Solar twins in M67
Key Words.:stars: fundamental parameters – open clusters and associations: individual: M67 – stars: late-type
Context:The discovery of true solar analogues is fundamental for a better understanding of the Sun and of the solar system. Despite a number of efforts, this search has brought only to limited results among field stars. The open cluster M67 offers a unique opportunity to search for solar analogues because its chemical composition and age are very similar to those of the Sun.
Aims:We analyze FLAMES spectra of a large number of M67 main sequence stars to identify solar analogues in this cluster.
Methods:We first determine cluster members which are likely not binaries, by combining proper motions and radial velocity measurements. We concentrate our analysis on the determination of stellar effective temperature, using analyses of line-depth ratios and H wings, making a direct comparison with the solar spectrum obtained with the same instrument. We also compute the lithium abundance for all the stars.
Results:Ten stars have both the temperature derived by line-depth ratios and H wings within 100 K from the Sun. From these stars we derive, assuming a cluster reddening , the solar colour and a cluster distance modulus of 9.63. Five stars are most similar (within 60 K) to the Sun and candidates to be true solar twins. These stars have also a low Li content, comparable to the photospheric abundance of the Sun, likely indicating a similar mixing evolution.
Conclusions:We find several candidates for the best solar analogues ever. These stars are amenable to further spectroscopic investigations and planet search. The solar colours are determined with rather high accuracy with an independent method, as well as the cluster distance modulus.
The specificity of the Sun and of our solar system have been the subject of active investigation over the last 5 decades. How typical is the Sun for a star of its age, mass, and chemical composition? How typical is that solar-type stars host planetary systems? Are they similar at all to ours?
The quest to find stellar analogues to the Sun has been going on for a long time (for an extensive review see, e.g., Cayrel de Strobel 1996), and it stems from the poor knowledge we have of the Sun when seen ‘as a star’ and from how typical the Sun is for a G2 type star, for its age, chemical composition, population. It is, however, after the discovery of the first exo-planets (Mayor & Queloz 1995) that this quest became even more compelling, because to find stars similar to our own would allow us to answer to fundamental questions related to the origin of the solar system, the frequency of planetary systems similar to ours, and eventually the formation of life in other exo-planetary systems (Cayrel de Strobel 1996). The need to identify in the night sky solar proxies to be used for spectroscopic comparison is also diffuse, in particular for the analysis of small solar system bodies (Böhnhardt, private communication).
Among the most recent results in this research, Meléndez et al. (2006) used high resolution, high signal-to-noise ratio Keck spectra to show that HD 98618 is a very close solar twin, and King et al. (2005) proposed HD 143436 after analyzing 4 stars pre-selected from literature. These stars seem to compare well with the best known solar twin, HR 6060, first analyzed by Porto de Mello & da Silva (1997), and subsequently confirmed by Soubiran & Triaud (2004), who made a comparative study of several hundreds of ELODIE spectra. Finally, Meléndez & Ramírez (2007) have shown HIP 56948 to be the best solar twin known to date both in stellar parameters and in chemical composition, including a low lithium abundance.
The open cluster M67 is a perfect target to search for solar analogues. Recent chemical analyses (Tautvaišiene et al. 2000; Randich et al. 2006; Pace et al. 2008), show that this cluster has a chemical composition (not only Fe, but also all the other elements) extremely similar to the solar one, as close as allowed by the high precision of the measurements. The analysis resulted in [Fe/H]=0.030.03 for Tautvaišiene et al. (2000), [Fe/H]=0.030.01 for Randich et al. (2006), and [Fe/H]=0.030.03 for Pace et al. (2008).
There are other two additional characteristics which make M67 strategical. The first one is that all the determinations of age give for this cluster an age encompassing that of the Sun (3.5-4.8 Gyr; Yadav et al. 2008), while the age determination for field stars is always uncertain. The second characteristic is that M67 is among the very few clusters showing Li depleted G stars (Pasquini et al. 1997). This is an important point because, as pointed out by Cayrel de Strobel (1996), even if many stars appear to have most characteristics similar to the Sun, their Li abundance is usually 10 times higher than in our star. Since Li is likely an indicator of the complex interaction taking place in the past between the stellar external layers and the hotter interior, the choice of stars which also share the same Li abundance with the Sun is an additional property to pinpoint the true analogues.
