BERYLLIUM AND ALPHA-ELEMENT ABUNDANCES IN A LARGE SAMPLE OF METAL-POOR STARS

Our stars have a range in temperatures (5500–6400 K) and metallicities (−0.4 to −3.5), so our original line lists were reduced slightly differently for each star due to the limits above. We were left with 28–86 lines of Fe i, 9–14 lines of Fe ii, 5–19 lines of Ti i, 5–13 lines of Ti ii, and 1–3 lines of Mg i.

We have written a collection of perl scripts that perform an iterative determination of T_eff, log g, [Fe/H], and ξ, using the line lists for each star. These scripts utilize the abfind driver in MOOG. We found T_eff from the agreement of the Fe abundance from Fe i lines with a range of excitation potentials, i.e., the slope between log Fe/H and excitation potential (χ) should be zero. We determined log g from the ionization balance of both Fe i with Fe ii and Ti i with Ti ii, i.e., the abundances from the lines of the two ionization stages agreed at the preferred log g value. For almost all our stars we used the log g values from Ti i and Ti ii in part because there were more lines of Ti ii than Fe ii in general. However, the differences in log g were typically <0.04 and the ensuing differences in A(Be) were typically <0.01. We found ξ by iterating so that the Fe i abundances were similar at all reduced equivalent widths. Our starting value was ξ = 1.5 km s⁻¹; for some stars, this did not converge to a slope of zero so the iterations stopped and 1.5 km s⁻¹ was used. The median value for the 42 stars where we did determine ξ is 1.42 km s⁻¹. This is virtually identical to the 1.47 km s⁻¹ value found by Magain (1989).

Model atmospheres were made for the specific parameters for each star by interpolation with the Kurucz (1993) grid. All elements were reduced by the amount that Fe is reduced relative to the Sun, except for Be and O.

Table 2 contains the derived values for the stellar parameters in Columns 2–5. We show in Figure 1 the distribution of our selected stars in the T_eff versus [Fe/H] plane. We note that there are six stars with [Fe/H] < −3.00. We limited our lower temperature bound to 5500 K because below that the metallic and molecular blending lines become too strong and the Be ii lines become too weak to obtain reliable Be abundances.

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We have compared our derived parameters with those determined by Stephens & Boesgaard (2002) for the seven stars in common. (We have two other stars in common, but we adopted their parameters for G 64-12 and G 64-37.) The average of the temperature differences is +10 K, of the log g differences is −0.02, and of the [Fe/H] differences is −0.02 dex (in the sense of this study minus theirs). One star, BD +34 2476, has a T_eff difference of 187 K. The other stars agreed well within the nominal uncertainty of ±50 K. The largest difference in [Fe/H] was only +0.16. The range in the differences in log g was ±0.36.

We have also compared our parameters with those used in the study by Smiljanic et al. (2009) for the 16 stars in common with theirs. (There are 18 stars in common but they used the Stephens & Boesgaard 2002 parameters for two of them.) For 14 of the 16 stars, they made use of the parameters derived spectroscopically by Fulbright (2002). For nine of the stars the agreement in temperature is excellent, within ±50 K. However, for seven stars their temperatures are systematically lower than ours by 250–600 K. For six of these seven stars, we were able to make comparisons with effective temperatures found by Casagrande et al. (2010) from the infrared-flux method (IRFM). Those temperatures were in between our values and the ones used by Smiljanic et al. (2009), with five being closer to ours and one closer to theirs. On average our spectroscopic temperatures were 138 K hotter than those from the IRFM, while those of Smiljanic et al. were 285 K cooler. The seventh star was analyzed by Nissen et al. (2000) who found temperatures with IRFM; that value is also intermediate between the two spectroscopically determined temperatures with ours again being hotter.

Thirteen of our stars were also observed by Nissen & Schuster (2010) in their sample of 106 stars from which they found evidence for two different populations of halo stars in the solar neighborhood. They also determined their parameters spectroscopically. On average our values for T_eff are 28 K hotter than theirs, our values for log g are smaller than theirs by 0.15 dex, and we find [Fe/H] lower by −0.05 dex. (If we exclude HD 241253 for which we differ in temperature by 224 K, our mean difference is +12 K; for that star we agree in [Fe/H] by 0.03 dex.)

The Be abundance is particularly sensitive to log g. As mentioned above, we found this parameter spectroscopically primarily from the ionization balance between Ti i and Ti ii, which compared well with what we found from Fe i and Fe ii. This study has 20 stars in common with Tomkin et al. (1992) who found log g values from the ionization balance between Fe i and Fe ii. The average difference in log g from the two studies is +0.008.

