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Chemical abundance analysis of the open clusters Cr 110, NGC 2099 (M 37), NGC 2420, NGC 7789, and M 67 (NGC 2682)^,

E. Pancino¹ - R. Carrera^1,2 - E. Rossetti¹ - C. Gallart²

1 - INAF - Osservatorio Astronomico di Bologna, via Ranzani 1, 40127 Bologna, Italy
2 - Instituto de Astrofisica de Canarias, via Lactea s/n, 38200, La Laguna, Tenerife, Spain

Received 23 July 2009 / Accepted 28 September 2009

Abstract
Context. The present number of Galactic open clusters thathave high resolution abundance determinations, not only of [Fe/H],but also of other key elements, is largely insufficient to enable aclear modeling of the Galactic disk chemical evolution.
Aims. To increase the number of Galactic open clusters with high quality measurements.
Methods. We obtained high resolution (), high quality (-100 perpixel), echelle spectra with the fiber spectrograph FOCES, at CalarAlto, Spain, for three red clump stars in each of five Open Clusters.We used the classical equivalent width analysis method to obtainaccurate abundances of sixteen elements: Al, Ba, Ca, Co, Cr, Fe, La,Mg, Na, Nd, Ni, Sc, Si, Ti, V, and Y. We also derived the oxygenabundance using spectral synthesis of the 6300 Å forbidden line.
Results. Three of the clusters were never studied previously with high resolution spectroscopy: we found(0.10) dex for Cr 110;(0.10) dex for NGC 2099 (M 37), and(0.10) dexfor NGC 2420. This last finding is higher than typical literatureestimates by 0.2-0.3 dex approximately and in closer agreementwith Galactic trends. For the remaining clusters, we find that(0.10) dex for M 67 and(0.10) dex for NGC 7789. Accurate (to0.5 km s^-1)radial velocities were measured for all targets, and we provide thefirst velocity estimate derived from high resolution data forCr 110, km s^-1.
Conclusions. With our analysis of the new clusters Cr 110,NGC 2099, and NGC 2420, we increase the sample of clusterswith high-resolution-based abundances by 5%. All our program starsshow abundance patterns which are typical of open clusters, very closeto solar with few exceptions. This is true for all the iron-peak ands-process elements considered, and no significant-enhancementis found. No significant (anti-)correlations for Na, Al, Mg, and Oabundances are found. If anticorrelations are present, the involvedspreads must be <0.2 dex. We then compile high resolution dataof 57 OC from the literature and find a gradient of [Fe/H] withGalactocentric radius of -0.06  0.02 dex kpc^-1,in agreement with past work and with results for Cepheids and B starsin the same range. A change of slope is seen outside kpc and [/Fe] shows a tendency to increase with.We also confirm the absence of a significant age-metallicity relation, finding slopes of -2.6  1.1  10^-11 dex Gyr^-1 and 1.1  5.0  10^-11 dex Gyr^-1 for [Fe/H] and [/Fe] respectively.

Key words:stars: abundances - Galaxy: disk - open clusters and associations: general

1 Introduction

Open clusters (hereafter OC) are idealtest particles in the study ofthe Galactic disk, providing chemical and kinematical information in differentlocations for different times. Compared to field stars, they have the obviousadvantage of being coeval groups of stars, at the same distance and with ahomogeneous composition. Therefore, their properties can be determined withsmaller uncertainties. Several attempts have been made to derive twofundamental relations using OC: themetallicity gradient along the diskand theage-metallicity relation (hereafter AMR) of the disk(e.g.,Friel et al. 2002;Panagia & Tosi 1980;Janes 1979;Salaris et al. 2004;Twarog et al. 1997;Chen et al. 2003), but they were hampered bythe lack of large and homogeneous high quality datasets.

Table 1:  Observing logs and program stars data.

In particular, the lack of ametallicity scale extending to solarmetallicity with comparable precision to that of the lower metallicity regime(i.e.,Zinn & West 1984;Carretta & Gratton 1997) represents the main problem from the point of view of(i) the study of the Galactic disk,(ii) tests of stellar evolutionmodels for younger and more metal-richsimple stellar populations, and(iii) the use of those stellar populations as templates for extragalactic studiesof population synthesis. Of the1700 known OC (Dias et al. 2002, and updates),only a subset of140, i.e., 8% of the total, possesses some metallicitydetermination. Most of these have been obtained by means of different photometricstudies in the Washington (e.g.,Geisler et al. 1991,1992), DDO(e.g.,Clariá et al. 1999), Strömgren (e.g.,Twarog et al. 2003;Bruntt et al. 1999), UBV(e.g.,Cameron 1985), and IR (e.g.,Tiede et al. 1997) photometric systems andpassbands, often giving rise to considerable differences from those obtained fromspectroscopy (seeGratton 2000, and references therein). In a far smallernumber of clusters, abundances have been derived from low-resolution spectroscopy(e.g.,Warren & Cole 2009;Carrera et al. 2007), and there have been admirable attempts to obtainlarge and homogeneous datasets (seeFriel et al. 2002;Friel & Janes 1993) in spite of thenon-negligible uncertainties involved in the procedure.

A few research groups (see Sect. 6 for more details) are presentlyobtaining high quality spectra and are deriving more precise abundancemeasurements. The study of elements other than the iron-peak ones (such as ,s-, andr-process, light elements) allows one to place strongerconstraints on the sites of production of those elements (SNe Ia, SNe II, giants,supergiants, and Wolf-Rayet stars) and therefore on their production timescales.These are fundamental ingredients to the chemical evolution modeling of theGalactic disk (Tosi 1982;Colavitti et al. 2009;Chiappini et al. 2001).

For these reasons, we obtained high resolution spectra for a sample of poorlystudied old OC. We present here the detailed abundance analysis of five clustersobserved during our first run at Calar Alto. Observations and data reductions aredescribed in Sect. 2; the linelist and equivalent width measurementsare described in Sect. 3, while the abundance analysis methods andresults are presented in Sect. 4; abundance results are then discussedand compared with literature results in Sects. 5-7; finally, we summarize our results and draw our conclusions inSect. 8.

2 Observational material

Three red clump stars wereselected in each of the target clusters using the WEBDA database (Mermilliod 1995) and the 2MASS surveydata for the infrared mag (Skrutskie et al. 2006). More details about thereferences for star names, coordinates and magnitudes can be found inTable 1, while the position of our targets in the color magnitudediagrams (CMDs) obtained from WEBDA are shown in Fig. 1.

	Figure 1: V, (B-V) Color Magnitude Diagrams of the program clusters(from the WEBDA), with the location of our target stars.
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Observations were performed between the 1st and 10th of January 2004 with thefiber echelle spectrograph FOCES at the 2.2 m Calar Alto Telescope, in Spain. Thesky was generally clear, although a few nights had thin cirrus and sometimesclouds, forcing us to increase the exposure times considerably. All stars wereobserved in 3-16 exposures lasting 15-90 min each, depending on the magnitude,until a globalS/N ratio between 70 and 100 (per pixel) was reached around6000 Å (Table 1). Each night, we took a sky exposure with anexposure time as long as that of the longest scientific exposure. The sky levelwas negligible for all exposures withS/N>20, therefore exposures withS/N<20were neglected and we did not subtract the sky, to avoid adding noise to thespectra. Sky emission lines, even in the red part of the spectrum, onlyoccasionally affected the measurements of some absorption lines, which werediscarded. The spectral resolution wasfor all spectra.

2.1 Data reduction

Data reductions were done with IRAF within theimredandechelle packages. The following steps were performed: bias subtraction,flatfielding, order tracing with optimal extraction, background subtraction,wavelength calibration with the help of a Thorium-Argon lamp, and final merging(and rebinning) of overlapping orders. The one-dimensional spectra obtained fromdifferent exposures (withS/N>20) were median-averaged to produce one singlehighS/N spectrum for each star, used for equivalent width measurements(Sect. 3.3). Finally, the noisy ends of each combined spectrum were cut,allowing for an effective wavelength coverage from 5000 to 9000 Å.

Sky absorption lines (telluric bands of O₂ and H₂O) were removed using theIRAF tasktelluric with the help of two hot, rapidly rotating stars,HR 3982 and HR 8762, chosen from theBright Star Catalogue (Hoffleit & Jaschek 1991).HR 3982 and HR 8762 were observed each night at an airmass not too different fromthe scientific targets. Residuals of the correction in the red part of thespectrum (for example, from the strong O₂ band around 7600 Å) prevented usfrom using most of the corresponding spectral regions in our abundance analysis.Also, after 8400 Å, the echelle orders do not overlap anymore and small gapsappear.

