Lithium abundances in the α Per cluster Free

Abstract

1 INTRODUCTION

Abundance measurements of lithium (Li) in stellar atmospheres have long been an active pursuit for observers and theoreticians alike. Much of the activity is directed at understanding the depletion of the atmospheric Li from its abundance, often an inferred quantity, acquired at birth. Open clusters serve as astrophysical laboratories in which to investigate the internal depletion of Li, because a given cluster provides a close approximation to a sample of coeval stars of a common age and initial composition, including that of Li, but spanning a range of masses and other properties, such as rotation. Crucially, the suite of clusters spans a large range of ages for a small range in composition. Three principal episodes of Li depletion are recognized: (i) depletion through destruction of Li at the base of the convective envelope of the pre-main-sequence (PMS) star; (ii) continued depletion by destruction in the MS phase; and (iii) depletion by a combination of diffusion and destruction in F-type MS stars in the narrow effective temperature range of about 6400–6900 K (the so-called Li-dip). Sestito & Randich (2005) assemble Li abundance data for 20 open clusters with ages from 5 Myr to 8 Gyr to confront theories for Li depletion with observations.

The cluster α Per was among the sample of 20 clusters with Li observations drawn from Balachandran, Lambert & Stauffer (1988, 1996, hereinafter BLS) and Randich et al. (1998). In this paper, we obtain and analyse high-resolution spectra from which Li abundances are obtained for about 50 stars. When the BLS and this new sample are combined in a uniform manner and a reconsideration is made of the cluster membership of the stars, Li abundances are provided for 70 cluster members.

Observations of Li in α Per were made initially by Boesgaard, Budge & Ramsay (1988) who analysed high-resolution spectra of six F-type stars to show that the Li-dip (Boesgaard & Tripicco 1986) has not yet developed in this young (age of about 50 Myr) cluster. Our principal goal was not to define the run of Li abundance along the MS, because that is already well known for F-, G- and K-type stars (BLS; Boesgaard et al. 1988; Randich et al. 1998) and M-type stars (García López, Rebolo & Martín 1994; Zapatero Osorio et al. 1996). Rather we sought to determine if the Li abundance at a given effective temperature has an intrinsic scatter.

Such a star-to-star variation in apparent Li abundances has been reported for the Pleiades, a cluster only slightly older than α Per (Butler et al. 1987; Soderblom et al. 1993; King, Krishnamurthi & Pinsonneault 2000). This variation appears for stars with effective temperatures less than about 5300 K and extends to the useful limit of the sample at about 4000 K. The peak-to-peak variation is about 1.5 dex in apparent Li abundance. Stars with the stronger Li i 6707 Å feature at a given temperature have higher projected rotational velocities (v sin i). The debate is ongoing as to whether the variation in Li i line strength in the Pleiades and other clusters reflects a real abundance difference or differences in atmospheric structure not modelled by classical atmospheres.

Randich et al. (1998) studied Li abundances in 18 very active, X-ray-selected members of α Per enlarging the original sample of BLS in the 5500–3900 K range of effective temperature and suggested that, at T_eff≤ 5300 K, there was indeed a significant dispersion in Li abundances in stars at the same temperature. They further suggested that rapid rotators had more Li and exhibited a smaller dispersion than slow rotators at the same T_eff. They inferred from these observations a likely relationship between Li, chromospheric activity and the rotational history of stars.

Examination of BLS's Li observations as re-analysed by Randich et al. (1998) led Xiong & Deng (2005) to suggest that star-to-star variations were also present among α Per members at effective temperatures of about 4700 K and that the variations primarily arose from atmospheric effects and not a real abundance variation. With our larger sample of cluster members, we re-examine the question of star-to-star variation in Li abundance.

In Section 2, we discuss a selection of the newly observed stars. In Section 3, we describe the new high-resolution spectra of α Per stars. Section 4 presents the stellar parameters with emphasis on the effective temperature. The abundance analysis is introduced in Section 5. The run of Li abundance with an effective temperature and the star-to-star variations are discussed in Section 6. This paper concludes with general remarks in Section 7.

2 CONSTRUCTION OF THE FINAL SAMPLE

In referring to members of the cluster, we follow the convention of ‘WEBDA’, a website devoted to stellar clusters.1Heckmann, Dieckvoss & Kox (1956) and Heckmann & Lübeck (1958) introduced a numbering scheme preceded by the letters ‘He’. Later, Stauffer, Hartmann & Jones (1985, 1989a) and Prosser (1992) identified fainter stars with the letters ‘Ap’. In WEBDA, the label He is replaced by #, thus He 12 becomes #12. In the case of the Ap stars, the numbering is increased by 1500 and Ap replaced by #, thus Ap 79 becomes #1579.

