The Solar Twin Planet Search. I. Fundamental parameters of the stellar sample
I. Ramirez, J. Melendez, J. Bean, M. Asplund, M. Bedell, T. Monroe, L. Casagrande, L. Schirbel, S. Dreizler, J. Teske, M. Tucci Maia, A. Alves-Brito, P. Baumann
aa r X i v : . [ a s t r o - ph . S R ] A ug Astronomy&Astrophysicsmanuscript no. ms c (cid:13)
ESO 2018September 18, 2018
The Solar Twin Planet Search
I. Fundamental parameters of the stellar sample
I. Ram´ırez , J. Mel´endez , J. Bean , M. Asplund , M. Bedell , T. Monroe , L. Casagrande ,L. Schirbel , S. Dreizler , J. Teske ⋆ , , , M. Tucci Maia , A. Alves-Brito , and P. Baumann McDonald Observatory and Department of Astronomy, University of Texas at Austin, USAe-mail: [email protected] Departamento de Astronomia do IAG / USP, Universidade de S˜ao Paulo, Brazil Department of Astronomy and Astrophysics, University of Chicago, USA Research School of Astronomy and Astrophysics, Mount Stromlo Observatory, The Australian National University, Australia Institut f¨ur Astrophysik, University of G¨ottingen, Germany Steward Observatory, Department of Astronomy, University of Arizona, USA Department of Terrestrial Magnetism, Carnegie Institution of Washington, USA The Observatories of the Carnegie Institution For Science, Pasadena, California, USA Instituto de Fisica, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, Brazil Una ffi liatedReceived — –, —; accepted — –, — ABSTRACT
Context.
We are carrying out a search for planets around a sample of solar twin stars using the HARPS spectrograph. The goal ofthis project is to exploit the advantage o ff ered by solar twins to obtain chemical abundances of unmatched precision. This survey willenable new studies of the stellar composition – planet connection. Aims.
We determine the fundamental parameters of the 88 solar twin stars that have been chosen as targets for our experiment.
Methods.
We used the MIKE spectrograph on the Magellan Clay Telescope to acquire high resolution, high signal-to-noise ratio spec-tra of our sample stars. We measured the equivalent widths of iron lines and used strict di ff erential excitation / ionization balance analy-sis to determine atmospheric parameters of unprecedented internal precision: σ ( T e ff ) = σ (log g ) = . σ ([Fe / H]) = .
006 dex, σ ( v t ) = .
016 km s − . Reliable relative ages and highly precise masses were then estimated using theoretical isochrones. Results.
The spectroscopic parameters we derived are in good agreement with those measured using other independent techniques.There is even better agreement if the sample is restricted to those stars with the most internally precise determinations of stellarparameters in every technique involved. The root-mean-square scatter of the di ff erences seen is fully compatible with the observa-tional errors, demonstrating, as assumed thus far, that systematic uncertainties in the stellar parameters are negligible in the study ofsolar twins. We find a tight activity–age relation for our sample stars, which validates the internal precision of our dating method.Furthermore, we find that the solar cycle is perfectly consistent both with this trend and its star-to-star scatter. Conclusions.
We present the largest sample of solar twins analyzed homogeneously using high quality spectra. The fundamental pa-rameters derived from this work will be employed in subsequent work that aims to explore the connections between planet formationand stellar chemical composition.
Key words. stars: abundances – stars: fundamental parameters — stars: planetary systems
1. Introduction
Planets form by sequestering refractory and volatile materialfrom protoplanetary disks. This process may a ff ect the chemi-cal composition of the gas accreted during the final stages of starformation. Therefore, it can potentially imprint its signatures onthe composition of the outermost layers of the host stars. Also,the composition of the nebula that stars and their accompany-ing planetary systems form out of may influence the number andtype of resulting planets. Thus, there may be a connection be-tween the chemical composition of stars and the presence andcomposition of di ff erent types of planets.The classic example of the relationship between stellar abun-dances and planets is the observed higher frequency of giantplanets around stars of higher metallicity (e.g., Gonzalez 1997;Santos et al. 2004; Valenti & Fischer 2005; Ghezzi et al. 2010). ⋆ Carnegie Origins Fellow
Other signatures of planet formation are harder to detect becausethey are expected to be at the 1 % level, or lower (Chambers2010). Nevertheless, this level of precision can be achieved bystudying solar twins (Cayrel de Strobel 1996), stars which arespectroscopically very similar to the Sun. This is because themany systematic e ff ects that plague classical elemental abun-dance determinations can be eliminated or minimized by a strictdi ff erential analysis between the solar twins and the Sun.In the past few years, the study of solar twins has revealedthree potential signatures of planet formation in addition to theplanet-metallicity correlation: – i) a deficiency of about 0.1 dex in refractory material rel-ative to volatiles in the Sun when compared to solar twins In the standard elemental abundance scale: [ X / H ] = A X − A ⊙ X , where A X = log( n X / n H ) +
