (models 2c and 2d) can reproduce the observed scatter in Li line strengths with spot coverage fractions of ∼60%; however, their Figure 2 shows that such stars would be subluminous by ΔV ⩾ 1 mag in the color–magnitude diagram. The photometric data in Figure 3 clearly excludes these large temperature contrast spot models. The large photosphere-spot temperature contrast models only modestly alter the star's color (Figure 2 of Barrado y Navascues et al. 2001). As a result, a similar degree of scatter is introduced into the Li and K line strengths (Figures 3 and 8 of Barrado y Navascues et al. 2001)—a prediction also excluded by our spectroscopic data.

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In sum, the marked difference between K i and Li i scatter cannot exclude a spot origin for the Li scatter in our Pleiades. While the indistinguishable spread of Li in the (V − I)– and V–Li EW planes (Figure 4) compared to that in the (B − V)-based plane of Figure 2 does not betray the presence of spots, two spectroscopic signatures do robustly exclude the analytic spot models 2a and 2b of Barrado y Navascues et al. (2001) as a source of the Li scatter. The first is the difference in Li abundances derived from the λ6707 Li i resonance line and the weaker blended 1.85 eV λ6103.6 Li i subordinate feature(s) previously investigated in the Pleiades by Ford et al. (2002). We selected several interesting sets of Pleiades of similar color but with significantly different λ6707 Li i line strengths (Table 2). Effective temperatures and microturbulent velocities are adapted from the spectroscopic parameters determined by Ford et al. (2002). Following these authors, we assumed log g = 4.5 for all stars since the derived Li abundances are insensitive to the assumed gravity. We determined Li abundances from the λ6707 resonance line from our measured equivalent widths via Dr. A. Steinhauer's $\sf {LIFIND}$ program discussed in King & Schuler (2005); these are given in Column 6 of Table 2.

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Abundances from the λ6104 Li i features were determined via spectral synthesis carried out with an updated version of the LTE analysis MOOG Sneden (1973) and Kurucz model atmospheres.⁶ The λ6104 region line list was formed utilizing atomic data from the Vienna Atomic Line Database (Kupka et al. 2000) and Kurucz line data,⁷ and CN data from Davis & Phillips (1963). The line list was calibrated by adjusting some oscillator strengths in order to produce solar syntheses matching the Kurucz solar flux atlas (Kurucz 2005) using input abundances from Anders & Grevesse (1989) except for CNO; solar values of log N(C) =8.39, log N(N) =7.78, and log N(O) = 8.68 were adopted from Asplund et al. (2005) and Allende Prieto et al. (2001). The Pleiades syntheses assumed input scaled solar abundances with [m/H] =−0.06 based on the results of Ford et al. (2002)

Sample λ6104 Li i spectra and syntheses are shown in Figure 5. Abundances are given in the penultimate column of Table 2, whose final column lists the λ6104- and λ6707-based Li abundance differences. There are two notable features in the abundance comparisons. First, the significant Li scatter persists when measured from the λ6104 feature. Second, we find no significant difference between the resonance line- and subordinate line-based abundances. The mean difference (6104–6707) is +0.01 dex with small scatter (±0.08 dex, s.d.).

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We find that the Barrado y Navascues et al. (2001) analytic spot models reproducing the observed Li dispersion of our sample in the range 0.7 ⩽ (B − V)₀ ⩽ 0.8, lead to significantly larger predicted 6104–6707 Li differences. Syntheses of the λ6104 and λ6707 Li i regions—the latter using the line list from King et al. (1997) updated with VALD atomic data and recalibrated to the solar flux spectrum—were performed using the photosphere and spot parameters of models 2a and 2b with 80% spot coverage from Barrado y Navascues et al. (2001) assuming log g = 4.5, ξ = 2.0 km s⁻¹, [m/H] =−0.06, and an input abundance of log N(Li) =2.80. The photospheric and spot spectra were weighted by their respective Planck functions and coverage fractions before adding and renormalizing.

The resulting λ6104 and λ6707 photosphere+spot spectra were analyzed as observed data via spectrum synthesis computed for T_eff = 5225 (the value of the spotted models consistent with flux conservation), log g = 4.5, ξ = 2.0, and [m/H] =−0.06. The λ6707 Li abundances deduced from the spotted synthetic spectrum are log N(Li) =2.90 and 3.02 for spot models 2a and 2b, respectively. The corresponding λ6104 Li abundances are 3.32 and 3.62. The Li differences (6104– 6707 Å) deduced from the two Li i lines—0.42 and 0.6 dex for spot models 2a and 2b—are significantly larger than the zero difference exhibited by our stars.

