BERYLLIUM ABUNDANCES IN STARS OF ONE SOLAR MASS

The stars in this study were chosen from the LR04 paper in which 451 F and G dwarfs were analyzed for the purpose of understanding the metallicity, mass, and age effects on the Li abundance. Their study determined ages and masses using the G00 tracks, and Hipparcos parallaxes for M_V. Our study focused on the stars that LR04 found to be within 0.9 ⩽ M_☉ ⩽ 1.1. Of the 451 stars in the LR04 study there were 156, or 35% in that mass range; we have Be observations of one-third of these stars.

Figure 1 is an H–R diagram showing the positions of our stars. They are separated into dwarfs and subgiants by the criterion of S04 at log g = 4.1. The circled dot indicates the Sun. They range from 5600 K < T_eff < 6600 K and most are somewhat evolved away from the zero-age main sequence. Due to the fact that most of the stars in LR04 are evolved beyond the zero-age main sequence, it was possible to determine stellar ages for them.

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In 2004, the HIRES spectrometer was upgraded with a 6144 × 4096 mosaic CCD, which is split into three chips with one optimized for the ultraviolet/blue end of the spectrum. The quantum efficiency is 94% for this chip in the Be region, about 12 times better than the old chip. Between 2005 January 31 and 2007 June 9, 40 Keck spectra were taken with the new HIRES detector on nine separate nights. Given the relative brightness of these stars, they were taken in evening and morning twilights and on partly cloudy nights. The decker used was B5 which has slit dimensions of 3.5 × 0.861 arcsec. These data have a spectral dispersion of 0.0132 Å pixel⁻¹ and a measured spectral resolution of ∼49,000 near 3130 Å. Exposure times ranged from 3 to 30 minutes to attain a signal-to-noise ratio (S/N) range from 33 to 277 and a median S/N of 146 and a mean of 168.

On each of the nine nights on which observations were made for this program, calibration frames were also taken. Typically 7–9 bias frames were recorded and Th–Ar spectra were obtained at the beginning and end of each night. The internal flat fields were taken with different exposure times for each of the three CCDs. In order to achieve sufficient flux for the Be ii line region exposures of 50 s were needed for the UV chip. The optimum exposure for the green chip was typically 3 s and that exposure would be useful for the longer orders of the UV chip. In order to not saturate the flat fields on the red chip exposures of 1 s were obtained. Seven to nine flat exposures were taken at each of the three exposure times to achieve the proper flux for the various orders on all three CCDs.

Table 1 gives the star name, V magnitude, date of observation, exposure time, and total S/N of the stars for which observations were taken using Keck I with the upgraded HIRES.

The Keck spectra from the upgraded HIRES were supplemented by spectra in the LR04 one-solar-mass range from the original HIRES and the CFHT. With the original HIRES on Keck I with a Tektronix 2048 × 2048 CCD (Vogt et al. 1994), five stars were observed between 1999 November 13 and 2002 January 5. These data have a spectral resolution of 0.022 Å pixel⁻¹, which gives a resolution of ∼48,000 per pixel. Exposure times for those stars ranged from 5 to 12 minutes with a median S/N of 140 and a mean of 122.

Five stars were observed on 15 and 16 October 1995 on the 3.6 m CFHT with the Gecko f/4 spectrograph with a resolution of ∼120,000 and a dispersion of 0.010 Å pixel⁻¹. The detector was a 2048 × 2048 array with 15 μm pixels that is UV sensitive with a quantum efficiency of 80% in the Be region. Exposure times for these five stars range from 15 to 45 minutes, with a median and mean S/N of 72. Information on these observations and data reduction can be found in Boesgaard et al. (2001). One additional star (HD 142860) was obtained with the f/8 coudé spectrograph at CFHT at a resolution of 24,000. Details of that observation can be found in Boesgaard et al. (2004b).

Table 2 includes the CFHT stars and Keck I stars that were previously included in Boesgaard et al. (2001, 2004a, 2004b). It lists the name, V magnitude, date of observation, exposure time, total S/N, telescope, and the reference to the paper from which the star was taken and where the earlier analyses were presented. The Be abundances for these stars have been redetermined here using the parameters determined by LR04.