12 and n X is the number density of X nuclei in thestellar photosphere. 1. Ram´ırez et al.: Fundamental parameters of solar twins (Mel´endez et al. 2009; Ram´ırez et al. 2009, 2010), with atrend with condensation temperature that could be ex-plained by material with Earth and meteoritic composition(Chambers 2010), hence suggesting a signature of terrestrialplanet formation (see also Gonz´alez Hern´andez et al. 2010,2013; Gonzalez et al. 2010; Gonzalez 2011; Schuler et al.2011b; Mel´endez et al. 2012); – ii) a nearly constant o ff set of about 0.04 dex in ele-mental abundances between the solar analog componentsof the 16 Cygni binary system (Laws & Gonzalez 2001;Ram´ırez et al. 2011; Tucci Maia et al. 2014), where the sec-ondary hosts a giant planet but no planet has been detectedso far around the primary (see also Schuler et al. 2011a); – iii) on top of the roughly constant o ff set between the abun-dances of 16 Cygni A and B, there are additional di ff erences(of order 0.015 dex) for the refractories, with a condensationtemperature trend that can be attributed to the rocky accre-tion core of the giant planet 16 Cygni B b (Tucci Maia et al.2014).In order to explore the connection between chemical abun-dance anomalies and planet architecture further, we have anongoing Large ESO Program (188.C-0265, P.I. J. Mel´endez)to characterize planets around solar twins using the HARPSspectrograph, the worlds most powerful ground-based planet-hunting machine (e.g., Mayor et al. 2003). We will exploit thesynergy between the high precision in radial velocities that canbe achieved by HARPS ( ∼ − ) and the high precisionin chemical abundances that can be obtained in solar twins ( ∼ .
01 dex). This project is described in more detail in Section 2.In this paper we present our sample and determine a homoge-neous set of precise fundamental stellar parameters using com-plementary high resolution, high signal-to-noise ratio spectro-scopic observations of solar twins and the Sun. In addition, weverify the results with stellar parameters obtained through othertechniques. Also, stellar activity indices, masses, and ages areprovided. The fundamental stellar properties here derived will beused in a series of forthcoming papers on the detailed chemicalcomposition of our solar twin sample and on the characterizationof their planets with HARPS.
2. HARPS planet search around solar twins
Our HARPS Large Program includes about 60 solar twins, sig-nificantly expanding the hunt for planets around stars closely re-sembling the Sun. This project fully exploits the advantage of-fered by solar twins to study stellar composition with unprece-dented precision in synergy with the superior planet hunting ca-pabilities o ff ered by HARPS.In the planet search program we aim for a uniform and deepcharacterization of the planetary systems orbiting solar twinstars. This means not only finding out what planets exist aroundthese stars, but also what planets do not exist. We have designedour program so that we can obtain a consistent level of sensi-tivity for all the stars, to put strict constraints on the nature oftheir orbiting planets. We emphasize that we are not setting outto detect Earth twins (this is about one order of magnitude be-yond the present-day capabilities of HARPS) but we will makeas complete an inventory of the planetary systems as is possi-ble with current instruments in order to search for correlationsbetween abundance signature and planet properties. This value of instrumental precision has in fact been confirmed inour existing HARPS data for the least active star.
Our HARPS Large Program started in October 2011 and itwill last four years, with 22 nights per year that are broken upinto two runs of seven nights and two runs of four nights. Oursimulations of planet detectability suggest that a long run persemester aids in finding low-mass planets, while a second shorterrun improves sampling of longer period planets and helps elim-inate blind spots that could arise from aliasing. We set the min-imum exposure times to what is necessary to achieve a photon-limited precision of 1 m s − or 15 minutes, whichever is thelongest. The motivation for using 15 minute minimum total ex-posure times for a visit is to average the five-minute p -modeoscillations of Sun-like stars to below 1 m s − (e.g., Mayor et al.2003; Lovis et al. 2006; Dumusque et al. 2011). For the bright-est stars in our sample we take multiple shorter exposures over15 minutes to avoid saturating the detector. Simulations indi-cate that the precision, sampling, and total number of measure-ments from our program will allow us to be sensitive to planetswith masses down to the super-Earth regime (i.e. < M ⊕ ) inshort period orbits (up to 10 days), the ice giant regime (i.e. 10– 25 M ⊕ ) in intermediate period orbits (up to 100 days), and thegas giant regime in long period orbits (100 days or more).In Figure 1, we show the radial velocities of four stars withvery low levels of radial velocity variability, corroborating thata precision of 1 m s − can be achieved. In Figure 2 we show theRMS (root-mean-squared scatter) radial velocities for all the lowvariability stars in our sample. Several stars in the sample showclear radial velocity variations. Some of these variations likelycorrespond to planets and will be the subject of future papers inthis series.