When the observations (see below) made for this paper are combined with those reported by BLS, we have spectra for 86 stars. Since our primary goal is to determine whether the run of Li abundance down the MS of the cluster exhibits scatter at a given effective temperature, it is vital to sort cleanly the cluster members from the non-members and also to separate out suitable from unsuitable (i.e. doubled-lined spectroscopic binaries) members.

As long recognized, clean separation of members from non-members is not an easy task for α Per, because it is at low Galactic latitude and has a small relative proper motion. In making the separation, we have called upon a variety of publications that have previously attempted the task. The primary source and the one used in selecting stars for observation was the seminal study of the cluster by Prosser (1992). He considered a variety of membership indicators among which the primary ones were proper motions and radial velocities of the stars.

Makarov (2006) re-analysed the cluster's proper motions using astrometry and photometry from the Tycho-2 Catalogue and the Second USNO CCD Astrometric Catalog (UCAC2). Makarov's table of ‘High-Fidelity’ members lists 139 stars with a V magnitude brighter than about 11.5; no table of non-members is provided. Of the stars in our sample with V < 11.5 and designated as members according to Prosser, all but 10 are among Makarov's high-fidelity members. Four of the 10 stars not listed as members by Makarov are categorized as non-members by Mermilliod, Queloz & Mayor (2008) (see below). It is unclear whether Makarov studied all stars from Prosser's list with V < 11.5, and therefore the absence of a star in Makarov's table is not necessarily an indication that it is not a member. We have included the remaining six stars in our sample in Table 1.

Mermilliod et al. (2008) undertook a radial velocity programme to check for spectroscopic binaries in the cluster. Their criteria for membership were three-fold: proper motions (from UCAC2), radial velocity and location in the color–magnitude diagram. These criteria were applied independently of Prosser's and Makarov's efforts at membership determination. 54 of our 86 stars were in Mermilliod et al.’s programme. Of these only four were identified as non-members in that program: # 143, 573, 1100 and 1181, with the first two shown to be spectroscopic binaries. We adopt Mermilliod et al.’s view that this quartet are non-members and list these stars in Table 2. Some members were shown to be spectroscopic binaries. Binaries not yet shown to be double-lined are included in the list of 70 members and identified in the final column in Table 1; all seven fall near the MS locus in a color–magnitude diagram, suggesting that the secondary star contributes very little to the composite spectrum.

Patience et al. (2002) report on an imaging search for close binaries among known cluster members; these authors made no independent determinations of membership. A large fraction of our stars was examined by Patience et al. with the majority reported not to have a companion that would have contributed to our spectrum, which we have assumed is that of a single star. Four stars were excluded as unsuitable for analysis on the basis of the reported imaging; these have companions separated by less than 0.5 arcsec and rather similar masses. The stars are # 696 (also known as #1538), 935, 1541 and 1598.

In summary, 70 of the 86 stars are considered to be cluster members (Table 1). Information provided in Table 1 is as follows: the WEBDA # is in column 1, and the adopted stellar parameters are in columns 2, 3 and 4. The projected rotational velocity (v sin i) in column 7 is primarily taken from Prosser (1992). The equivalent width (EQW) of the Li i 6707 Å feature is given for stars with low v sin i in column 8 and the derived Li abundance is given in column 9. Columns 10–12 summarize the membership status of the star as given by Prosser (1992), Makarov (2006) and Mermilliod et al. (2008). The final column identifies the seven stars that are spectroscopic binaries. These seven stars are members and it is assumed that the secondary star is too faint to contribute to the spectrum. They are therefore included with the single stars in Table 1 and in our analyses.

16 stars, originally classified as members by Prosser (1992), have subsequently been identified as non-members, single-lined or double-lined spectroscopic binaries (SB2s), or close double stars. The nature of these stars and the source of the revised information is listed in Table 2, which has the same format as Table 1. The stars are not rejected outright from our sample. Rather, temperatures, rotational velocities and Li and Fe abundances were determined as for the members and the results are discussed with caveats and questions in Sections 6.2 and 6.3.

Our sample of 70 certain members and 16 stars, possibly of questionable status, represents the largest selection to date for which Li abundances are available in α Per.

3 OBSERVATIONS

High-resolution spectra were obtained between 1992 and 1994. Observations were made during 1992 December and 1993 November for 30 stars at the 2.7-m telescope at the W. J. McDonald Observatory with the Robert G. Tull cross-dispersed echelle spectrograph (Tull et al. 1995) at a resolving power of about 60 000 with exposure times chosen to provide a signal-to-noise ratio (S/N) of 100 or higher. In 1994 January, observations were carried out for 21 stars at the 4-m telescope at KPNO with the Casségrain echelle spectrograph, the red long-focus camera and the Tex 2048 × 2048 CCD chip to give a 2-pixel resolution of 0.16 Å (R∼ 40 000). Integration times were chosen to provide an S/N close to 150 for most stars and even higher in a few cases.

