The chemical compositions of Galactic disc F and G dwarfs

Abstract

Photospheric abundances are presented for 27 elements from carbon to europium in 181 F and G dwarfs from a differential local thermodynamic equilibrium (LTE) analysis of high-resolution and high signal-to-noise ratio spectra. Stellar effective temperatures (T_eff) were adopted from an infrared flux method calibration of Strömgren photometry. Stellar surface gravities (g) were calculated from Hipparcos parallaxes and stellar evolutionary tracks. Adopted T_eff and g values are in good agreement with spectroscopic estimates. Stellar ages were determined from evolutionary tracks. Stellar space motions (U, V, W) and a Galactic potential were used to estimate Galactic orbital parameters. These show that the vast majority of the stars belong to the Galactic thin disc.

Relative abundances expressed as [X/Fe] generally confirm previously published results. We give results for C, N, O, Na, Mg, Al, Si, S, K, Ca, Sc, Ti, V, Cr, Mn, Co, Ni, Cu, Zn, Sr, Y, Zr, Ba, Ce, Nd and Eu. The α elements — O, Mg, Si, Ca and Ti — show [α/Fe] to increase slightly with decreasing [Fe/H]. Heavy elements with dominant contributions at solar metallicity from the s-process show [s/Fe] to decrease slightly with decreasing [Fe/H]. Scatter in [X/Fe] at a fixed [Fe/H] is entirely attributable to the small measurement errors, after excluding the few thick disc stars and the s-process-enriched CH subgiants. Tight limits are set on ‘cosmic’ scatter. If a weak trend with [Fe/H] is taken into account, the composition of a thin disc star expressed as [X/Fe] is independent of the star's age and birthplace for elements contributed in different proportions by massive stars (Type II supernovae), exploding white dwarfs (Type Ia supernovae) and asymptotic red giant branch stars.

By combining our sample with various published studies, comparisons between thin and thick disc stars are made. In this composite sample, thick disc stars are primarily identified by their V_LSR in the range −40 to −100 km s⁻¹. These are very old stars with origins in the inner Galaxy and metallicities [Fe/H]≤−0.4. At the same [Fe/H], the sampled thin disc stars have V_LSR∼ 0 km s⁻¹, and are generally younger with a birthplace at about the Sun's Galactocentric distance. In the range −0.35 ≥[Fe/H]≥−0.70, well represented by present thin and thick disc samples, [X/Fe] of the thick disc stars is greater than that of thin disc stars for Mg, Al, Si, Ca, Ti and Eu. [X/Fe] is very similar for the thin and thick disc for — notably — Na and iron-group elements. Barium ([Ba/Fe]) may be underabundant in thick relative to thin disc stars. These results extend previous ideas about composition differences between the thin and thick disc.

1 Introduction

Lower main-sequence stars have lifetimes comparable to the age of the Galaxy and presumably atmospheric compositions that are essentially identical to those of their natal interstellar clouds. Spectroscopic and photometric analyses of these stars provide a sensitive probe of the major processes that have shaped the chemical evolution of our Galaxy. This paper, which describes a survey of 181 F and G main-sequence stars, was inspired by the analysis of Edvardsson et al. (1993, hereafter EAGLNT) of abundances for 13 elements for 189 F and G disc dwarfs with metallicities in the range −1.1 ≤[Fe/H]≤+0.25. We sought to examine more closely several conclusions advanced by EAGLNT.

One conclusion concerned the variation of chemical composition with the distance of a star's birthplace from the Galactic centre. EAGLNT gave estimates of this distance (R_m) derived from a star's kinematics and a model of the Galactic potential. A striking dependence on R_m was found for the relative abundances of α elements (Si and Ca) and iron. As was already known (cf. Lambert 1989; Wheeler, Sneden & Truran 1989; McWilliam 1997), [α/Fe] increases with decreasing [Fe/H], rising from [α/Fe]= 0 at [Fe/H]= 0 to about 0.3 at [Fe/H]=−1. EAGLNT found that the trend of [α/Fe] with [Fe/H] depends on R_m, being more marked for small R_m than large R_m. They interpreted this dependence of [α/Fe] on R_m at a given [Fe/H] as due to an early rapid rate of star formation in the inner parts of the Galactic disc resulting in Type II supernovae (SNII) dominating the enrichment of the interstellar gas to a greater extent than they did locally where the more slowly evolving Type Ia supernovae (SNIa) have been important contributors. Models of the Galactic chemical evolution have predicted abundance gradients of the kind inferred by Edvardsson et al. (e.g. Chiappini, Matteucci & Gratton 1997).

Others have examined this and other of EAGLNT's conclusions. Fuhrmann (1998) finds that [Mg/Fe] gets successively smaller in halo, thick disc and thin disc stars, and there is a segregation of [Mg/Fe] between two disc populations such that even at the same [Fe/H] their [Mg/Fe] are distinct. Chen et al. (2000), who analysed a sample of 90 F and G disc dwarfs for 13 elements, found a group of stars in the metallicity range −1.0 ≤[Fe/H]≤−0.6 having small R_m (≤7 kpc) that are older than other disc stars and probably belong to the thick disc.

Our present survey covers 181 nearby F and G dwarfs observed with the McDonald Observatory's 2.7-m telescope and 2dcoudé spectrometer at a resolving power of about 60 000 with broad spectral coverage, and at signal-to-noise (S/N) ratios of 300–400 for most stars. The wavelength coverage and S/N ratios are a significant improvement over EAGLNT's observations, which covered four or five spectral regions of 100 Å each at an S/N ratio of about 200. Also, EAGLNT's northern stars were observed at a resolving power of about 30 000, and only the southern stars were observed at the resolving power of 60 000. Our new spectra lead to more accurate abundances for more elements. Our analysis benefits also from the use of improved fundamental parameters for the stars. In particular, the effective temperatures are determined from the b—y colour and a recent calibration based on the infrared flux method, while surface gravities come from a comparison of the positions of the stars in the colour—magnitude diagram, which are precisely fixed by the Hipparcos parallaxes, with theoretical isochrones.

2 Observations

2.1 Stellar spectra

Programme stars were selected from the uvbyβ catalogue of Olsen (1983, 1988). Among the selection criteria were an effective temperature in the range 5600–7000 K, and a surface gravity indicative of little or moderate evolution off the zero-age main sequence (ZAMS) (see Fig. 1).

All the observations were made at the Harlan J. Smith 2.7-m telescope at McDonald Observatory, using the 2dcoudé echelle spectrometer (Tull et al. 1995) with a 2048 × 2048 pixel Tektronix charge-coupled device (CCD) as detector. A resolving power of ≈60 000 was attained. Spectral coverage was complete from 4000 to 5600 Å and substantial but incomplete from 5600 Å to about 9000 Å. In order to minimize the influence of cosmic rays, two observations in succession, rather than one longer observation, were generally made of each star. From about 5500 Å to about 9000 Å the extracted stellar spectra have a typical S/N ratio of about 400, while at wavelengths shorter than about 5500 Å the S/N ratio decreases with decreasing wavelength. We also observed the asteroid Iris in order to have a solar spectrum recorded under similar circumstances as the stellar spectra. The data were processed and wavelength calibrated in a conventional manner with the iraf1 reduction package. Double-lined spectroscopic binaries and broad-lined stars (v sin i≥ 20 km s⁻¹) were dropped from the programme. The remaining 181 stars were subjected to an abundance analysis, and are listed in Table 1.

Absorption lines suitable for measurement were chosen for having clean line profiles, as judged by inspection of the solar flux spectrum at extremely high resolving power and S/N ratio (Kurucz et al. 1984), that could be reliably measured in all, or most of, the programme stars. Moore, Minnaert & Houtgast (1966) was our primary source for line identification. The equivalent width of each line was measured with the irafsplot measurement option most suited to the situation of the line. This was usually the fitting of a single (or multiple) Gaussian profile(s) to the stellar line, but for stronger lines with significant damping wings a Voigt profile was used; for a few lines direct integration provided the best method of measurement and was preferred. Table 2 gives basic information for the selected lines; the list includes 170 lines of 27 elements. The spectrum of Iris, which was reduced and measured in the same manner as the programme stars, provided solar equivalent widths.

2.2 Stellar kinematics

The space motions of the programme stars can be used to calculate their Galactic orbits. In order to determine the space motions we need the stellar distances, proper motions and radial velocities.

Parallaxes and proper motions for nearly all the programme stars are available from the Hipparcos Catalogue (ESA 1997). All the stars in our sample are within 150 pc from the Sun, so their Hipparcos parallaxes are accurate; the average error is 6.1 ± 3.2 per cent. The proper motion errors are much less. For the few (seven) programme stars not in the Hipparcos Catalogue uvbyβ photometry was used to calculate photometric distances following the prescriptions of EAGLNT. A comparison of photometric and Hipparcos distances showed that the average ratio d(phot)/d(Hip) is 1.10 ± 0.15 (20 stars, standard deviation).

Accurate CORAVEL radial velocities have been taken from the survey of kinematical data for F and G dwarfs in the solar neighbourhood by Pont et al. (1999). These data were kindly provided by J. Andersen prior to publication. The CORAVEL data show that 19 of the programme stars2 have variable radial velocities, presumably a result of their membership in low-amplitude spectroscopic binary systems. Small corrections (<1 km s⁻¹) to the observed velocities due to gravitational or convective shifts were neglected.