3. Data
Our sample stars were chosen first from our previous dedicatedsearches for solar twins at the McDonald (Mel´endez & Ram´ırez2007; Ram´ırez et al. 2009) and Las Campanas (Mel´endez et al.2009) observatories. Those searches were mainly based on mea-sured colors and parallaxes, by matching within the error barsboth the solar colors (preliminary values of those given inMel´endez et al. 2010, Ram´ırez et al. 2012, and Casagrande et al.2012) and the Suns absolute magnitude. We also added moretargets from our spectroscopic analysis of solar twins from theS N database (Allende Prieto et al. 2004) and the HARPS / ESOarchive, as reported in Baumann et al. (2010). Finally, weselected additional solar twins from the large samples ofValenti & Fischer (2005) and Bensby et al. (2014). For the lat-ter two cases we selected stars within 100 K in T e ff , 0.1 dex inlog g , and 0.1 dex in [Fe / H] from the Suns values.We selected a total of 88 solar twins for homogeneous highresolution spectroscopic observations. The sample is presentedin Table 2. From this sample, about 60 stars are being observedin our HARPS planet search project; the rest have been alreadycharacterized by other planet search programs.
The high-quality spectra employed for the stellar parameter andabundance analysis in this paper were acquired with the MIKEspectrograph (Bernstein et al. 2003) on the 6.5 m Clay MagellanTelescope at Las Campanas Observatory. We observed our tar-gets in five di ff erent runs between January 2011 and May 2012(Table 1). The observational setup (described below) was identi-cal in all these runs.
2. Ram´ırez et al.: Fundamental parameters of solar twins
Fig. 1.
Radial velocities measured with HARPS for four of thesolar twins in our sample. Dashed lines correspond to each star’saverage radial velocity (RV) value. The low RMS scatters andlack of apparent instrumental trends in RV demonstrate the highprecision achieved with HARPS.
Fig. 2.
Distribution of RMS scatter in radial velocities for 46 ofthe solar twins currently being monitored with HARPS. An ad-ditional 15 stars being monitored have RMS ranging from 10 to230 m s − . The dashed line corresponds to the median RMS ofthe 46 stars shown.We used the standard MIKE setup, which fully covers thewavelength range from 320 to 1 000 nm, and the 0.35 arcsec(width) slit, which results in a spectral resolution R = λ/ ∆ λ =
83 000 (65 000) in the blue (red) CCD. We targeted a signal-to-noise ratio ( S / N ) per-pixel of at least 400 at 6000 Å in order toobtain spectra of quality similar to that used by Mel´endez et al.(2009), who were the first to detect the proposed chemical sig-nature of terrestrial planet formation. Multiple consecutive ex-posures of each of our targets were taken to reach this very high S / N requirement.The spectra were reduced with the CarnegiePython MIKEpipeline, which trims the image and corrects for overscan, ap-plies the flat fields (both lamp and “milky”) to the object im-ages, removes scattered light and subtracts sky background. Itproceeds to extract the stellar flux order-by-order, and it appliesa wavelength mapping based on Th-Ar lamp exposures takenevery 2-3 hours during each night. Finally, it co-adds multipleexposures of the same target. Hereafter, we refer to these data asthe “extracted” spectra.We used IRAF’s dopcor and rvcor tasks to compute andcorrect for barycentric motion as well as the stars’ absolute radialvelocities. The latter were derived as described in Section 3.4.Each spectral order was then continuum normalized using 12thorder polynomial fits to the upper envelopes of the data. We ex-cluded ∼
100 pixels on the edges of each order to avoid their lowcounts and overall negative impact on the continuum normaliza-tion. This did not compromise the continuous wavelength cover-age of our data. However, we excluded the 5 reddest orders of thered CCD and discarded the 19 bluest order of the blue CCD. Thereason for this is that our continuum normalization is not reliablebeyond these limits and we found no need to include those wave-lengths for our present purposes. Thus, the wavelength coverage http://code.obs.carnegiescience.edu/mike Milky flats are blurred flat-field images that illuminate well the gapsbetween orders and are used to better correct the order edges. IRAF is distributed by the National Optical AstronomyObservatory, which is operated by the Association of Universitiesfor Research in Astronomy (AURA) under cooperative agreement withthe National Science Foundation. 3. Ram´ırez et al.: Fundamental parameters of solar twins
Table 1.