2.2 Radial velocities

Radial velocities were measured with the help of DAOSPEC (Stetson & Pancino 2008, see alsoSect. 3.3). Measurements were based on360 absorptionlines of different elements (see Sect. 3) with typical measurementerrors on the mean of about 0.1 km s^-1. All measurements were performedseparately on the one-dimensional spectra extracted from the single exposures foreach star, including those withS/N<20, which were not used in the abundanceanalysis. In this way, we could check that no significant radial velocityvariations were present.

Table 2:  Heliocentric radial velocities measurements and their 1errors()for each program star.

Table 3:  Stellar parameters for the program stars.

Heliocentric corrections were computed with the IRAF taskrvcor,which bears a negligible uncertainty of less than 0.005 km s^-1. Sincewe did not observe any radial velocity standard and our calibration lamp datawere not acquired simultaneously, we used telluric absorption lines to findthe absolute zeropoint of our radial velocity measurements. Inparticular, laboratory wavelengths of the H₂O absorption bands around5800, 6500, 7000, 7200, 8000, and 8900 Å and the O₂ absorptionbands around 6300, 6900, and 7600 Å were obtained from theGEISA database(Jacquinet-Husson et al. 2005,1999) and we measuredtheir radial velocity in our program stars. The resulting zeropointcorrections, based on 200-250 telluric lines, amount to generally no morethan1 km s^-1 with typical errors in the mean of about0.5 km s^-1, approximately five times larger than those in the radialvelocity measurements.

After applying the above corrections, and propagating the correspondinguncertainties, we computed a weighted average of the heliocentric velocitiesestimates for each exposure (see Table 2). All the program starsappear to be radial velocity members of the observed clusters, the possibleexception being star 2108 in Cr 110, which has a slightly higher velocity thanboth 2129 and 3144. However, since the value for 2108 is within 3of themean value for the cluster, we decided not to reject this star. We can provide thefirst radial velocity estimate based on high resolution for Cr 110: km s^-1. Our determinations are generally in goodagreement with literature values within 3,except maybe for star 5237 inNGC 7789, which is marginally dicrepant with the estimate byGim et al. (1998b).However, there is perfect agreement between the two studies for theother twostars of NGC 7789, and our estimate appears more consistent withmembership of 5237. In conclusion, we considered all the programstars as likely radialvelocity members of their respective clusters.

2.3 Photometric parameters

We first computed the dereddened colors(B-V)₀, ()₀, and(V-K_TCS)₀. The adoptedE(B-V) valuesare indicated in Table 4, where)was obtained with thereddening laws byDean et al. (1978), andE(V-K_TCS) withCardelli et al. (1989). We werethen able to obtainand the bolometric correction BC_V foreach program star, using both theAlonso et al. (1999) and the (theoretical andempyrical)Montegriffo et al. (1998) color-temperature relations, taking into account theuncertainties in the magnitudes and reddening estimates. The average differencebetween theAlonso et al. (1999) and theMontegriffo et al. (1998) temperatures was K (for the empirical calibration ofMontegriffo et al. 1998) and K (for the theoretical calibrationofMontegriffo et al. 1998). We averaged all the aboveestimates to obtain ourphotometric reference values and their 1uncertainties(Table 3).

Gravities were obtained fromand BC_V using the fundamentalrelations

where red clump masses were derived using Table 1 ofGirardi & Salaris (2001),and are also shown in Table 3. We assumed that,,and,in conformitywith IAU recommendations (Andersen 1999). The difference between theAlonso et al. (1999) and the (empirical and theoretical, respectively)Montegriffo et al. (1998)estimates wasand.As above, we averaged all our estimates to obtain photometricgravities(Table 3) and their 1uncertainties.

Table 4:  Input cluster parameters.

Finally, a photometric estimate of the microturbulent velocitiesv_t wasobtained using the prescriptions of bothRamírez & Cohen (2003), i.e.,,andCarretta et al. (2004), i.e.,.The latter takes into account the systematic effect discussed byMagain (1984)and is on average lower by km s ^-1 than the one byRamírez & Cohen (2003). However, the correction for theMagain (1984) effect dependsstrongly on the data quality (i.e., resolution,S/N ratio, number of lines used,log gf values etc.). Therefore we chose not to average the two estimates, but touse them as an indication of the (wide)v_t range to explore in our abundanceanalysis (see Sect. 4.1).

3 Linelist, atomic data and equivalent widths

We created a masterlist of absorption lines by visually comparing our spectra withthe the UVES solar spectrum inthe range 5000-9000 Å, and with the linelists extracted from theVALD database (Kupka et al. 1999) andthe Moore (Moore et al. 1966)solar atlas. The masterlist was fed to DAOSPEC, andEW were measured for all ourprogram stars. A first selection was applied to reject all lines measured for 10stars or less (out of 15) and that hadEW systematically larger than 250 mÅ.Later, after performing a rough abundance analysis (see Sect. 4.1), werejected all lines that inferred systematically discrepant abundances, especiallyif the formal DAOSPEC relative error (,Fig. 2) was around 15% or more, and the DAOSPEC quality parameter was above 1.5 (for more detailsabout the DAOSPEC error and quality parameter, see Sect. 3.3). The finallinelist, including atomic data andEW measurements for all program stars,contains 358 absorption lines of 17 species, and can be found in the electronicversion of Table 5. Atomic data include laboratory wavelengths,excitation potentials, andvalues, which are always taken from the VALDdatabase with the exceptions listed below.

3.1-elements atomic data

The only-element for which we had clear problems with the atomic data wasmagnesium. The lines with eV (7060 and 7193 Å) gave discrepantabundances by1.5 dex with respect to the average of all Mg lines. Wecompared our VALD log gf with the NIST database of atomic data andnoticed a difference of 1.4 dex for the eV lines, while all theother Mg I lines had very similar log gf values in both databases. The NISTlog gf values abundances of the eV lines gave abundances inmuch closer agreement with the other Mg I lines and the literature Mgabundances for OC, therefore we used the NIST values for those lines, instead ofthe VALD ones.

Another element with uncertain log gf values is calcium.As an example, for the 9lines that we use, there is an average difference oflog gf-log gf dex, which is not statisticallysignificant given the large .The NIST log gf values for those 9 linesalso range from D to E, which means that they are largely uncertain. Finally, oursolar abundance (Sect. 4.6) gives(0.03) dexif we use the VALD log gf and [Ca/H] = +0.08  0.03 (0.03) dex with the NISTones, which is equally compatible with zero within 3.Summarizing, thereis large uncertainty in the calcium log gf determinations, and we shouldkeep in mind that there is an additional0.2 dex uncertainty in all [Ca/Fe]determinations in the literature.

For the synthesis of the [O I]-Ni I blend at 6300 Å, we used the VALD log gfvalue for oxygen, but we chose to use theJohansson et al. (2003) log gf for Ni I at6300.35 Å, which is lower (-2.11 dex instead of -1.74) and gives oxygenabundances more in line with the other-elements.

Table 5:  Equivalent widths and atomic data of the program stars. Thecomplete version of the table is available at CDS. Here we show a few linesto illustrate its contents.

Figure 2: The behavior of DAOSPEC relative errorsversus EW isshown ( top panel) and the 15error limit is marked with a dotted line. Thebehavior of the quality parameterQ is shown versus EW ( middle panel) andwavelength ( bottom panel), and theQ=1.5 limit is marked with a dotted line. SeeSect. 3.3 for more details. In all panels, grey dots represent all thelines measured by DAOSPEC, while black dots represent lines cross-identified withour input linelist.

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3.2 Heavy element atomic data

For neodymium, we could only find three reliable lines, which apparently did notneed any detailed HFS (hyperfine splitting) analysis (Aoki et al. 2001), at 5092,5249, and 5485 Å. However, the spread in their abundances was quite high(Table 7). The laboratory log gf value published byDen Hartog et al. (2003) arevery similar to those from VALD, except for the 5485 Å line, where they differby 0.14 dex. Therefore, since the log gf values byDen Hartog et al. (2003) slightlyreduced the spread in the [Nd/Fe], we used them instead of the VALD ones (seeTable 5).

3.3 Equivalent widths with DAOSPEC

The full description of how DAOSPEC works, including comparisons withthe literature and several experiments with artificial and real spectra,can be found inStetson & Pancino (2008). The instructions on how to install,configure and use DAOSPEC can be found in``Cooking withDAOSPEC''. Inshort, DAOSPEC is a Fortran program that automatically finds absorptionlines in a stellar spectrum, fits the continuum, measuresEW, andidentifies lines with a laboratory linelist; it also provides a radialvelocity estimate (Sect. 2.2).