Data reduction was carried out following standard iraf procedures.2 The frames were trimmed and overscan corrected. Bias frames were combined and subtracted from the raw spectrum. The spectrum was divided by the normalized flat-field image to account for the pixel-to-pixel sensitivity difference of the detector and then corrected for scattered light. No sky subtraction was done as the sky signal was negligible in all cases.

19 and 24 echelle orders were extracted, respectively, from the McDonald and the KPNO data. The wavelength-scale for all the orders was derived using the Thorium–Argon spectrum. The wavelength-calibrated spectrum was then normalized to a continuum of one.

The measured EQWs of the Li i line at 6707.8 Å are given in Tables 1 and 2 for stars with low projected rotational velocities (v sin i < 25 km s⁻¹). The EQWs include the contribution of the Fe i blend at 6707.435 Å. The contribution of the Fe i blend was removed by the program moog (Sneden 1973) during the derivation of the Li abundance. In the slow rotators (v sin i < 25 km s⁻¹), the uncertainty in the EQW, largely caused by the placement of the continuum, was 2–3 mÅ at ∼15 mÅ, 6 mÅ at ∼130 mÅ and 10 mÅ at ∼200 mÅ. In the spectra of the more rapidly rotating stars in which lines were still measurable, the EQW uncertainty was estimated to be as large as ∼15 mÅ. EQWs were not measured in these stars, rather Li abundances were determined by spectral synthesis, and the EQWs listed in Tables 1 and 2 for stars with v sin i > 25 km s⁻¹ were calculated from the derived abundance using moog (Sneden 1973).

The analysis of the 6707 Å line was done for all the stars with spectrum synthesis fits to the observed spectrum. For the 36 slowly rotating stars for which spectroscopic analysis was possible, the Li abundance was determined in addition from the Li EQW. The match between the two measurements of Li abundance was in excellent agreement.

4 STELLAR PARAMETERS

The Li abundance determined from the 6707-Å feature is primarily sensitive to the adopted effective temperature T_eff. An error of ±200 K in T_eff results in an uncertainty in log N(Li) between ±0.28 to ±0.14 over the 4500–6500 K temperature range. Thus, we devoted considerable effort to a determination of T_eff. The Li abundance is quite insensitive to the adopted surface gravity; a variation in log g of ±0.5 dex results in a change in Li abundance by less than ±0.02 dex. The adopted microturbulence has a small influence on Li, when the 6707-Å feature is strong.

4.1 Effective temperature

The effective temperature is derived from photometry, primarily the (V−K) index, and checked by use of the Strömgren β index and spectroscopy.

4.1.1 Photometry

Our principal photometric indicator of the effective temperature is the (V−K) colour index, which is available for all the stars. All of the observed stars have a K_s magnitude in the 2MASS catalogue.3 The K_s magnitudes were transformed to Johnson K magnitudes by the Koornneef transformations (Carpenter 2001). The V magnitudes were taken from Prosser (1992).

The literature contains various estimates of the reddening affecting the cluster. Several authors refer to a variable reddening across the cluster. Cluster members are slightly reddened, but there is little solid evidence that the reddening is significantly different from star to star. BLS adopted E(B−V) = 0.08 (Mitchell 1960) for all their stars and remarked that Crawford & Barnes (1974) suggested a range from 0.04 to 0.21. BLS note that the extremities of the range correspond to effective temperatures lower by 100 K and hotter by 450 K. Thus, the larger reddenings are a concern in the search for the origin of a scatter in Li abundances.

Inspection of Crawford & Barnes (1974) shows, however, little evidence for a variation in reddening. In their table III, they list measurements of E(b−y) for 21 F-type stars. 15 stars are members and six are non-members according to Makarov (2006). (12 of the 15 members are in Table 1.) The mean E(b−y) for the 15 is 0.054 ± 0.017 with extremes of 0.032 and 0.091. In contrast, larger reddening is seen among non-members with the six non-members exhibiting a range in E(b−y) from 0.023 to 0.148. Crawford & Barnes did note that 18 A-type and 31 B-type cluster members gave higher and similar reddening: 14 A-type stars, members according to Makarov (2006), give a mean E(b−y) = 0.089 ± 0.036 with extreme values of 0.038 and 0.139. The factor of 1.7 between the mean values for the F- and A-type stars points to an issue with the calibration. Possibly, the larger standard error in the A stars may indicate non-uniform colours resulting perhaps from diffusion or metallicity effects. Trullols et al. (1989) provide E(b−y) for 12 F star members: the mean E(b−y) is 0.065 ± 0.012, where the standard error again indicates little if no variation from star to star. Peña & Sareyan (2006) provided Strömgren photometry for cluster stars from a combination of their own measurements and published values and obtained a mean reddening from 169 stars of E(b−y) = 0.073 ± 0.038. However, for the 15 F stars in common, their reddening [E(b−y) = 0.086 ± 0.029] differs from that of Crawford & Barnes, suggesting calibration differences.