The space velocities with respect to the Sun were then calculated. A solar motion (−10.0, +5.2, +7.2) km s⁻¹ in (U, V, W),3 derived from Hipparcos data by Dehnen & Binney (1998), was adopted in adjusting the space velocities to be with respect to the local standard of rest (LSR). Table 1 gives (U_LSR, V_LSR, W_LSR). Our space velocities may be compared with those of Chen et al. (2000) who use the same solar motion. For the 19 stars common to our investigation and theirs, which are also in the Hipparcos Catalogue and also show no sign of radial velocity variation so their space velocities are based on identical proper motions and distances and very similar radial velocities, the (U, V, W) velocities agree to about 1 km s⁻¹ or better.

The Galactic orbital parameters, R_p and R_a (peri- and apogalactic distances), Z_max (maximum distance from the Galactic plane) and e (orbital eccentricity), were computed using a Galactic potential integrator developed by D. Lin in 1999 (provided by Jon P. Fulbright with the kind permission of D. Lin).

In computing orbital parameters we have adopted the above solar space motion, a solar Galactocentric distance of 8.5 kpc, and a solar circular velocity of 225.2 km s⁻¹. Grenon (1987) argues that R_m= (R_p+R_a)/2 is a likely stable quantity and, hence, a measure of a star's birthplace. In Table 1, we give the orbital parameters R_m, Z_max and e.

We have only three stars in this study that are common with EAGLNT's sample. The orbital parameters derived in this study are different from EAGLNT's by ≤5 per cent, except for Z_max, which differs by ∼25 per cent. The differences become smaller (≤2 per cent) if we adopt the same values for the Sun as that of EAGLNT [EAGLNT used (U, V, W) = ( − 10, +6, +6 km s⁻¹), 8.0 kpc for Galactocentric distance, and 226 km s⁻¹ for the solar circular velocity].

3 Analysis

3.1 Introduction

Elemental abundances are derived from an LTE analysis of equivalent widths using the code moog (Sneden 1973). atlas9 (Kurucz 1998) plane-parallel, line-blanketed, flux-constant LTE model atmospheres with convective overshooting are used. The models are linearly interpolated for the appropriate values of the fundamental atmospheric parameters (T_eff, log g, [M/H],4ξ_t), which are determined independently of the spectroscopy. The effective temperatures T_eff and metallicities [M/H] are derived from uvbyβ photometry. The surface gravities g are determined from the comparison of the position of the star in the (B−V) versus M_V plane with calculations of stellar evolution, using Hipparcos parallaxes to determine M_V. The microturbulence ξ_t is set by an empirical relation between ξ_t, T_eff and log g derived from spectroscopic analysis of a subset of the programme stars. The large number of lines available for elements such as iron allows an independent spectroscopic determination of T_eff and log g, and hence a comparison of the photometric estimates of these quantities.

3.2 Selection of the model atmosphere grid

Over the past decade we have witnessed exciting developments in stellar atmosphere modelling well beyond classical LTE one-dimensional models. Full non-local thermodynamic equilibrium (NLTE) structures (e.g. Hauschildt, Allard & Baron 1999), LTE 3D time-dependent hydrodynamical models (e.g. Asplund et al. 2000), and 1.5D and 3D NLTE radiative transfer calculations (e.g. Shchukina & Trujillo Bueno 2001) are examples of the recent advances. Application of these modelling techniques to a large sample of stars and elements is still impracticable for several reasons: the new models are available only for a few values of the atmospheric parameters, NLTE calculations with realistic model atoms are generally time-consuming and, for some species, such calculations are unreliable, due to uncertainties in the atomic data. Recent studies (Nissen et al. 2002; Chen et al. 2002) provide comparisons for some elements of abundances derived from 1D and 3D models. For stars with [Fe/H], T_eff and log g corresponding to our dwarfs, these authors find that [O/Fe], [S/Fe] and [Si/Fe] from 3D are lower by less than 0.04 dex than results from an equivalent 1D model. The differential effect on such abundance ratios across our sample of similar stars should be small. Effects of replacing 1D models by 3D models may vary from element to element. While we are confident that the situation will change in the near future, we have considered only well-tested flux-constant 1D model atmospheres: the marcs models originally developed by Gustafsson et al. (1975), and the atlas9 models incorporating improvements to the treatment of convection and convective overshoot (Kurucz 1998). We also tested recently developed atmospheric models known as nextgen models by Hauschildt et al. (1999).

In comparisons against observations of the Sun, the atlas9 solar model fares better than the marcs solar model. This is clearly the case for limb darkening in the continuum at optical and near-infrared wavelengths (Blackwell, Lynas-Gray & Smith 1995). A better fit to limb-darkening data is achieved with the empirical model atmosphere known as the Holweger—Müller model (Holweger 1967; Holweger & Müller 1974); this is a not surprising result given that the model was derived in large part from limb-darkening measurements. Models may also be compared by their ability to fit those Fe i lines having an accurately determined gf value from laboratory experiments. Iron abundances derived from lines of different lower excitation potential are less dependent on the lower potential in the case of the atlas9 than for the marcs model (Blackwell et al. 1995). The empirical Holweger—Müller model, as revised by Grevesse & Sauval (1999), and the miss (Allende Prieto et al. 2001a) empirical model also return iron abundances that are independent of the lower excitation potential. Ionization equilibrium, as measured by the iron abundance derived from Fe i and Fe ii lines, is well satisfied by the atlas9 and the Grevesse—Sauval or miss empirical models, but less well by the marcs and nextgen models. atlas9 models come in two flavours — with and without convective overshooting considered as part of the treatment of convection. Castelli, Gratton & Kurucz (1997) suggest that the model with overshooting (over model) reproduces observed properties (limb darkening, etc.) of the Sun better than the model without overshooting (nover model).

Our choice of over atlas9 in preference to marcs models for the abundance analysis is based on the solar comparison. It should be noted, however, that almost all of the programme stars are within ±500 K of the Sun's temperature. If the difference between an atlas9 and a marcs model is partly attributable to the different treatments of line blanketing, the differences in abundances derived from them should be smaller for the typical star in our sample than they are for the Sun. Similarly, the small differences between nover and overatlas9 solar models will become even smaller for the programme stars where we are concerned with differential abundances relative to the Sun. We comment below on the effects of replacing the preferred over with the nover models.

3.3 Fundamental atmospheric and other parameters

Three of the four parameters listed above are used to select a model from the overatlas9 grid. These —T_eff, log g and [M/H]— are first determined from photometry, and checked subsequently against the spectroscopic analysis. Microturbulence, the fourth parameter, is only determined spectroscopically. In addition, it is not used in the selection of a model from the grid; the grid was computed for a single value of the microturbulence (ξ_t= 2.0 km s⁻¹), which is fairly representative of values determined here spectroscopically.

3.3.1 The effective temperature

The uvbyβ photometry, especially the b—y colour, is used to determine T_eff. First, we must consider and, if necessary, correct for the effects of interstellar reddening. The programme stars are all within 150 pc of the Sun, with the majority within 100 pc. Interstellar reddening is negligible within 100 pc (Schuster & Nissen 1989). In order to check for reddening at greater distances, we considered the average value and distribution of E(b—y) for stars closer than 100 pc and likewise for stars further away than 100 pc. E(b—y) came from the observed b—y and the unreddened (b—y)₀ derived from the β index, which is unaffected by reddening, together with the calibration of Olsen (1988).

For stars within 100 pc, the average E(b—y) is very small, E(b—y) =−0.005 ± 0.010 mag from 170 stars, and the distribution is essentially Gaussian with the dispersion explained by the errors in the photometry. For the more distant 21 stars, E(b—y) is positive, E(b—y) =+0.010 ± 0.013 mag, and the distribution is asymmetric, with a tail of positive E(b—y) caused by a few stars with significant reddening. In the light of these results, we assume that all of our programme stars are unreddened and use the observed b—y to determine T_eff, except for five stars5 beyond 100 pc with significant reddening, E(b—y) ≥ 0.025, for which we use the corrected b—y.

We use the calibration of Strömgren indices given by Alonso, Arribas & Martinez-Roger (1996). This calibration, which uses a large number of lower main-sequence stars and subgiants whose temperatures were measured by the infrared flux method, spans ranges of 4000 K ≤T_eff≤ 7000 K and −2.5 ≤[Fe/H]≤ 0, and is well suited to the programme stars. The calibration relates T_eff with b—y, c₁ and [Fe/H], with b—y making the major contribution to the calibration and c₁, the gravity-sensitive index, and [Fe/H] making minor contributions. To apply the calibration, b—y and c₁ were taken from Hauck & Mermilliod (1998), while [Fe/H] values were estimated from Strömgren photometry (see below). (The effect of reddening on c₁ is negligible.) The error in the derived T_eff may come from different sources: uncertainties in the Strömgren photometry, reddening and the calibration of the absolute flux in the infrared. Alonso et al. (1996) estimated an uncertainty of 1.5 per cent (90 K) by taking into account both the systematic and accidental errors in the calibration.