Observing runs and reference star observations
Run Dates Spectra Reference(s)1 1–4 Jan 2011 35 Iris2 23–24 Jun 2011 13 Vesta and 18 Sco3 9–10 Sep 2011 18 Vesta4 23 Feb 2012 4 18 Sco5 29-30 Apr, 1 May 2012 17 18 Sco ( × (1) Number of spectra acquired other than that of the reference target(s). of these spectra is reduced to ≃ − scombine task was used to merge all orders and create a finalsingle-column FITS spectrum for each star. Hereafter, these dataare referred to as the “normalized” spectra. To ensure the consistency of our data between di ff erent observ-ing runs we acquired spectra of asteroids Iris and / or Vesta, whichare equivalent to solar spectra, and / or the bright solar twin star18 Sco (HIP 79672) in each one of the runs (Table 1). Asteroidswere observed if they were bright ( V ∼ . − .
3) during our runs;otherwise only 18 Sco was observed in a given run. We acquiredasteroid spectra in three runs and 18 Sco in three runs as well,with only one of them in common with an asteroid observation.Two observations of 18 Sco were made in di ff erent nights in oneof the runs. Thus, there are four available 18 Sco spectra. We didnot produce solar or 18 Sco spectra by co-adding data taken indi ff erent runs. Instead, we analyzed them independently. Estimates of the absolute radial velocities (RVs) of our samplestars are required as a starting guess for the HARPS data reduc-tion. We obtained those values using our MIKE extracted spectraas follows.Twenty two of our solar twins are listed in the Nidever et al.(2002) catalog of RVs of stable stars (their Table 1). The RVsof these objects had been monitored for four years and theywere found to be stable within 0.1 km s − . The zero point of theNidever et al. RVs is consistent with the accurate RV scales ofStefanik et al. (1999) and Udry et al. (1999) within 0.1 km s − ,while their internal uncertainties are only about 0.03 km s − . Weused these 22 stars as RV standards.The absolute radial velocities of our stars were determinedby cross-correlation of their extracted spectra with the 22 RVstandards mentioned above. We employed IRAF’s fxcor taskto perform the cross-correlations. Orders significantly a ff ectedby telluric absorption were excluded. The order-to-order relativeRVs were averaged to get a single RV value. The 1 σ error ofthese averages ranges between 0.1 and 0.6 km s − depending onthe standard star used in the cross-correlation. Thus, for eachprogram star, 22 RVs were measured, each corresponding to adi ff erent standard reference. These 22 RV values were weight-averaged to compute the final RV of each star. The average 1 σ error of these final averages is 0.6 km s − , i.e., larger than the 1 σ errors of the cross-correlations, suggesting that the uncertaintiesof the final averages are dominated by systematic errors in theRVs adopted for the standard stars and not by our observationalnoise. Table 2 lists our derived absolute radial velocities.Instead of adopting the Nidever et al. (2002) RVs for thestandard stars, we re-derived their RVs with the same proceduredescribed above, but using for each standard star the other 21 −5.0 −4.8 −4.6 −4.4log R ′HK N Fig. 3.
Histogram of log R ′ HK values for our sample stars. Thedashed lines limit the range of values covered by the 11-yearsolar cycle.standards for cross-correlation. The average di ff erence betweenthe Nidever et al. (2002) RVs and those we re-derived for the 22standard stars is + . ± .
58 km s − . We used the MIKE extracted spectra to calculate chromosphericactivity indices for our stars. Naturally, the actual level of activitywill be better determined using the time-series measurements ofthe HARPS spectra. At this stage, we are only interested in aninitial reference estimate of these values.First, we measured “instrumental” S = ( H + K ) / ( R + V )values using the Ca ii H & K fluxes ( H , K ) and their nearbycontinuum fluxes ( R , V ). The former were computed by fluxintegration using triangular filters of width = K ) and 3968.5 Å ( H ). The (pseudo-)continuum fluxeswere estimated as the flux averages at 3925 ± V ) and3980 ± R ); as the regions are broad, spectral lines alsofall in the pseudo-continuum. We used IRAF’s sband task forthese calculations. Then, we searched for standardized S MW val-ues (i.e., S values on the Mount Wilson scale) previously pub-lished for our sample stars. We found S MW values for 62 ofour stars in the catalogs by Duncan et al. (1991); Henry et al.(1996); Wright et al. (2004); Gray et al. (2006); Jenkins et al.(2006, 2011) and Cincunegui et al. (2007). Measurements of thesame object found in more than one of these sources were aver-aged. We used these values to place our instrumental S valuesinto the Mount Wilson system via a second order polynomial fitto the S vs. S MW relation.To calculate log R ′ HK values (given in Table 2) we employedthe set of equations listed in Section 5.2 of Wright et al. (2004),using our calibrated S MW measurements and the stars’ ( B − V )colors given in the Hipparcos catalog (Perryman et al. 1997).The average di ff erence between our log R ′ HK values and thosepreviously published in the papers mentioned in the paragraphabove is 0 . ± . R ′ HK span of about 0.1 (Hall et al. 2009).A histogram of our log R ′ HK values is given in Figure 3.As an independent check of our log R ′ HK calculations,we compared the values we derived with those computedby Lovis et al. (2011), who used multi-epoch HARPS spec-tra. Fifteen of our sample stars are included in the study byLovis et al. They all show low levels of chromospheric activ-ity (log R ′ HK . − . R ′ HK values are, on average, only 0 . ±
4. Ram´ırez et al.: Fundamental parameters of solar twins .
025 higher, i.e., in excellent agreement with theirs consideringthe calibration errors and potential activity cycle variations.