Crawford (1975) used the available uvby Hβ photometry for bright stars and cluster members to calibrate Hβ in terms of the intrinsic colour (b−y) and other indices, applicable for β between 2.59 and 2.72. Using this calibration, we made fresh estimates of E(b−y) for 40 stars with the available Stromgren photometry (from WEBDA, which essentially includes the observations of Crawford & Barnes 1974; Trullols et al. 1989) in the above range of β, taking care that the sample contained no binaries or possible non-members. We found that E(b−y) ranged from 0.02 to 0.12, very similar to previous studies, with an average E(b−y) of 0.075 and a standard deviation of the measurements (standard error) of ±0.04. For the normal interstellar reddening law, A_V = 0.32, this translates to E(V−K) = 0.284 ± 0.15. The standard error may be used as one estimate of the reddening uncertainty for each star.

Prosser (1992) derived E(V−I) for about 75 M cluster dwarfs from a somewhat unusual process. Low-dispersion spectra provided spectral types, which with a colour–spectra type relation gave the intrinsic (V−I) colour of a star. A comparison of intrinsic and observed (V−I) gave a star's reddening. The mean E(V−I) ≃ 0.18 corresponds to E(b−y) ≃ 0.08 and E(V−K) ≃ 0.3, values consistent with other reddening measures from traditional techniques applied to earlier spectral types. Given that the reddenings are described by Prosser as ‘preliminary values’, one may attach little weight to his suggestion that the reddening is not uniform for cluster members.

The intrinsic (V−K) colour was calculated assuming an average interstellar reddening of E(V−K) = 0.284. The photometric calibrations (V−K) −T_eff of Alonso, Arribas & Martínez-Roger (1996) given below were used to derive the (V−K) effective temperature T_eff(V−K) for all the stars. This procedure was applied to all stars including those previously analysed by BLS:

1

for 0.4 ≤ (V−K) ≤ 1.6 and

2

for 1.6 ≤ (V−K) ≤ 4.1, where θ_eff = 5040/T_eff. We denote this photometric temperature by T_eff(V−K) (see Table 1 for cluster members). The photometric error in K is 0.02 mag4 and in V it is 0.058 mag (Prosser 1992), yielding a standard deviation in (V−K) of 0.06 mag. An error in (V−K) of 0.06 results in an error of 125 K at 6600 K, 50 K at 4500 K and 75 K at 5500 K. We caution that the presence of a cool companion may increase the (V−K) colour of the primary component of a binary and therefore the temperature derived for these stars (Table 2) may be systematically low. We note here that the standard deviation of 0.15 in E(V−K) derived from the reddening calculation is substantially higher than the uncertainty in the photometric measurement determined above and translates to temperature uncertainties of 325 K at 6600 K, 180 K at 5500 K and 125 K at 5500 K.

Other colour indices might be considered as thermometers. Several previous studies of α Per (and other clusters) have employed (B−V) for which measurements are available for all but five of our stars. However, the V versus (B−V) colour–magnitude diagrams for young clusters are fundamentally different from the V versus (V−I) plots when overlaid by theoretical isochrones. The best-fitting isochrone in the V versus (B−V) diagram for young clusters, such as α Per, follows the observed MS down to the late-K stars, which lie conspicuously to the left of the theoretical MS; they are consistently fainter and bluer. This is seen in the Pleiades and α Per (S. V. Mallik, private communication). Stauffer et al. (2003) first pointed out this blue anomaly in the Pleiades and suggested it may be due to a flux contribution (larger in B than in V) not represented by the model atmospheres. This so-called (B−V) anomaly is predominant in the younger clusters, but is absent in clusters as old as Praesepe: α Per is about 0.05 Gyr to Praesepe's 0.6 Gyr. If this interpretation rather than a more deep-seated deficiency in the models providing the isochrones is correct, the anomaly is likely related to stellar surface activity that decays as stars age. This has two obvious consequences for deriving and interpreting Li abundances. First, (B−V) may be a poorer temperature indicator for the cooler stars than (V−K); the colour–temperature calibration is likely dependent on a star's age, but may also vary from star to star with changes in stellar activity. These dependencies may then provide a star-to-star scatter in Li abundance.