3.3.2 The surface gravity

The surface gravity of a programme star is estimated by comparing its position in the colour—magnitude diagram with theoretical isochrones. This comparison provided the stellar masses and radii, and thus the surface gravities. Isochrones were taken from Bertelli et al. (1994); they span all required stellar masses and metallicities. Allende Prieto & Lambert (1999) have used these isochrones similarly to determine fundamental parameters for stars in the Hipparcos Catalogue within 100 pc.

3.3. Photometric metallicity

The metallicity6[M/H] was determined from the b—y, m₁ and c₁ indices using either equation (2) (for F stars) or equation (3) (for G stars) of Schuster & Nissen (1989) with photometric data from Hauck & Mermilliod (1998). Using the quoted uncertainties in (b—y), m₁ and c₁ from Hauck & Mermilliod, we estimate an uncertainty of ≃0.2 dex in our photometric metallicity. Hauck & Mermilliod estimate a standard deviation of 0.16 dex in the [Fe/H] derived from their calibration.

3.3.4 Microturbulence

Earlier studies of the microturbulence in the atmospheres of F and G dwarfs have shown that similar stars have very similar levels of microturbulence, which depends weakly on T_eff and g (Nissen 1981). The microturbulence is determined spectroscopically from the condition that the abundance derived from lines of the same species should be independent of a line's equivalent width. Often, Fe i lines are used for obvious reasons.

A similar linear regression has been used by others. Use of published formulae results in slightly different results. For example, adoption of EAGLNT's recipe gives a mean ξ_t that is about 0.2 km s⁻¹ greater. Nissen's original expression (Nissen 1981) returns greater values but by only 0.1 km s⁻¹. Chen et al. (2000) remark that their ξ_t are 0.3 km s⁻¹ greater than EAGLNT's. Quite possibly, the lower values of ξ_t found here are due to our use of rather weak lines which are inherently less sensitive to microturbulence. The difference is unimportant as far as the abundance analysis is concerned; a change of ξ_t by ±0.25 km s⁻¹ changes the abundance of lines with equivalent widths of 50 m Å or less by less than 0.01 dex. Even at 100 m Å, the abundance changes by no more than 0.04 dex.

3.3.5 Comparison of photometry and spectroscopy

As a check on the photometrically derived fundamental parameters we used Fe i and Fe ii lines to determine T_eff and log g by the classical conditions that the Fe abundance be independent of the lower excitation potential for Fe i lines, and Fe i and Fe ii lines yield the same abundance. Lines with reliable gf values (see below) and equivalent widths less than 60 m Å were used, a restriction that effectively eliminates the sensitivity to the microturbulence. About 25–30 Fe i and four Fe ii lines were used.

Photometric and spectroscopic T_eff values and metallicities [Fe/H] are compared in Fig. 2. On average, spectroscopic temperatures are hotter than their photometric counterparts by 71 ± 47 K with a hint that the difference is T_eff-dependent. For [Fe/H], the mean difference between spectroscopic and photometric estimates is merely 0.05 ± 0.09 dex with no detectable trend over the range −0.2 to −0.8 in [Fe/H].

Surface gravity is checked using Fe i–Fe ii and Cr i–Cr ii lines. The comparison is made in Fig. 3. It is seen that the neutral lines give a slightly lower abundance: log ε (Fe i) − log ε(Fe ii) =−0.02 ± 0.05 with just a hint of a dependence on [Fe/H]. Chromium gives a very similar result: log ε (Cr i) – log ε(Cr ii) =−0.04 ± 0.06. We conclude that the surface gravities do not introduce appreciable systematic errors into the abundance analysis. Reducing the differences to exactly zero calls for adjustments to the adopted atmospheric parameters that are within their estimated uncertainties given above. Additionally, the negative differences may signal departures from LTE effects, principally the overionization (relative to LTE) of the neutral atoms (see e.g. Shchukina & Trujillo Bueno 2001).

3.4 Stellar ages

We have estimated ages for the sample by comparison with the isochrones published by Bertelli et al. (1994). As most of our stars have already evolved off the main sequence, we can constrain their age very precisely. For some of the stars that are too close to the main sequence we can, at most, obtain upper limits. Our method resembles that described by Lachaume et al. (1999). Some aspects, however, are different, and therefore we describe it below.

Finally, the derived P( log t) was normalized and, whenever appropriate, fitted with a Gaussian to derive the mean and a 1σ uncertainty for the age of the star, which are included in Table 1. Fig. 4 shows an example of the practical application to two well-known nearby stars, the Sun and Procyon A. The upper panels show the position of the star in the log T_eff versus log g plane. The dots are grid points within the 3σ error bar ellipse, which therefore were included in the solution. In the lower panels, the probability density for the age is displayed, as well as a best estimate and 1σ limits. Given the typical error bars for our sample, a star with the solar parameters is too close to the ZAMS to determine but an upper limit. For a star with the parameters of Procyon A (see e.g. Allende Prieto et al. 2002a), it is possible to constrain the age very precisely — a case more representative of our sample regarding the evolutionary status. The ages derived in this study show a range consistent with those published by Chen et al. (2000) and EAGLNT for thin disc stars, but small differences are noticeable in Fig. 8.

4 Atomic Data

The critical atomic datum is the gf value of a line. Our general procedure was to search the literature for accurate theoretical calculations or laboratory measurements of the gf values. Our search left gaps, which were filled in various ways, including an inverted solar analysis.

References to the principal sources of data on gf values for individual elements are given in Table 2. We comment here on the Fe i and Fe iigf values because these lines play a special role in the abundance analysis, as already noted. Our search uncovered accurate gf values for 33 of the 56 Fe i and two of the eight Fe ii lines in our lists of measured weak unblended stellar lines. In the case of the Fe i lines, these values come mainly from three sources (see references in Table 3). These and other sources were reviewed by Lambert et al. (1996), who remarked on their inter-agreement and suggested corrections to put all gf values on a common scale. To obtain gf values for the remaining Fe i and Fe ii lines, we calculated astrophysical gf values from the solar (Iris) spectrum using average abundances derived from Fe i and Fe ii lines that have accurate theoretical or laboratory gf values.

We chose nine Fe ii lines that are unblended and measurable in most stars in the sample. For three of the Fe ii lines (6369.46, 6432.68 and 7515.84 Å) laboratory measured gf values are available. For the Fe ii line at 6369.46 ÅHeise & Kock (1990) measure a log(gf) value of −3.55, which is significantly higher than our derived solar value of −4.10. Our derived value is in fair agreement with the predicted log(gf) value of −4.25 (Kurucz 1998) and solar value of −4.36 (Blackwell, Shallis & Simmons 1980). By adopting the laboratory gf value, this line yields a lower abundance than the mean Fe abundance (7.42) derived from 6432 and 7515 Å. The 6369.46 Å Fe ii line appears to be blended with another Fe ii line at 6369.375 Å (Kurucz 1998), but the blend's contribution is negligible. For this line, we adopted the gf value derived in this study (Table 3). A search for laboratory Fe ii lines at λ > 3000 Å has been presented by Allende Prieto et al. (2002a). They noticed that Fe ii 5234.6 Å was measured by Kroll & Kock (1987) and Heise & Kock (1990). The rescaled and averaged value (−2.23 ± 0.08) is in excellent agreement with our astrophysical determination (−2.22).

Astrophysical gf values were also determined from the spectra of two of the programme stars: HD 145937 with [Fe/H]=−0.55, and HD 217877 with [Fe/H]=−0.14. The iron abundances and the model atmospheres were derived using the Fe i and Fe ii lines with accurate experimental gf values. For the Fe i and Fe ii lines lacking measured or accurate theoretical gf values, we have computed them by inverting the two stellar spectra, and using the mean Fe i and Fe ii abundances, respectively. Finally, a mean of the solar and stellar gf values was adopted. A similar procedure is adopted for the rest of the elements. Results are given in Table 3.

In addition to the gf values, hyperfine splitting (HFS) and/or isotopic splitting must be considered for a few lines. Lines of Sc ii, V i and Co i are broadened by HFS, but test calculations showed that the effect on the abundances is negligible for lines of the observed equivalent widths. This is not the case for the Mn i and Cu i lines. In these cases, equivalent widths were calculated from synthetic line profiles and abundance found by matching these widths to the observed values. For the Mn i lines, the data on the splitting and strengths of the HFS components were taken from Kurucz (1998). The lines show so much HFS that without this detailed treatment they would return erroneous abundances. In the case of the Cu i lines, the 5105 Å line required thorough consideration of the HFS and isotopic splitting: the HFS data were taken from Kurucz (1998) and the isotopic ratio was assumed to be the Solar system value for all stars (⁶³Cu/⁶⁵Cu = 2.24). The effect of the HFS on the final abundances can be as large as 0.6 dex for the stronger Mn lines where the spacing between HFS components is large. In the case of the 6021 Å Mn line and the 5218 Å Cu line, the separation between the components is very small.

5 The Solar Abundances

The spectrum of Iris for the Sun was treated in the same way as the programme spectra, using an atlas9 model for the accepted solar parameters T_eff= 5780 K, log g= 4.44 and a solar composition [log ε(Fe) = 7.50 was adopted]. Equivalent widths were measured for the lines in Table 2. The microturbulence adopted was ξ_t= 1.22 km s⁻¹, which was derived using the Fe i lines having accurate gf values. Analysis of the iron lines returned the parameters T_eff= 5760 ± 50 K, log g= 4.44 ± 0.10 and log ε(Fe) = 7.45 ± 0.06. The parameters T_eff and log g are, within their uncertainty, equal to the accepted values. The derived solar Fe abundance log ε(Fe) = 7.45 ± 0.05 is close to the Grevesse & Sauval (1998) photospheric value of log ε(Fe) = 7.50 ± 0.05. The difference of 0.05 dex is partly attributable to the use of different model atmospheres. Replacing atlas9 by Holweger—Müller, the abundance increases to log ε(Fe) = 7.53.