4. Model atmosphere analysis
A very important component of our work is the determination ofiron abundances in the stars’ atmospheres. To compute these val-ues, we used the curve-of-growth method, employing the 2013version of the spectrum synthesis code MOOG (Sneden 1973)for the calculations (specifically the abfind driver). We adoptedthe “standard composition” MARCS grid of 1D-LTE model at-mospheres (Gustafsson et al. 2008), and interpolated modelslinearly to the input T e ff , log g, [Fe / H] values when necessary. Asshown in previous works by our group, the particular choice ofmodel atmospheres is inconsequential given the strict di ff eren-tial nature of our work and the fact that all stars are very similarto the Sun. A set of 91 Fe i and 19 Fe ii lines were employed in this work(Table 3). These lines were taken from our previous studies andmost of them have transition probabilities measured in the lab-oratory. Nevertheless, the accuracy of these values and the factthat some lines have log g f values determined empirically areboth irrelevant for our work. All these lines are in the linear partof the curve-of-growth in Sun-like stars and therefore their un-certainties cancel-out in a strict line-by-line di ff erential analysis.Most of our iron lines are completely unblended. However,our Fe i linelist includes a few lines that are somewhat a ff ectedby other nearby spectral features. The reason to keep these linesis that they balance the excitation potential ( χ ) vs. reduced equiv-alent width ( REW = log EW /λ , where EW is the line’s equiv-alent width) distribution of the Fe i lines. This is important toavoid degeneracies and biases in the determination of stellar pa-rameters using the standard excitation / ionization balance tech-nique, which is described in Section 4.3.The χ vs. REW relation of our iron linelist is shown inFigure 4. In addition to retaining as many as possible low- χ lines,even if they are di ffi cult to measure, we had to exclude a num-ber of very good (i.e., clean) lines on the high- χ side, also toprevent biasing the stellar parameter determination. Having anunbalanced χ distribution would make the T e ff more sensitive toone particular type of spectral line, which should be avoided.The positive correlation between excitation potential and transi-tion probability is expected. Lower χ lines tend to be stronger;to avoid saturated lines, lower log( g f ) features are selected. Equivalent widths were measured “manually,” on a star-by-star,line-by-line basis, using IRAF’s splot task. Gaussian fits werepreferred to reduce the impact of observational noise on thelines’ wings, which has a stronger impact on Voigt profile fits. Atthe spectral resolution of our data, Gaussian fits are acceptable.The deblend option was used when necessary, making sure thatthe additional lines were consistently fitted for all stars (i.e., weused the same number and positions of blending lines). For somespectral lines a relatively low pseudo-continuum assessment wasnecessary due to the presence of very strong nearby lines. Wealso made sure to adopt consistent pseudo-continua for all stars. http://marcs.astro.uu.se −6.0−5.5−5.0−4.5 l og ( E W / λ ) χ (eV)−5−4−3−2−10 l og ( g f ) Fig. 4.
Excitation potential versus reduced equivalent width (toppanel) and transition probability (bottom panel) relations for ourFe i (circles) and Fe ii lines (squares). The equivalent widths cor-respond to our solar reference, which is based on spectra of sun-light reflected from asteroids, as described in Section 4.2.Our experience shows that manual measurement of EW s is supe-rior to an automated procedure in terms of achieved consistencyand accuracy. Given the characteristics of our data, the predicted error inour EW measurements is about 0.2 mÅ. This value was com-puted using the formula by Cayrel (1988), who points out thatthe true error is likely higher due to systematic uncertainties,for example those introduced by the continuum placement. Thespectra of our reference stars were used to get a better estimateof our EW errors.The EW s measured in our three solar (asteroid) spectra wereaveraged to create our adopted solar EW list, which is providedin Table 3. The error bars listed there for EW ⊙ correspond tothe 1 σ scatter of the three equivalent width measurements avail-able for each spectral line. Similarly, we averaged the EW s ofthe four spectra of 18 Sco. The di ff erence between these average EW s and those measured in the individual spectra are shown inFigures 5 and 6. The 1 σ scatter of the EW di ff erences shownin Figures 5 and 6 ranges from 0.4 to 0.5 mÅ and from 0.5 to0.7 mÅ, respectively.Assuming that the scatter values quoted above arise frompurely statistical errors, the EW uncertainty for the 18 Sco spec- Our team has employed a number of automated tools to calculateequivalent widths in the past. Although these procedures are extremelyhelpful when dealing with very large numbers of stars and long spectralline-lists, we have found that even minor issues with the continuum de-termination or other data reduction deficiencies always result in a smallfraction of spectral lines with incorrect EW values (or at least not pre-cise enough when investigated in chemical abundance space). Sigma-clipping could be invoked to get rid of these outliers, but this intro-duces star-to-star inconsistencies in the derivation of stellar parameters.Despite being extremely ine ffi cient, visual inspection of every spectralline and “manual measurements” have proven to be the most reliableand self-consistent techniques for EW determination in our works. 5. Ram´ırez et al.: Fundamental parameters of solar twins −4−2024 ∆ E W Iris (UT110104) −4−2024 ∆ E W Vesta (UT110624)
20 40 60 80 100 120EW (mÅ)−4−2024 ∆ E W Vesta (UT110909)
Fig. 5.