In our opinion, the search of analogues to the Sun and to the solar system can be well performed in open clusters (OCs), which show a homogeneous age and chemical composition, common birth and early dynamical environment. As a consequence, they provide an excellent laboratory for investigating the physics of solar stars and of planetary system evolution, besides being excellent probes of the structure and evolution of the Galactic disk.
M67 is a rich cluster, therefore it provides us with the opportunity to find many stars candidates sharing similar characteristics, and not only one. This is fundamental to obtain some meaningful statistics, and the cluster hosts many main sequence (MS) stars of mass around the solar mass, which form a continuous distribution (Fig. 1).
Finding several solar analogues in M67 will also help in providing an independent estimate of the solar colors, a quantity which still suffers of some relevant uncertainty (see, e.g., Holmberg et al. 2006), as well as an independent estimate of the distance modulus of the cluster.
The present paper is the culmination of a work, which involved the chemical determination of this cluster (Randich et al. 2006; Pace et al. 2008), photometry and astrometry (Yadav et al. 2008) to obtain membership, and FLAMES/GIRAFFE high resolution spectroscopy to clean this sample from binaries, and to look for the best solar analogues using the line-depth ratios method (Gray & Johanson 1991; Biazzo et al. 2007) and the wings of the H line (Cayrel de Strobel & Bentolila 1989) to determine accurate temperatures with respect to the Sun. In addition, the Li line is used to separate Li-rich from Li-poor stars.
2 Observations and data reduction
We obtained 2.5 hours in three observing nights in service mode with the DDT program 278.D-5027(A). Observations
were carried out with the multi-object FLAMES/GIRAFFE spectrograph at the UT2/Kueyen ESO-VLT (Pasquini et al. 2002)
in MEDUSA mode
We selected from the catalog of Yadav et al. (2008) the main sequence stars () with close to that of the Sun (0.60–0.75) with the best combination of proper motions parameters, that is a membership probability superior to 60%, and exclusion of candidates with a proper motion larger than 6 mas/yr with respect to the average cluster members. Full details about proper motion errors and selection criteria can be found in the original Yadav et al. (2008) work.
The log of the observations is given in Table 1. The observations were reduced using the ESO-GIRAFFE pipeline.
Radial velocities were measured using the IRAF
We note that the GIRAFFE solar spectrum
3 Data analysis and membership
3.1 Radial velocity
Out of the 90 stars observed, all selected on the proper motion and membership criteria given above, we found that 59 of them are probable single radial velocity (RV) members. We have retained all the stars which show RV variations smaller than 1 km s in the three exposures acquired and which have a mean velocity within 2 sigma (1.8 km s) from the median cluster RV. In Fig. 2 the histogram of the radial velocity distribution of these stars is shown, together with a Gaussian fit with =32.90 km s and a km s. In Table 4 the RV values are listed for the stars of the final sample, while in Table 5 the values of the single RV measurements are given for the stars we discarded.
In Fig. 3 we show the enlarged portion of the colour-magnitude diagram CMD containing the original sample; in this Figure the discarded and the retained stars are indicated with different colours. Many of the discarded stars tend to occupy the brighter side of the main sequence, where binaries are indeed expected to be present. On the other hand, our procedure still leaves several stars which are apparently above the photometric main sequence. This is because the radial velocity measurements are not of superb quality and because the time span by the observations is of only 18 days. Long period binaries will not be discovered by our three radial velocity observations. We shall see as seven stars clearly stand up also in the Magnitude – Temperature diagram (see Fig. 5) and they are best candidates for binaries of similar mass. We have kept them in the sample, and we anticipate that their presence does not influence our analysis or conclusions.