As described in Sect. 3, we used the DAOSPEC errors and qualityparameter,Q, to select good absorption lines from our master linelist. Since ourspectra are rebinned linearly in wavelength, we scaled the FWHM with .Figure 2 shows their behavior. The formal error in the Gaussian fit thatDAOSPEC outputs is given by,andcan be used to selectgood measurements, since smaller lines are noisier and tend to have higherrelative errors. The quality parameter Q, instead, is the result of comparinglocal residuals around each line with average residuals for the whole spectrum. Asa resultQ tends to be worse for strong lines, because the Gaussian approximationdoes not hold so well. Also,Q becomes poorer at the blue side of the spectrum,where theS/N ratio is lower. In the region around 7700 Å, where the residualsof the prominent O₂ telluric band affect the measurements,Q reaches itsmaximum. The measuredEW for our program stars are shown in the electronic versionof Table 5 along with theandQ parameter estimated byDAOSPEC.

3.4 EW uncertainties

We used the formal errors in the Gaussian fit computed by DAOSPEC only toreject unreliable measurements from our initial line list. The actual abundanceerrors due to theEW measurement process itself were instead computed later,as explained in Sect. 4.3.

To compute theEW uncertainty related to the continuum placement, we used Eq. (7)fromStetson & Pancino (2008) to derive the effective uncertainty in the continuumplacement ()which was found to be significantly smaller than 1%. We first lowered the ``best-fit'' continuum level byandmeasured theEWs again, obtainingEW<sub>(-)</sub>, then we raised the level by the sameamount and measuredEW<sub>(+)</sub>. The differences from the ``correct''EWmeasurements,andwere averaged to estimatefor each line. The typical resultant uncertainty, due only to thecontinuum placement, was approximately constant withEW and mÅ approximately (see also Fig. 2 byStetson & Pancino 2008).This small uncertainty was neglected because it had a much smaller impact on theresulting abundances than other sources of uncertainty considered inSects. 4.3 and 4.4.

3.5 Comparison with literature EW

To our knowledge, only one of our target stars was studied before byYong et al. (2005) andTautvaisiene (2000), with a resolution andS/N similar to ours,i.e., star 141 in M 67. WhileYong et al. (2005) do not publish theirEWmeasurements, we can compare with those byTautvaisiene (2000). The authorsprovided two sets ofEW, the former derived from a spectrum with 000,and the latter from a spectrum with 000. We have 48 lines in commonwith the 000 set and 36 with the 000 set.

Figure 3 shows good agreement between ourEWs and the 000set. We only found a systematic offset ofEW_T00-EW mÅ, which corresponds to a continuumplacement difference of about 1% (see also Sect. 3.4). A possibletrend withEW was visible when comparing ourEWs with the 000 set,with no systematic offset ( mÅ). On the one hand, thismeans that our continuum placement is in far closer agreement with the 000 continuum determined byTautvaisiene (2000) than with the 000 one. On the other hand, we note that a possible trend is alsovisible when comparing theTautvaisiene (2000) measurements at 000 withthose at 000. In conclusion, we considered ourEW measurements to bein good agreement with theTautvaisiene (2000) ones, given the involved uncertainties(see also Table 6).

Figure 3: Comparison of our EW measurements withTautvaisiene (2000), for star 141 inM 67. The top panel shows the comparison of DAOSPEC EW with the set byTautvaisiene (2000), based on 48 lines in common. The middle panel show thesame comparison, but for theset byTautvaisiene (2000), based on 36 lines. The bottom panel shows the 15 lines in common between theand the 000 EW sets, considering only the lines included in the two upper panels.

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4 Abundance analysis

4.1 Best model search

A preliminary abundance determination was done using the photometric parameters(Sect. 4), which allowed us to identify and remove those lines in ourlist that gave systematically discrepant abundances. We found largely discrepantFe I and Fe II values when using the photometric parameters (by0.5-0.9 dex), indicating that something was wrong with the photometricgravities (Sect. 2.3).

As a second step, we calculated Fe I and Fe II abundances for a set ofmodels with parameters extending more than 3around thephotometric estimates of Table 3, i.e., about300-500 K in ,0.3-0.6 dex inand0.5 km s^-1in v_t, depending on the star. This large grid of calculatedabundances was used to refine our photometric estimate of theatmospheric parameters.

We chose the model that satisfied simultaneously (within theuncertainties) the following conditions:(i) the abundance of Fe I lines should not vary with excitation potential;(ii) the abundance of Fe I lines should not vary significantlywithEW, i.e., strong and weak lines should infer the same abundance;(iii) the abundance of Fe I lines should not differ sigificantly from theabundance of Fe II lines;(iv) the abundance of Fe I lines should not varysignificantly with wavelength.

Table 6:  Comparison of our results for star 141 in M 67 with the analysis ofTautvaisiene (2000) andYong et al. (2005).

Using the spreads in the Fe I and Fe II abundances of various lines, and theuncertainties in the slopes of the above conditions, we estimated the typical 1uncertainties in the spectroscopic parameters: about100 K for,0.2 dex for,and0.1 km s^-1 forv_t.

The resulting spectroscopic parameters (Table 3) were always in goodagreement with the photometric ones, within the quoted uncertainties, with atendency for the spectroscopic gravities to be systematically higher by0.3-0.5 dex (see above). However, these differences are always easilyaccommodated within the uncertainty ranges (related to photometric errors,uncertainties in distance moduli and reddenings, and bolometric corrections).

4.2 Abundance calculations

Abundance calculations and spectral synthesis (for oxygen) were performed usingthe latest version of the abundance calculation code originally described bySpite (1967). We used the model atmospheres byEdvardsson et al. (1993). We also made use ofABOMAN, a tool developed by Rossetti at the INAF, Bologna Observatory, Italy,that allows the semi-automatic processing of data for several objects, using theabove abundance calculation codes. ABOMAN performs all the steps needed to choosethe best model automatically, and provides all the graphical tools to analyze theresults.

Table 7:  Abundance ratios for sigle cluster stars, with their internal uncertainties (Sect. 4.3). For externaluncertainties see Table 9.

When the best model was found for each star, abundances and abundance ratios ofall the species of interest were calculated, by averaging the results for eachline of that element (Table 7). Abundance ratios were always computedwith respect to Fe I. Cluster averages were computed as weighted averages of theresults for each star in the cluster and, if necessary, of different ionizationstages of each element (Table 8). In all tables, [/Fe] isthe weighted average of all-elements abundances.

We can compare our results for star 141 in M 67 (see also Sect. 3.5)with those ofTautvaisiene (2000) andYong et al. (2005). We find general agreement forboth the atmospheric parameters and abundance ratios, with the only significantexception of barium (but see the discussion in Sect. 6.3), calcium(discussed in Sect. 6.2), and titanium. For all the elements discussed,our results, as discussed in Sect. 6, are in broad agreement with theentire collection of high resolution abundances for OC, so we consider our resultsto be robust.

Table 8:  Average cluster abundances, obtained with the weighted average of thesingle stars abundances.

4.3 Internal abundance uncertainties

Random uncertainties in theEW measurement process and in the loggfdeterminations were taken into account by averaging the abundances determinationsobtained for different lines and usingas the finalinternal error. These are reported in Table 7, and they are ofthe order of0.01 dex for Fe I, which had the highest number of lines, andcould reach up to0.2-0.3 dex for elements relying on a handful of linessuch as Nd, for example. Additional systematic (from line to line) and random(from star to star) uncertainties inEW measurements, related to continuumplacement, had a negligible impact on the final abundances in our specific case(Sect. 3.4).

For the spectral synthesis of oxygen, the uncertainty in the fit was computed bychoosing two spectra, one with abundance higher than the best fitting spectrum,and another one with lower abundance, each chosen to differ by approximately 1(of the poissonian noise) from the observed spectrum. The abundancedifference of the two ``altered'' spectra with the best-fit spectrum were averagedtogether to produce the estimated uncertainty, reported in Table 7 (andin our solar analysis, Table 10).

4.4 Uncertainties due to the choice of stellar parameters

The choice of stellar parameters implies systematic (from line to line) and random(from star to star) uncertainties in the final abundances. To estimate the impactof the stellar parameters choice on the derived abundances, each parameter isusually altered by its estimated uncertainty and the resulting abundancedifferences with respect to the best model parameter abundance set are summed inquadrature to obtain a global uncertainty. We applied this method to our coolest(508 in NGC 2099) and warmest star (2129 in Cr 110) and obtained various abundanceratio uncertainties ranging from 0.05 to 0.45 dex, with a typical value around0.10 dex.