Equivalent width di ff erences for our asteroid (solar) spec-tra. In each panel, the di ff erences between the EW s measured ina given spectrum and the average EW values are shown. On thetop left side of each panel, the name of the target is followed bythe UT date of observation (in YYMMDD format). −4−2024 ∆ E W
18 Sco (UT110624) −4−2024 ∆ E W
18 Sco (UT120223) −4−2024 ∆ E W
18 Sco (UT120429)
20 40 60 80 100 120EW (mÅ)−4−2024 ∆ E W
18 Sco (UT120430)
Fig. 6.
As in Figure 5 for our 18 Sco spectra.tra can be estimated as √ / × (0 . − . Since the individual18 Sco spectra are typical of all our other sample star observa-tions, we estimate an average EW uncertainty of about 0.5 mÅ,which corresponds to 1 % for a line of EW =
50 mÅ.The good agreement found in our EW measurements madeon multiple spectra for the same stars (Sun and 18 Sco) ensures ahigh degree of consistency in the derived relative stellar param-eters, as will be shown quantitatively in Section 4.4. If the EW precision of each spectrum is σ , that of the average of n has a precision of σ n = σ/ √ n −
1. The scatter of the average mi-nus individual spectrum measurement di ff erences is then p σ + σ n = σ √ n / ( n − σ is proportional to √ ( n − / n , with n = We employed the excitation / ionization balance technique to findthe stellar parameters that produce consistent iron abundances.We started with literature values for the stars’ fundamental at-mospheric parameters T e ff , log g, [Fe / H] , v t and iteratively mod-ified them until the correlations with χ and REW were mini-mized, while simultaneously minimizing also the di ff erence be-tween the mean iron abundances derived from Fe i and Fe ii linesseparately. The stellar parameters derived in this manner areoften referred to as “spectroscopic parameters.”We used a strict di ff erential approach for the calculations de-scribed here. This means that the stars’ iron abundances weremeasured relative to the solar iron abundance on a line-by-linebasis. Thus, if A Fe , i is the absolute iron abundance derived for aspectral line i , the following quantities: [Fe / H] i = A Fe , i − A ⊙ Fe , i were employed to perform the statistics and to calculate the finalrelative iron abundances by averaging them. Strict di ff erentialanalysis minimizes the impact of model uncertainties as well aserrors in atomic data because they cancel-out in each line calcu-lation. This is particularly the case when the sample stars are allvery similar to each other and very similar to the star employedas reference, i.e., the Sun in our case. We adopted T ⊙ e ff = g ⊙ = . v ⊙ t = . − , and the absolute solar abun-dances by Anders & Grevesse (1989). The particular choice ofthe latter has no e ff ect on the precision of our relative abun-dances.In each iteration, we examined the slopes of the [Fe / H] vs. χ and [Fe / H] vs.
REW relations. If they were found positive (neg-ative), the T e ff and v t values were increased (decreased). At thesame time, if the mean Fe i minus Fe ii iron abundance di ff erencewas found positive (negative), the log g value was increased (de-creased). We stopped iterating when the standard deviations ofthe parameters from the last five iterations were all lower than0.8 times the size of the variation step. The first set of itera-tions was done with relatively large steps; the T e ff , log g , and v t parameters were modified by ±
32 K, ± .
32, and ± − ,respectively. After the first convergence, the steps were reducedin half, i.e., to ±
16 K, ± ± − , and so on, untilthe last iteration block, in which the steps were ± ± ± − .The average [Fe / H] resulting in each iteration was com-puted, but not forced to be consistent with the input value.While this condition should be enforced by principle, within ourscheme one could save a significant amount of computing timeby avoiding it. After all, the final iteration loop has such smallsteps that the input and resulting [Fe / H] values will not be sig-nificantly di ff erent. Indeed, the average di ff erence between inputand output [Fe / H] values from all last iterations in our work is0 . ± . / H]values is 0.02 dex (including both Fe i and Fe ii lines). Formal er-rors for the stellar parameters T e ff , log g , and v t were computedas in Epstein et al. (2010) and Bensby et al. (2014). On averagethese formal errors are σ ( T e ff ) = σ (log g ) = . σ ( v t ) = .
