Free Access
Issue
A&A
Volume 590, June 2016
Article Number A32
Number of page(s) 8
Section Stellar structure and evolution
DOI https://doi.org/10.1051/0004-6361/201527848
Published online 04 May 2016

© ESO, 2016

1. Introduction

Solar twins are stars that have spectra very similar to the Sun, with stellar (surface) parameters (temperature, surface gravity, and metallicity) around the solar values (Teff within ±100 K, log  g and [Fe/H] within ±0.1 dex, as arbitrarily defined in Ramírez et al. 2014)1. Since they have about 1 M and roughly solar chemical composition, they follow a similar evolutionary path to the Sun, from the zero age main sequence to the end of their lives. The highly precise atmospheric parameters that one can derive for these objects allows a reliable determination of their ages using the traditional isochrone method (Ramírez et al. 2014; Nissen 2015). Thus, we can take advantage of this very special group of stars to better understand the nucleosynthesis of s- and r-elements throughout the Galaxy (e.g. Mashonkina & Gehren 2000; Battistini & Bensby 2016).

Another important potential application of the heavy elements is their use for age dating. By investigating the abundances of several elements using high precision differential abundances for a sample of 21 solar twins, Nissen (2015) finds a very tight correlation of [Y/Mg] as a function of stellar age. There have also been previous studies at standard precision that indicate a correlation between the s-process elements, like Ba and Y, with stellar age (Mashonkina & Gehren 2000; Bensby et al. 2005; D’Orazi et al. 2009). More recently, Maiorca et al. (2011) reinforced the above results using open clusters in a broad age range.

The aim of this work is to analyze the abundances of the heavy element yttrium and the α-element magnesium in a sample of 88 solar twins with ages covering 0.3 Gyr to 10.0 Gyr, which thus have important implications for astronomy, such as for dating exoplanet host stars, studying stellar evolution effects, Galactic chemical evolution, and different studies of stellar populations.

2. Data and analysis

2.1. Observations and data reduction

The observations for the 88 stars of our sample of solar twins were carried out with the Magellan Inamori Kyocera Echelle (MIKE) spectrograph (Bernstein et al. 2003) on the 6.5 m Clay Magellan Telescope at Las Campanas Observatory on five runs between January 2011 and May 2012. See Ramírez et al. (2014) for a more detailed description of our sample, the observations, and data reduction.

The same instrumental setup was employed for all stars, achieving a signal-to-noise ratio of at least 400 around 600 nm. The resolving power is R = 83 000 in the blue, and R = 65 000 in the red. The spectra of the Sun, which served as a reference for the differential analysis, were obtained through the observation of the asteroids Iris and Vesta using the same instrumentation setup2. The orders were extracted with the CarnegiePython MIKE pipeline3, and Doppler correction and continuum normalization was performed with IRAF.

2.2. Stellar parameters

Stellar parameters were obtained by Ramírez et al. (2014) through differential excitation and ionization equilibrium using the abundances of FeI and FeII, with the Sun as reference. The abundances were determined using the line-by-line differential method, employing EW that were measured by hand with the task splot in IRAF. The Fe abundances and stellar parameters from Ramírez et al. (2014), were determined with the 2014 version of the LTE code MOOG (Sneden 1973), adopting the MARCS grid of 1D-LTE model atmospheres (Gustafsson et al. 2008). The Y and Mg abundances were determined with same grid, but we note that the exact grid of model atmospheres is irrelevant for differential abundances, since the mean abundance difference is lower than 0.001 dex (Meléndez et al. 2012). We have repeated our calculations using Kurucz ODFNEW model atmospheres (Castelli & Kurucz 2004) and found that the mean differential [Mg/H] and [Y/H] abundance change in only (Kurucz – MARCS) −0.0006 dex (σ = 0.0031) and –0.0003 dex (σ = 0.0045), respectively.