Smiljanic et al. (2009) used gravities derived from Hipparcos parallaxes or adopted literature values. The agreement for all but one of the 16 stars is within ±0.30 and the mean difference is −0.04. For that one star, G 63-46, our log g value is higher by 0.93 dex and our Be abundance is higher by a factor of four. We have also tried their log g from Hipparcos in our analysis, which we present in the following section. Neither our Be abundance nor theirs produce an outlier in the relationships produced in Section 4.

We also compared our derived values of [Fe/H] for the 16 stars. All but one star agree to within ±0.12 with a mean difference of −0.03. For BD +2 4651 we find [Fe/H] = −1.90 while they find −1.50. This star is also not an outlier in any of the figures in Section 4 with either set of values.

We used MOOG with the synth driver to find Be and O abundances. We used the appropriate model for each star to create a synthetic spectrum from 3129 to 3133 Å to compare with the observed intensity-wavelength files. For Be we used four abundances to find the best match. We then plotted the best fit to the data with comparisons of A(Be) of +0.30 dex and −0.30 dex and one with no Be at all. For O we tried four abundances differing by 0.20 dex (or in some cases 0.10 dex). As part of the fitting procedure we could adjust the width of the Gaussian we used for the line profile, the continuum level, and the exact wavelength. For some stars there was some broadening beyond the instrumental width, but the determination of the continuum level was not a problem in the metal-poor stars and the wavelength corrections made during the data reduction were very accurate.

In Figure 2 we show the syntheses for two stars of very different metallicities: [Fe/H] = −1.01 and −2.79. This illustrates the complexity of the spectra in the more metal-rich stars and the concomitant difficulty in getting a good synthetic fit. The metal-poor stars can be well fit, as seen in the figure for BD −10° 388 and reliable Be abundances can be determined. However, the Be ii lines grow weaker as the metallicity decreases (see, e.g., Gilmore et al. 1991, 1992; Molaro et al. 1997; Boesgaard & King 1993; Boesgaard et al. 1999; Rich & Boesgaard 2009). The need for very high S/N is clear for the lowest metallicity stars. For example, our spectrum of BD −10° 388, shown in Figure 2, has an S/N of 120.

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Figure 3 shows the observed spectra and synthetic spectra for two stars with the same temperature, but different values for log g and [Fe/H]. The lower metallicity star has the lower Be and O abundances. In BD +28° 2137 the value for [Fe/H] is lower by 0.41 dex, for [O/H] by 0.39 dex, and for A(Be) by 0.31 dex compared to those values in BD −17° 484.

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For stars with lower log g values, the Be ii lines are stronger for a given Be abundance, which can be seen in Figure 4. For G 180-24 log g is 3.77, which is lower than 3.98 for G 24-3 and the Be ii lines can both be seen to be stronger in G 180-24. The Be abundances are comparable; G 180-24 does have a higher A(Be), but not by much: 0.10 dex. The syntheses for these two stars are shown in Figure 5. This implies that Be ii will be more easily detected in subgiants than in dwarfs at low metallicities.

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One of our stars, G 268-32, with [Fe/H] = −2.51 seemed to be very difficult to fit with an ordinary synthetic spectrum. According to the analysis by Aoki et al. (2002), it is a carbon-enhanced metal-poor (CEMP) star with [C/Fe] = 2.1 and [N/Fe] = 1.2. When we used those values in the synthesis, we derived a much better fit. Our parameters are very similar to those of Aoki et al. (2002): we derive 6230/4.60/−2.51/1.46, while they find 6250/4.5/−2.55/1.5 for T_eff, log g, [Fe/H], and ξ.

Then following the example of Ito et al. (2009), we removed the CH (and CN) lines from the line list in order to find an upper limit for the Be abundance. Figure 6 shows an expanded view of the region of the 3131 line of Be ii. The feature at 3130.8 Å, primarily Ti ii, is well fitted. For Be the synthetic spectrum with no Be best matches the observed spectrum, but we adopt an upper limit of A(Be) <−1.5. This is now the second CEMP star with no Be; Ito et al. (2009) found A(Be) < −2.00 in BD +44° 493. Unlike BD +44° 493, G 268-32 has enhanced s-process elements; Aoki et al. (2002) find [Ba/Fe] = +1.98. The group of CEMP stars that are enhanced by s-process nucleosynthesis, CEMP-s, are thought to result from mass transfer from an asymptotic giant branch (AGB) companion. This AGB connection may provide an answer to the problem of the low (or no) Be in light of a normal Li abundance in G 268-32; Thorburn (1994) found A(Li) = +2.09, but with a lower temperature, 5841 K, and a lower [Fe/H] = −3.50. When we use our model with her Li equivalent width, we find A(Li) = 2.32.