Elemental abundances derived for the Sun from lines with adopted gf values and equivalent widths measured from the solar Iris spectrum (Table 2) are summarized in Table 4. Agreement with the solar photospheric abundances given by Grevesse & Sauval was taken as evidence of reliable gf values. Their analysis uses an empirical solar model atmosphere, and this difference in models introduces small differences in the abundances derived from identical sets of atomic data. In general, our results from a few lines are in good agreement with standard results from usually more lines.

6 Stellar Abundances

Elemental abundances for all the programme stars were determined using the overatlas9 model computed for the T_eff and log g derived from the photometry and Hipparcos parallaxes, respectively. Adopted model parameters are given in Table 1. The stellar abundance results are referenced to the solar abundances determined in the current study (Table 4) using the same lines, and a similar procedure as for the programme stars, i.e. we derive and discuss differential abundances [X/H] and [X/Fe]. Abundances relative to iron for the entire sample are presented in Tables 5 and 6. Before discussing the astrophysical implications of our results, we assess their accuracy, and present a few comparisons with some recent analyses of F and G disc dwarfs.

6.1 Internal assessment of the errors

This assessment of the errors afflicting the derived abundances is made without questioning the assumptions in the approach (i.e. LTE is accepted as valid). In what is now a standard procedure, we calculate the effect on the abundances of the errors in the observed equivalent widths, the defining model atmosphere parameters and the atomic data.

6.1.1 Equivalent widths

An external check is possible using our measurements of the Iris (solar) spectrum with those from lunar/day sky spectra by EAGLNT and Chen et al. (2000). We have 47 lines in common with EAGLNT and 59 with Chen et al. Equivalent widths are compared in Fig. 5 (upper panels). The solar abundance differences using a common model and atomic data are shown in the lower panels of Fig. 5. EAGLNT's W_λ values are on average 1.4 m Å smaller than ours. Chen et al.'s measurements are close to ours: the mean difference in W_λ is just 0.3 m Å. Our stellar spectra are typically of the quality of the Iris spectrum.

6.1.2 Atmospheric parameters

In Section 3.3, we derived the atmospheric parameters and discussed their uncertainties, concluding that δT_eff≃±100 K, Δ log g≃±0.1, Δξ_t≃±0.25 km s⁻¹ and Δ[M/H]≃±0.2. Assuming that the effects of these errors on the derived abundances are uncorrelated for the small range of the various Δs, it is a simple matter to determine their effect on the abundances. We have done this for a sample of stars spanning the parameter range of the entire sample. Predicted values of the total abundance uncertainty are summarized in Table 7.

6.2 External errors

Before making intercomparisons of our abundances with earlier studies, we compare the abundances derived from the adopted Kurucz over models with those derived from nover models. For 16 stars in our sample, spanning the full range of T_eff and [Fe/H] of the sample, we recomputed abundance ratios [X/Fe] using the same atmospheric parameters, but with nover models. The abundance differences from over and nover models are very small (see Fig. 6 for representative elements). In the case of high excitation lines (see [C/Fe] and [O/Fe]), there appears to be a trend of the abundance difference with [Fe/H], which is possibly due to the fact that these excited lines are formed deep in the atmosphere where differences between over and nover models are larger. Differences may be overestimated, as we have used atmospheric parameters and gf values derived from over models in computing abundances from nover models.

The Chen et al. (2000) sample of 90 F—G dwarfs includes 23 from our collection. Intercomparison of their and our results offers a check on our results, but it must be deemed incomplete in that the methods of analysis are very similar. First, we note that there is close agreement over the adopted atmospheric parameters. In the sense Chen — ours, we find δT_eff= 7 ± 42 K, Δ log g= 0.04 ± 0.13, Δ[Fe/H]=−0.02 ± 0.06 and Δξ_t= 0.39 ± 0.22 km s⁻¹. This broad agreement reflects the similarity in the approaches to the determination of atmospheric parameters. For example, both studies use (b–y) and the calibration of Alonso et al. (1996) to obtain T_eff.

Secondly, there is good agreement over the derived abundances for elements in common. Both studies adopt a differential approach using the solar spectrum. There is partial overlap in the lists of selected lines. Model grids differ: Chen et al. (2000) used new marcs models, and we used the overatlas9 models. In this initial comparison, we consider the mean differences between the two studies. Later, we comment on a few specific elements. Mean abundance differences from the 23 stars are given in Table 8. These small zero-point differences probably arise from a combination of factors: differences in the adopted solar equivalent widths, use of different grids of model atmospheres for the Sun and the programme stars, and selection of different lines with differing sensitivity to the various atmospheric parameters. We apply the appropriate zero-point difference in cases where we combine Chen et al.'s results with ours as a way to increase the sample size.

A direct comparison was made with EAGLNT's results for three stars (HD 69897, 216385 and 218470) that are in common with the present study. EAGLNT's T_eff and log g are found to be greater than our values by 96 ± 41 K and 0.13 ± 0.07 dex, respectively. The difference in T_eff and log g can possibly be attributed to differences in adopted methods: EAGLNT determined both the T_eff and log g using Strömgren indices. The differences in abundance ratios, [X/Fe], are small (<0.1 dex). For a more reliable transformation of EAGLNT's abundances to our scale, we take advantage of the fact that the Chen et al. (2000) selection of stars included 26 from EAGLNT. The principal difference in the adopted atmospheric parameters is in the effective temperatures, for which the difference in the sense Chen — EAGLNT is —88 ± 56 K. Other differences are quite minor: Δ log g=−0.07 ± 0.08 and Δ[Fe/H]=−0.02 ± 0.07. Abundance differences Chen − EAGLNT (see table 2 of Chen et al.) are small. The abundance differences Chen − ours and EAGLNT − ours are given in Table 8.

7 Chemical Evolution of the Disc

Several signatures of chemical evolution of the Galactic disc may be looked for using our data. Here, we comment briefly on the age—metallicity relation, aspects of the evolution of the relative abundances (i.e. [X/Fe] versus [Fe/H]), the scatter in relative abundances at a fixed [Fe/H], and the difference in compositions of thick and thin disc stars.

Our sample is nearly homogeneous, as it comprises thin disc stars to the almost total exclusion of thick disc representatives (see below for our definition of the thick disc). Furthermore, our sample was selected to cover only a part of the [Fe/H] range spanned by thin disc stars. As appropriate, we combine our data with published results.

7.1 Age—metallicity relation

EAGLNT's age—metallicity relation, which hinted at a slow drop in metallicity with increasing age of the star, was marked by a large spread in metallicity at a fixed age. Our sample taken at face value offers a cleaner relation — see Fig. 7, where the relation is shown for [Ca/H], [Fe/H] and [Ba/H]. Fig. 8 shows this relation with earlier results from Chen et al. (2000) and EAGLNT with their marked scatter in [Fe/H] at a fixed age. The appearance of a cleaner age—metallicity relation is attributable to two selection effects. First, and more important, we chose stars in a restricted [Fe/H] range and, in particular, [Fe/H] > − 0.2 are poorly represented. Secondly, our sample is kinematically homogeneous to the almost complete exclusion of thick disc stars. In short, we support earlier conclusions that the age—metallicity relation offered directly by local thin and thick disc stars is characterized by a large scatter about a slow monotonic decrease of metallicity with increasing age.

7.2 Relative abundances

In discussing the variation of [X/Fe] versus [Fe/H] (Figs 9, 10 and 11), we begin by making brief comparisons with published results, principally those from the recent extensive surveys of disc F and G dwarfs by EAGLNT, Feltzing & Gustafsson (1998), Fulbright (2000) and Chen et al. (2000) over the common interval in [Fe/H]. Note that our stars sample well the interval [Fe/H]≃−0.1 to −0.6. EAGLNT's stars covered a slightly broader range ([Fe/H]=−0.8 to +0.2) with Feltzing & Gustafsson adding metal-rich stars ([Fe/H]= 0.0 to +0.2). EAGLNT considered O, Na, Mg, Al, Si, Ti, Fe, Ni, Y, Zr, Ba and Nd. Chen et al. provided good coverage for [Fe/H]=−1.0 to +0.1 for O, Na, Mg, Al, Si, K, Ca, Ti, V, Cr, Ni and Ba. Fulbright analysed a sample of disc and halo stars with a wide range in T_eff, log g and metallicity, and provided abundances for 13 elements (Na, Mg, Al, Si, Ca, Ti, V, Cr, Ni, Y, Zr, Ba and Eu). From his study we have selected 77 disc dwarfs/subgiants that have −1.0 ≤[M/H]≤+0.2, and 3.8 ≤ log g≤ 5.0. For elements (C, N, S, Sc, Mn, Co, Cu, Zn and Ce) not covered by these surveys, we compare with other studies.