We also employed the recently introduced python q2 code4 (Ramírez et al. 2014), which makes the abundance determination and analysis considerably more efficient, by calling MOOG drivers and performing the line-by-line analysis, including corrections by hyperfine structure (HFS) and also computing the associated errors. Both observational and systematic uncertainties were considered. Observational errors are due to uncertainties in the measurements (standard error) while the systematic errors are uncertainties coming from the stellar parameters, as described in Ramírez et al. (2015). Observational and systematic errors were added in quadrature.

The age and mass for the sample were determined using Yonsei-Yale isochrones (Yi et al. 2001), as described in Ramírez et al. (2013, 2014). This method provides good relative ages, due to the high precision of the atmospheric parameters, by comparing the location of the star on the Teff, log g, [Fe/H] parameter space, with the values predicted by the isochrones, computing mass, and age probability distribution functions. As shown below, these ages can also be made accurate (i.e. almost insensitive to the choice of models) by forcing different isochrone sets to reproduce the solar parameters exactly.

Figure 1 shows the location of the Sun in the Teff − log g plane along with 4.6 Gyr Yonsei-Yale (YY) and 4.5 Gyr Darmouth (DM) isochrones (Dotter et al. 2008). These ages are the closest to solar age found in each grid. Solid lines represent the isochrones of solar composition in each case. Clearly, they do not exactly pass through the solar location, but a minor shift of the [Fe/H] of the isochrone sets by –0.04 in the case of YY (dashed line) and +0.08 for DM (dot-dashed line) brings these isochrones to excellent agreement with the solar parameters at the well-known solar age (e.g. Sackmann et al. 1993). We applied these offsets to both isochrone grids before using them to determine stellar parameters5.

thumbnail Fig. 1

The 4.6 Gyr Yonsei-Yale (dashed line) and 4.5 Gyr Darmouth (dot-dashed line) isochrones shifted in [Fe/H] by –0.04 dex and +0.08 dex, respectively. We note the agreement after the change.

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As shown in Fig. 2, our solar twin data set spans a narrow range of Teff and log g, but it is enough to cover the very wide range of ages from 0 to 10 Gyr. YY (dashed lines) and DM (dot-dashed lines) isochrones are also shown in this plot. These isochrones have [Fe/H] = −0.04 for Yonsei-Yale and [Fe/H] = + 0.08 for DM, which, as explained above, pass through the solar location at solar age. We note the excellent agreement between these two sets of isochrones for ages younger than 6 Gyr. For older stars, the DM isochrones are shifted to somewhat higher effective temperatures, which implies that the ages inferred from them will be somewhat older, compared to those obtained from the Yonsei-Yale set.

thumbnail Fig. 2

Distribution of our sample with the 1 to 10 Gyr Yonsei-Yale (dashed lines) and Darmouth (dot-dashed lines) isochrones.

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Figure 3 compares the YY and DM isochrone ages derived for our solar twin stars. On average, the mean difference of the most probable ages (DM–YY) is + 0.2 ± 0.5 Gyr, which would suggest good agreement within the errors. However, there is a clear systematic offset at older ages, albeit small, of + 0.4 ± 0.2 Gyr.

If the [Fe/H] offsets to the isochrones are not applied, the YY and DM isochrones are systematically off by 1 Gyr at solar age, and up to 2 Gyr for the oldest stars. On the other hand, when these corrections are applied to the isochrones, the anchor points are the solar parameters, which give us relative accurate ages. We note that, for the pair of old solar twins 16 Cyg, our method gives an age of Gyr (from the combined age-probability distributions; Ramírez et al. 2011), which is in excellent agreement with the seismic ages recently determined for this pair (average of 7.0 ± 0.1 Gyr; van Saders et al. 2016). Even though the typical error for both isochronal ages set is ~0.6 Gyr, we decided to use the YY grid instead of DM because the former has a more consistent sampling of the isochrones, which makes the age determination less likely to suffer from statistical biases.

thumbnail Fig. 3

Upper panel: comparison of ages estimated by Yonsei-Yale and Darmouth isochrones for our solar twin sample. Lower panel: differences between the YY and DM isochronal ages.