016 km s − . For [Fe / H], the formal error was com-puted by propagating the errors in the other atmospheric pa-rameters into the [Fe / H] calculation; adding them in quadrature(therefore assuming optimistically that they are uncorrelated) A Python package (qoyllur-quipu, or q ) has been developed by I.R.to simplify the manipulation of MOOG’s input and output files as wellas the iterative procedures. The q source code is available online at https://github.com/astroChasqui/q2 .6. Ram´ırez et al.: Fundamental parameters of solar twins eff (K)05101520 N N −0.2 −0.1 0.0 0.1 0.2[Fe/H]05101520 N Fig. 7.
Histograms of stellar parameters for our sample stars. Thedashed lines correspond to the canonical solar values.and including the standard error of the mean line-to-line [Fe / H]abundance. On average, σ ([Fe / H]) = .
006 dex. The stellar pa-rameter uncertainties are the main source of this error, not theline-to-line scatter.The errors quoted above are extremely low due to the highquality of our data and our precise, consistent, and very careful EW measurements. One should keep in mind, however, that thetrue meaning of these formal errors is the following: inside theirrange, the [Fe / H] versus χ / REW slopes and Fe i minus Fe ii ironabundance di ff erences are consistent with zero within the 1 σ line-to-line scatter. In other words, they just correspond to theprecision with which we are able to minimize the slopes and ironabundance di ff erence. Rarely do they represent the true errorsof the atmospheric parameters because they are instead largelydominated by systematic uncertainties (e.g., Asplund 2005). Theonly possible exceptions, as argued before, are solar twin stars ifanalyzed relative to the Sun or relative to each other.Our derived spectroscopic parameters, and their internal er-rors, are given in Table 4. Figure 7 shows our sample histogramsfor these stellar parameters. The reliability of our error esti-mates and detailed accuracy assessments are discussed later inthis paper. For now, it is interesting to compare our spectro-scopic parameters with those determined by Sousa et al. (2008),who employed essentially the same technique used in this work,but with some di ff erences regarding the ingredients of the pro-cess. Nineteen stars were found in common between our workand the study by Sousa et al.. The average di ff erences in stel-lar parameters, in the sense Sousa et al. minus this work, are: EP = χ (eV) [ F e / H ]
18 Sc − Sun −5.8 −5.6 −5.4 −5.2 −5.0 −4.8 −4.6
REW = l g (EW/λ) [ F e / H ] Wavelength (Å) [ F e / H ] Fig. 8.
Line-to-line relative iron abundance of 18 Sco as a func-tion of excitation potential (top panel), reduced equivalent width(middle panel), and wavelength (bottom panel). Crosses (circles)are Fe i (Fe ii ) lines. The solid lines in the top and middle panelsare linear fits to the Fe i data. In the bottom panel, the solid lineis a constant which corresponds to the average iron abundanceof this star. ∆ T e ff = − ±
12 K (5660 to 5875 K), ∆ log g = . ± .
04 (4.16to 4.49), and ∆ [Fe / H] = − . ± .
015 (–0.13 to + Figure 8 shows an example of a final, fully converged solution.It corresponds to the “closest-ever” (Porto de Mello & da Silva1997), bright solar twin star 18 Sco. Since the EW values em-ployed in this calculation for 18 Sco correspond to the averageof four independent observations, each made with a S / N ∼ T e ff = ± g = . ± .
01, [Fe / H] = . ± . v t = . ± .
01 km s − .The precision of our results for all other stars is typically half asgood, yet still extremely precise.As a test case, we determined the stellar parameters of 18 Scousing each of its four available individual spectra. These aremore representative of our sample stars’ data in general. Theparameters derived from these individual spectra have the fol-lowing mean and 1 σ values: T e ff = ± g = . ± . / H] = . ± . v t = . ± .
015 km s − .This is fully consistent with the values and errors derived for
7. Ram´ırez et al.: Fundamental parameters of solar twins the case when the average EW values of 18 Sco are employed,which ensures that our formal error calculation is reliable.We performed a similar test calculation for the three avail-able solar spectra relative to their average EW s. We found thefollowing averages for the three individual spectra: T e ff = ± g = . ± . / H] = − . ± . v t = . ± .