3.2 Effective temperature
Given that our targets are on the main sequence of a cluster of solar metallicity and age, the critical astrophysical parameters for the selection of the best solar analogues is the effective temperature. We have used two spectroscopic methods to compute the stellar effective temperature: the line-depth ratios and the H wings. To calibrate these methods we have used a grid of synthetic spectra, computed with SYNTHE from a grid of 1D LTE model atmospheres computed with version 9 of the ATLAS code (Kurucz 1993a, b) in its Linux version (Sbordone et al. 2004; Sbordone 2005). All the models have been computed with the “NEW” Opacity Distribution Functions (Castelli & Kurucz 2003) which are based on solar abundances from Grevesse & Sauval (1998) with 1 micro-turbulence, a mixing-length parameter of 1.25 and no overshooting. The grid of synthetic spectra covers the temperature range 5450–6300 K with [Fe/H]=0, =4.4377, =1 km s and was degraded to the resolution of the FLAMES/GIRAFFE spectra. We stress that for both methods these models are used to quantify the difference between the stellar spectra and the solar spectrum. Zero point shifts are most likely present, due, for instance, to limitations in the atmospheric models or to not perfect treatment of the H lines. While these inaccuracies will reflect in a wrong temperature for the Sun, the difference between the stars and the Sun will be much less affected.
It has been demonstrated that for stars with line-depth ratios (LDRs) are a powerful temperature
indicator, capable to resolve temperature differences lower than 10 K
(Gray & Johanson 1991; Catalano et al. 2002; Biazzo et al. 2007). Since our stars are within this range, we have
applied the LDR method to the members previously selected by radial velocity measurements (see
Table 4). To convert the line-depth ratios of our stars into effective temperature we
need to calibrate a temperature scale for the measured LDRs. To this purpose we have considered an initial
sample of about 100 lines of iron group elements (which are usually temperature sensitive) present in the
spectral range covered by our observations, from which we selected lines with the following characteristics:
weak (to avoid saturation effects), sensitive to temperature variations, and at the same time well measurable
in our spectra. The final selection contains six line pairs suitable to apply the LDR method; we measured
them in the synthetic spectra and then derived an LDR calibration for each pair.
In Table 2 we list for these six line pairs the wavelength, the element and the excitation
potential, as taken from the NIST
With this method the effective temperature of the observed GIRAFFE solar spectrum results in 579227 K, i.e. 15 K higher than the synthetic one (5777 K is the theoretical effective temperature of the solar atmosphere; Wilson & Hudson 1991).
We computed the temperature difference between the FLAMES/GIRAFFE targets and the Sun (as obtained from the six line-depth ratios and the summed spectra of the targets) as a function of the de-reddened colour (; Taylor 2007). The relationship for our targets is well described by a linear fit, which gives and an rms of 100 K.
In Fig. 5 the temperature-magnitude diagram is shown. The two colours of the symbols are referred to stars with lower and higher presence of lithium. Seven stars clearly stand out of the main sequence, suggesting a parallel binary sequence. They most likely are long period binaries with components of similar mass not detected as RV variable by our observations, because of the limited time base of our observations.
The wings of the H line profile are very sensitive to temperature, like all the Balmer lines, and depend only slightly on metallicity and gravity (Cayrel et al. 1985; Fuhrmann et al. 1993; Barklem et al. 2002). In particular, the spectral region in the range between 3 and 5 Å from the H line center is a good effective temperature diagnostic (Cayrel de Strobel & Bentolila 1989). With respect to the higher members of the series, the H line has considerable less blending in the wings, making easier the placement of the continuum. A further advantage, over other members of the series, is that it is rather insensitive to convection and in particular to the adopted mixing length parameter in 1D model atmospheres (Fuhrmann et al. 1993). Thus, we selected this region as temperature indicator and for each star we have compared the H line profile outside the core in our real spectrum against the synthetic profile. The hydrogen line profiles are computed in SYNTHE by routine HPROF4, which, for resonance broadening uses essentially the Ali & Griem (1965, 1966) theory, and for Stark broadening it calls routine SOFBET, written by Deane Peterson, which uses essentially the theory of Griem (1960), with modified parameters, so as to provide a good approximation to the Vidal et al. (1973) profiles (F. Castelli, private communication). For further details on the computations of hydrogen lines in SYNTHE, see Castelli & Kurucz (2001) and Cowley & Castelli (2002). The dominant broadening for H is resonance broadening, while Stark broadening becomes relevant for higher members of the series. In order to minimize the subjectiveness of the measurement, we have quantified the comparison between the synthetic profile and the observed one minimizing the rms of the subtraction. Continuum normalization is not easy for such a broad line, however, the fact of using a fiber instrument with a large coverage, minimize the subjectiveness of the process and makes it quite reproducible. Given the limited ratio of the observations, it is however very difficult to provide a realistic estimate of the involved uncertainties. The systematic errors in the effective temperature obtained from the H wings is given by Gratton et al. (2001), and the errors associated to the method have been discussed by, e.g., Bonifacio et al. (2007), where the dominant source of error for échelle spectra has been identified in residuals in the correction of the blaze function. The GIRAFFE spectra are fiber-fed and the flat-field is obtained through the same optical path as the stellar spectra, thus flat-fielding allows a better removal of the blaze function than it is possible for slit spectra. We have estimated for our stars an average error of 100 K. With this method the effective temperature of the Sun results in 5717100 K, i.e. 60 K lower than the solar real value. We note that the absolute temperature determined in this way depends critically on a number of assumptions in the model, and on the adopted broadening theory for H, and these produce a zero point shift of the Sun. The relative measurements, which are made with respect to the observed solar spectrum, are instead rather insensitive to all the assumptions used to build the synthetic profile.