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Smiljanic et al. (2008) discovered a Be-rich halo dwarf, HD 106038, which has [Fe/H] = −1.26 (Nissen & Schuster 1997). They found a Be abundance of A(Be) = 1.40 near the meteoritic value of 1.42 (Grevesse & Sauval 1998) and 1.41 (Lodders 2003). We observed this star on our 2008 January 16 Keck night and obtained an S/N of 100 in a 25 minute integration. Our derived parameters (T_eff = 6085 K, log g = 4.63, [Fe/H] = −1.34, ξ = 1.46) are very similar to the ones they used and our Be abundance is similar, A(Be) = 1.47. Tan et al. (2009) also analyzed HD 106038 and derived A(Be) = 1.37.

The upper part of Figure 7 shows our observed spectrum of HD 106038 compared to BD −8° 4501, which has similar parameters. The difference in the Be ii lines is dramatic. The lower half of the figure is our spectrum synthesis for HD 106038, showing good fits for both Be and OH. This OH line gives [O/H] = −0.95; the other two OH features give −0.92 and −0.90 (see Section 3.3).

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In Section 3.1, we noted that our spectroscopic log g was quite different from the Hipparcos one used by Smiljanic et al. (2009) for G 63-46. The parallax for this star is 7.44 ± 1.70 mas resulting in their value of 3.77 (±0.10). We have done a Be- and O-synthesis with that log g and find A(Be) = 0.66, lower than the +0.98 with our log g but higher than the +0.37 found by Smiljanic et al. The OH lines are not fitted as well using the lower log g, however. We also tried a synthesis with all four parameters used by Smiljanic et al. that does not fit our data at all well, mostly because their temperature is so low that all the blending lines near the 3130 line of Be ii are too strong.

Beryllium is a direct by-product of O via spallation so it is useful to find the abundance of O in our stars. As pointed out in Rich & Boesgaard (2009) determining reliable O abundances in stars is not easy and the three common features used (O i triplet, [O i], and the electronic transitions of OH in the UV) all have drawbacks. Our spectra do not extend beyond 6000 Å, so we could only use the OH features in the UV. In addition to the OH feature between the two Be ii lines at 3130.6 Å, we used two additional OH features at 3139 and 3140 Å. There are seven OH lines in the 3139 Å region and five OH transitions in the 3140 Å region as well as atomic lines. Our line lists for the OH regions are from B. Gustafsson (1996, private communication).

Figure 8 shows the syntheses for these regions in two of our stars with different values of [Fe/H]. We used the value for the Gaussian smoothing that we found in the Be ii synthesis because it was constrained there by many more features. Similarly, if needed, we used those values for the continuum and wavelength adjustments. In the figure we show the best fit for O and for amounts of ±0.20 dex as well as the result with no O at all.

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We derive an average [O/H] abundance by weighing the O abundance derived from 3130 Å region by a factor of two. That extra weight was used because (1) the 3130 Å line list is better determined and (2) that region is closer to the center of the echelle order and thus has a somewhat higher S/N. Generally, the O abundance from these two OH features agrees well with that found from the 3130 Å feature.

We used our spectrum of the Moon (see Table 1) to find a solar abundance of O from the same three OH features. From this we find log O/H + 12.00 = 8.63 ± 0.08. This is in good agreement with the revised value for the Sun of Asplund et al. (2009) of 8.69. The work of Asplund & García Peréz (2001) indicates that the use of three-dimensional model atmospheres reduces the O abundance found from the OH lines, and also reduces it more at lower values of [Fe/H].

The O abundances are quite sensitive to the values for log g and T_eff (see Section 3.5). There is an additional uncertainty from using one-dimensional instead of three-dimensional model atmospheres. We decided to use two other alpha-elements as surrogates for O and thus have determined the abundances of [Ti/H] and [Mg/H].

We have measured equivalent widths of 5–19 Ti i lines and 5–13 Ti ii lines. We found Ti abundances with the abfind driver in MOOG. The standard deviation of the Ti abundance from the agreement of the Ti i lines is 0.06–0.11 dex and from the Ti ii lines is 0.08–0.11 dex. Table 3 gives our results for [Ti/H] for the newly observed stars and for the stars in Rich & Boesgaard (2009).