However, as noted byCayrel et al. (2004), this method produces a very conservativeestimate of the uncertainty, because it neglects the natural correlation betweenstellar parameters that occurs when the so-called ``spectroscopic method''(Sect. 4.1) is adopted. Covariance terms should therefore be includedto properly take into account these dependencies among the parameters(seeMcWilliam et al. 1995, for a detailed treatment of the problem). The practical methodproposed byCayrel et al. (2004) assumes that, among the atmospheric parameters,has by far the strongest effect on the abundance results and,therefore,must be varied by its estimated uncertainty(100 K in our case, Sect. 4.1). A new ``second best'' modelmust then be identified with the new value ofby varyingv_t andaccordingly, to minimize as much as possible the slopes of the relationsdescribed in Sect. 4.1. This method naturally and properly takes intoaccount both the main terms of the error budgetand the appropriatecovariance terms.

We therefore altered the temperature of our hottest and coolest stars (see above)by both +100 K and -100 K. We reoptimized all the parameters and recalculated allthe abundance ratios. The final uncertainties are the average of the uncertaintiescalculated with the higher and lower temperature and are shown inTable 9. The average between the uncertainties in these two cases istaken as a reliable estimate of the impact of the choice of stellar parameters onour abundance ratios. We added theseexternal uncertainties betweenparentheses after each abundance ratio and we summed them in quadrature with theinternal errors to produce the errorbars in each figure.

Table 9:  Uncertanties due to the choice of stellar parameters for the coolest(second column) and the warmest (third column) of our programs stars (seeSect. 4.4).

4.5 Other sources of uncertainty

The following additional sources of systematic uncertainties are not explicitlydiscussed here, but should be taken into account when comparing our abundanceestimates with other works in the literature:

• systematic uncertainties related to the choice of the solar referenceabundances, which are not discussed here. Our abundances can be shifted to anysolar reference abundance with the information in Table 10;

• uncertainties due to the choice ofvalues, which can be estimatedby comparing ourvalues with other literature values (seeSect. 3.1);

• uncertainties in the entire analysis due to more sophisticated effects suchas, NLTE, HFS, isotope ratios, which are difficult to evaluate in some cases(these are mentioned whenever known or relevant in Sects. 3 and 6;

• small additional uncertainties related to the particular choices ofatmospheric model and abundance calculation code.

Table 10:  Solar abundance values.

4.6 The Sun

To test the entire abundance determination procedure, includingEW measurement,the choice of lines and atomic parameters, and the uncertainty determinationcriteria, we performed an abundance analysis of the Sun, and checked that weobtained solar values for all elements, within the uncertainties. We used the solarspectrum from the ESO spectrograph HARPS, in La Silla, Chile, obtained byobservingGanymede.The spectral resolution,,is comparable to ours, while theis much higher.

To measureEWs, we used DAOSPEC and the same linelist used for our program stars.We then compared our solarEWs with two different literature sets, the first byMoore et al. (1966) and the second byRutten & van der Zalm (1984). The median difference between ourEW and the ones by Moore is- mÅ (with aninterquartile range of2.7 mÅ), based on 225 lines in common, while the onewith theRutten & van der Zalm (1984) measurements is- mÅ (with an interquartile range of2.1 mÅ), based on 112 lines in common. Forcompleteness, we note that- mÅ (with aninterquartile range of2.8 mÅ), based on 390 lines in common. We aretherefore satisfied with our solarEW measurements.

We then performed our abundance analysis (as in Sect. 4.2) by exploringthe following atmospheric parameter ranges:-5800,in steps of 50 K;-4.5, in steps of 0.1 dex; andv_t=0.5-1.5, in steps of 0.1 km s^-1. The resulting best model has K, dex, andv_t=0.8 km s^-1, in good agreement with the accepted values (Andersen 1999).Our adopted reference solar abundances (Grevesse et al. 1996) are shown in Table 10,along with the abundance ratios derived as described. As can be seen, all thederived abundance ratios are compatible with zero, within the uncertainties, withthe exception of Al and Ba. For Al, only one ( Å) very weak(EW=18 mÅ)line could be measured in the solar spectrum, while we used about8 lines in the analysis of our red clump giants. The linesat 6696 and 6698 Å areknown to generally infer lower values than the other Al lines (Gratton et al. 2001;Reddy et al. 2003),so we do not worry too much about our lone 6698 Å solar line giving a low [Al/Fe] result. Wediscuss Ba in Sect. 6.3. For some elements (La, Mg, Nd, Y), no ratiocould be determined either because their lines appear too weak in the sun orbecause the solar spectrum range (5000-7000 Å) does not contain the lines thatwe used in this paper.

Table 11:  Literature abundance determinations for M 67 based on high resolutionspectroscopy.

5 Cluster-by-cluster discussion

5.1 Cr 110

Collinder 110 is a poorly studied, intermediate-age OC located atand:01:00.We could not find any high resolution spectroscopic study of this cluster in theliterature, but photometric studies were conducted byTsarevskii & Abakumov (1971),Dawson & Ianna (1998) andBragaglia & Tosi (2003). Reddening, distance, and ages determined bythese authors are included in Table 4. Concerning metallicity, whilethe first two studies assume solar metallicity,Bragaglia & Tosi (2003) find, as a resultof their synthetic diagram analysis, two equally good solutions, one at solarmetallicity and the other at slightly subsolar metallicity (Z=0.008). Are-evaluation of the same data byBragaglia & Tosi (2006) favours the slightly subsolarvalue.

Low resolution spectroscopy using the infrared calcium triplet byCarrera et al. (2007)gave: [Fe/H] = -0.01  0.07 dex in theCarretta & Gratton (1997) scale,[Fe/H] =  dex in theZinn & West (1984) scale, and [Fe/H] = -0.19  0.21 dex in theKraft & Ivans (2003) scale. Our determination of [Fe/H] = +0.03  0.02(0.10) dex is in good agreement with all these estimates, given the largeuncertainties involved in photometric and low-resolution spectroscopic metallicityestimates. The other element ratios determined here have no previous literaturevalues with which to compare, but the comparisons in Sect. 6 showthat they behave as expected for a solar metallicity OC. Our radial velocityestimate for Cr 110, km s^-1 (Sect. 2.2),is in good agreement with the CaT value determined byCarrera et al. (2007) of km s^-1.

5.2 NGC 2099 (M 37)

NGC 2099 (M 37) is located in the Galactic anticenter direction in Aurigaand.Since it is close-by and appears to be a relatively rich and large cluster, it hasbeen photometrically studied by several authors to derive accurate magnitudes andproper motions, and to complete a census of variable stars (for historicalreferences seeKalirai et al. 2001). All the papers that derived reddening, distance, andage are also cited in Table 4. Photometric studies generally attribute asolar metallicity to NGC 2099 (e.g.,Mermilliod et al. 1996). Metallicity estimates basedon photometry can only be found inJanes et al. (1988), who infer [Fe/H] = 0.09 dex,Marshall et al. (2005), who infer [M/H] = ,andKalirai & Tosi (2004), who inferZ<0.02.

Surprisingly, when considering the wealth of photometric studies, M 37 lacks anylow or high resolution spectroscopic study, designed to determine its chemicalcomposition. Our values therefore fill this gap, and show that in all respectsthis cluster has a typical solar metallicity, with all element ratios close tozero within the uncertainties. On the other hand, radial velocity determinationsfor this cluster have been quite numerous (Sect. 2.2) and appear in goodagreement with our determination.

5.3 NGC 2420

NGC 2420 (:38:23 and:34:24) has always been considered the definitiveexample of the older, moderately metal-deficient OC beyond the solar circle.Several good quality imaging studies appeared already in the 60 s and 70 s(Cannon & Lloyd 1970;van Altena & Jones 1970;West 1967b;McClure et al. 1978,1974;Sarma & Walker 1962, to name a few), and more recentphotometries appeared in a variety of photometric systems (the most citedbeingAnthony-Twarog et al. 1990). Its intermediate status between the solar-metallicity OC near thesun and the clearly metal-deficient population of globular clusters indicated itearly on as a potential transition object between the two populations, withmetallicity determinations - both photometric and spectroscopic - placing itat an [Fe/H] value around the one of 47 Tuc(e.g.,Cohen 1980;Smith & Suntzeff 1987;Pilachowski et al. 1980;Canterna et al. 1986). Photometric studies infer somewhathigher [Fe/H] values, ranging from -0.5 to -0.3 dex(e.g.,Friel et al. 2002;Twarog et al. 1997;Anthony-Twarog et al. 2006), but still significantly lower than the valueof [Fe/H] = -0.05  0.03 (0.10) dex that we found here.