The second spectroscopic signature that is inconsistent with the analytic spot models reproducing the observed Li spread in our stars is the strength of CN lines in both the λ6104 and λ6707 region. The CN line depths in the T_eff = 5225 spotted synthetic spectra are some 3–5 times deeper than observed in our actual object spectra. Figure 6 illustrates a related important point: while the warmer photosphere (T_phot = 5655 K; 20% coverage) and cool spots (T_spot = 4870 K; 80% coverage) in model 2a of Barrado y Navascues et al. (2001) conspire to yield a spotted star of T_eff ∼ 5225, the spectrum of such a model is not equivalent to that of an unspotted model with T_eff = 5225. Figure 6 indicates the CN features are significantly stronger in the spotted model.

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Schuler et al. (2004) find that our cool Pleiades' O abundances derived from the high-excitation O i λ7774 triplet in our spectra show a dramatic increase with declining T_eff and significant star-to-star scatter. Schuler et al. (2006b) show that photospheric hot spots provide a plausible explanation for this behavior. In order to examine whether the Li and O scatter are related, the λ6707-based Li and λ7774-based O abundances were fit as functions of T_eff using low-order polynomials. To ensure consistency for this purpose, Li abundances were determined with $\sf {LIFIND}$ using the stellar parameters of Schuler et al. (2004); these were updated for H ii 298 using our (B − V)₀ value, adjusting the Schuler et al. (2004) O abundance (to [O/H] =+0.80) in the process. The resulting abundance residuals (observed minus fitted), shown in Figure 7, are not correlated. Moreover, the rms dispersion of the observed Li abundances (∼0.22 dex) is twice that of the O abundances (∼0.12 dex) despite the fact that the temperature sensitivity of the (logarithmic) O abundances is 2–3 times larger than that for Li. We conclude that the dispersion in our Pleiades' Li is not associated with that in O i.

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We have utilized high-resolution and high-S/N spectroscopy to measure λ6707 Li i and λ7699 K i line strengths and λ6707- and λ6104-based Li abundances in 17 slowly (projected) rotating cool Pleiades dwarfs. A significant factor of ∼2 dispersion is seen in the λ6707 Li i line strengths over the 0.72 ⩽ (B − V)₀ ⩽ 0.82 color range; this large Li scatter is also inferred from λ6104 subordinate line-based abundances. The scatter in our selected sample eliminates line blending due to rapid projected rotation as a source of Li dispersion in our Pleiades. In contrast to previous studies, our high-resolution and S/N data evince no substantial scatter in the λ7699 K i line strengths of our particular Pleiad sample. This stark distinction relative to the Li line strengths excludes simple color or T_eff errors or line formation effects due to an overlying chromosphere as the source of Li scatter in our stars.

The difference in the dispersions of the K i and Li i line strengths does not, however, exclude spots as a source of the Li scatter; in particular, the analytic spot models 2a and 2b of Barrado y Navascues et al. (2001) can produce the Li scatter we observe without leading to significant scatter in K i line strengths or in the color–magnitude diagram. The equivalence of the λ6707- and λ6104-based Li abundances in our stars does, however, exclude these spot models, which predict a factor of ⩾3 difference in the resonance and subordinate line-based Li abundances. These spot models also would lead to CN line strengths significantly larger than observed in our spectra.

The simplest explanation of the Li i dispersion in our Pleiades is scatter due to real abundance differences. There are numerous candidate mechanism(s) to explain these pre- or near-zero-age main sequence abundance differences: chemical inhomogeneities, magnetic field differences, variable mass accretion, and individual rotational histories (Ventura et al. 1998; Garcia Lopez et al. 1994). While the effects of chromospheres on Li i line formation and the effects of rotation on measurements of the Li i line strength espoused by King & Schuler (2004) and Margheim et al. (2002) may contribute to an (illusory) Li dispersion, our results suggest that there must also be a real component to the Pleiades Li dispersion—at least over the range 0.7 ⩽ (B − V)₀ ⩽ 0.8 seen in Figure 2.

The size of the real component is difficult to determine directly; however, future work can deduce the size and mass range of real scatter since sources of possible illusory dispersion are amenable to observation. Systematic effects of rotation on Li abundance measurement of rapid rotators or from low spectral resolution (neither characterize our data) can be mitigated by determining abundances from spectrum syntheses with suitable accounting of macroscopic broadening. The influence of chromospheric emission and surface magnetic activity (spots and plages) on Li i (and K i) lines can be measured by searching for correlated temporal variations in alkali line strength and chromospheric emission and photometric indices via a simultaneous spectroscopic and photometric monitoring program of the Pleiades (Jeffries 1999). Our Li equivalent widths and those of Soderblom et al. (1993) for five stars (H ii 152, 263, 2126, 2311, and 2366) differ at the ⩾2σ level, providing impetus for such a program. Additional constraints may be gleaned from observations of ⁹Be in our cool Pleiades, as well as in similarly cool Hyades stars, whose degree of Li scatter is unknown due to vanishingly weak Li line strengths (Soderblom et al. 1995).