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The stellar parameters and [Fe/H] abundances for most of our sample stars were determined in our previous work (Ramírez et al. 2014), except for HIP 108158, HIP 55409, HIP 72043, and HIP 68468. As these stars were outliers in the [Y/Mg] versus age plot (there are other outliers, but they can be explained owing to to binarity), we decided to verify their parameters by remeasuring the EW of FeI and FeII lines for those stars (the reanalysis of HIP 68468 is presented in Meléndez et al. 2016). For HIP 72043, we didn’t find any difference, meaning that it is a true outlier in the [Y/Mg]-age plane; for the other three stars, their parameters were revised (Table 1).

Table 1

Revised parameters for HIP 108158, HIP 55409, and HIP 68468.

We also updated the ages for HIP 109110 and HIP 29525, two young solar twins, for which more precise ages, which were determined through rotational periods, are available in Baumann et al. (2010)6. According to Barnes (2007), the errors from gyrochronology is 15% in the age of solar analogs, which is significantly better than those found in Ramírez et al. (2014), which are about 40–70% for these two young stars (isochrone ages have larger error bars at a younger age, as seen in Fig. 3). We note also that, for those two stars, the rotational ages agree better with the [Y/Mg] ages.

2.3. Abundance analysis

Yttrium abundances were obtained using the 485.48 nm, 520.04 nm, and 540.27 nm YII lines and corrected for HFS adopting the HFS data from Meléndez et al. (2012).

For magnesium we used the 454.11 nm, 473.00 nm, 571.11 nm, 631.87 nm, and 631.92 nm lines, paying extra attention to the latter two lines owing to the influence of telluric features in this region, as shown in Fig. 4. We note that the separation between theses telluric lines is 0.74 Å  and their line ratio is 1.05.

Once the initial set of differential abundances was obtained, we verified the presence of outliers and, when present, the EW of those lines were verified and q2 was executed again.

thumbnail Fig. 4

Mg I lines around 631.9 nm and telluric lines in this region for HIP 64713 (black dots) and HIP 89650 (red line). We advise caution swhen measuring these Mg I lines.

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3. Results and discussions

As shown in Fig. 5, there is a clear correlation between both [Y/Fe] and [Mg/Fe], and stellar age, for the sample of 88 stars, confirming the result found by Nissen (2015), which is based on a smaller sample. The behaviour of yttrium is due to the increasing contribution of s-process elements from low and intermediate mass AGB stars, which most efficiently produce Y (Fishlock et al. 2014; Karakas & Lattanzio 2014) and which slowly became more important with time (Travaglio et al. 2004; Nissen 2015).

On the other hand, the correlation of [Mg/Fe] with age is an effect of the increasing number of Type Ia SNe in comparison to the number of Type II SNe, as discussed by Kobayashi et al. (2006). This is because Type II SNe produces mainly α-elements (O, Mg, Si, S, Ca, and Ti), enhancing the interstellar medium with these species in the early Galaxy, while Type Ia SNe produce yields with high Fe/α ratio. Complementary to this, we show with the [Fe/H] vs. age plot that there is no age-metallicity correlation for the stars in our data, independently of its population (Fig. 5).

thumbnail Fig. 5

[Y/Fe] (upper panel), [Mg/Fe] (middle panel), and [Fe/H] (lower panel) as function of age. The red open circles are spectroscopic binary stars and the green triangles are visual binaries. [Fe/H] vs. age do not show any correlation with age. We also present the linear fit for [Y/Fe] and [Mg/Fe] versus age on their respective panels.

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In Fig. 5, there is a gap around 8.5 Gyr that could be important when distinguishing different populations. This gap in the [Mg/Fe] vs. age plot was used to identify 10 stars that display a high-α abundance that, according to Haywood et al. (2013), may belong to the thick disk population. On the other hand, Adibekyan et al. (2011) classify these high-α metal-rich stars (hαmr) as being a different population of stars, that do not belong to either the thin or the thick disk. These stars share some properties with both thin and thick disks stars and might have migrated from the inner parts of the Galaxy (Adibekyan et al. 2013). However the detailed study of these stars by Haywood et al. (2013) indicates that they may have formed at the end of the thick disk.