For Mg we have used three lines of Mg i at 4571, 4703, and 4730 Å. For the most metal-poor stars ([Fe/H] ≲ −2.7) only the line at 4703 Å was strong enough to use. Conversely, in the more metal-rich stars ([Fe/H] ∼−0.5 to ∼−1.0) that line was too strong to use. Table 3 also gives the Mg abundances.

Uncertainties in the abundances are due to uncertainties in the stellar parameters and the quality of the data, including the S/N. We have calculated the errors in the abundances for all five elements which are due to the uncertainties in the stellar parameters. We have used ±100 K as the uncertainty in T_eff, ±0.2 dex as the uncertainty in log g, ±0.10 dex as the uncertainty in [Fe/H], and ±0.2 km s⁻¹ as the uncertainty in ξ. We have chosen three representative stars that cover a range in parameters from 5768 to 6222 K in temperature, 3.04 to 4.07 in log g, −1.35 to −2.79 in [Fe/H], and 1.14 to 1.54 km s⁻¹ in ξ; the results are in Table 4. The adopted abundance error is the quadrature sum of the uncertainty from each parameter.

We can estimate the uncertainty in the equivalent width measurements from the S/N values and the spectral resolution. Eighty-seven percent of our stars have spectra with S/N > 80 and 60% are >100.

As can be seen from Figure 2, the more metal-rich stars have many blended lines in the Be ii region; to determine reliable Be abundances, the stellar parameters and the line list used in the synthesis must therefore be well determined. For the metal-poorer stars the spectrum is less crowded, making the Be abundances easier to determine. However, in the most metal-poor stars, the Be lines become very weak so it is especially important to obtain high S/N spectra. As can be noticed in Table 4, the Be abundance is particularly sensitive to the log g value used.

The abundance of O from the OH features is particularly sensitive to the model temperature and gravity. Even though the three OH features we used give very similar abundances in each star, the uncertainties in the stellar parameters contribute substantial error. In addition there is the possibility of a more systematic trend seen when the three-dimensional model atmospheres are used (Asplund & García Peréz 2001) as mentioned in Section 3.3.

In the figures that follow we adopt these values as mean errors: [Fe/H] ± 0.09; [Ti/H] ± 0.09; [Mg/H] ± 0.07; A(Be) ± 0.12; and [O/H] ± 0.22. For the element ratios we adopt these values: [Ti/Fe] ± 0.13; [Mg/Fe] ± 0.11; [Be/Fe] ± 0.15; and [O/Fe] ± 0.24.

Figure 9 shows the relationship between [Fe/H] and A(Be) for our stars. Two stars with enriched Be (HD 106038 and HD 132475) were not included in the determination of the least-squares fit to the data. A linear fit between these two logarithmic quantities is a good match over three orders of magnitude in [Fe/H]:

$$\begin{equation} A({\rm Be}) = 0.877 (\pm 0.030) [{\rm Fe/H}] + 1.207 (\pm 0.060). \end{equation} \tag{ 1 }$$

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As Rich & Boesgaard (2009) pointed out, there is no substantial evidence for a plateau of Be at the lowest metallicities.

Smiljanic et al. (2009) list the linear relations found between Be and Fe by several different studies and for four subsets of their own data. Those slopes are all steeper than ours because none of those studies has the large number of very metal-poor stars that we have here. Our single-slope fit is influenced by our stars with [Fe/H] < −2.2. When we just consider the more metal-rich stars with [Fe/H >−2.2, we find a slope of 1.04 ± 0.06. This agrees, within the errors, with the slope of 1.16 ± 0.07 found by Smiljanic et al. (2009) for their thick disk star sample.

When the Be results are normalized to the Fe abundance, [Be/Fe], as seen in Figure 10, we can see that Be is somewhat enriched over Fe from [Be/Fe] = +0.19 at [Fe/H] ∼ −3.3 and reducing to [Be/Fe] = 0 at [Fe/H] = −1.7. The formation of Be can occur in the earliest generations of massive stars during SNe when CNO atoms accelerate out from the explosion into the ambient gas. These ejecta strike protons and neutrons at high energies and split into smaller atoms like Li, Be, and B. So it is not surprising that Be is enhanced relative to Fe in the most metal-poor stars. According to Tsujimoto et al. (1995), the relative contribution of SNe Ia to the solar Fe abundance is 57%.