We believe that the most likely theoretical explanation of a real star-to-star Li dispersion in the Pleiades is a range in pre-MS lithium depletion. Such a range would naturally emerge if the radii of protostars of the same mass, composition, and age during the epoch of pre-MS lithium depletion were somehow different. To explain the empirical trend, one would also require the more rapidly rotating and active stars to have been larger. There is now emerging evidence that activity impacts the radii of both main-sequence and pre-MS stars in precisely this sense. Torres & Ribas (2002) found that the radii of the near-twin stars in YY Gem were far too large to be consistent with the predictions of standard stellar theory. Subsequent data confirmed this result, and Morales et al. (2008) found a correlation between activity and the radius excess in low mass stars. Berger et al. (2006) also found this to be a relatively common phenomenon in their measurements of the radii of field M stars, although it is more challenging to perform a rigorous test in the absence of direct mass constraints in such systems. Andronov & Pinsonneault (2004), in a study of cataclysmic variable systems, found that excess activity could induce radius changes of the proper order of magnitude (see also Chabrier et al. 2007).

The physical mechanism linking activity-related radii differences with those in Li depletion is that spots inhibit convective energy transport, requiring the star to carry the flux through a smaller effective volume. The star therefore requires a larger radius, corresponding to an effective reduction in the mixing length or efficiency of energy transport. This in turn reduces pre-MS lithium burning because the central temperature and pressure of a star is decreased if the radius is increased. We performed a simple numerical test of this phenomenon. A 10% difference in radius (of order seen in active eclipsing binaries) during standard pre-MS convective burning for a 0.9 M_☉ solar abundance model led to a factor of 2.5 increase in the remaining surface lithium abundance at an age of 100 Myr relative to an inactive model with the same mass but a smaller radius. How the spot properties of single pre-MS stars (the precursors of our Pleiad sample) compare to those of active binaries remains an open question. Some meaningful context, however, might be provided by chromospheric emission fluxes. We note that the log R'(HK) indices for active solar-type binaries widely range from −4.4 to −3.3 at a given color or Rossby number (Figure 4 of Montes et al. 1996), while the corresponding Pleiades (pseudo-)indices (which must be transformed from Hα and Ca ii infrared triplet data) widely range from −4.5 to −3.5 (Figure 3 of King et al. 2003); i.e., active binaries show wide chromospheric emission at the same levels and with similar wide dispersion as present-day Pleiades.

When/if spot filling factors are reduced subsequent to pre-MS Li depletion, stars would converge to similar radii, but would retain a fossil record of their differences in earlier stages. If more spotted stars on the main sequence retained their lower effective temperatures, one would also shift more massive (and less depleted) stars to the same effective temperature as less massive (and more depleted) bare stars, further amplifying the apparent Li dispersion. There is evidence that activity can differentially impact protostellar radii. Stassun et al. (2007) found a reversal in the predicted T_eff–radius relationship between a more active primary and a less active secondary of a brown dwarf binary system in the young (1 Myr) Orion Nebula Cluster.

Our suggested explanation of the Pleiades Li dispersion has several attractive features. It explains why the dispersion is large among cooler stars, which experience significant pre-MS depletion, compared to hotter stars, and the propensity for more rapidly rotating (and perhaps more spotted) cool dwarfs to exhibit larger Li line strengths. It can also qualitatively explain the apparent narrowing of dispersion in cool main-sequence stars in older open clusters as follows. Beyond the Pleiades age, more heavily spotted and rapidly rotating stars deplete more Li than barer and more slowly rotating stars due to rotationally induced main-sequence mixing; as spottedness declines with increasing age and stellar radii concomitantly relax, the former stars also become hotter relative to the latter stars. The combined effect would be a reduction in the star-to-star dispersion in cool cluster Li abundances that is controlled by the timescales of stellar angular momentum loss and spot coverage diminution. Because the former timescale could, in principle, be longer than the latter, the passage of additional time would then witness the resurgence of substantial Li dispersion due to rotationally induced main-sequence mixing acting in stars whose radii and temperatures are no longer scattered due to surface inhomogeneities. This is not inconsistent with the observation that the ratio of rapid and slow rotators in the ∼100 Myr Pleiades is the inverse of that of Li-rich and -poor solar mass stars in the 4.6 Gyr cluster M67 (Jones et al. 1999). Our suggested explanation, which recognizes the importance of surface inhomogeneities on stellar radii and possible differences in time evolution of rotationally induced mixing and spot coverage, dovetails with the important observational picture painted by Jones et al. (1999): a significant Li dispersion in cool dwarfs in very young clusters such as the Pleiades that markedly declines in intermediate age clusters such as M34 and the Hyades, and then reappears in older clusters such as M67. We caution, though, that the dwarf Li abundances in M67 are available only for stars of T_eff ⩾ 5500–5600 K; abundances in lower mass M67 dwarfs akin to our cooler Pleiades have not yet been determined. It should also be noted that a variety of observational studies (e.g., Piau et al. 2003; Randich et al. 2007; Jeffries et al. 2002) have suggested other mechanisms besides or in addition to rotationally induced mixing as the source of main-sequence Li depletion and explaining the resulting main-sequence Li–T_eff morphologies manifested by open cluster data.