A linear fit well describes the relationship between the temperature difference of the FLAMES/GIRAFFE targets and the Sun as obtained from the H wings, and the de-reddened colour: with an rms of 81 K.
The calibrations vs. obtained with the two methods agree quite well, as shown in Fig. 7; they have slightly different slopes which produce a maximum difference at the red edge () of the sample of 40 K (H temperatures are cooler). These relationships can be used to calibrate stars with metallicity close to solar. Our LDR vs. relationship has almost exactly the same slope of the Alonso et al. (1996) relationship, but it is hotter than this by 60 degrees. As a reference, the Alonso et al. (1996)’s scale produce an effective temperature for the Sun of 5730 K for a .
Lithium is an important element because it is easily destroyed in stellar interiors, and its abundance indicates the amount of internal mixing in the stars. Lithium in Pop I old solar stars varies by a factor 10 (Pasquini et al. 1994) and M67 is one of the few clusters which clearly shows this spread among otherwise similar stars (Pasquini et al. 1997).
Equivalent widths (EWs) of the lithium line at nm were computed using the IRAF task SPLOT; from measured EWs we derived Li abundances using the curves of growth (COGs) of Soderblom et al. (1993). At the GIRAFFE resolution the Li i lines are blended with the Fe i 670.744 nm line, whose contribution to the lithium blend was subtracted using the empirical correction of the same authors. Lithium abundances were then corrected for the NLTE effects using the prescriptions of Carlsson et al. (1994).
Fig. 6 shows the lithium abundance for the summed spectra of the 59 targets as a function of the effective temperature, as derived by the LDR method. The filled symbols refer to the LTE abundance, while the empty ones represent the non-LTE abundance. The difference between LTE and non-LTE values is minor. The blue points are the solar twins (see Section 4). The position of the Sun is shown at and K (see Section 3.2). The lithium abundance is listed in Table 4. Several solar twin candidates have Li abundances which are comparable with the Sun, whose value is 0.84 as measured by us on the GIRAFFE spectrum (see above), and 1.0 as measured in high resolution solar atlas (Müller et al. 1975). In most investigations the error associated to the effective temperature is usually the dominant one (100 K correspond to about 0.1 dex in ), but in this case, since we have good determination, but limited resolution and ratio, the uncertainty in the abundance associated to the equivalent width measurements is not negligible. The expected uncertainty in the measured lithium equivalent widths has been estimated from Cayrel (1988)’s formula:
where is the signal-to-noise ratio per pixel, is the full width of the line at half maximum, and the pixel size. The predicted accuracy, , is 3.0 mÅ for a typical ratio of 80 and of 1.6 mÅ for a ratio of 150. However, it should be noted that this formula neglects the uncertainty on the continuum placement. We estimate that, using homogeneous procedures for the determination of the continuum and the line widths, the statistical error for the weak lithium line is of the order of 2-3 mÅ, depending on the ratio of the co-added spectrum. This will correspond to an asymmetric error dex for a star with a line as weak as the Sun, and of dex for a star with a =2.2. Since the line is weak, the error (in percentage) is inversely proportional to the line strength. Given the errors, all the stars with upper limits in our sample may have a Li comparable to the solar one.