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Oxygen is directly connected to Be as a major "mother" nucleus for the rare light elements through various spallation reactions. The relationship we found between A(Be) and [O/H] is shown in Figure 11. There is more scatter in this diagram than in Figure 9, which is due in part to the larger uncertainties in [O/H] as seen in Table 4. [O/H] is sensitive to both T_eff and log g; the error bar shown here is ±0.22.

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The linear single-slope fit shown is

$$\begin{equation} A({\rm Be}) = 1.037 (\pm 0.053) [{\rm O/H}] + 0.893 (\pm 0.073). \end{equation} \tag{ 2 }$$

The scatter of the data in Figure 11 does not seem to be random, but rather the low O points are above the best-fit line as are the high O points. We therefore tried a two-slope fit shown in Figure 12. This was also done by Rich & Boesgaard (2009). This change could be expected if the dominant source of Be in the O-poor and Be-poor stars is the acceleration of CNO atoms from SNe II in the early days of Galactic evolution. The number of Be atoms would be proportional to the number of SNe II and thus the number of O atoms. The slope would be ⩽1 (as modified to lower values by processes like mass outflow during star formation). When the dominant source of Be atoms is from the classical GCR method with energetic cosmic rays hitting CNO atoms in the ambient interstellar gas as detailed by Meneguzzi et al. (1971), the number of O atoms would depend on the cumulative rate of SNe and the number of energetic cosmic rays proportional to the instantaneous rate of SNe. The slope for the O-rich and Be-rich stars would be ⩽2. The slope we find between [O/H] and A(Be) for the O- and Be-poor stars is 0.69 ± 0.13 and for the O-rich and Be-rich stars is 1.30 ± 0.10, consistent with the notion of a change in the dominant production mechanism.

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Those expressions are as follows.

High-O and high-Be:

$$\begin{equation} A({\rm Be}) = 1.295 (\pm 0.100) [{\rm O/H}] + 1.127 (\pm 0.104). \end{equation} \tag{ 3 }$$

Low-O and low-Be:

$$\begin{equation} A({\rm Be}) = 0.690 (\pm 0.129) [{\rm O/H}] + 0.275 (\pm 0.252). \end{equation} \tag{ 4 }$$

The slope change does seem to be caused by the Be abundances rather than the O abundances. In Figure 13, we show the relationship between [Fe/H] and [O/H]. There is less scatter than found in Figures 9 (Be versus Fe) and 11 (Be versus O) and a well-defined linear fit given by

$$\begin{equation} [{\rm O/H}] = 0.749 (\pm 0.025) [{\rm Fe/H}] + 0.126 (\pm 0.050). \end{equation} \tag{ 5 }$$

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We have done two statistical tests (χ² and BIC (Bayesian information criterion)) to evaluate whether the data for A(Be) and [O/H] are better fit by a single power law or a broken power law. Both tests indicate that the one-slope fit is better.

Figure 14 shows the O abundances normalized to the Fe abundances as a function of the Fe abundances. This too can be well represented by a linear fit with the scatter due to the mean error in [O/Fe]:

$$\begin{equation} [{\rm O/Fe}] = -0.252 (\pm 0.025) [{\rm Fe/H}] + 0.121 (\pm 0.050). \end{equation} \tag{ 6 }$$

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As mentioned previously, the O abundance from the OH features has a large dependence on both T_eff and log g from the models; in addition, there is the issue of the abundance found from three-dimensional models versus one-dimensional models as discussed above in Section 3.3. Therefore, we have used two alpha-elements, Ti and Mg, as surrogates for O.

Figure 15 shows the relationship between the abundance of Ti and Fe as well as the Ti normalized to Fe compared to Fe. There is a remarkably tight correlation between [Ti/H] and [Fe/H] with a slope of 0.86 ± 0.01. The closeness of this relationship, and that between [Mg/H] and [Fe/H] (shown in Figure 17), indicates that the stellar parameters we have derived are well determined. The relationship between [Ti/Fe] and [Fe/H] with a slope of −0.14 ± 0.01 is less steep than the one between [O/H] and [Fe/H] which has a slope of −0.25 ± 0.02.