It is also tempting to speculate that the starspot-radius mechanism might be connected with other puzzling stellar phenomena. The alleged existence of a gap (or gaps) in the number distribution of Pop I main-sequence stars Mendoza (1956); Bohm-Vitense (1970); Rachford & Canterna (2000) around (B − V) ∼ 0.3 could be accommodated if this color corresponds to the onset of surface spot formation driving stars to lower T_eff values compared to bluer barer stars. The accompanying increase in stellar radii might give rise to the surprising number of luminosity class II–IV stars that reside in the main-sequence region of the Hipparcos-based H–R diagram (Newberg & Yanny 1998). The precipitous rise in apparent [Fe ii/H] abundances and more gradual but nevertheless surprising rise in apparent [Fe i/H] abundance in the Hyades with declining T_eff (Yong et al. 2004), the rise in high-excitation permitted [O i/H] abundances with declining T_eff in the Hyades and the even steeper rise in the younger Pleiades (Schuler et al. 2006b), the rise in forbidden line-based [O i/H] abundances with declining T_eff in the Hyades (Schuler et al. 2006a), the rise in [Si i/H] abundances with declining T_eff in M34 (Schuler et al. 2003) are at least qualitatively consistent with a T_eff-dependent disparity between spot-adjusted radii and assumed standard stellar radii. Such a disparity would lower log g with declining T_eff; the sensitivity of the features noted above is such that lowering log g increases their line strengths in cool dwarfs.

Future observational work is needed to confirm these speculative connections; quantifying or parameterizing spot coverage and properties rather than chromospheric emission indices per se that are used as measures of "activity" will be of particular importance. Such work includes: continued exploration of the reality of main-sequence gaps in open clusters, their evolution with age, and the spot properties of stars adjacent to these gaps; understanding the nature of luminosity class II–IV stars, in particular spot properties and physical radii, near the main-sequence region of the H–R diagram; the spot properties of stars as a function of T_eff in the Pleiades, M34, and Hyades open clusters, and their association with the abundance anomalies (especially star-to-star variations in permitted line [O i/H] values in cool Pleiades and Hyads) listed above.

A possible signature of the mechanism we propose here is the Li/Be ratio in stars sufficiently cool and old to suffer main-sequence mixing of ⁹Be, but not so cool as to have suffered pre-MS convective burning of ⁹Be. Such rotationally induced main-sequence mixing would deplete more Be (and Li) in stars with larger initial rotational velocities; however, if such stars were more heavily spotted, they suffered reduced pre-MS convective burning of Li; depending on the balance of spot-induced retarded pre-MS Li depletion and rotation-induced enhanced MS Li depletion, this effect could create a population of higher Li/lower Be stars whose number depends upon the initial distribution of rotation, its time evolution, and age. Identifying such stars using extant disk field abundance data is difficult given differences in stellar structure due to metallicity differences, unknown relative initial Li and Be abundances, and a dispersion in age. Such a search is best carried out in cool dwarfs of open clusters of at least intermediate (e.g., Hyades) age. For the purpose of constraining the origin of Li scatter in the Pleiades, a monitoring program to identify short- (days) and long- (years) term variations in Li i line strengths and spot properties is critical. If our proposed origin of the Pleiades Li dispersion is correct, we expect to see variations in Li line strength that are consistent only with changes in photospheric structure/parameters and the details of spot-included radiative transfer alone; once these variations are accounted for, a significant dispersion in Li line strength should remain as a relic of spot-induced differences in pre-MS Li burning. While observationally challenging, these future observational programs (accompanied by detailed modeling of pre-MS Li depletion in stars of various spotted conditions) will be required to fully understand the magnitude, mass distribution, and thus the ultimate origin of real star-to-star Li dispersion in the Pleiades.