For many elements, inspection of the plots of [X/Fe] versus [Fe/H] shows that published results differ from ours by only a small zero-point correction. Table 8 lists the zero-point corrections between Chen et al. (2000) and us, and between EAGLNT and us. Since we have only three stars in common with EAGLNT, we infer the mean zero-point correction between our and EAGLNT's results by combining the corrections between Chen et al. and us, and between Chen et al. and EAGLNT. Each of the three analyses is a differential analysis conducted relative to the solar spectrum. Given that theories of Galactic chemical evolution should not pretend to challenge observations at the 0.1 dex level, we shall not attempt to pin down the origins of the zero-point corrections; possible sources of a zero-point difference were discussed above. For applications where the largest possible sample size may be useful, we shall apply the zero-point correction to place published results on our system of abundances.

Our results are in good agreement for elements in common with EAGLNT. The trends of [X/Fe] versus [Fe/H] are identical for O, Na, Mg, Al, Si, Ca, Ti, Ni and Ba. Differences may be noticeable for Y and Zr. In the case of Y and Zr, we find [X/Fe] to decline slightly with decreasing [Fe/H], but EAGLNT found either no (Y) or an opposite (Zr) trend. The most striking differences with respect to EAGLNT are not in the trends but in the scatter about a mean trend. Most notably, the scatter found here is considerably smaller than reported by EAGLNT for Mg, Al and Ti, especially at [Fe/H]≤−0.4. The scatter in [X/Fe] for these and other elements is discussed below.

There is also very good agreement with the results of Chen et al. (2000). After allowing for a small zero-point difference, two differences are noted. First, there is a small but distinct difference between our (and EAGLNT's) and Chen et al.'s run of [Al/Fe] versus [Fe/H]: we find [Al/Fe] to increase slightly with decreasing [Fe/H], but Chen et al. find an initial decrease from [Al/Fe]≃+0.15 at [Fe/H]= 0 to [Al/Fe]≃−0.1 at [Fe/H]≃−0.4, from which point [Al/Fe] may increase slightly. Secondly, there are elements for which the analyses agree about the trends but give different results for the scatter in [X/Fe] at a fixed [Fe/H]: notably, Cr, for which Chen et al. report a flat trend but with stars spanning the range [Cr/Fe]≃−0.1 to +0.2, in contrast to our results (Fig. 10).

Remarks on [X/Fe] versus [Fe/H] are offered for those elements not covered by either EAGLNT or Chen et al. Our reference is usually to the most recent work on an element. The elements in question are C, N, S, K, Sc, Mn, Co, Cu, Zn, Ce, Nd and Eu. Oxygen is also discussed.

Carbon Our results are in good agreement with abundances derived by Gustafsson et al. (1999) from the 8727 Å[C i] line in 80 stars of EAGLNT's sample. We confirm the increase of [C/Fe] with decreasing [Fe/H]. Scatter about the mean trend is larger from our C i lines than from the forbidden line, a difference attributed to the different sensitivities of the lines to the atmospheric parameters. The slight offset — our [C/Fe] are larger by about 0.03 dex — is in line with the systematic difference in the adopted T_eff values.

The analysis by Tomkin et al. (1995) of C i lines in 105 of EAGLNT's stars gave a very similar slope for the [C/Fe]–[Fe/H] relation as found by us and by Gustafsson et al., but Tomkin et al.'s results are offset to lower [C/Fe] by about 0.15 dex from ours. This offset arises because EAGLNT's T_eff scale is about 80 K hotter than ours.

Nitrogen Atomic nitrogen is represented in spectra of F—G dwarfs by weak N i lines. Our [N/Fe] values show considerable scatter at a fixed [Fe/H], which is largely attributable to the weakness of the two N i lines, and the T_eff sensitivity of the derived abundances. At those metallicities ([Fe/H]≃−0.2) well represented in our sample, [N/Fe] is about 0.2, which implies that, if [N/Fe]= 0 at [Fe/H]= 0, then [N/Fe] increases as [Fe/H] falls below the solar value. The N i lines are not detectable in our stars with [Fe/H]≤−0.4.

A selection of N i lines was used previously by Clegg, Lambert & Tomkin (1981) to measure [N/Fe] in 15 stars over the [Fe/H] spanned by our stars to give [N/Fe]≃ 0.0, a value smaller than ours by about 0.2 dex. Considering the similar sensitivities of the C i and N i lines to the adopted atmospheric parameters, [N/C] is robustly model-independent. Our result [N/C]≃ 0 is consistent with that given by Clegg et al.

Oxygen The forbidden [O i] 6300 Å line in our spectra falls near the gap between the spectral orders, and the line can be measured reliably only in stars where lines are blueshifted. This and the weakness of the line limited us to measure the 6300 Å line in 60 stars ranging in metallicity from 0.0 to −0.5 dex. In analysing the W_λ of 6300 Å we have considered the blend caused by a Ni i line at 6300.335 Å with the gf value reported by Allende Prieto, Lambert & Asplund (2001b). The effect of the blend on the [O i] abundance is significant, especially in stars of solar metallicity. The abundance ratio [O/Fe] is found to increase with decreasing [Fe/H], in general agreement with other studies where the blend was recognized (Nissen et al. 2002).

Direct comparisons with the majority of the published analyses of the [O i] lines are compromised by their neglect of the Ni i blending line. Our results are in fair agreement with Nissen et al. (2002).

Sulphur Recently, Chen et al. (2002) reported S abundances for a sample of 26 disc stars. Our current results, based on three S i lines that are common with Chen et al. (2002), in general agree with their results. However, the scatter appears higher in our data. A difference between Chen et al. (2002) and our analysis is the [S/Fe] offset from [S/Fe]= 0 even at [Fe/H]∼ 0. We discuss below the possible reasons for the small offsets.

Potassium In spite of a large scatter, a weak trend of increasing K abundance with decreasing [Fe/H] is noticeable (see Fig. 9).

Scandium Nissen et al. (2000) obtained Sc abundances for stars in the Chen et al. (2000) sample. These were revised by Prochaska & McWilliam (2000) using accurate hyperfine splittings for the Sc ii lines. The revised results in the common [Fe/H] interval are in good agreement with ours. Inspection of Fig. 10 shows that Sc, as noted by Nissen et al. but disputed by Prochaska & McWilliam, behaves like the α elements Ca and Ti. This similarity may not hold for stars with [Fe/H] < −1 (Gratton & Sneden 1991; Prochaska & McWilliam 2000).

Manganese A decrease of the Mn abundance (relative to Fe) for decreasing [Fe/H] was noted by Beynon (1978), explored with high-quality spectra of a few stars by Gratton (1989), and defined for F—G disc dwarfs by Nissen et al. (2000) and Prochaska & McWilliam (2000). For [Fe/H] > − 0.6, the limit of our sample, the [Mn/Fe] measured by us and by Prochaska & McWilliam are in good agreement as to slope and absolute value.

Cobalt Data on cobalt in F—G disc dwarfs are especially sparse. Gratton & Sneden (1991) obtained [Co/Fe]≃−0.1 from a few stars in our [Fe/H] range. This early result is consistent with ours.

Copper Our results show little variation of [Cu/Fe] with [Fe/H]. Earlier discussions have focused on the run of [Cu/Fe] with [Fe/H] for halo stars for which [Cu/Fe] declines steadily for decreasing [Fe/H] (Sneden, Gratton & Crocker 1991): [Cu/Fe]= 0.38 [Fe/H]+ 0.15. This slope is at odds with our results, but close inspection of the few results available to Sneden et al. for stars with [Fe/H] > − 1 shows that a change of slope might have been anticipated.

Zinc This element appears to behave similarly to the α elements; [Zn/Fe] increases slightly with decreasing [Fe/H]. This result is consistent with the analysis by Sneden et al. (1991) of Zn in disc and halo dwarfs and giants, which gave [Zn/Fe] constant (= 0.04) from [Fe/H]=−0.1 to −2.9.

Cerium In solar material, Ce is principally an s-process product. Thus, it is the expected result that [Ce/Fe] and [Ba/Fe] vary in very similar fashions. That the scatter at a given [Fe/H] is larger for [Ba/Fe] than for [Ce/H] is probably due (see below) to the fact that the Ba ii but not the Ce ii lines are strong, and so dependent on the adopted microturbulence and other factors.

Neodymium Extending the argument just given for Ce, we note that the s-process contributions to solar abundances of Ba, Ce, Nd and Eu are 81, 77, 56 and 6 per cent, respectively. Noting the opposite slopes of [Ba/Fe] and [Eu/Fe] versus [Fe/H], it is not surprising that [Nd/Fe] appears to be independent of [Fe/H].

Europium Recently, Eu abundances for samples of EAGLNT's stars using their atmospheres were published by Woolf, Tomkin & Lambert (1995) and Koch & Edvardsson (2002). Their results for [Eu/Fe] are consistent with ours.