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Figure 16 shows how A(Be) tracks [Ti/H] well with a slope of 1.00 ± 0.04. As in Figure 11 of A(Be) versus [O/H], both the lowest values of [Ti/H] and the highest ones lie above the best fit but not as dramatically as for [O/H]:

$$\begin{equation} A({\rm Be}) = 1.002 (\pm 0.042) [{\rm Ti/H}] + 1.069 (\pm 0.072). \end{equation} \tag{ 7 }$$

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The relationship between [Mg/H] and [Fe/H] and the one between [Mg/Fe] and [Fe/H] are shown in Figure 17. There is a surprisingly close correlation between [Mg/H] and [Fe/H] with a slope of 0.94 ± 0.01. This is impressive in part because we have only 1–3 Mg i lines and only the strongest one could be used in the Fe-poor stars. The relationship between [Mg/Fe] and [Fe/H] (slope = −0.07 ± 0.01) is even flatter than those of [Ti/Fe] with [Fe/H] and [O/H] with [Fe/H].

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The plot of [Mg/H] (as a surrogate for [O/H]) with A(Be) is shown in Figure 18. The slope of this relationship is 0.87 ± 0.03, which is very similar to the slope between A(Be) and [Fe/H] of 0.87 ± 0.03. The relation between A(Be) and [Mg/H] is

$$\begin{equation} A({\rm Be}) = 0.870 (\pm 0.033) [{\rm Mg/H}] + 0.815 (\pm 0.056). \end{equation} \tag{ 8 }$$

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Table 3 also gives the abundance of Li from the literature for most of our stars along with the reference for each. This is not meant to be a comprehensive compilation where multiple studies of a given star are combined in some way. We did make use of the compilation done by Charbonnel & Primas (2005) when the Li abundances were available for our stars to give some consistency. Our purpose here is only to compare the Li and Be abundances in a general way and to check for potential Be depletions in Li-depleted stars.

In Figure 19, we show our Be abundances compared to Li abundances found in the literature. Most of our sample have values of A(Li) near 2.2, corresponding to the halo star Li plateau reflecting the big bang production of Li as first found by Spite & Spite (1982). There are seven stars in our sample that are Li-deficient: BD +37° 1458 at A(Li) = 1.37, HD 64090 at 1.21, HD 109303 at <1.65, HD 188510 at 1.61, HD 201889 at 1.04, G 74-5 at 1.48, and Ross 390 at 1.15. Although Li is depleted in those seven stars, the Be abundances are apparently normal for their [Fe/H] values. Four of the seven have T_eff < 5600 K (HD 64090, HD 188510, HD 201889, and BD +37° 1458); these temperatures are cool enough for Li depletion to have occurred (e.g., Boesgaard et al. 2005). Only the coolest, BD +37° 1458 at 5492 K, might be mildly Be-deficient as judged by its position in Figure 9 where it is 0.35 dex below the fit. The other three stars have [Fe/H] values < −0.9, which are too metal-rich to be part of the halo star Li plateau; they may have suffered Li depletion like that in Population I stars.

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We could not find Li abundances in the literature for 21 of our 117 stars. Only one, HD 184499, may be cool enough to have had Li depletion, but it has normal Be. Our two stars with enhanced Be are also enhanced in Li. HD 106038 with A(Be) = 1.47 has A(Li) = 2.48 (Asplund et al. 2006) and 2.55 (Tan et al. 2009). HD 132475 was found by Novicki (2005) to have enhanced Li with A(Li) = 2.39. Boesgaard & Novicki (2006) determined a Be abundance of A(Be) = +0.57 and Tan et al. (2009) found A(Be) = +0.62, i.e., it is Be-rich for its [Fe/H] of −1.50, as seen in Figure 9.

Our kinematic classification of these stars is drawn from Gratton et al. (2003), who use Galactic orbit calculations to determine criteria for distinguishing between stellar populations corresponding to different Galactic components. Stars with a galactic rotation velocity larger than 40 km s⁻¹ and an apogalactic distance (R_apo) less than 15 kpc comprise a kinematic class associated with the dissipative collapse population (Eggen et al. 1962), including stars from the classical thick disk and halo. The remainder of the stars in our sample can be associated with the accretion-process population first proposed by Searle & Zinn (1978). These are mainly halo stars, a subset of which can be further distinguished due to their retrograde orbits. Retrograde stars have a V velocity of < −220 km s⁻¹. The UVW velocities have positive U values away from the Galactic center, positive V values in the direction of the solar motion, and positive W values paralleling the direction of the north Galactic pole. To convert these values relative to the local standard of rest, we used solar values of U_☉ = −9 km s⁻¹, V_☉ = +12 km s⁻¹, and W_☉ = +7 km s⁻¹. Here we define a star's Galactic rotation velocity as v_rot = V + 220 km s⁻¹, where 220 km s⁻¹ is the rotational velocity of the local standard of rest with respect to the Galaxy (Fulbright 2002). The Galactic rest-frame velocities, v_RF, are [U² + (V + 220)² + W²]^1/2.