However, bothCohen (1980) andPilachowski et al. (1980) noted that NGC 2420 should besignificantly more metal-rich than the globular clusters they analyzed, i.e., M 71(Cohen 1980) and 47 Tuc (Pilachowski et al. 1980), by some0.5 dex. Since they placedM 71 and 47 Tuc around [Fe/H] = -1.3, they consequently placed NGC 2420 at[Fe/H] = -0.6. The resolution of their spectra (R<10 000) was much lower thanours, but if we trust their analysis in a relative sense, and consider more recentmetallicity estimates for 47 Tuc and M 71 (-0.76 and -0.73,respectively,Harris 1996), we would then place NGC 2420 around [Fe/H]  -0.1or -0.2. Having said that, it is surprising that there are no modern highresolution studies of a cluster that was considered so important in the past. Thehighest spectral resolution employed to study NGC 2420 is(Smith & Suntzeff 1987), with a spectral coverage of only 200 Å, giving [Fe/H] = -0.57. Onlythe preliminary work ofFreeland et al. (2002) suggested a higher, slightly subsolar [Fe/H]value for NGC 2420. We also note that our [Fe/H] brings NGC 2420 more in line withother OC in the Galactic trends discussed in Sect. 7. Also, wecannot ignore the similarity with the case of NGC 7789 (Sect. 5.5),where analyses of high resolution spectroscopy byTautvaisiene et al. (2005) and us provide much higher abundances than the previous photometric and low/medium-resolutionstudies. Clearly, additional high resolution spectroscopy with modern instruments,possibly withandis needed for this cluster.

5.4 NGC 2682 (M 67)

Among the old OC, M 67 (,)is quite close to us, with low reddening(Table 4) and solar metallicity, so it is one of the most well studiedopen clusters, and a good target when searching for solar twins and analogs(Pasquini et al. 2008). Since the first pioneering studies at the beginning of XX century,a few hundred papershave been published to date (seeBurstein et al. 1986;Carraro et al. 1996;Yadav et al. 2008, for morereferences). Therefore, we have included M 67 in our samplebecause it acts as a fundamental comparison object that enables us to place ourmeasurements in a more general framework.

Among the vast literature on M 67, there are several determinations of itsmetallicity, with various methods (e.g.,Garcia Lopez et al. 1988;Friel et al. 2002;Foy & Proust 1981;Janes & Smith 1984;Cohen 1980;Janes & Phelps 1994;Balaguer-Núñez et al. 2007;Demarque 1980;Burstein et al. 1986;Friel & Boesgaard 1992;Friel & Janes 1993;Brown 1987;Marshall et al. 2005;Cayrel de Strobel 1990;Hobbs & Thorburn 1991;Burstein et al. 1984, to name afew),all typically converging to a solar value. high resolution abundancedeterminations have been derived for both giants and dwarfs, with many studiesbeing devoted to light elements such as lithium and beryllium and theirimplications for mixing theories (Randich et al. 2007;Jones et al. 1999;Pasquini et al. 1997).

Table 11 shows a comparison of our results with some of the most recenthigh resolution ( 000) determinations(Santos et al. 2009;Randich et al. 2006;Tautvaisiene 2000;Shetrone & Sandquist 2000;Pace et al. 2008). The overall comparison is extremelysatisfactory for all elements, except maybe for Mg, Na, Ba, and Ca (see alsoSect. 3.1). For Mg, Na, and Ba, the large spread in literaturedemonstrates the difficulties in measuring these elements. For Ca, we see that ourvalue is marginally lower than other literature deterrminations. As explained inSect. 3.1, this is most probably due to the large uncertainties on thecalcium log gf values.

Table 12:  Literature abundance determinations for NGC 7789 based onhigh resolution spectroscopy.

5.5 NGC 7789

NGC 7789 (and,orl=115.53 andb=-5.39) is a richand intermediate-age OC, with a clearly defined giant branch, a well-populatedmain-sequence turnoff, and a substantial population of blue stragglers(Twarog & Tyson 1985;McNamara 1980;Milone & Latham 1994). Several photometric studies have been carried out(some examplesareKustner 1923;Jahn et al. 1995;Bramich et al. 2005;Bartasiute & Tautvaisiene 2004;Gim et al. 1998a;Martinez Roger et al. 1994;Vallenari et al. 2000;Janes 1977;Burbidge & Sandage 1958;Reddish 1954) and itsparameters are reasonably well known.

Table 13:  Literature sources and [Fe/H] values for high resolution ()based abundance ratios of old OC.

Abundance determinations obtained from photometry and low/medium-resolutionspectroscopy all give subsolar values around [Fe/H]  -0.2(Friel et al. 2002;Friel & Janes 1993;Pilachowski 1985;Schönberner et al. 2001), i.e., much lower than our(0.10) dex. However, a more conforting comparison withTautvaisiene et al. (2005) is shown in Table 12. Their spectra have a resolution andS/N that is similar to ours, and most abundance ratios in common show excellentagreement. Minor discrepancies arise for some elements such as Ca (but see thediscussion in Sects. 3.1 and 5.4), Al (but they used onlyone doublet while we used four), Na, and O. Since they do not list their log gfvalues, and other ingredients of the abundance analysis were similar to ours, wecannot explain the Na-O discrepancies, but we suspect that they must be caused bylog gf differences.

6 Discussion of abundance ratios

We compared our abundance ratios with data from the literature, which wereassembled as follows. For the Milky Way field stars, we used the thick and thinGalactic disc measurements fromReddy et al. (2003) andReddy et al. (2006), who performedhomeogeneous abundance calculations of a few hundred F/G dwarfs selected from theHipparcos catalogue. We added abundance ratios, based on high resolutionspectroscopy, for 57 old OC from various literature sources(Table 13). When more than one determination was available for onecluster, we simply plotted them all to obtain a realistic idea of theuncertainties involved in the compilation.

Figure 4: Comparison between our iron-peak element results (large black dots), thehigh resolution measurements of other OC listed in Table 13 (largedark grey dots), and field stars belonging to the thin Galactic disc (lightgrey dots,Reddy et al. 2003) and to the thick Galactic disc (tiny light greydots,Reddy et al. 2006). Errorbars on our results are the quadratic sum of internaluncertainties and uncertainties due to the choice of stellar parameters(Sect. 4).

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6.1 Iron-peak element ratios

When compared with literature data (Fig. 4), our iron-peak elementsappear all solar and in good agreement with the results for the Galactic disc andother OC. In particular, cobalt and chromium are in the closest agreement and havethe smallest spreads. Although Sc, V, and Co are known to possess HFS that maylead to an increased scatter and an overestimated ratio, they do not appear todiffer significantly from solar for our target stars, so we did not attempt anydetailed HFS analysis. Nevertheless, the effect of increased scatter andoverestimated abundances are visible, expecially for vanadium, both in our dataand in the discs stars, as well as in the other clusters from the literature.

A puzzling effect is seen in Fig. 4 in the [Ni/Fe] ratio. All the datafor disc stars are very close to solar ( = -0.02  0.02), and so areour determinations (), but the other OC high resolutiondata appear slightly enhanced (), lying systematicallyabove the disc ones. Such a0.05 dex offset is well within theuncertainties of abundance determinations in general, but since it appearssystematic in nature, we are still left without a clear explanation. Our [Ni/Fe]ratios are slightly lower than the other OC determinations, although stillcompatible within the uncertainties.

	Figure 5: Comparison between our-element ratios and the literatureones. Symbols are the same as in Fig. 4.
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6.2-element ratios

We obtained abundances of Ca, Mg, O, Si, and Ti. As can be seen fromFig. 5, Si and Ti appear practically solar, within their respectiveuncertainties, and in very good agreement with literature determinations for boththe discs stars and those of the other OC. For O, Ca and Mg we instead findmarginally discrepant enhancements.

For O, we note that the spread in both our data and that of the literature isgreater that in any other-element. This is partly due to the well knownproblems of determining O from the single 6300 Å line, or the 6363 Å weakline, or from the IR triplet at 7770 Å(which requires NLTE corrections).Moreover, some literature works use Solar reference abundances that are as high as8.93, which may explain some of the lowest [O/Fe] literature estimates. Given thelarge spread, the tendency of our [O/Fe] measurements to lie on the upper envelopeof the other OC high resolution data is probably irrelevant. Solar O enhancementswould probably be more in line with those of the other-elements, whilethe subsolar values found generally in the literature suggests Wolf-Rayet asadditional contributors of O, with a stronger metallicity dependence of the O yields (McWilliam et al. 2008).

In the case of Ca, our values are marginally inconsistent with the bulk of fieldand OC literature determinations. A few literature measurements of OC ratios arehowever as low as our values. These inconsistencies could be explained by thelarge uncertainties in the literature log gf values for calcium lines(0.2 dex, see discussion in Sect. 3.1). Given these largeadditional uncertainties, we finally conclude that [Ca/Fe] is basically compatiblewith solar values in all the clusters examined.