7.3 Offsets in [X/Fe]

Given the differential analysis and the absence of cosmic scatter in our sample (see next section), one would expect stars of solar [Fe/H] to have [X/Fe]= 0. However, Figs 9, 10 and 11 show [X/Fe] of Mg, Al, Si and S offset by 0.03–0.05 dex at [Fe/H]= 0.0, and [X/Fe] of elements Sc, V, Mn and Cu offset by ∼0.05 at [Fe/H]= 0.0. A key to the origins of the small offsets may be the fact that the Sun is not fully representative of our sample. With T_eff= 5780 K, log g= 4.44 and [Fe/H]= 0, the Sun is in a tail of the stellar distribution in all three parameters (Fig. 1). This has several consequences. The equivalent widths of some lines in the stellar spectra may differ considerably from their strengths in the solar spectrum. Systematic errors such as those arising from the neglect of stellar granulation and departures from LTE, which would cancel in a strictly differential analysis of quite similar stars, may leave a small imprint here in the form of the offset in [X/Fe] at [Fe/H]= 0. A leading NLTE effect may be overionization of the metals in the iron group. One might suppose similar degrees of overionization such that [Ni/Fe] may be reliably estimated from a combination of Ni i and Fe i lines. In the case of Mg, Si and S, the offset disappears when [X/Fe] is computed using iron abundance derived from Fe ii lines.

7.4 Outliers

There are few stars in our sample whose abundances for one or more elements differ significantly from the mean abundances of the rest of the stars at the same [Fe/H] (see Figs 9–11). Two stars, HD 110989 and 136925, are enhanced only in abundances of Mg, Al, Si, S and Ti, and the rest of the abundances are normal. The kinematics of these stars suggest that they belong to the thick disc population, for which such enhancements are characteristic (see below). Figs 9, 10 and 11 also reveal that half a dozen stars are enhanced in s-process elements, i.e. Sr, Y, Zr, Ba, Ce and Nd. Abundances of these stars are summarized in Table 9. HD 88446 is known to be an s-process-enriched CH subgiant (Smith, Coleman & Lambert 1993). The current abundances are in very good agreement with the literature values. We assume that the other stars are also s-enriched dwarfs. The higher s-process abundances in unevolved stars are attributable to mass transfer from a companion asymptotic giant branch (AGB) star that is now an unseen white dwarf.

7.5 Cosmic scatter?

A first step towards an understanding of the scatter in the abundance ratios [X/Fe] is to quantify the scatter. To do this we fit a linear relation to the data and examine the residuals about the relation. A histogram of the residuals is fitted with a Gaussian. In very few cases is a Gaussian not a good fit. Fig. 12 shows [X/Fe] versus [Fe/H] for X = Mg and Si with the fitted linear relation, the residuals about this relation, and a histogram of these residuals with its fitted Gaussian. The σ_gau of the Gaussian varies from element to element. Table 10 summarizes the results. Note that in computing the measurement errors σ_mod for individual stars, we have not included the uncertainty in the EW measurements. Except for two elements, K and Sr, abundances are computed using two or more lines and the net random error due to the EW measurement is very small.

An obvious question occurs. Is there information about Galactic chemical evolution (GCE) in the σ_gau estimates, or do abundance measurement errors dominate? To address this, we compare the error σ_mod previously calculated (Table 10) with σ_gau.

Values of σ_gau are well matched to the estimates of σ_mod for almost every element (Fig. 13). This is especially true for Cr and Ni, two elements spectroscopically similar to Fe with similar nucleosynthetic origins (i.e. intrinsic star-to-star differences in [X/Fe] are minimized). For C and N, σ_gau is less than the estimated σ_mod, which suggests that the latter are overestimates. In these cases where the abundance is based on high excitation lines, we suspect that the T_eff errors are significantly overestimated: the adopted error is probably an upper limit (see Alonso et al. 1996) to the combination of the random and systematic errors, but only the latter is a weak contributor to σ_mod. In the case of Cu and Sr, σ_gau exceeds σ_mod. Abundance of Sr is dependent on a single line and it is therefore difficult to argue that there is a real star-to-star scatter in [Sr/Fe].

The implication for GCE is clear: The intrinsic or cosmic scatter in [X/Fe] among these thin disc stars with birthplaces concentrated at Galactocentric distances of 7–10 kpc is small, say σ_cosmic < σ_gau. Noting that the sampled ejecta come in differing proportions from the three principal sites of stellar nucleosynthesis — SNII, SNIa and AGB stars — the lack of cosmic scatter implies that the ejecta from the different sites were well mixed into the gas from which the stars formed.

That there is cosmic scatter was suggested by EAGLNT's study, which showed a noticeably larger scatter in [Mg/Fe], [Al/Fe] and [Ti/Fe] (relative to similar elements such as Si and Ca) for stars with [Fe/H]≤−0.4.7 Reconciliation of this suggestion with the evident lack of comparable scatter in our sample is attempted below.

7.6 Chemical evolution of the thin disc

Chemical evolution as portrayed by Figs 9–11 is broadly interpreted as the consequence of mixing into the interstellar medium of ejecta from three principal sites of nucleosynthesis: SNII, SNIa and AGB stars. Qualitatively, the key features of Figs 9, 10 and 11 are widely accepted as understood. For example, the gradual decline in [X/Fe] for α elements (O, Mg, Si, Ca and Ti) with increasing [Fe/H] is taken to reflect the delayed contribution from SNIa with a lower α/Fe ratio than the ejecta from SNII which dominated the chemical evolution at earlier times and hence low [Fe/H]. Detailed modelling has been attempted by many authors – see, for example, Timmes, Woosley & Weaver (1995), Chiappini et al. (1997), Goswami & Prantzos (2000) and Alibés, Labay & Canal (2001). Quantitative matching of predictions to observations of [X/Fe] remains elusive.

Contributions from the AGB stars must be reflected in the abundances of C, N and heavy elements synthesized predominantly by the s-process. Carbon and nitrogen are also synthesized by massive stars. These stars may also contribute Sr, Y and Zr through the weak s-process and Eu through the r-process. While AGB stars also synthesize these ‘light’ elements, they dominate synthesis of ‘heavy’ s-process nuclides such that, as noted above, AGB stars control production of Ba, Ce and Nd in thin disc stars. In contrast, europium is an r-process or SNII product.

Inspection of Fig. 11 shows, as mentioned in Section 7.2, that Sr, Y, Zr, Ba and Ce show very similar declines in [X/Fe] with decreasing [Fe/H]. Europium shows an increase, as expected of this r-process product. Increasing Ba and Ce (relative to Fe) surely indicates the increasing prominence of AGB star ejecta relative to SNII and SNIa ejecta which contribute Fe but very little Ba and Ce. The ratio of heavy to light s-process abundances is shown in Fig. 14. The similarity of the slopes of [X/Fe] versus [Fe/H] for light (Sr, Y, Zr) and heavy (Ba, Ce) elements may reflect either unchanging relative contributions from AGB stars or a change in these contributions that is offset by a change in the weak s-process contribution from the massive stars. On the assumption that the AGB stars are the controlling influence, the unchanging abundance ratio of heavy to light elements indicates that the exposure to neutrons in the s-process site is essentially independent of the metallicity of the contributing AGB stars.

7.7 Thin and thick discs

The thick disc is considered by many to be the result of heating of the thin disc by accretion of, or merger with, small stellar systems. Freeman & Bland-Hawthorn (2002) refer to the resulting thick disc as a ‘snap frozen’ relic of the state of the (heated) early disc. The labels ‘thin’ and ‘thick’ were introduced by Gilmore & Reid (1983) and denote the different vertical scaleheights of the populations: 300 pc for the thin disc and 1450 pc for the thick disc. The ratio of stellar density of thick to thin disc is a few per cent near the Sun. The thick disc is broadly described as slightly metal-poor and old relative to the thin disc.

In our sample, the lack of cosmic scatter in [X/Fe] at a fixed [Fe/H] is striking and in apparent conflict with results obtained by others. We noted above the contrast with EAGLNT's results for Mg, Al and Ti where a larger scatter (apparently, cosmic) was reported for stars with [Fe/H] less than about −0.4 and more metal-rich than about −0.8; the lower bound is uncertain due to the paucity of very metal-poor stars in their sample. Fuhrmann (1998), in a notable contribution, attributed the scatter in [Mg/Fe] to a mixing of thin with thick disc stars and a different chemical evolution of these two stellar populations [see also Gratton et al. (2000) for remarks on O and Mg with respect to Fe]. He suggested that at [Fe/H]≈−0.4 the [Mg/Fe] was either ‘high’ or ‘low’ with no stars having an intermediate value.

Prochaska et al. (2000) report results from the initial phases of a survey of thick disc main-sequence stars in the solar neighbourhood. Stars are selected to have V_LSR from −20 to −100 km s⁻¹, metallicities in the interval −0.4 to −1.1, and a W_LSR that takes a star to at least 600 pc above the Galactic plane. The latter criterion in particular takes out thin disc stars. A colour selection provides stars generally cooler than those comprising our and other surveys. Ten stars were analysed using model atmospheres and high-resolution spectra, obtaining abundances for 20 elements. Presently, the sample lacks stars in common with other surveys, and hence there may be small offsets between the [X/Fe] and those of the surveys considered here. Results8 are incorporated into Figs 15, 16 and 18.