The Keck I data from the upgraded HIRES were reduced using IRAF and using two different reduction pipelines: the new MAKEE Data Reduction Software and the IDL-based HIRES Redux software. Both software routines were designed for the new chip. We used our own master flat fields (one for each chip), biases, and arcs rather than adopt archival ones. It is critical to have long flat-field exposures, typically 50 s, in order to have sufficient flux at the UV wavelengths of the Be II lines, while 3 s is enough for the green chip and 1 s for the red chip. Our wavelength calibrations were found from our Th–Ar exposures at the beginning and end of the each night. The wavelength solution was applied for each night. Cosmic ray removal was also performed on the stars in the Be region using the IDL version of L.A. Cosmic⁴ (van Dokkum 2001). The data were then Doppler corrected and continuum fit in IRAF using the onedspec package and the echelle package.

The data reduction for the stars discussed in Section 2.3 has been described in the original papers; see Boesgaard et al. (2001), B04a, and B04b for the details of the procedures used regarding the CFHT stars and the earlier Keck I HIRES stars.

In order to measure the Be abundance in these stars, we interpolated atmospheric models from the Kurucz grid point models (Kurucz 1993). These require metallicity ([Fe/H]), effective temperature (T_eff), surface gravity (log g), and microturbulence (ξ). The [Fe/H], T_eff, and log g were adopted from LR04; however, the microturbulence parameter was not included. Microturbulences were determined using the following relation derived by Edvardsson et al. (1993):

$$\xi = 1.25 + 8 \times 10^{-4}({T}_{\rm eff} - 6000) - 1.3(\log { g} - 4.5)\,.$$

A complete list of the stellar parameters (T_eff, log g, [Fe/H], and ξ) for all our stars is found in Table 3.

We determined the abundance of Be by fitting the Be ii resonance lines at 3130.421 and 3131.065 Å using the spectral synthesis software MOOG⁵ (Sneden 1973) as updated in 2002 (in "synth" mode). Due to the considerable blending around the 3130.421 Å line, the stronger line of the doublet, the fit of the 3131.065 Å line gave a more reliably determined Be abundance.

Our line list includes 307 atomic and molecular lines between 3129.5 and 3132.5 Å. It was adopted largely from Kurucz to best fit the Be region with some modifications to the list from former studies of Be abundances in stars covering a wide range of temperatures and gravities., e.g. the log gf value of the 3129.763 Å  Zr ii line. During the synthesis fitting a Gaussian profile was used for the instrumental and other broadening. The instrumental broadening has a full width at half-maximum (FWHM) of 0.08 Å and most of the stars were fit with FWHM 0.08 to 0.10 Å. The largest broadening was 0.18 Å for HD 218470, an F5 V star in the Li–Be dip region with T_eff = 6495 K.

Figures 2–5 show examples of the synthetic spectra that were created for each star. For each spectrum, the dots represent the data points while the solid line is the synthesis with the best fit. The dash-dotted lines represent a factor of 2 in the Be abundance above and below the best-fit Be abundance and the dotted line represents a synthetic spectrum without any Be. The Be abundance is represented in terms of A(Be); the meteoritic value is A(Be) = 1.42 (Grevesse & Sauval 1998).

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In Figure 2 HD 693 and HD 103799 are compared. They have essentially the same T_eff, [Fe/H], age (6.1 Gyr), and A(Be). The main discernible difference is in the rotation as is seen in the line broadening in HD 103799 where its FWHM Gaussian is 0.13 compared to that of HD 693 at 0.09. Shown in Figure 3 are HD 186379 and HD 94012 which have nearly identical [Fe/H] and the same A(Be) and vary only slightly in age (10 Gyr versus 8 Gyr) even though they differ in T_eff by 250 K. In Figure 4 are HD 199960 and HD 15335. They have the same age (6.5 Gyr), and T_eff; however, they differ in both [Fe/H] and A(Be) by a factor of 2. This supports the trend of an increasing Be abundance with increasing [Fe/H] for halo and disk stars (e.g., see Boesgaard & Novicki 2006, their Figure 7). Finally, in Figure 5 are HD 209320 and HD 30743. These stars have the same age but differ in [Fe/H] by 0.4 dex, T_eff by 225 K, and in A(Be) by 0.2 dex.