Concerning Mg, we know already that the log gf values of some lines are stillnot very well determined (Sect. 3.1). We also know (Gratton et al. 1999) thatsome lines require NLTE corrections. We could find no correction factors for thelines that we were able to measure in our spectra, but we noticed that those linesexamined byGratton et al. (1999), which havevalues similar to our lines,require NLTE corrections of about +0.1-0.5 dex. This correction would make our[Mg/Fe] values even higher, reaching an enhancement of 0.2-0.6 dex with respectto solar. Another possibility is that our lines have a non-negligible HFS, becausethey are dominated by odd isotopes, but we could find no further information inthe literature. We only noted that other authors find such relatively high valuesof [Mg/Fe] in OC (such asBragaglia et al. 2008).

When the average [/Fe] values are calculated, however, all the programstars and the cluster averages appear perfectly compatible with solar, within therelatively small uncertainties, as expected (see Tables 7 and 8). The [/Fe] ratio is discussed also inSect. 7.

	Figure 6: Comparison between our s-process elements ratios and the literatureones. Symbols are the same as in Fig. 4, except for the blackstar-like symbols in the top [Ba/Fe] panel, which represent the revision of Ba abundances with spectral synthesis performed byD'Orazi et al. (2009).
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6.3 Heavy element ratios

We measured the heavy s-process elements Ba, La, and Nd and the light s-processelement Y. Lanthanum does not require any synthesis to take into account HFS,since the three lines that we used are always in the linear part of the curve ofgrowth, and Fig. 6 shows indeed good agreement with the sparseliterature values. Yittrium and neodimium are also in agreement with theliterature data, although the measurements of Nd in OC are few in number andexhibit significant scatter. Our values of [Nd/Fe] have a tendency to lie towardsthe upper envelope of the disc stars, but this is not significant if we considerthe large uncertainties involved (see also the discussion inSect. 3.2).

Concerning Ba, we find high values in both our program stars and the Sun itself(Sect. 4.6). The same result has been found by other authors(e.g.,Bragaglia et al. 2008). While a detailed study of the barium abundance is beyondthe scope of the present paper, we note that recentlyD'Orazi et al. (2009) used adetailed HFS analysis of barium in OC to show that the overabundance can thus bereduced by roughly0.2 dex. Looking at Fig. 6, we can see thatour [Ba/Fe] values are in general sligthly higher than the literature OC data,which in turn have a huge spread. Data fromD'Orazi et al. (2009), who revised the Baabundances for 20 OC using spectral synthesis to take HFS into account, aretowards the lower envelope of the OC abundances (open stars inFig. 6). As can be seen, some [Ba/Fe] enhancement remains in theirhigh quality data, which is apparently well correlated with the cluster ages (seetheir Fig. 1). However, no clear explanation is available yet, since the currentevolution models and yields do not reproduce the data correctly at young ages,where the enhancement is higher and more uncertain (up to [Ba/Fe]  0.6 dexfor ages around 10⁸ yr).

To summarize, most of the [Ba/Fe] enhancement that we see in our measurementsshould be produced by HFS effects, but some could be real (up to 0.2 dex,see Fig. 2 byD'Orazi et al. 2009).A hint of a negative slope of [Ba/Fe] vs. [Fe/H] in OC appears,that is not appareent among disc stars. Further studies similar to thatofD'Orazi et al. (2009) are necessary for large samples of disc and OC stars to placefirmer constraints on the chemical evolution of Ba in the Galactic disc.

	Figure 7: Comparison between our [Na/Fe] and [Al/Fe] ratios and the literaturevalues. Symbols are the same as in Fig. 4.
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6.4 Ratios of Na and Al and anticorrelations

We also derived Na and Al abundances, since these elements are quite easy tomeasure in OC and there is a vast body of literature measurements to compare with.Figure 7 shows that for Al there is general agreement between ourdata, the disc ratios, and the OC ratios, although there is a large scatter in theliterature data. The NLTE corrections for the four Al doublets and the type ofstars studied here could not be found in the literature.Baumüller & Gehren (1997) givecorrections for hotter ()and higher gravity ()stars, which suggest that either the corrections are negligible, or they areslightly negative at lower temperatures and gravities.

In the case of Na, the spread in the literature data is even larger, and there aredata points with both significant Na enhancement and typical solar values. Partof the scatter depends on the need for NLTE corrections. According toGratton et al. (1999), the 5682-5688 Å and the 6154-6160 Å doublets with mÅ both require corrections of about0.05-0.10 dex, forsolar stars such as those considered here. The NLTE-corrected abundances should behigher than the LTE-uncorrected ones: this should bring our [Na/Fe] LTEmeasurements to closer agreement with literature measurements. If the observedenhancement in [Na/Fe] should prove to be real for OC, this would set OC starscompletely apart form disc stars (De Silva et al. 2009). If the large spread were inaddition intrinsic, this would suggest that light element chemical anomalies aresimilar, although much less pronounced, to those found in globular clusters.

	Figure 8: A search for (anti)-correlations of Al, Mg, Na and O among our targetsstars. The four panels show different planes of abundance ratios, where starsbelonging to each cluster are marked with different symbols. Dotted lines showsolar values, solid lines show linear regressions and the typical uncertainty(0.1 dex) is marked on the lower right corner of each panel.
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Together with Mg and O (and C and N), Al and Na show puzzling (anti)-correlationsin almost all of the studied Galactic globular clusters (Gratton et al. 2004). The mostinteresting property of the chemical anomalies, is that they have never been foundoutside globular clusters. They are not present in the field populations of theMilky Way and its surrounding dwarf galaxies, and they have only more recentlybeen found in Fornax and LMC clusters (Letarte et al. 2006;Mucciarelli et al. 2009;Johnson et al. 2006). Dedicatedsearches for anticorrelations in OC include that ofMartell & Smith (2009), on the strengthof CH and CN bands in NGC 188, NGC 2158, and NGC 7789, that ofSmiljanic et al. (2009),based on high resolution spectroscopy of C, N, O, Na, and¹²C/¹³C andthat ofDe Silva et al. (2009), which compiles and homogenizes literature Na-O highresolution data. No clear-cut sign of any anticorrelation has yet been found.

If we make the usual (anti)-correlation plots for our five OC(Fig. 8), we find no clear sign of chemical anomalies, and in allfour plots the spread in each ratio is still compatible with the typicaluncertainty in our measurements, which is of the order of 0.1-0.2 dex, dependingon the element. In particular, in the [O/Fe]-[Na/Fe] plane, all 15 stars roughlyoccupy the solar region around zero that in Fig. 5 byCarretta et al. (2006) contains onlynormal only (see alsoDe Silva et al. 2009). A possible exception to this total absenceof correlations is the [Na/Fe]-[Al/Fe] plane, where a hint of a correlation canbe discerned. Statistically, this is not significant and small variations incould induce a similarly weak correlation. For this reason,anticorrelations are usually a more robust sign of chemical anomalies. In light ofthe discussion bySmiljanic et al. (2009) about a Na-O anticorrelation, our Na-Al results issuggestive. If future studies show that some chemical anomalies of these elementsare present in Galactic OC, our analysis (together with that ofSmiljanic et al. 2009)implies that they must be of a much smaller extent than in globular clusters,i.e., 0.2-0.3 dex at most in [Al/Fe], [Mg/Fe], [Na/Fe], and [O/Fe] for the kindof clusters studied here. In any case, the lack of relations for OC would pointtowards one or more of the following environmental causes for the presence ofanticorrelations in globular clusters:(i) relatively low metallicity (belowsolar);(ii) a dense local environment;(iii) total cluster mass ofthe order of10⁴ or more;(iv) an undisturbed positionin the Galaxy (e.g., away from the disc, see alsoCarretta 2006).

Figure 9: Trends in [Fe/H] ( top panel) and [/Fe] ( bottom panel) withGalactocentric Radius. Light grey dots in the top panel are OC fromFriel et al. (2002), grey dots are the OC compiled in Table 13 and blackdots are our data. NGC 2420 estimates by us andSmith & Suntzeff (1987) are connected with athick dotted line. A linear fit with its uncertainty range is drawn across allpoints in both panels.

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7 Galactic trends

As said earlier, OC are fundamental test particles in the study of the chemicalevolution of the Galactic disc, and as such, they produce two of the strongestconstraints on chemical models: the Galactic radial trends and the age-metallicityrelation (AMR). Since a careful homogeneization of literature data (including notonly element ratios, but also ages and Galactocentric radii) is beyond the scopeof the present paper, we used the literature data of Table 13,averaging all estimates for a single cluster together. We complemented our resultswith data byFriel et al. (2002) for those OC lacking high resolution measurements.Using 28 OC in common between the two datasets, we found an average offset of[Fe/H] = - dex, in the sense that the measurements byFriel et al. (2002)are on average lower than those based on high resolution data. We correctedFriel et al. (2002) data by this amount before plotting them. We extracted OC agesfrom the compilation ofDias et al. (2002), and for the Galactocentric radii()data we used primarilyFriel et al. (2002), complemented by the WEBDA,and obtained data points for the few missing clusters from the papers ofTable 13. The resulting radial trends and AMR for [Fe/H] and[/Fe] (computed as in Sect. 4.2) are plotted inFigs. 9 and10 and discussed below.