Using the Adibekyan et al. (2013) criteria, nine stars from our sample are hαmr (Fig. 6)7. With this method, we identify the same hαmr stars as we did using the [Mg/Fe] vs. age plot (Fig. 5), with the exception of HIP 109821. Adopting a binomial distribution (e.g. Bevington 1969, Chap. 3). the occurrence of hαmr in our sample is 10/88 (11.4 ± 3.4%) which is consistent with the 3/21 (14.3 ± 7.6%) from Nissen (2015) and 60/413 (14.5 ± 1.7%) from Adibekyan et al. (2012), using the same metallicity range of our sample.

thumbnail Fig. 6

[Mg/Fe] vs. [Fe/H] plot of the data from Adibekyan et al. (2012; filled symbols) matching the [Fe/H] range from our work (empty points). The circles represents the thin disk stars and the triangles the hαmr stars.

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We also show the Toomre diagram for the sample (Fig. 7) highlighting the hαmr stars (open circles). The hαmr group does not seem to be particularly separated from the rest of the group and its kinematic properties are in agreement with the findings by Adibekyan et al. (2011, 2013), as well as Bensby et al. (2014).

thumbnail Fig. 7

Toomre diagram for our sample. The open circles are the high-α metal rich star stars.

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The red open circles on the [Y/Fe] and [Mg/Fe] plots (and in Fig. 9) are binaries, pinpointed through radial velocity changes. The majority of the stars from our MIKE sample overlap with our HARPS Large Program (Ramírez et al. 2014), in which we search for exoplanets in a sample of about 60 solar twins using the HARPS spectrograph (Mayor et al. 2003). Thanks to the radial velocity data of our sample (and previous works), we identified some binary or multiple system stars (red open circles), indicated in Table A.1. From our visual inspection, all spectroscopic binaries seem single-lined. Also, the single-lined nature of the spectra is apparent in the iron abundance analysis; the EWs do not appear to be contaminated in any significant manner.

We also note that in the [Y/Fe] plot, all outliers are spectroscopic binaries (red open dots). This is probably because their companion transfered Y material to what is now the primary star. Thus, [Y/Fe] seems to be a good method to identify potential multiple star systems where mass transfer has taken place, but this is possible only when precise ages are available. We note that the stars HIP 77052, HIP 74432, and HIP 83276, which seem to be outliers in the [Y/Fe] plot, are identified as visual binaries (Tokovinin 2014).

Figure 8 shows an age histogram of the whole sample. The red solid curve shows the thin disk, while the blue dashed line represents the stars assigned to the hαmr population. It is possible to distinguish a clear age gap at 8.0 Gyr, separating the thin disk and the hαmr stars. The hαmr population show a star-to-star scatter in age of only 0.3 Gyr, showing that this population formed quickly. Nevertheless, the hαmr stars cover an [Fe/H] range similar to that of the younger thin disk stars that formed during the last 8 Gyr.

thumbnail Fig. 8

Age histogram for the thin disk (red solid line) and hαmr stars (blue dashed line).

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In Fig. 9 we present the [Y/Mg] vs. stellar age plot. A linear fit to our data, excluding the spectroscopic and visual binary stars, gives the following relation using the YY ages8: (1)This is practically the same fit found by Nissen (2015), within 1σ, but with better precision and a scatter of 0.037 dex. A remarkable significance level of about 41σ is found for the slope and a Spearman coefficient of rS = −0.96, with a probability of 10-35 of our results arising by pure chance, showing that this behaviour cannot occur randomly. We note that the hαmr stars were not excluded from the fit, meaning hat the [Y/Mg] relation seems to also be valid for this population. The relation of age (in Gyr) as function of [Y/Mg] is (2)The scatter of this relation is 0.9 Gyr, which is larger then the average error of the isochronal ages (0.6 Gyr). Subtracting these errors, we find an intrinsic uncertainty of 0.7 Gyr for the age determination (this value should be added to the error in the age determination from Eq. (1). For [Y/Mg], we have a mean error of 0.017 dex, which translates to a typical error in age of 0.4 Gyr. Thus, the total error expected is ~0.8 Gyr for data with quality similar to the those employed in this work.