Table 4 includes the parameters such as mass, age, and absolute visual magnitude as determined by LR04, including their value for A(Li). The final column has the Be abundance determined in this work.

In the temperature regime of our stars, an error of 100 K results in a negligible error in A(Be) ⩽ 0.01 dex. However, an uncertainty in log g of ± 0.5 produces an error between 0.044 and 0.052 dex depending upon T_eff. A combination of errors due to uncertainties in T_eff, log  g, [Fe/H], ξ, S/N of the observed spectrum, and the goodness of fit of the synthetic spectrum combine to give errors in A(Be) of 0.1 to 0.2 dex. There are nine stars analyzed here with Be detections that can be compared with the results in B01, B04a, and B04b. The average differences in the parameters used are ΔT = 5 K, Δlog  g = −0.05, and Δ[Fe/H] = −0.03 (in the sense of LR04 minus previous publications); these are insignificant differences. The differences in the values of A(Be) for the nine stars are −0.12 ± 0.12.

We have found Be abundances in 46 of our 50 stars ranging from A(Be) = 0.57 up to the meteoritic abundance of 1.42. This represents a spread in A(Be) of almost an order of magnitude in one-solar-mass stars. The four upper limits to A(Be) extend this range down to <−0.2 or a factor of more than 40. In our sample there are six stars with only upper limits on the Li abundance and four of them also have only upper limits on Be, while the two others have measured Be. Two of the Li- and Be-deficient stars, HD 182101 and HD 218470, are in the Li–Be dip region of T_eff.

Histograms of the Li and Be abundance distributions are shown in Figure 6. For this sample of 44 Li detections of one-solar-mass stars the median value of A(Li) = 2.39 and for the 46 Be detections the median A(Be) is 0.92. Both of these values are lower than their meteoritic counterparts of 3.31 and 1.42, respectively; this indicates considerable stellar depletion relative to the meteoritic values. All the stars are Li depleted and all but one are Be depleted.

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When we narrow the mass range to those stars that are within ±0.03 solar masses (0.97–1.03 M_☉) and select those within ±100 K of the Sun, there are six in our sample. For these six the mean A(Li) = 2.24 ± 0.23 and the mean A(Be) = 1.03 ± 0.14. These values compare well, within the errors, with the medians from the whole sample. The six stars (HD 22521, 26421, 94835, 100180, 186379, and 217877) are all older than the sun by 3–4 Gyr (except HD 94835, which is only 2.3 Gyr older) according to the G00 tracks and isochrones. Their old age and relatively high mean Li abundance, A(Li) = 2.24, only deepens the mystery of the large solar Li depletion, A(Li)_☉ ∼ 1.0.

In the LR04 study, masses and ages were determined via the G00 isochrones and evolutionary tracks. We have put our Be results in the familiar context of the H–R diagram by showing the relative Be abundances along with the G00 evolutionary tracks and isochrones in Figures 7 and 8. We have used tracks for [Fe/H] of 0.0 and −0.4 and include stars with [Fe/H] > −0.2 in Figure 7 and < −0.2 in Figure 8. The evolutionary tracks that cover our range of mass of 0.9–1.1 M_☉ are shown for the respective values of [Fe/H]. Isochrones for 100, 700, 2500, and 4500 Myr are also shown in each figure. The four sizes of symbols indicates the size of A(Be).

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In Figure 8, two stars appear to be >1.1 M_☉ for this survey, but this is due to the metallicity dependence of the evolutionary tracks; in LR04 smaller intervals were chosen for the tracks and therefore better constraints on the mass in LR04 were made. Although stars that fall near the cutoff between the two tracks in this study do not appear to be in the right mass range, the masses for these stars are indeed in the correct range and have been adopted from the LR04 paper.

As can be seen in Figure 1, many of the stars in our sample have evolved away from the zero-age main sequence (which is the reason why evolutionary ages can be assigned). In S04, the cutoff between dwarfs and subgiants is given as log g = 4.1. There are 17 stars in this sample that accordingly would be classified as subgiants. These stars generally have lower Be abundances with a mean A(Be) of 0.82 (excluding the two with upper limits). The stars with log g ⩽ 4.1 separate out in the distribution shown in the Be histogram in the lower portion of Figure 6; the lower three bins have 3, 8, and 4 stars that are subgiants.