	Figure 10: Trends in [Fe/H] ( top panel) and [/Fe] ( bottom panel) withcluster ages. Symbols are the same as in Fig. 9.
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7.1 Trends with Galactocentric radius

The trends in the abundances with Galactocentric radiusprovide strong constraints on the models of Galactic chemical evolution as far as the discformation mechanism is concerned. It is now widely accepted (see forexampleFriel et al. 2002;Sestito et al. 2008;Magrini et al. 2009;Twarog et al. 1997;Yong et al. 2005) that there is a clear trend ofdecreasing metallicity, measured by [Fe/H], with increasing.Such atrend is clearly detected not only in OC, but also in field stars (B-stars andCepheids), H II regions, and planetary nebulae (seeAndrievsky et al. 2004;Lemasle et al. 2008;Chiappini et al. 2001;Yong et al. 2005, for some reviews of literaturedata).

The first large studies of homogeneous OC abundances (summarized in thereview byFriel 1995), found that old OC (older than the Hyades) extend outwards inthe disc, much farther out than young OC, and they found a clerly defined slopeout to kpc. The spread about this slope was at the time0.2 dex, i.e., generally compatible with (or perhaps slightly larger than)the measurement uncertainties. This slope follows naturally from most Galacticchemical evolution models (Tosi 1996;Andrievsky et al. 2004;Colavitti et al. 2009;Chiappini et al. 2001;Matteucci & Francois 1989;Tosi 1988,1982;Magrini et al. 2009), when different starformation and infall rates are assumed for the inner and outer disc. To reproducemost of the observational constraints, a differential disc formation mechanism isoften assumed, in which either the inner disk formed first and then grew in radius(inside-out formation) or the whole disk evolved simultaneously, but with a farmore intense (and sometimes fast) evolution in its central, denser parts. Aprediction of all models is that the metallicity gradient should change with time(although different models predict very different time changes;Tosi 1996)and some predict that it should flatten out at large radii. Indeed, the firststudies of anticenter and distant clusters (Sestito et al. 2008;Carraro et al. 2007;Yong et al. 2005;Carraro et al. 2004)showed that after kpc, the relation flattens to around avalue of [Fe/H]  -0.3 dex.

Not much can be said with the present data about the slope variation with time,but the exact value of the slope has been a matter of some debate. As said,earlier studies found a value of around -0.09  0.01 dex kpc^-1, or-0.07  0.01 dex kpc^-1 for the homogenous measurements byFriel et al. (2002).An alternative interpretation of a different data compilation (Twarog et al. 1997)describes the trend as two disjoint plateaux, one around solar metallicitycomprising OC within kpc, and a second one at [Fe/H]  -0.3 outside the solar circle. More recent work based on highresolution compilations of OC data (Sestito et al. 2008) find a steeper slope of-0.17  0.01 dex kpc^-1 within kpc, which still holds whenconsidering only the 10 clusters analyzed homogeneously by that group. A sort ofbimodal distribution is observed in their Fig. 9, where between the very steepslope of the inner clusters and the plateau of the outer ones there is a small gapthat is almost devoid of OC ( kpc).

Our results are plotted in Fig. 9, where we consider the trend in[Fe/H] and [/Fe] with.We do see a distinct slope in theinner clusters and a flattening out for the outer ones. However, our samplecontains15 more OC than that ofSestito et al. (2008), and most of them(including our five determinations) fall into the gap around kpc, discussed above. With the addition of these clusters,we find a gentler slope of -0.05  0.01 dex kpc^-1, in good agreement withprevious work (Friel et al. 2002;Friel 1995) and with the disk Cepheids within  11 kps (Andrievsky et al. 2004;Lemasle et al. 2008). If we exclude the clustersoutside kpc and remove the low resolution OC data fromFriel et al. (2002), the slope does not steepen significantly, becoming-0.06  0.02 dex kpc^-1. The flattening also does not seem so abrupt as inFig. 9 bySestito et al. (2008). The paucity of OC in the flat part of the relation (wehave only Be 20, Be 22, Be 29, and Saurer 1 in our compilation) surely calls formore high resolution studies, since as the data stand now, they look compatiblewith both a plateau and a gradual change in slope. We note that NGC 2420 (alreadydiscussed in Sect. 5.3) was found to have [Fe/H] = -0.57 dex bySmith & Suntzeff (1987), based on 000 spectra, while we find -0.05 dex, inmuch better agreement with the global Galactic trend. This goes in the directionof filling the gap in theSestito et al. (2008) compilation, and also in theTwarog et al. (1997) dataset, pointing more towards a gentle and continuous decrease in [Fe/H].

The trend in-enhancement withis also of some importance,because it constraints the role of SNe Type Ia and II and their relativecontributions.Yong et al. (2005) found a tendency for the-enhancement toincrease with,as didMagrini et al. (2009), who found this tendency to bein good agreement with their chemical evolution model. Model A byChiappini et al. (2001)also predicted an increase in [/Fe] with.In ourcompilation, the trend appears as a weak slope that is perfectly compatible with aflat distribution at the 1 level. This, together with the study of slopechanges with time, is one typical case in which a high quality, homogeneousanalysis of100 OC could provide a clear and definitive answer.

7.2 Trends with age

In spite of all models predicting an evolution of disk metallicity with time,albeit maybe only in the first Gyrs, and that this variation is indeed observed indisk stars (Reddy et al. 2003;Bensby et al. 2004), there appears to be no correlation at all betweenold OC abundances and ages (see the review byFriel 1995). More recent resultshave not changed this picture substantially. If confirmed, the lack of an AMR inOC would point towards a different source of chemical enrichment for OC stars(Yong et al. 2005) with respect to the disc stars. In essence, the metallicity of OC stars seems to be more dependent on the location in which they formed, than by thetime at which they formed.

What we find here is quite encouraging, although still not statisticallysignificant. We recall that our compilation includes 57 high resolution abundancedeterminations, plus a handful of low resolution determinations byFriel et al. (2002). Although we have made no attempt to homogeneize the data, exceptfor a -0.16 dex correction to the low resolution abundances, this sample is50% larger than any compilation presented before (seee.g.,Sestito et al. 2008;Magrini et al. 2009;De Silva et al. 2009) and shows that the community is proceeding fast infilling up the gaps in our knowledge of OC. Figure 10 indeed shows aweak trend of decreasing [Fe/H] and increasing [/Fe] with increasing age.The slopes are very gentle at most and are still compatible with no trends at all.Nevertheless, if these trends exist, we can place some constraints on them: for[Fe/H], the gradient should not be significantly greater than-2.6   dex Gyr^-1 and for [/Fe] no greater than dex Gyr^-1.

8 Summary and conclusions

We have analyzed high resolution spectra of three red clump giants in five OC,three of them lacking any previous high-resolution-based chemical analysis. Giventhe paucity of literature data, such a small sample is enough to increase theentire body of high resolution data for OC by5%. To compare our resultswith the literature, we have compiled chemical abundances based on high resolutiondata of 57 clusters from the literature. Given the rapid progress in the field,this sample is50% larger than previous literature compilations(e.g.,Friel et al. 2002;Sestito et al. 2008;Magrini et al. 2009). The main results drawn from the analysisof our five clusters are:

• We provide the first high-resolution-data based abundance analysis of Cr 110([Fe/H] = +0.03  0.02 (0.10) dex), NGC 2099 ([Fe/H] = +0.01  0.05(0.10) dex) and NGC 2420 ([Fe/H] = -0.05  0.03 (0.10) dex), whichpreviously had only measurements based on low resolution data, and the 000 analysis bySmith & Suntzeff (1987); our new determination of themetallicity of NGC 2420 places data for this cluster in far closer agreement withglobal Galactic trends.
• The abundances found for NGC 7789 ([Fe/H] = +0.04  0.07(0.10) dex) and M 67 ([Fe/H]= +0.05  0.02 (0.10) dex) are in goodagreement with past high resolution studies.
• We provide the first high-resolution-data based radial velocitydetermination for Cr 110 ( km s^-1).
• We found that all our abundance ratios, with few exceptions generallyexplained by technical details of the analysis procedure, are near-solar, as istypical of OC with similar properties; we also found solar ratios for Na, which isgenerally found to be overabundant, and for O, which is generally found to beunderabundant.
• We detected no significant anticorrelation (or correlation) among Na, Al,Mg, and O, in general agreement with past and recent results, and we can say thatif these correlations are indeed present in OC, they must be far less extendedthan in globular clusters, amounting to no more than 0.2-0.3 dex at most.