After the early works on M67, several Li surveys have been carried out of additional clusters well sampling the age metallicity space (Randich 2008 and references therein): out of nine clusters older than the Hyades with available Li measurements, only two, besides M67, show a significant dispersion. The latter seems to be an exception, rather than a rule and its occurrence does not depend on age, nor on metallicity, nor on global cluster parameters.
In this context, the novel result of our analysis and, in particular, of the careful selection and cleaning of the sample as well as of the precise effective temperature determination, is that the large spread is clearly present only for stars cooler than 6000 K. Stars warmer than 6200 K seem to show a decay, probably indicating the red side of the “Li-gap”, while stars in the 6000 K do not show any major scatter.
It is now well ascertained on empirical grounds that, in order to explain the MS Li depletion in solar-type stars, an extra or non-standard mixing mechanism must be at work. No consensus so far has been found on the nature of this mechanism; it is nevertheless clear that, whatever this process is, it must be driven by an additional stellar parameter besides mass and chemical composition. The presence of the Li spread indeed indicates that this parameter must vary from star to star, and that, depending on it, some stars (including the Sun) undergo a much more efficient mixing than others, while the absence of a dispersion for stars warmer than 6000 K suggests that this parameter is more uniform among F-type stars.
Recent modeling have had some success in reproducing the solar Li abundance by using fairly complex models which include internal gravity waves (Charbonnel & Talon 2005), however, those models are not able to reproduce the observed evolution of Li with age, and, in particular, the “plateau” in Li abundances at old ages (Randich 2008). We are not aware of similar models for a grid of masses, to be compared to our observations; since the number of possible parameters which influence the Li evolution is very large (depth of convective zone, initial rotation, magnetic field, mass losses and torques just to mention a few), we cannot really predict at present why the extra mixing takes places at a given in M67 stars.
4 Solar analogues
With the aim to find the best solar analogues, we have compared to (Fig. 7).
There are in our sample 10 stars for which both the and are within 100 K of the solar values (285, 637, 1101, 1194, 1303, 1304, 1315, 1392, 1787, 2018). We will use these stars to find the best solar analogues and our best evaluation for the solar colours and the cluster distance. These stars are indicated in bold face in Table 4.
The average difference between these 10 stars and the solar is of 13 K (with a sigma of 60 K), while the average is =9 K, with a sigma of 58 K. The average characteristics of these 10 stars should therefore well represent the solar values.
The average of the ten analogues is (), their average magnitude is mag (), and the (). The spread is larger than the formal errors in the photometry, indicating a possible real spread in the stellar characteristics. This is not surprising because, formally, these stars may span a range of up to 200 K in temperature.
If we take our results of Table 3, two stars (637 and 1787) have both determinations within 50 K from the solar values, and three additional ones (285, 1101, 1194) within 60 K; these 5 stars are overall the closest to the Sun, with nominal effective temperatures derived with both methods differing less than 60 K from the solar one. Their average magnitude (14.557 mag) is very similar to what found for the full subsample of 10, as well as their average colour (0.688) just 0.007 magnitude bluer than the whole subsample.
All the data in our possession indicate that some of these stars have a metallicity very close (within 0.03 dex; note that also their Li abundance is comparable; see previous Section) to the Sun, they have a very similar temperature (within 50 K), as well as a comparable age to the Sun, and they are true main sequence stars. To the best of our knowledge they are the best candidates in M67 to be the closest analogues to our star.
In Figure 8 we compare the GIRAFFE spectrum of the Sun with the sum of the spectra of the 10 best stars analogues and of the 5 best analogues in a portion of the spectra which includes H and in another including the Li lines. The extremely small difference between the solar spectrum and these co-added spectra confirm quantitatively the very close resemblance of these stars to the Sun.