Given the large stellar sample that may be assembled from various sources, we explore in greater detail the evidence for cosmic scatter in [Mg/Fe] and other elements arising from the mixing at a fixed [Fe/H] of thin and thick disc stars. Fig. 15 shows [Mg/Fe] and [Ti/Fe] versus [Fe/H] for stars drawn from the samples referenced in the caption. With the exception of the data from Prochaska et al. (2000) and Fulbright (2000), the published abundances have been adjusted to our scale using small corrections. Common stars among the samples were identified, and treated only once: for common stars in our study and others, we have adopted our values, and for common stars in Chen et al. (2000) and EAGLNT, we have adopted the Chen et al. values. The appearance of cosmic scatter at [Fe/H]≃−0.4 is intimately related to the mixing of stellar populations. For [Fe/H] > − 0.4, the stars belong to the thin disc. At [Fe/H] < −0.4, thick disc stars comprise the majority. In simplest terms stars with the higher [Mg/Fe] at a given [Fe/H] are old thick disc stars from the inner Galaxy. To justify this identification, we divide the stars into two groups according to whether [Mg/Fe] is greater than or less than +0.2 dex as shown in Fig. 15.

In the four panels of Fig. 16, we identify a star by its group membership in plots of V_LSR, W_LSR, R_m and age. We have calculated these quantities when authors of the selected samples did not provide them. Low and high [Mg/Fe] stars occupy almost non-overlapping areas of the panels showing V_LSR, R_m and age. Many stars of high [Mg/Fe] (large symbols in the plots) have a circular velocity less than that of the Sun, a range in W_LSR that shows they make excursions to about 1 kpc above the plane, an age that places them among the oldest stars in the Galaxy (log τ₉≈ 1.0–1.3), and an origin in the inner Galaxy (R_m∼ 5–7 kpc). The high [Mg/Fe] stars are primarily representatives of the Galaxy's thick disc. The low [Mg/Fe] stars of the same [Fe/H] as the thick disc stars are predominantly thin disc stars from Galactocentric distances closer to the radius of the Sun's orbit. This difference in populations is, as Fuhrmann (1998) recognized, responsible for the appearance of cosmic scatter in [Mg/Fe] among slightly metal-poor stars. The difference between two disc populations is also clear from Fig. 17, where the stars are binned in 0.5 kpc intervals of R_m. For this we have considered star samples of EAGLNT, Chen et al. (2000), Fulbright (2000) and our work, totalling around 500 disc stars. The entire sample is grouped into two classes: stars with [Mg/Fe]≥ 0.2 dex as thick disc stars, and stars with [Mg/Fe] < 0.2 dex as thin disc stars. Thin disc stars fit a Gaussian centred at R_m= 8.1 kpc and thick disc stars peak at R_m= 6.7 kpc. The distribution suggests that thin disc stars are likely to have circular orbits and thick disc stars are relatively eccentric and formed closer to the Galactic Centre.

The dispersion in W_LSR for thin disc stars increases progressively for lower [Fe/H] in agreement with the correlation between σ_W and age determined by Gómez et al. (1997), who studied several thousand B- to F-type stars with Hipparcos data, and the [Fe/H] versus age relationship depicted in Fig. 8. Gómez et al. found the σ_W—age relationship to saturate at ∼4–5 Gyr, which is also consistent with the scatter in W flattening for thin disc stars with [Fe/H]≤−0.3 in Fig. 16.

To quantify the differences between the thin and thick disc samples, we choose a sample of thick disc stars as having [Fe/H]≤−0.35 and a V_LSR from −40 to −100 km s⁻¹, R_m of 5.5–7.0 kpc, and an age log τ₉≥ 1.0. The upper bound chosen for [Fe/H] is seemingly the maximum [Fe/H] of thick disc stars seen in the solar neighbourhood; we are not aware of selection effects compromising the considered surveys which would have led to the exclusion of stars of high [Mg/Fe] with [Fe/H] > − 0.3. The lower bound on [Fe/H] for thick disc stars is unknown and unimportant to our measurement of the difference in [X/Fe] between the two samples. Our comparison sample of thin disc stars has V_LSR between −40 and +40 km s⁻¹. Mean values for the thin disc stars are R_m= 8.1 kpc and log τ₉= 0.6 for those stars with [Fe/H] between −0.35 and −0.7, the metallicity range for which present samples of thin and thick disc stars have an overlap.

Thin and thick disc stars with [Fe/H] between −0.35 and −0.7 differ in [X/Fe] (Fig. 18). Table 11 gives the mean [X/Fe] for those elements well represented in both samples and the difference Δ[X/Fe]=[X/Fe]_thick−[X/Fe]_thin between the mean values. Our Δ values are similar to those suggested by Prochaska et al. (2000) from a comparison between their [X/Fe] and those of published surveys of disc stars. Δ[X/Fe] is positive for several elements: Mg, Al, Si, Ca, Sc, Ti, V and Eu. To within the uncertainty, Δ[X/Fe] is zero for Na, Cr, Mn and Ni, and possibly negative for Ba. Particularly striking is the contrast between the odd-Z light elements Na and Al, a difference noted by EAGLNT. The Δ values for Sc and V are largely dependent on Prochaska et al.'s results for thick disc stars and may be affected by a systematic offset arising from different abundance analysis techniques. We note in Fig. 18 that our results and those of Chen et al. (2000) suggest a smaller Δ value for V.

Thick disc stars have a narrow spread in [Ba/Eu]. The spread in [Eu/Fe] evident from Fig. 18 is much reduced when [Ba/Eu] is considered. Fig. 19 shows this. A few thin disc stars share the [Ba/Eu] of the thick disc stars. For a pure r-process solar-like mix, [Ba/Eu]≈−0.7. Evidently, the thick disc stars have a smaller fraction of s-process heavy elements than disc stars of the same [Fe/H]. This is an expected result given that the thick disc stars are older than the thin disc companion stars; the s-process elements are contributed by the more slowly evolving low-mass AGB stars.

Our primary aim here was to establish that previous reports of cosmic scatter in [Mg/Fe] and similar ratios arise from the mixing of stellar populations. Cosmic scatter, as shown here, is undetectable in [X/Fe] at fixed [Fe/H] among local thin disc stars. It is apparently small for thick disc stars but a large sample subjected to a uniform analysis must be made available to test this suspicion.

Our selection of thick disc stars by negative V_LSR, high τ₉, low [Fe/H] and small R_m excludes two interesting groups of stars. First, there are stars with [Mg/Fe] > 0.2 with positive V_LSR and low [Fe/H] (Fig. 16). Secondly, there are a few stars with V_LSR characteristic of the thick disc but higher [Fe/H].

The first group by virtue of their generally positive V_LSR appears to originate from outside the solar circle (R_m≃ 8.5–10 kpc). They share the lower [Fe/H] of the thick stars; none are present with [Fe/H]≥−0.3. Although the sample size is small, there is a hint that, in contrast to the thick stars, these stars are not exclusively old. The amplitude in W_LSR across the sample appears to be smaller than that of the thick disc stars. However, it is interesting to note that the abundance pattern of this group is very similar to that of thick disc stars as in Fig. 18 and Table 11. This group appears to be related to the thick disc stars discussed above with R_m of 5–7 kpc.

The second group are apparently ambiguous. Additional stars belonging to this group are to be found in Feltzing & Gustafsson (1998). Their V_LSR (∼−50 km s⁻¹) would identify them as belonging to the thick disc; but by their W_LSR, R_m, spread in ages and [Fe/H], they would be linked with the thin disc stars. These stars do not show the [X/Fe] of the thick disc stars.

8 Concluding Remarks

Our stellar sample primarily comprises thin disc stars, but, by drawing on samples that include thick disc stars, we may compare and contrast chemical compositions of thin and thick disc stars.

8.1 Thin disc — questions

Three aspects of the compositions of the thin disc stars attract our attention: (i) the lack of cosmic scatter in [X/Fe], (ii) the dispersion in the age—metallicity relation, and (iii) the origin of the gas from which the most metal-poor thin disc stars were formed.

The thin disc, as sampled by stars that are passing through the solar neighbourhood, has a lower limit of [Fe/H]∼−0.7, an upper bound to the age of about 10 Gyr, and origins from Galactocentric distances of between about 7 and 10 kpc. The restriction to 7 < R_m < 10 emerges as a direct consequence of the small eccentricity of the orbits. Between these limits on the metallicity and age, variations in [X/Fe] are small (Figs 9–11). A more remarkable result concerning the thin disc is the confirmation of earlier work, showing that, although the thin disc stars sample a range in metallicity and age, and originate from different Galactocentric distances, these identifying characteristics vanish almost entirely when the relative abundances of elements are considered. In particular, apart from weak trends with [Fe/H], [X/Fe] exhibits no scatter in excess of that attributable to measurement errors.9 This fact stands as a challenge to models of Galactic chemical evolution.

Lack of scatter in [X/Fe] suggests that the Galactic thin disc is chemically homogeneous at a given time, and mixing of the various ejecta into star-forming clouds in the disc is very efficient. This homogeneity refers to abundance ratios [X/Fe] not to the abundances [Fe/H] or [X/H]. As noted in the discussion of the age—metallicity relation, there is a spread in the latter quantities at a given age and a given Galactocentric distance.