We warmly thank A. Bragaglia and A. Mucciarelli for their useful comments andsuggestions.We thank M. Tosi and D. Romano for their insights on the chemicalevolution modelling of the Milky Way and its Disks. We also warmly thank theCalar Alto Support staff for their hospitality and a good time together. R.C., C.G.and E.P. acknowledge support by the Spanish Ministry of Science and Technology(Plan Nacional de Investigación Científica, Desarrollo, e InvestigaciónTecnológica, AYA2004-06343). E.P. acknowledges support from the Italian MIUR(Ministero dell'Universitá e della Ricerca) under PRIN 2003029437,``Continuities and Discontinuites in the Formation of the Galaxy.'' R.C.acknowledges funding by the Spanish Ministry of Science and Innovation under theMICINN/Fullbright post-doctoral fellowship program.

References

Footnotes

... 2682)

Based on data collected with the fiber spectrograph FOCES at the 2.2 m Calar Alto Telescope. Also based on data from the 2MASS survey and the WEBDA, VALD, NIST, and GEISA online databases.

...

Full Table 5 is only available in electronic form at the CDS via anonymous ftp tocdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/511/A56

... stars

Although fainter than the brightest giants, redclump stars have the advantage of a higher gravity and temperature thatconsiderably reduces line crowding. Clump stars are also easy to identify even inthe sparsest clusters, maximizing the chance of choosing cluster members.

... WEBDA

http://www.univie.ac.at/webda

... 2MASS

http://www.ipac.caltech.edu/2mass. 2MASS (Two Micron All Sky Survey) is a jointproject of the University of Massachusetts and the Infrared Processing andAnalysis Center/California Institute of Technology, funded by the NationalAeronautics and Space Administration and the National Science Foundation.

... IRAF

Image Reduction and AnalysisFacility. IRAF is distributed by the National Optical Astronomy Observatories,which is operated by the association of Universities for Research in Astronomy,Inc., under contract with the National Science Foundation.

...GEISA

http://ara.lmd.polytechnique.fr/htdOC-public/products/GEISA/HTML-GEISA/

... colors

SinceR magnitudes are availablefor less than half of our sample, we decided to ignore them in the following.

...0

After dereddening, ()was alsoconverted into (V-I_J) using the prescription byBessell (1979), to be used withthe color-temperature relations byAlonso et al. (1999).

...V

We computed theK_TCS magnitudes from the 2MASS TCSmagnitudes using the prescription byKinman & Castelli (2002).

... spectrum

http://www.eso.org/observing/dfo/quality/UVES/pipeline/solar_spectrum.html

...VALD

http://www.astro.uu.se/ vald/

... Moore

ftp://ftp.noao.edu/fts/linelist/Moore

... NIST

http://physics.nist.gov/PhysRefData/ASD/index.html

...DAOSPEC''

http://www3.cadc-ccda.hia-iha.nrc-cnrc.gc.ca/community/STETSON/daospec/;http://www.bo.astro.it/ pancino/projects/daospec.html

...uncertainties

We basically considered a slope consistent with zero whenthe 3spread around the fit was larger than the maximum [Fe/H] differenceimplied by the fitted slope at the extremes of the interval covered by theabscissae (be it,EW or).

... abundance

Wedecided not to use theMagain (1984) effect, because we prefer to have internallyconsistent abundances from each line, and the difference in the measurements forthe two methods in our case appears small ( km s^-1).

...Ganymede

http://www.ls.eso.org/lasilla/sciops/3p6/harps/monitoring/sun.html

...Å

Because of the shorterspectral range of the solar spectrum and to spectral defects, we could onlymeasure one Al line in the Sun.

...Dias et al. (2002)

We are aware that at least in thecase of NGC 6791, the age given byDias et al. (2002) is quite different from otherliterature estimates (citations in Table 13), being lower by at least2 Gyr. However, building a homogeneous age scale is a non-trivial task, which isbeyond the scope of the present paper.

... concerned

A far stronger constraint would be thevariation in this trend with age. Such a study is at the moment not possible,given the small number of clusters studied with high resolution in a homogenousway.

... nebulae

However, we know of atleast one dataset in which PNe show flat trends in oxygen and neon abundances with(Stanghellini et al. 2006).

All Tables

Table 1:   Observing logs and program stars data.

Table 2:   Heliocentric radial velocities measurements and their 1errors()for each program star.

Table 3:   Stellar parameters for the program stars.

Table 4:   Input cluster parameters.

Table 5:   Equivalent widths and atomic data of the program stars. Thecomplete version of the table is available at CDS. Here we show a few linesto illustrate its contents.

Table 6:   Comparison of our results for star 141 in M 67 with the analysis ofTautvaisiene (2000) andYong et al. (2005).

Table 7:   Abundance ratios for sigle cluster stars, with their internal uncertainties (Sect. 4.3). For externaluncertainties see Table 9.

Table 8:   Average cluster abundances, obtained with the weighted average of thesingle stars abundances.

Table 9:   Uncertanties due to the choice of stellar parameters for the coolest(second column) and the warmest (third column) of our programs stars (seeSect. 4.4).

Table 10:   Solar abundance values.

Table 11:   Literature abundance determinations for M 67 based on high resolutionspectroscopy.

Table 12:   Literature abundance determinations for NGC 7789 based onhigh resolution spectroscopy.

Table 13:   Literature sources and [Fe/H] values for high resolution ()based abundance ratios of old OC.

All Figures

	Figure 1: V, (B-V) Color Magnitude Diagrams of the program clusters(from the WEBDA), with the location of our target stars.
Open with DEXTER
In the text

	Figure 2: The behavior of DAOSPEC relative errorsversus EW isshown ( top panel) and the 15error limit is marked with a dotted line. Thebehavior of the quality parameterQ is shown versus EW ( middle panel) andwavelength ( bottom panel), and theQ=1.5 limit is marked with a dotted line. SeeSect. 3.3 for more details. In all panels, grey dots represent all thelines measured by DAOSPEC, while black dots represent lines cross-identified withour input linelist.
Open with DEXTER
In the text

	Figure 3: Comparison of our EW measurements withTautvaisiene (2000), for star 141 inM 67. The top panel shows the comparison of DAOSPEC EW with the set byTautvaisiene (2000), based on 48 lines in common. The middle panel show thesame comparison, but for theset byTautvaisiene (2000), based on 36 lines. The bottom panel shows the 15 lines in common between theand the 000 EW sets, considering only the lines included in the two upper panels.
Open with DEXTER
In the text

	Figure 4: Comparison between our iron-peak element results (large black dots), thehigh resolution measurements of other OC listed in Table 13 (largedark grey dots), and field stars belonging to the thin Galactic disc (lightgrey dots,Reddy et al. 2003) and to the thick Galactic disc (tiny light greydots,Reddy et al. 2006). Errorbars on our results are the quadratic sum of internaluncertainties and uncertainties due to the choice of stellar parameters(Sect. 4).
Open with DEXTER
In the text

	Figure 5: Comparison between our-element ratios and the literatureones. Symbols are the same as in Fig. 4.
Open with DEXTER
In the text

	Figure 6: Comparison between our s-process elements ratios and the literatureones. Symbols are the same as in Fig. 4, except for the blackstar-like symbols in the top [Ba/Fe] panel, which represent the revision of Ba abundances with spectral synthesis performed byD'Orazi et al. (2009).
Open with DEXTER
In the text

	Figure 7: Comparison between our [Na/Fe] and [Al/Fe] ratios and the literaturevalues. Symbols are the same as in Fig. 4.
Open with DEXTER
In the text

	Figure 8: A search for (anti)-correlations of Al, Mg, Na and O among our targetsstars. The four panels show different planes of abundance ratios, where starsbelonging to each cluster are marked with different symbols. Dotted lines showsolar values, solid lines show linear regressions and the typical uncertainty(0.1 dex) is marked on the lower right corner of each panel.
Open with DEXTER
In the text

	Figure 9: Trends in [Fe/H] ( top panel) and [/Fe] ( bottom panel) withGalactocentric Radius. Light grey dots in the top panel are OC fromFriel et al. (2002), grey dots are the OC compiled in Table 13 and blackdots are our data. NGC 2420 estimates by us andSmith & Suntzeff (1987) are connected with athick dotted line. A linear fit with its uncertainty range is drawn across allpoints in both panels.
Open with DEXTER
In the text

	Figure 10: Trends in [Fe/H] ( top panel) and [/Fe] ( bottom panel) withcluster ages. Symbols are the same as in Fig. 9.
Open with DEXTER
In the text

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