At the request of the referee we performed also a direct comparison between the solar spectrum and the spectrum of our solar analogs. We used a minimization using a Doppler shift and a re-adjustment of the continuum of the stars of M67 as free parameters, in order to match the observed spectra to the observed GIRAFFE solar spectrum. The reduced of the fit, or the associated probability, then provides a mean to rank the M67 stars. We restricted the comparison to a range of 10 Å centered on H. While in the fitting of the synthetic spectra the core of the line was excluded from the fitting range, it was here included. The LTE synthetic spectra fail to reproduce the core of H due to the presence of a chromosphere (absent in the model atmospheres employed by us) and to NLTE effects. Instead, the sought-for solar analogs must behave exactly like the Sun, including in the core of H. With this method the three M67 stars which are most similar to the Sun are the stars 1194, 1101 and 637. The result is thus very similar to what obtained by comparing the observed spectra to synthetic spectra, confirming that the stars we selected are very similar to the Sun. We prefer the method based on synthetic spectra, since the direct comparison to the solar spectrum is affected by the noise present in the latter.
5 Solar Colour
We would like finally to use the observed colour of the solar analogues to derive in an independent way the colour of the Sun, and this requires to evaluate the cluster reddening.
The reddening towards M67 has been evaluated by many authors in the last 50 years, and a thorough discussion is given by Taylor (2007). M67 reddening is evaluated by this author in , which is accidentally the same value obtained by An et al. (2007) as the average point of the traditionally accepted range for the cluster. We will therefore adopt this value. This implies that the de-reddened colour for the average of our 10 solar analogues is .
The value is in excellent agreement with what found by inverting the fit of all the stars using the , which would have predicted and the value obtained by inverting the fit of , which would give .
It is not simple to evaluate a realistic error estimate for this colour. This should include: the spread (0.020 mag) around our determination, the uncertainty in the cluster reddening, plus other systematics originating from stellar evolution and photometry. We evaluate the evolutionary effects by investigating the expected variations of the solar color with age and metallicity by using evolutionary models. Photometric uncertainties are estimated by comparing Yadav et al. (2008) photometry with what obtained for this cluster by other groups.
We use the tracks from Girardi et al. (2000) for analyzing differential evolutionary effects. Because our stars have a similar effective temperature to the Sun, age has no influence: for stars younger than 5 Gyr of solar , the visual absolute magnitudes and colours do not change in any appreciable way. If M67 were younger than the Sun, the only effect would be that the masses of our stars were higher, by about 1%, than the solar one, but no difference is predicted in magnitude or colours. The other source of systematic uncertainty is the possibility that metallicity is not exactly solar. In this case, for a fixed effective temperature, we do expect that a star more metal rich by 0.05 dex would be slightly brighter (0.08 magnitude in ) and slightly redder (0.01 mag) than the Sun.
Our photometry is taken by Yadav et al. (2008), which was calibrated on Sandquist et al. (2004). In order to check for photometric systematic errors, we have compared our values for the 10 best analogues with Montgomery et al. (1993), finding that using their photometry an average =0.650 would have been found, i.e. only 1 mmag bluer than our value. Sandquist et al. (2004) made on the other hand a general comparison between his colours and those of Montgomery et al. (1993), finding an overall zero point shift in of 8 mmag (the Sandquist’s are bluer than the Montgomery ones). The fact that the agreement for these 10 solar stars is better than this systematic shift might be due to a statistical fluctuation, it is on the other hand quite common that calibrations agree at best for solar stars. We will nevertheless consider a 0.008 uncertainty in the colour as introduced by the adopted photometry.
The simple average of the most recent estimate of the M67 metallicity gives [Fe/H]=0.01. This would require a correction of 2 mmag towards the blue for the solar colors derived from the M67 stars to compensate for their higher metallicity. We conclude that a solar is our present best estimate. The uncertainties associated are 0.006 magnitudes given by the spread of our solar analogues divided by the square root of number of our solar analogues (namely 10); a 0.007 magnitudes given by a generous uncertainty in the cluster metallicity (0.03). Zero points uncertainties in photometry are the dominant source and they account for 0.008. All these errors are summed quadratically. To this, the uncertainty in the cluster reddening determination, which is assumed to be 0.004 mag (Taylor 2007; An et al. 2007), is linearly added.
An additional hidden source of systematic effects, which might add a bias towards redder colours, might be present, and this is the presence of unidentified binaries. A typical red, faint companion will make the stars to appear slightly brighter and slightly redder than what they should be, still influencing very little the spectroscopic determination. Given our radial velocity selection, only a few binaries should be left in our sample, and with low mass objects. We cannot quantitatively account for their presence, but we shall keep this possibility in mind.