4.1.2 The Strömgren β index

As a reddening-free index, the Strömgren β index is a useful measure of the effective temperature for stars hotter than about 5000 K. Measures of β are taken from Crawford & Barnes (1974) and Trullols et al. (1989). The β versus T_eff calibration is taken from Alonso et al. (1986; see also Castelli & Kurucz 2006). T_eff(β) is listed in column 6 of Table 1 for 24 cluster members and the comparison T_eff(β) versus T_eff(V−K) is shown in Fig. 1. T_eff(β) is also listed for four stars of questionable status in Table 2 and included in Fig. 1.

Figure 1

Comparison of the effective temperatures derived from the (V−K) and β indices. The line corresponds to perfect correspondence between the two measurements. The symbols are described in the key.

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While there is a good agreement between (V−K) and Hβ temperatures at the cool end of the useful range of the β index, there is a surprisingly larger scatter, at the warm end, with temperature differences as large as 500 K for the same star from the two calibrations. The difference is also surprising, because the two calibrations come from a common paper. We have no leads on whether this difference is due to calibration issues or photometry errors, but we surmise it is unlikely to be caused by variable reddening as it is confined to a small temperature range. The non-members and SB2s lie within the scatter defined by the members.

4.1.3 Spectroscopy

Our spectroscopic temperature is based on the usual condition that the Fe i lines in the observed spectra return the same Fe abundance independent of a line's lower excitation potential. The McDonald spectra provide about 30 Fe i lines spanning about 4 eV in the lower excitation potential. The KPNO spectra with their greater wavelength coverage yield about 130 Fe i lines. These numbers pertain to slowly rotating stars (v sin i≤ 20 km s⁻¹); more rapidly rotating stars have broader lines that lead to blending and a difficulty in measuring EQWs accurately, especially of weak lines. The T_eff determination has to be made simultaneously with that for the microturbulence ξ_t. For this exercise in determining T_eff and ξ_t, we used astrophysical gf-values for Fe i and Fe ii lines. The gf-values were determined using moog (Sneden 1973) with measurements of Fe i and Fe ii EQWs from the high-resolution digital solar atlas (Delbouille, Roland & Neven 1990), the Kurucz solar model atmosphere with no convective overshoot (Castelli, Gratton & Kurucz 1997) and requiring the lines to yield Fe/H = 7.50 at ξ_t = 0.8 km s⁻¹.

We derived spectroscopic temperatures for 24 cluster members including eight stars observed by BLS for which we were able to retrieve their spectra (Table 1), and for 12 binaries, doubles or non-members (Table 2). The microturbulence and spectroscopic temperatures are listed in columns 4 and 5, respectively. A 100 K change in the effective temperature resulted in a significant non-zero slope of Fe i versus lower excitation potential to allow us to constrain temperatures to ±100 K. Errors in the EQW measurement, gf-values and microturbulence would result in random and systematic temperature errors and we feel that ±200 K conservatively constrains the error in our derived T_eff(spec). The ξ_t is determined to about ±0.1 km s⁻¹.

A comparison of T_eff(V−K) and the spectroscopic temperature T_eff(spec) is presented in Fig. 2. On average, T_eff(V−K) is cooler than T_eff(spec) by about 250 K. The temperature difference appears to vanish for the hotter stars, say, T > 6000 K. This level of agreement is consistent with the estimated uncertainty from the analysis of the Fe i lines and lends support to the assertion that reddening is not very variable across the cluster. The visual doubles, the SB2s and three of the four non-member stars lie within the scatter defined by the cluster members. Only #1181 has a much cooler T_eff(spec) compared to T_eff(V−K).

Figure 2

Comparison of the effective temperatures derived from the (V−K) index and the Fe i lines [T_eff(spec)]. The line corresponds to perfect correspondence between the two measurements. The symbols are described in the key.

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4.2 Surface gravity

With the inclusion of Fe ii lines in the spectroscopic analysis, it is possible to determine the surface gravity log g. Spectra of 18 stars provide an adequate number of eight to 10 Fe ii lines. A log g determination requires the same Fe abundance from Fe i and Fe ii lines and this is possible to an accuracy of ±0.25 dex. For the stars without a spectroscopically determined log g, we adopt the log g = 4.5 for the T_eff determination from the Fe i lines. This value was adopted for all stars without a spectroscopic determination of the surface gravity.

4.3 Microturbulence

The microturbulence is taken either from the analysis of the Fe i lines or a value of 1.5 km s⁻¹ was assumed.

5 ABUNDANCE ANALYSIS

5.1 Lithium abundances

The abundance analysis from which we extract the Li abundance takes the standard form.