The evolutionarily older subgiants show typically lower Be abundances at a given T_eff than the dwarf stars. The older age of the subgiants allow them to have had more time for slow mixing of the light elements, leading to depletion on the main sequence while the more advanced evolutionary stage allows them to have enlarged the surface convection zones leading to light-element dilution.

It may also just be a reflection of small number statistics; S04 do not see a similar depletion in their subgiants as seen in their Figure 4. Indeed, there would not be as much Be dilution in evolved stars compared to Li dilution. Figures 7 and 8 show little sign of a correlation between Be abundance and evolutionary age along the mass tracks.

This solar-mass sample was selected from a survey of F and G stars in the local thin disk. This resulted in a temperature range for our stars from 5600 to 6400 K. When plotted against temperature, an upper envelope for the Be abundance becomes apparent as seen in Figure 9. The highest Be abundances are present near 5800–600 K, with reduced amounts of Be in the hotter stars of our sample, 6300–6500 K, in the Li–Be dip region. For the Hyades this dip region is about T_eff ∼ 6300–6800 K (e.g., Boesgaard & Tripicco 1986), but for older stars the dip region may enlarge toward cooler temperatures (e.g., Michaud 1986) and show a larger spread in A(Li) (e.g., Jones et al. 1999).

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The lowest Be detections for this sample are A(Be) ∼0.5 dex and the Be abundances range up to 1.42. This order-of-magnitude spread can be seen particularly in the cooler stars (i.e., T_eff⩽ 5900 K). The stars in the S04a paper have T_eff in the range of 4800–6300 K. They find a abundance peak in A(Be) near 6100 K, with a gentle decline toward lower temperatures approaching 5000 K. Their sample includes planet-host stars, many of which are metal-rich, whereas our sample has only two stars with [Fe/H] >0.00. Those metal-rich stars show enhanced Be. Although our sample shows no such Be abundance peak and decline we note that our sample covers a specific mass range and thus a smaller range in temperature than that of S04a; we would not expect to see the decline in Be with decreasing temperature that they found.

Both slow mixing and convection zone depth vary with the stellar metallicity at a given mass or T_eff. There is evidence of a correlation between [Fe/H] and A(Be) (e.g., Boesgaard et al. 2008; Boesgaard & Novicki 2006; Section 4.4). That correlation needs to be considered when evaluating the temperature relation. The range for metallicity for our stars is −0.65 ⩽ [Fe/H] ⩽ +0.11. In Figure 10, we show the Be abundances normalized to Fe as [Be/Fe] versus T_eff. (We used the meteoritic A(Be) for the solar system normalization.) The normalized ratio, [Be/Fe], shows some spread at a given temperature, but no dramatic trend with temperature. And unlike Figure 9, the dwarfs and subgiants show similar relations with temperature. This plot of [Be/Fe] against T_eff does not yield the same trend as seen in S04a.

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The stars of this sample are members of the thin disk and generally have considerably higher metallicities than those of the thick disk and halo populations. These stars are of metallicity [Fe/H] > −0.65, with two positive metallicity stars. However, when the Be abundance is plotted against [Fe/H] in Figure 11, the metal-rich stars of this survey match the trend with the halo stars sampled in Boesgaard et al. (2008) remarkably well. The slope of the relation between A(Be) and [Fe/H] is 0.86 ± 0.02. The most metal-rich star (at [Fe/H] = 0.11) in our sample is HD 199960 whose Be abundance is equivalent to that of the meteoritic value of 1.42 dex (Grevesse & Sauval 1998). This value is also the highest Be abundance in this sample, supporting the idea that A(Be) increases with [Fe/H]. This is a remarkable trend, extending over nearly 4 orders of magnitude in [Fe/H] and over 3 orders of magnitude in A(Be).