thumbnail Fig. 9

[Y/Mg] versus age for the sample for 88 solar twins. The slope is −4.13 × 10-2 ± 1.12 × 10-3 with a scatter in age of 0.9 Gyr. The red open circles are spectroscopic binary stars and the green triangles are visual binaries.

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The age – [Y/Mg] relation shown in Fig. 9 and described by Eqs. (1) and (2) was determined using a sample of solar twins for which highly precise Y and Mg abundances, as well as ages, could be derived. Its origin is explained by nucleosynthesis and the chemical evolution of the solar neighbourhood. Thus, we do not expect this relation to be restricted to solar twins. Since nucleosynthetic yields can be metallicity-dependent, it is possible that this relation could be different for samples with non-solar [Fe/H]. We tested this possibility by dividing our sample into metal-rich and metal-poor groups, finding no significant differences. Thus, it is possible that the metallicity dependency is mild, if it is present at all. This means that, at least for the metallicity interval of our sample, the [Fe/H] does not have an impact on the age determination using Eq. (2). However, more studies are needed to determine if this remains true to metallicities other than solar. The [Y/Mg] abundance ratio can be measured with a precision of about 0.05 dex in non-solar twins. Our Eq. (2) can be used on those stars to determine their ages with a precision of 1.4 Gyr. With less precise [Y/Mg] measurements, for example assuming errors of 0.1 dex, we can still constrain the stellar age to 2.5 Gyr.

4. Conclusions

We confirm the tight relation of [Y/Mg] vs. age, first found by Nissen (2015). This relation seems to apply even for the thick disk population. Although we used a bigger sample of solar twins, the relation found is practically the same as Nissen’s, with a slope of −0.041 ± 0.001 dex/Gyr and a scatter in ages of σ = 0.9 Gyr.

The mean uncertainty expected for data with precision similar to ours is ~0.8 Gyr. This level of precision for the abundances, stellar parameters, and age determination as well, could only be achieved through a strict differential analysis of solar twin stars. We note that our careful work allowed us to find a good correlation of [Y/Mg] abundances with stellar age. However, extremely high-precision abundances are not necessary to have a satisfactory age determination. Even with a [Y/Mg] ratio with error of 0.05 dex, it is possible to obtain an age with a uncertainty of 1.4 Gyr.

Tests were made to verify if this relation has some dependence with metallicity. For this we divided the group into metal-poor and metal-rich stars, but no significant trend with [Fe/H] was detected, meaning that the age determination, at least in the −0.14 ≤ [Fe/H] ≤ 0.14 dex interval, should not be metallicity-correlated.

More investigation is needed to verify the applicability of the [Y/Mg] clock relation to stars with metallicities that are different from solar. Also, this correlation may be more complex than just a simple linear fit. Nevertheless, with regard to solar twins and solar analogs, the [Y/Mg] ratio is a promising new metric to reliably estimate relative ages independent of isochrones, and could be used alongside other age determination methods.

Our work provides important observational constraints to the yields of s-process elements in models of low- and intermediate-mass AGB stars (e.g. Maiorca et al. 2012).


1

We note that some stars in Ramírez et al. (2014) fall slightly outside the solar twin definition. They are also included in this work because they are close enough to the Sun for a high-precision abundance analysis.

2

In this work we only use the light reflected on Iris as our reference spectrum for the differential analysis.

4

https://github.com/astroChasqui/q2; a tutorial is available on this site with detailed information on the capabilities of this code.