Kinematic properties for our full sample are given in Table 5, which lists the stellar radial velocity, the U_lsr, V_lsr, and W_lsr velocities relative to the local standard of rest, all in km s⁻¹, the distance to the apogalacticon of the orbit (R_apo), and the distance above the Galactic plane Z_max, both in kiloparsecs. The reference for the orbital parameters is included in Table 5, with the majority from the compilation of Carney et al. (1994). For each star we also list v_RF in km s⁻¹. We include our final classification of each star as dissipative (D) or accretive (A) or accretive/retrograde (A,R). In total our sample consists of 57 dissipative stars and 57 accretive stars (33 of which are also classified as retrograde). For two stars in our sample (HD 24289 and BD −13 3442), we were unable to make a conclusive kinematic classification as no data were available in the literature.

The distribution of A(Be) with [Fe/H] for the four groups—all stars, dissipative, accretive, and retrograde—is shown in Figure 20. The stars in the dissipative group span nearly the full range in [Fe/H]. The slope we find for them is 0.94 ± 0.04. However, the slopes for the accretive and retrograde stars are both lower at 0.68 ± 0.04. These slopes are different at the 4.6σ level. For comparison, in Figure 21 we have plotted the accretive stars and the dissipative stars with the best-fit linear relations overplotted. They separate well into two distinctive groups. The slopes intersect at [Fe/H] near −2.2, which somewhat blurs the distinction in A(Be) for low-metallicity stars in the two populations. We suggest that the accretive stars may have originated in environments where less Be was formed. They may have had their Be formed in the vicinity of SN II through the acceleration of CNO atoms into the surrounding gas as discussed in Section 4.2.

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Similar plots between A(Be) and [O/H] are shown in Figures 22 and 23. In Figure 22, we see that the stars in the dissipative group span nearly the full range in [O/H]. The slope between A(Be) and [O/H] for this group is 1.13 ± 0.08. As with Be and Fe, the accretive and retrograde stars have a shallower slope for Be and O of 0.76 ± 0.06. These slopes are different at the 3.6σ level. The two-slope fit that we see in Figure 12 of 1.30 ± 0.10 and 0.69 ± 0.13 may be partly due to the fact that there are two populations of stars. And this in turn may result from the formation of a larger fraction of Be made by the CNO cosmic rays produced by SNe II for the accretive stars while most of the dissipative stars inherited Be from the GCRs. A direct comparison between those two groups in Figure 23 shows that they follow distinct relations, but again the intersection of the two fits occurs at [O/H] ∼ −1.9 and the differences at low [O/H] are cloudy.

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In Figure 24, we show the distribution of the Be abundances with the rest-frame velocity (v_RF). There are four panels showing the distribution for all stars, for just the dissipative stars, for just the accretive stars, and for just the retrograde stars. For the dissipative stars the full range of Be abundances is present, but there are no stars with v_RF > 280 km s⁻¹ (by definition). For the accretive and retrograde stars there are no stars with A(Be) > +0.35 with the exception of the two with enriched Be (HD 106038 and HD 132475). Based on the A(Li) values and the positions in the A(Be)–[Fe/H] plane, there is no evidence that there has been Be depletion (with the possible exception of BD +37° 1458). Therefore, it seems plausible that the accretive and retrograde stars come from an environment that has not been as enriched in Be as the dissipative sample was. This is in qualitative agreement with Tan & Zhao (2011) who find that low-α (accretive) stars have generally lower Be abundances than high-α although their sample is only from [Fe/H] = −0.49 to −1.55.

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Figure 25 shows the distribution of Be normalized to Fe ([Be/Fe]) with the rest-frame velocity (v_RF). The accretive stars and their subset of retrograde stars show a flat distribution of [Be/Fe] with v_RF; the star with the highest velocity at 409 km s⁻¹ is G 64-12, which has low values of A(Be) = −1.43 and [Fe/H] = −3.45 but a comparatively high value for [Be/Fe] = +0.60. The dissipative stars may be connected to v_RF with the lower velocity stars showing higher values of [Be/Fe].

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Pasquini et al. (2005) have suggested that A(Be) in stars can track early star formation in the Galaxy. They use [O/Fe] to reveal the variation in the star formation rate and A(Be) as a measure of time, a cosmochronometer, from the beginning of star formation. They use the Galactic evolution model of Travaglio et al. (1999). Model predictions have been made by Valle et al. (2002) for Li, Be, and B. They take the stellar production of Fe and O from Thielemann et al. (1996) for SNe I and from Woosley & Weaver (1995) for SNe II.