The value found is somewhat in the middle between the majority of the ‘old’ determinations (see Table 2 of Barry et al. 1978, which found =0.667 averaging most of previous measurements), and the most recent determinations, which, as summarized, for instance, by Holmberg et al. (2006), tend to find in the range between 0.62 and 0.64. None of these results are formally in disagreement with ours, but we can exclude the estimates at the edges of the distribution.
We think that this estimate is very robust, because our results are based on a very few steps and assumptions. We assume that the metallicity of M67 is essentially solar, and this fact is agreed on by all latest works. We determine the in a differential way from the Sun, on spectra taken with the same instrument, and using two sensitive methods (line-depth ratios and H wings). We prove that the stars are indeed very close to the Sun showing how their spectra overlap with the solar one. The stars observed are still on the main sequence.
6 Cluster distance
The average magnitude of the 10 solar analogues is 14.583 mag, which must be corrected for reddening: =3.10.041=0.127, implying a de-reddened magnitude of 14.456. With a solar absolute magnitude of 4.81 (Bessell et al. 1998), the distance modulus of M67 is of 9.65. As mentioned in the previous Section, a correction might be needed if the metallicity differs substantially from the solar one (of up to 0.08 magnitudes for [Fe/H]=0.05, but we consider such a large difference in metallicity very unlikely). A correction of 0.002 mag, corresponding to a metallicity of [Fe/H]=0.01 (used in the previous Section) would bring to a distance modulus of 9.63.
This determination is in excellent agreement with two recent determinations: An et al. (2007) who estimate a distance modulus of 9.61 and Sandquist et al. (2004), who find 9.60, both using the same reddening we adopted.
The associated error given by the spread around the average magnitude is of 0.060 (i.e. 0.19/) magnitudes. Other sources of uncertainty in the distance modulus will be given by the error in reddening, which accounts for 0.012 magnitudes, and by the uncertainty on [Fe/H]. If we assume an error on [Fe/H] of 0.03 dex, this accounts for 0.05 magnitudes in the distance modulus. Summarizing, our best estimate of the distance modulus is: 9.63.
A full comparison of our estimate with those present in literature is beyond the scope of this work. We find however remarkable the agreement between our distance estimate and the ones of Sandquist et al. (2004) and An et al. (2007) in particular when considering that our method is independent with respect to theirs.
By using selected observations with FLAMES/GIRAFFE at the VLT, we have made a convincing case that the open cluster M67 hosts a number of interesting potential solar twins, and we have identified them. We have computed spectroscopic accurate effective temperatures for all the stars with two methods. The color-temperature relationships we derive can be used to determine temperatures for MS solar-metallicity stars.
By computing the average solar twin colours, we have obtained a precise estimate of the solar : .
By averaging the magnitude of the solar twins, we have determined an accurate distance modulus for M67: 9.63, which is in excellent agreement with the most recent estimates, which were based on different, independent methods and data sets.
We have determined for all the stars Li abundances, confirming the presence of a large Li spread among the solar stars of this cluster, but showing for the first time, that the Li extra-depletion appears only in stars cooler than 6000 K. The candidate solar twins have Li abundance similar to that of our star, indicating that they also share with the Sun a similar mixing history.
Acknowledgements.We are grateful to F. Castelli for helping us to understand how hydrogen profiles are computed in SYNTHE. KB has been supported by the ESO DGDF 2006, and by the Italian Ministero dell’Istruzione, Università e Ricerca (MIUR) fundings. PB acknowledges support from EU contract MEXT-CT-2004-014265 (CIFIST). This research has made use of SIMBAD and VIZIER databases, operated at CDS (Strasbourg, France).
Appendix A On line material
- thanks: Based on observations collected at the ESO VLT, Paranal Observatory, Chile, program 278.D-5027(A).
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- This is the observing mode in FLAMES in which 132 fibers with a projected diameter on the sky of 12 feed the GIRAFFE spectrograph. Some fibers are set on the target stars and others on the sky background.
- IRAF is distributed by the National Optical Astronomy Observatory, which is operated by the Association of the Universities for Research in Astronomy, inc. (AURA) under cooperative agreement with the National Science Foundation.
- National Institute of Standards and Technology.
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