Model atmospheres were generated in 100 K intervals in temperature and 0.1 dex intervals in gravity using the program atlas9, written and supplied by R. L. Kurucz. Standard solar opacity distribution functions were used with overshoot turned off (see Castelli et al. 1997). The appropriate model was chosen for each star according to the stellar parameters listed in Tables 1 and 2.

The line analysis program moog (Sneden 1973) was used to convert EQWs of the 6707-Å Li i resonance doublet to an abundance. Throughout the assumption of local thermodynamic equilibrium (LTE) is adopted. The gf-values and wavelengths of the fine- and hyperfine-structure components of the Li i feature were taken from Andersen, Gustafsson & Lambert (1984). The Li abundance was chosen by the best fit of a synthetic spectrum to a region around the 6707-Å feature with the line list adopted by BLS. It is most unlikely that there is any ⁶Li in stars, where ⁷Li is even slightly depleted. Therefore, ⁶Li was included in the line list only for stars with log N(Li) > 3.0.

Li abundances were computed for the model parameters listed in Tables 1 and 2. An error of ±100 K in T_eff, ±0.25 dex in log g, ±0.1 km s⁻¹ in ξ_t and 5 mÅ in Li i EQW results in Li abundance errors of ±0.1, ±0.01, ±0.00 and ±0.09, respectively. As these estimates show, the two principal sources of uncertainty affecting the derived Li abundances arise from the effective temperature and the measured EQW. The effect of a 200-K spread in effective temperature is shown in Fig. 3 by the shaded area at the bottom of the figure. At the lowest temperatures, where the stars of the same effective temperature can show Li lines of quite different strengths, the uncertainty in measurement of the EQW may have a larger effect on the derived abundance than the temperature uncertainty, especially for those few stars where the Li line is weak. The reddening uncertainty estimated from Hβ increases the temperature error over 200 K only at the hottest temperatures; the uncertainty in E(V−K) of 0.15 translates to a temperature uncertainty of 325 K at 6600 K. This uncertainty would merely increase the Li abundance uncertainty at 6600 K to roughly the same magnitude as in the cooler stars (Fig. 3), and would not affect the discussion on Li abundance dispersion that follows in Section 6. In the temperature and gravity range of our sample, non-LTE corrections to the Li abundance are estimated to be small (Carlsson et al. 1994); non-LTE corrections would lower the LTE abundances by 0.019 at the cool end of our sample and by 0.009 dex at the hot end. Again, not incorporating these relatively small corrections would not affect our discussion on the dispersion in Li abundance that follows.

Figure 3

The effective temperature versus Li abundance relation for α Per. The projected rotational velocity (v sin i) of the stars is represented as in the legend. The shaded strip at the bottom of the figure shows the Li abundance spread resulting from an effective temperature uncertainty of 200 K. Several stars are labelled by the membership number for easy reference.

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Li abundances for the single-lined binaries in Table 1 and the non-members and double stars in Table 2 were determined as for the single stars. The Li abundances of non-members should have the same accuracy as the remainder of our sample and the Li abundance errors on the doubles is unknown. However, if a cool companion lowers the temperature estimated for single-lined and double-lined binaries, those Li abundances will be proportionately lowered. In addition, double-lined binaries may have weaker Fe i and Li i lines due to continuum dilution. We have therefore marked the Li abundances of the SB2s as uncertain in Table 2. If anything, the Li abundances of these stars are likely to be larger than our estimates. A stronger Li i line may result if a neighbouring feature line from the companion falls on the Li i line, but we have measured the wavelength separation of the two components and are certain that the Li i feature is not contaminated in any of our SB2s.

5.2 Iron abundance

Iron abundances were determined for 25 cluster members (Table 3). The typical measurement uncertainty in the EQW of a 40–60 mÅ Fe i line is ±5 mÅ. An error of ±100 K in T_eff, ±0.25 dex in log g, ±0.1 km s⁻¹ in ξ_t and ±5 mÅ in Fe i EQW results in Fe abundance errors of ±0.07, ±0.02, ±0.02 and ± 0.05, respectively. When these uncertainties are combined, the resulting error in the Fe abundance is ±0.09.

The mean Fe abundance is 7.40 ± 0.08 dex where this standard error is comparable to the estimate of the precision of a single determination. There may be a slight decrease in the derived Fe abundance with decreasing temperature; stars with T_eff > 5500 K give a mean that is 0.09 dex higher than stars with T_eff < 5500 K. A similar suggestion of a temperature dependence was made by BLS. Since our Fe abundance is based on astrophysical gf-values for Fe i and Fe ii lines and is derived using the solar abundance of log N(Fe) = 7.50, the mean Fe abundance may be quoted as [Fe/H]=−0.10, with [Fe/H]=−0.04 for T_eff > 5500 K and [Fe/H]=−0.13 for stars with T_eff < 5500 K. BLS obtained a mean Fe abundance about 0.13 dex higher with astrophysical gf-values calculated from the empirical Holweger & Müller (1974) and a microturbulence of 1.2 km s⁻¹. Our result is in good agreement with Boesgaard & Friel's (1990) spectroscopic determination by an essentially equivalent technique, including the use of the Kurucz grid, though with fewer (15) Fe i lines. They obtained [Fe/H]=−0.054 ± 0.046 from six stars with T_eff from 6415 to 7285 K; our result from four stars hotter than 6000 K is [Fe/H]=−0.04 ± 0.08.