From observations of Be, Fe, and O from Boesgaard et al. (1999), they compare [O/Fe] with A(Be) and find good agreement between the data for the dissipative stars and the model for the thick disk (see their Figure 2). That sample was only eight stars, however. Our sample size here is 116, excluding the CEMP star, G 268-32.

Figure 26 shows our data for [O/Fe] and A(Be) for all 116 stars. We show a linear fit and the 1σ error bars for [O/Fe]. The relationship is

$$\begin{equation} [{\rm O/Fe}] = -0.269 (\pm 0.029) \textit {A}({\rm Be}) + 0.476 (\pm 0.023). \end{equation} \tag{ 9 }$$

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We have also separated the data into dissipative, accretive, and retrograde subsamples of 57, 57, and 33 stars. There is virtually no difference between the fits for the full sample and these subsamples. The slopes are −0.26 ± 0.04, −0.25 ± 0.05, and −0.29 ± 0.08, respectively. The curve fit from Pasquini et al. (2005) does not match the data as well as the straight-line fit. Note that in Figure 14 we have plotted [O/Fe] with [Fe/H] as the abscissa (as opposed to A(Be) as the abscissa in Figure 26). In both plots there is a larger spread at higher values of the abscissa: [Fe/H] >−1.4 and A(Be) > 0.0. The vast majority of these stars belong to the dissipative population. We conclude that Be is no better as a cosmochronometer than Fe, and may in fact be worse.

Our Figure 7, top panel, shows two stars with similar metallicity and log g values, but very different Be abundances. Smiljanic et al. (2009) show four pairs of stars from their paper in Figure 14 with similar parameters and very different values for A(Be). Another compelling example can be seen in Figure 14 of Boesgaard & Hollek (2009) of two stars differing by 35 K in temperature, 0.07 in log g, 0.06 in [Fe/H], but differing by a factor of two in both A(Li) and A(Be); their masses are similar at 0.95 and 0.96 M_☉ as are their ages at 9.17 and 9.35 Gyr. These examples seem to indicate that there is a real spread in the Be abundance in stars of similar stellar parameters.

We have examined the possibility that there is a real spread in Be at a given interval of [Fe/H], [O/H], [Ti/H], and [Mg/H]. Our approach is to determine whether the data show unusually large scatter within a given range of [X/H] compared to the rest of the observations outside that interval. This is done using a prediction interval, which is the expected range of an unobserved random variable Y (here abundance of Be) at a given confidence (defined by 100(1–α)%) based on a set of observed data (Casella & Berger 2002, Section 11.3). We assume the data are independent, obey a linear relationship, and are normally distributed about the line in y.

For each interval of interest Δ[X/H] and confidence limit α we use observations outside that region to derive the best-fit slope, y-offset, and prediction interval in that region of interest. We determine how many points within Δ[X/H] lie inside and outside the prediction interval and then use the binomial distribution to calculate the probability of this occurring by chance. If the probability is <0.0063% (>4σ) and is not highly sensitive to either the width of Δ[X/H] or the chosen confidence limit α, then we interpret that as evidence for a spread in A(Be) for that particular Δ[X/H].

We ran our analysis for [Fe/H], [O/H], [Ti/H], and [Mg/H] with a running interval in steps of 0.01 in [X/H] for Δ[X/H] = 0.50, 0.30, and 0.20 (±0.25, ±0.15, ±0.10) and confidence levels α = 0.01, 0.05, and 0.10 (99%, 95%, 90%). No significant spread in A(Be) was observed in [Fe/H], [Ti/H], or [Mg/H]. We did, however, find evidence of a spread for [O/H] from ∼−0.5 to −1.1 dex. In Figure 27, we show an example of the analysis for A(Be) versus [O/H]. At the [O/H] value of −0.8 dex, an interval of Δ[O/H] = 0.50, and a confidence limit of 95% for the prediction interval, 10 out of 30 stars fall outside the prediction interval (top panel). The probability of this occurring by chance given the 5% expectation rate is 1.1 × 10⁻⁶ (middle panel). Our results are independent of whether we include or exclude the two anomalously Be-rich stars HD 106038 and HD 132475 (bottom panel). The spread is real at the 4⁺σ level of confidence. It is also real at the 3σ level of confidence when our Δ[O/H] = 0.30.

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The interval where there is the most spread in Be is between [O/H] = −0.5 and −1.0, which corresponds to −0.9 and −1.6 in [Fe/H].