If the mild evolution of [X/Fe] with [Fe/H] is ignored, [X/Fe] is independent of the birthplace (R_m) and birthdate of a thin disc star, always bearing in mind that we are sampling a small range in R_m. This independence extends to the present time. Massive stars, being young and therefore observed at or very close to their birthplace, may be used to trace the present composition of the Galaxy's thin disc. Observations show that [X/Fe]≃ 0.0 irrespective of position in the Galaxy. This result is well shown by the analyses by Andrievsky et al. (2002a,b) of Cepheids with locations corresponding to Galactocentric distances of 4–10 kpc. (These authors assume the Sun to be at 7.9 kpc.) The mean [Fe/H] of the Cepheids at the Sun's Galactocentric distance is not significantly different from zero. The authors suggest that the spread of about ±0.15 dex in [Fe/H] at this and other well-sampled distances exceeds the measurement errors. A spread is reported from observations of young open clusters (Friel 1995; Edvardsson 2002). Iron abundance decreases slightly with increasing Galactocentric distance: Andrievsky et al. obtain a slope for [Fe/H] of −0.029 ± 0.004 dex kpc⁻¹, a value of the same sign but slightly smaller than a majority of earlier measurements of this gradient. Other metals show rather similar gradients except that the heavy elements La, Ce, Nd, Eu and Gd show a positive gradient (mean value of +0.013 dex kpc⁻¹). Extension of the abundance analyses to Cepheids in the inner Galaxy shows that higher metallicity prevails inside about 6 kpc (Andrievsky et al. 2002b): [Fe/H]≃+0.3 from five stars at Galactocentric distances of 4.4–5.7 kpc, but [X/Fe]≃ 0.0 with the exception of a few elements represented by very few lines. In short, the Cepheids, young stars sampling a wide range in Galactocentric distances, have a composition expressed as [X/Fe] not distinctly different from that of thin disc stars. Examination of Andrievsky et al.'s results shows that the spread in [X/Fe] is small and probably dominated by measurement errors.

The existence of a (weak) abundance gradient is pertinent to the question of scatter in the age—metallicity relation. Most determinations put the slope at a larger value than the above value from Cepheids, say −0.1 dex kpc⁻¹ is typical. Grenon (1987, 1989) has adduced evidence that the gradient was of a similar magnitude in the past. EAGLNT's analysis offered supporting evidence. Presence of a shallow gradient is now widely linked to the presence of a stellar bar in the inner Galactic disc. Observationally, it is found that spiral galaxies with bars have flatter gradients than those without bars (Martin & Roy 1994). Theoretically, bars have been shown to homogenize the gas (Martinet & Friedli 1997). Recently, Cole & Weinberg (2002) have argued that the Galactic bar is younger than 6 Gyr, which, if the bar were the only mechanism for homogenizing the gas, would seem to imply the possibility of a different abundance gradient at very early times. However, there are other postulated ideas for maintaining a flat abundance gradient (see Andrievsky et al. 2002a).

Attention was drawn to the large spread in the age—metallicity relation by EAGLNT. At a fixed age, there is a spread of about 0.5 dex in [Fe/H], or at a fixed [Fe/H] there is a range in ages over about 8 Gyr. If stars migrate in Galactocentric distance and a Galactic abundance gradient existed over part of the time sampled by the age—metallicity relation, scatter in that relation would result. Feltzing, Homberg & Hurley (2001) from their analysis of nearly 6000 stars argue that stellar migration cannot account in full for the scatter, and interpret the scatter as ‘intrinsic to the formation processes of stars’. One might wonder if a contributing factor is an inability to predict accurately the Galactocentric distance R_m, especially for stars from the inner Galaxy that reach the Sun on ‘hot’ orbits thanks to the action of the inner bar of the Galaxy (Sparke & Sellwood 1987; Raboud et al. 1998).

Discovery of the earliest manifestation of the thin disc would provide an important datum about the disc's history. According to our sample, the oldest stars (Fig. 16) are slightly younger than the average thick disc star. These thin disc stars extend in [Fe/H] to −0.7 with, on average, a birthplace outside the solar circle. The vertical velocities W_LSR are those of the thin disc and not the thick disc. The lower bound to [Fe/H] was imposed as a selection criterion by EAGLNT, Chen et al. (2000) and ourselves. There are stars known at lower [Fe/H] with thin disc kinematics (cf. Chiba & Beers 2000; Beers et al. 2002). Clearly, an important task is to measure compositions for a selection of these metal-poor stars, and, in particular, to determine accurately those [X/Fe] which distinguish thin from thick disc stars. As important will be tracing the evolution of [X/Fe] with [Fe/H] and finding where (or if) [X/Fe] merges with halo values.10

8.2 Thick disc — questions

Thick disc stars selected by V_LSR relative to thin disc stars of the same [Fe/H] are older, exhibit a large dispersion in W_LSR, and originate from smaller Galactocentric distances (Fig. 16). Given the larger eccentricity and velocity dispersion of the thick disc stars compared to the thin disc population, we would expect a larger range in R_m. If ρ_thick(R) is nearly as flat as ρ_thin(R), Fig. 17 would reveal a wider Gaussian for the thick disc, but still centred at 6.5R_m. The fact that the distribution of thick disc stars is shifted to smaller mean Galactocentric distances can be explained by assuming a steeper dependence of ρ_thick with Galactocentric distance. Furthermore, the shift could be interpreted as the direct observation of the truncation radius of the thick disc, which, as pointed out by Freeman & Bland-Hawthorn (2002), may be different from the thin disc's, marking the size of the thin disc when the thick disc formed.

As we noted already, we confirm and extend an earlier result (Fuhrmann 1998; Gratton et al. 2000; Prochaska et al. 2000) that there are differences in [X/Fe] between thick and thin disc stars of the same [Fe/H]. These differences are summarized in Table 11. Especially notable is the different behaviour of Na, Mg and Al (relative to Fe) between the thick and thin disc. In particular, as first stressed by EAGLNT, [Na/Mg] at a fixed [MgH] is lower by about 0.2 dex for the thick relative to thin disc stars, but [Al/Mg] is the same for both groups. These differences are clues to the origins of the populations, and to the nucleosynthesis of Na, Mg, Al and other elements. The reader is referred to Prochaska et al. (2000) for discussion of these points.

Following Fuhrmann (1998), one may harbour the view that distribution functions for [X/Fe] are non-overlapping for samples of thin and thick disc stars for elements such as Mg for which Δ[X/Fe] is large. Quantitative spectroscopy of a large sample of thick disc stars and a control sample of thin disc stars is now needed to establish the distribution functions. Thick disc stars at the low [Fe/H] limit discussed here appear to merge with bulge/halo stars as far as [X/Fe] is concerned. The analysis by Feltzing & Gustafsson (1998) of metal-rich F—G stars shows no change in [X/Fe] with V_LSR, and so hints that the thick—thin disc differences disappear by [Fe/H]≃ 0.0, but the low W_LSR of their stars imply that their stars do not travel far from the Galactic plane, and hence attribution to the thick disc may be questionable.

Prochaska et al. (2000) discuss at some length the implications for the evolution of the Galaxy of the different [X/Fe] in thin and thick disc stars. As long noted, the extension of the halo [X/Fe] for α elements to higher [Fe/H] in thick disc than thin disc stars is suggestive of a delay in the contribution made by SNIa to the thick disc. Certainly, the thick—thin differences in [X/Fe] raise interesting questions about the nucleosynthesis by SNII. A key point stressed by Prochaska et al. concerns the closely similar ages and [X/Fe] for bulge, thick disc and (the majority of the) halo stars, which suggests that these populations formed from the same gas at about the same time. Several speculations may be offered to account for the lack of thin disc stars with thick disc abundances: (i) the gas from which thick disc stars formed did not contribute to the thin disc; (ii) a delay in star formation in the thin disc enables SNIa to enrich the gas in Fe-group elements and so reduce the Mg/Fe ratio for the first generation of thin disc stars; and perhaps (iii) the thick disc gas was diluted with gas in the thin disc before the observed stars formed.

8.3 New challenges

New challenges to the observer are presented by our survey of thin disc stars and the comparisons with published analyses of thick disc stars. A particular challenge is to find and survey the composition of thick disc stars over more of the space defined by R_m, τ_a, W_LSR and [Fe/H]. Given the availability of high-resolution spectrographs and large telescopes and tools for standard abundance analysis, it should not be difficult to provide the compositions.

A different challenge should be noted: the need to step beyond a classical abundance analysis with its reliance on the classical model atmosphere and method of line analysis. One step is taken by replacing the assumption of LTE by NLTE (i.e. statistical equilibrium) in analysing the absorption lines. A more challenging step involves using three-dimensional hydrodynamic model atmospheres in place of the classical atmosphere, which adopts hydrostatic equilibrium among its defining assumptions. Ultimately, the combination of the hydrodynamical models with NLTE is desired. Consummation of this marriage may be necessary in order to detect and quantify the cosmic scatter in the abundance ratios [X/Fe], and to obtain finally definitive results for [X/Fe].

Acknowledgments

We thank Bengt Edvardsson for providing a list of stars with Strömgren photometry, from which the current sample is taken, and the code for calculating the U, V, W space motion components. We are grateful to Johannes Andersen and Stephane Udry for providing the CORAVEL radial velocities prior to publication. We thank Jon Fulbright for making available computer code, with the kind permission of D. Lin, to calculate orbital parameters. We thank David Yong, Gajendra Pandey and Nils Ryde for many useful discussions. This research has been supported in part by the National Science Foundation (grants AST 96-18414, AST 99-00846, AST 00-86321) and the Robert A. Welch Foundation of Houston, Texas. This research has made use of the Simbad data base, operated at CDS, Strasbourg, France, and the NASA ADS, USA.

References

Author notes