Also listed in Table 3 are the Fe abundances of the non-members, visual doubles and binaries from Table 2 for which spectroscopic analysis was possible. The mean Fe abundance of the four non-members is [Fe/H]=−0.13 ± 0.15, of the two double stars is [Fe/H]=−0.07±0.04, and of the six double-lined spectroscopic binaries is [Fe/H]=−0.14 ± 0.21. The mean Fe abundances are not very different from that of the cluster members; the standard errors are slightly larger than for the cluster mean.

6 THE LITHIUM ABUNDANCE VERSUS TEMPERATURE RELATION

The general nature of the relation between the Li abundance and effective temperature was discussed previously by BLS and Randich et al. (1998).

In Fig. 3, we show the Li versus T_eff(V−K) relation for the 70 stars in Table 1, where the symbol's size reflects v sin i as depicted in the legend on the figure. The shaded region at the bottom of the figure displays the effect of a correction to T_eff of 200 K across the range from 6400 to 4500 K.

6.1 The hot stars

The Li versus T_eff(V−K) relation asymptotically approaches a constant abundance at the high-temperature end. In analysing this approach, we calculate mean abundances in four temperature bins for stars hotter than 6250 K (Table 4). Each bin has roughly the same number of stars, and the mean Li abundance in the four bins is essentially the same within the errors. In the three hottest bins, the dispersion within each bin can be easily accounted for by a combination of temperature errors (±200 K corresponds to ±0.14 dex), S/N of the spectra and small reddening variations. Whether the slightly larger dispersion is the coolest of the four bins is significant cannot be determined from our relatively small sample size. Within our errors, there appears to be no dispersion in the Li distribution or significant change in the mean Li value of these hottest stars.

Within these stars, there is an indication from Fig. 3 that the most massive rapidly rotating stars [at T_eff(V−K) > 6400 K] have a slightly lower Li abundance than the slow rotators. Taken as a whole, the results in Fig. 3 may suggest that the rapidly rotating stars provide a relation with a shallower slope for T_eff > 5500 K than the slowly rotating stars.

The Li abundance in the hottest stars is equal to the meteoritic value [log N(Li) = 3.25 ± 0.06 according to Grevesse, Asplund & Sauval 2007]. It is this value that has often been taken as a fair representation of the initial value for young open clusters, like α Per. Some authors also quote a very similar Li abundance derived from T Tauri stars (see e.g. Magazzu, Rebolo & Pavlenko 1992; Martín et al. 1994). These two data points suggest that the local value of the Galactic Li abundance has changed little in the last 4.5 Gyr.

6.2 The middle third

Three temperature bins define the middle third of the sample between 5500 and 6250 K (Table 4). The mean Li trend declines by 0.5 dex in this range. The dispersion in Li appears to be larger than can be accounted for by the uncertainties in the stellar parameters and the S/N of our spectra. In order to understand this dispersion, we examined four cluster members, #1589, #1604, #56 and #93, with T_eff between 5400 and 5750 K. These appear to be outliers to what would otherwise be a fairly narrow mean Li trend similar to that seen in the hotter stars; in the absence of these stars, the decline in the mean Li trend between 6250 and 5500 K would be 0.3 dex and the dispersion in the coolest bin be only ±0.13.

It is worth noting that these four stars have much lower Li EQWs compared to other stars in the same temperature range. We therefore begin by examining three possible explanations for these outliers: (i) their assigned effective temperature is in error; (ii) the stars are non-members that have experienced normal Li depletion for their age; (iii) the dispersion in Li is not real but a reflection of differences in chromospheric activity levels, which affect the formation of the Li i line and thereby the EQWs of the line; and (iv) an unusual amount of Li depletion has occurred in these cluster members. We comment on each of these in turn.