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Another illustration of this relation is to sort the sample into metallicity bins. We created four metallicity bins and took the mean A(Be) from the three most Be-rich stars per bin. Table 5 shows again that A(Be) increases as [Fe/H] increases. LR04 created similar [Fe/H] bins for their data with the Li abundance and found that as the [Fe/H] increased, the Li abundance increased (which was expected), and so did the mass. Given that our data were selected based on mass, it was not possible to see the mass trend; however, we did apply the same [Fe/H] bins to the 157 LR04 solar-mass stars that had Li abundances. A(Li) is shown to increase with increasing [Fe/H] as well, but it is less obvious in our smaller data set.

One of the aims of this study was to understand the relationship between A(Be) and age. The mass constraint was placed at 1 ± 0.1 M_☉ in order to parameterize the A(Be)–age relation. Of our stars, all but one are older than the 4.5 Gyr Sun, eight (or 15%) have ages < 6 Gyr, and two (4%) have ages < 5 Gyr. This fits well with the larger sample of LR04 stars with masses between 0.9 and 1.1 M_☉. The full LR04 sample includes 451 stars, with 157 (or 35% of the sample) within our mass constraints; of those 157 stars, only 34 (22%) have ages < 6 Gyr and only six (4%) have ages <5 Gyr.

Figure 12 plots A(Be) and [Be/Fe] against age. The spread in A(Be) (including upper limits) is nearly 1.5 dex for the entire range of ages; including only the Be detections, the spread is still 0.9 dex. It should be noted that only one star (HD 199960) has larger A(Be) than the Sun with the rest being below the solar A(Be) value of ∼ 1.3 dex (e.g., Boesgaard et al. 2003). These stars that have evolved away from the zero-age main sequence have continued to lose Be. In the lower panel one can see that the scatter is reduced by using [Be/Fe], correcting for each star's metallicity. A small trend is found such that the older stars have more Be relative to Fe in our one-solar-mass sample. The ratio of [Be/Fe] is two times larger in the stars of 10 Gyr compared to those of 5 Gyr.

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Understanding the correlation between Be and Li is key to understanding the nature of light-element depletion and slow mixing in these stars. Figure 13 shows a plot of A(Be) versus A(Li).

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B05 found a linear relationship between A(Li) and A(Be) for field and cluster stars in the T_eff ranges of 5900–6300 K (the Li "plateau") and 6300–6650 K (the cool side of the Li-dip) with slopes of 0.365 ± 0.036 and 0.404 ± 0.034, respectively. We can combine our data with the field stars of B04 in the temperature range of 5900 K < T_eff < 6300 K. Figure 13 shows those results for a total of 60 stars. The triangles are stars from this study. For the combined data we find a slope of 0.34 ± 0.05, which compares well with the slope for 31 field stars in this same temperature range in B04: 0.36 ± 0.05. Note that the three most Li- and Be-depleted stars in Figure 13 all have solar metallicity: [Fe/H] = −0.03, +0.09, +0.12. It appears that metallicity is not an important factor in the Li–Be correlation. The trend shown in Figure 13 is consistent with the predictions of Li and Be depletion caused by rotationally induced mixing of Deliyannis & Pinsonneault (1997).

There is clear evidence that astration of Be is taking place in these one-solar-mass stars. The spread in A(Be) and [Be/Fe] at a given temperature shows that. The spread in A(Be) covers more than 1.5 dex, while the typical errors are ±0.15. There are two stars in our sample that have nearly identical stellar parameters, yet they differ in both A(Be) and A(Li) by a factor of 2. The Be region of the spectra of these two stars, HD 200580 and HD 204712, are shown in Figure 14. Only the two Be ii lines show meaningful differences between these two spectra. Their full set of stellar parameters are given in Table 4. They differ in T_eff by only 35 K, in log g by 0.07, and in [Fe/H] by only 0.06, all within the precision of their determinations. Their respective masses are 0.95 and 0.96 M_☉ and their ages are 9.17 and 9.35 Gyr, with the slightly older one having more Be.

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This pair may indicate that another parameter plays a role in Be astration; it has been suggested by B04a that rotational velocity is that parameter. Stars are formed with differing initial velocities and spin down to their present-day values. During the spin-down, extra mixing occurs, which increases the amount of Be (and Li) that can reach the critical temperature for destruction. As found by B04a the depletion of Li and Be observed in cluster and field stars is well matched by the rotation-model predictions of Deliyannis & Pinsonneault (1997); see Figure 12 of B04a.