5

In R14, the –0.04 dex offset in the YY isochrone [Fe/H] values was applied after selecting the isochrone points to use in the probability density (PD) calculations. This led to a very minor offset (−0.1 ± 0.2 Gyr) in the ages derived with respect to the more precise case where the isochrone [Fe/H] values are all shifted before selecting the points to use in the PD computation. This minor change makes the ages reported in R14 slightly different from those employed in this work, but these small differences do not affect the results presented in this paper in any significant way.

6

We note that HIP 109110 is not used in the linear fit because it was identified as a spectroscopic binary. For HIP 29525, even if we adopt the more uncertain isochronal age, the linear fit is not changed because of the large error bar in age for this star.

7

Using data from Adibekyan et al. (2012), that matches the range of metallicities of our sample (–0.140 to 0.140 dex). Notice that we use [Mg/Fe] rather than [α/Fe] (which is the average of Mg, Si and Ti).

8

We have made tests using DM and YY ages with [Y/Mg] abundances to identify which would have the better fit with age, but we found the same scatter (0.038 dex in [Y/Mg]) and the same slope within 1σ. Since the differences in the age determination are small, they do not affect the final result.

Acknowledgments

M.T.M. thanks support by CNPq (142437/2014-0). J.M. thanks for support by FAPESP (2012/24392-2). M.A. has been supported by the Australian Research Council (grants FL110100012 and DP120100991). M.B. is supported by the National Science Foundation (NSF) Graduate Research Fellowships Program (grant No. DGE-1144082). J.B. and M.B. acknowledge support for this work from the NSF (grant No. AST-1313119). J.B. is also supported by the Alfred P. Sloan Foundation and the David and Lucile Packard Foundation.

References

Appendix A

Table A.1

[Y/H], [Mg/H], stellar parameters, and age for the 88 solar twins sample.

All Tables

Table 1

Revised parameters for HIP 108158, HIP 55409, and HIP 68468.

Table A.1

[Y/H], [Mg/H], stellar parameters, and age for the 88 solar twins sample.

All Figures

thumbnail Fig. 1

The 4.6 Gyr Yonsei-Yale (dashed line) and 4.5 Gyr Darmouth (dot-dashed line) isochrones shifted in [Fe/H] by –0.04 dex and +0.08 dex, respectively. We note the agreement after the change.

Open with DEXTER
In the text
thumbnail Fig. 2

Distribution of our sample with the 1 to 10 Gyr Yonsei-Yale (dashed lines) and Darmouth (dot-dashed lines) isochrones.

Open with DEXTER
In the text
thumbnail Fig. 3

Upper panel: comparison of ages estimated by Yonsei-Yale and Darmouth isochrones for our solar twin sample. Lower panel: differences between the YY and DM isochronal ages.

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In the text
thumbnail Fig. 4

Mg I lines around 631.9 nm and telluric lines in this region for HIP 64713 (black dots) and HIP 89650 (red line). We advise caution swhen measuring these Mg I lines.

Open with DEXTER
In the text
thumbnail Fig. 5

[Y/Fe] (upper panel), [Mg/Fe] (middle panel), and [Fe/H] (lower panel) as function of age. The red open circles are spectroscopic binary stars and the green triangles are visual binaries. [Fe/H] vs. age do not show any correlation with age. We also present the linear fit for [Y/Fe] and [Mg/Fe] versus age on their respective panels.

Open with DEXTER
In the text
thumbnail Fig. 6

[Mg/Fe] vs. [Fe/H] plot of the data from Adibekyan et al. (2012; filled symbols) matching the [Fe/H] range from our work (empty points). The circles represents the thin disk stars and the triangles the hαmr stars.

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In the text
thumbnail Fig. 7

Toomre diagram for our sample. The open circles are the high-α metal rich star stars.

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In the text
thumbnail Fig. 8

Age histogram for the thin disk (red solid line) and hαmr stars (blue dashed line).

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In the text
thumbnail Fig. 9

[Y/Mg] versus age for the sample for 88 solar twins. The slope is −4.13 × 10-2 ± 1.12 × 10-3 with a scatter in age of 0.9 Gyr. The red open circles are spectroscopic binary stars and the green triangles are visual binaries.

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In the text

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