Errors in the estimated temperatures appear to be the least likely cause of the outlier stars. An increase in the effective temperature would increase the estimated Li abundance of the outlier, but as the mean Li trend increases with increasing temperature, the required temperature increase is larger than that indicated simply by the temperature difference between the outlier abundance and the mean trend at that temperature. Consider the case of #1589, which is about 0.4 dex below the mean relation. A 500-K increase in effective temperature eliminates this deficit but at the new temperature of 5900 K, the star remains about 0.3 dex below the mean relation. A similar problem arises if the effective temperature is lowered. The temperature change required to meet the mean Li trend is even larger in #56 and it cannot be reconciled with the errors we have derived for our estimated temperatures. For example, the estimated temperatures of #56, T_eff(spec) = 5600 K and T_eff(V−K) = 5703 K are in good agreement and we see no reason to consider them to be in error by 700 K or larger. The other outliers would require similar and unacceptably large increases or decreases in temperature to put them on the mean Li trend. An added constraint against such a large increase in temperature is the measured Fe abundance. The 700-K increase in the effective temperature required for #56 would increase [Fe/H] from the measured value of +0.06 to an extraordinarily high value of +0.42. Similarly, #1604 has a measured metallicity of [Fe/H]=−0.09, consistent with the cluster mean, and the even larger increase in effective temperature increase would result in an unbelievable Fe abundance. An explanation for the quartet in terms of an error in their effective temperatures is therefore not credible.

Possibly, these outliers are not in fact cluster members. In the case of #56, Prosser (1992) assigned it a questionable status as a member on the basis of its radial velocity but full status on the basis of proper motion. If #56 is an interloper star with normal Li depletion for its age, it should be roughly the age of the Hyades cluster (600 Myr) (Boesgaard & Tripicco 1986; Boesgaard & Budge 1988; Thorburn et al. 1993). Similarly, at roughly the same temperature, #1604 with a slightly lower Li abundance would be a somewhat older star. However, neither #56 nor #1604 could be as old as NGC 752 (2.4 Gyr) or M67 (4.5 Gyr), because by that age solar-temperature stars have Li abundances of log N(Li) = 1.5 or lower (see Balachandran 1995 and references therein). The likelihood of Hyades-age interlopers in the field of view of the α Per cluster and at the distance of the α Per cluster is small. Although Prosser (1992) assigned cluster membership to #93 without a radial velocity measurement, the moderate rotational velocity of the star (v sin i = 25 km s⁻¹) increases the likelihood that it is a young star and therefore a cluster member; G stars are observed to have spun down by the age of the Pleiades (Stauffer et al. 1984). As noted in Table 1, Mermilliod et al. (2008) questioned the cluster membership of #1589. The relatively high Li abundance [log N(Li) = 2.24] relative to field stars at the same temperature suggests that the star is young; the abundance of Li is of the order of log N(Li) = 1.0 at 5300 K even in a cluster as young as the Hyades. Therefore, even if the quartet are rejected as members on this flimsy evidence, it is obviously no simple matter to account for their Li abundance as field stars.

The effect of chromospheric activity, in particular, surface inhomogeneities in the form of spots and plages, on the formation of the Li i line, and the subsequent effect on the EQW of the line has been the focus of several studies (Randich 2001; Hünsch et al. 2004; King & Schuler 2004; Xiong & Deng 2006; King et al. 2010). Typically, the K i resonance line that is formed in the same part of the atmosphere as Li i is measured for comparison. Although a spread in K i EQWs has been observed in stars of the same temperature in the Pleiades (Jeffries 1999) and IC 2602 (Randich 2001), the authors state that while there is a need to understand K i differences, there is no conclusive evidence that the spread in Li abundances in these young clusters can be attributed to differences in chromospheric activity alone. In a recent study of the high-resolution spectra of 17 cool Pleiades dwarfs, King et al. (2010) found that the Li i line strengths had a larger scatter than the K iλ 7699 Å line strengths. They concluded that there must be a true abundance component to the Pleiades Li dispersion and suggested that it may be due to differences in PMS Li burning caused by the effects of surface activity on stellar structure. Here we add a few nuggets to that discussion. Our KPNO spectra contain the 7699 Å K i resonance line at the edge of one of the echelle orders. We were able to measure this K i feature in 14 stars. The data show the expected increase in EQW with decreasing temperature, but the sparsity of the data precludes a detailed analysis. In addition to the two outliers, #1604 and #1589, we were able to measure the K i EQWs of two normal stars at the same temperature, #1086 and #1185. The data are shown in Table 5. There are two findings of relevance. First, while the Li i EQW of #1604 is a factor of 3 smaller than that of #1086 and #1185, the K i EQWs of all three stars are within about 15 per cent of each other. Secondly, comparing the K i lines in the two stars with low Li, #1589 and #1604, we find the ratio of their K i EQWs is 1.6, perhaps reflecting the lower T_eff(V−K) of #1589. The Li i EQW ratio of the two stars is 1.7 and mirrors the K i EQW ratio. Thus, we are able to discern no reason to attribute the low Li abundances to #1589 and #1604 to the effects of chromospheric activity.