014 km s − , which further demonstrates that theformal errors we derived fully correspond to the observationalnoise.Mel´endez et al. (2014a) have recently used spectra of 18 Scotaken with the UVES and HIRES spectrographs on the VLT andKeck Telescopes, respectively, to determine highly precise pa-rameters of this star. The reference solar spectra in their studyare reflected sunlight observations from the asteroids Juno (forthe VLT case) and Ceres (for HIRES). The parameters found for18 Sco in that study are T e ff = ± g = . ± . / H] = + . ± . σ preci-sion errors. For T e ff , note that the 1 σ lower limit of the valuefrom Mel´endez et al. (2014a) is exactly the same as the 1 σ up-per limit from our work (our most precise value, that from theaverage EW measurements, is T e ff = ± The most common approach to derive stellar masses and ages oflarge samples of single field stars is the isochrone method (e.g.,Lachaume et al. 1999). In most implementations, this methoduses as inputs the observed T e ff , M V (absolute magnitude), and[Fe / H] values, along with their errors. To calculate M V , a mea-surement of the star’s parallax is required. The latter is availablein the Hipparcos catalog (van Leeuwen 2007) for most Sun-likestars in the solar neighborhood.Each data point in an isochrone grid has stellar parametersassociated to it, including T e ff , M V , and [Fe / H], but also mass,radius, age, luminosity, etc. Thus, one could find the isochronepoint with T e ff , M V , and [Fe / H] closest to the observed valuesand associate the other stellar parameters to that particular ob-servation. To achieve higher accuracy, one can calculate a prob-ability distribution for each of the unknown parameters using asweights the distances between observed and isochrone T e ff , M V ,and [Fe / H] values (normalized by their errors). Then, the proba-bility distributions can be employed to calculate the most likelyparameter values and their formal uncertainties.Isochrone age determinations are subject to a number ofsampling biases whose impact can be minimized using Bayesianstatistics (e.g., Pont & Eyer 2004; Jørgensen & Lindegren 2005;da Silva et al. 2006; Casagrande et al. 2011). While correctingfor these biases is crucial for statistical stellar population stud-ies, their importance is secondary for small samples of field starsspanning a narrow range in parameters where the main goal is tosort stars chronologically (e.g., Baumann et al. 2010). Becauseof the small internal errors of our observed stellar parameters,this is possible with our approach.To derive a precise stellar parameter using isochrones, thestar must be located in a region of stellar parameter space wherethe parameter varies quickly along the evolutionary path. In par-ticular, a precise age can be calculated for stars near the main-sequence turn-o ff . On the main-sequence, isochrones of di ff erentages are so close to each other that a typical observation cannotbe used to disentangle the isochrone points that correspond tothat star’s age. It is for this reason that it is often assumed thatisochrone ages of main-sequence stars are impossible to calcu-late. Age (Gyr) P r o b a b ili t y d e n s i t y
18 Sco
Fig. 9.
Age probability distribution of 18 Sco. The dashed lineis at the most probable age. The probability density units arearbitrary. The dark (light) gray shaded area corresponds to the1 σ (2 σ ) confidence interval.Nevertheless, solar twin stars o ff er the possibility of de-riving reasonably precise isochrone ages, at least on a rela-tive sense. The most important step to achieve this goal con-sists in replacing M V for log g as one of the input parameters.The latter can be derived with extremely high precision, as wehave done in Section 4.3. Thus, even though main-sequenceisochrones are close to each other in the T e ff versus log g plane,the high precision of the observed T e ff and log g values ensuresthat the age range of the isochrones that are consistent withthese high-quality observations is not too wide. For example,Mel´endez et al. (2012) showed that the isochrone age of “thebest solar twin star” HIP 56948 can only be said to be youngerthan about 8 Gyr if its Hipparcos parallax is employed to cal-culate M V , which is in turn used as input parameter, but con-strained to the 2.3–4.1 Gyr age range if its very precise spec-troscopic log g value is adopted as input parameter instead (seetheir Section 4.3 and Figure 10).Isochrone masses and ages depend on the grid employed.This is true regardless of which input parameters are used.However, this leads mostly to systematic errors and, by defi-nition, does not a ff ect the internal precision of the parametersderived.In this work, we employed the isochrone method implemen-tation by Ram´ırez et al. (2013), but adopting the spectroscopiclog g instead of M V as input parameter. Ram´ırez et al. (2013) im-plementation uses the Yonsei-Yale isochrone set (e.g., Yi et al.2001; Kim et al. 2002). Figure 9 shows the age probability dis-tribution of 18 Sco as an example. The asymmetry of this curveis a common feature of isochrone age probability distributions.We assign the most probable value from this distribution as theage of the star. Confidence intervals at the 68 % and 96 % lev-els can then be interpreted as the 1 σ and 2 σ limits of the star’sage. They are represented by the dark- and light-gray shadedareas in Figure 9. Mass probability distributions are nearly sym-metric; thus a single value is su ffi cient to represent its internaluncertainty. The derived isochrone masses and ages ( τ ) for oursample stars are given in Table 4. Sample histograms for theseparameters are shown in Figure 10.The internal precision of our ages varies widely from star-to-star. On average, the 1 σ age range from the probability distribu-tions is 1.3 Gyr, with a maximum value of 3.1 Gyr and a mini-mum at 0.5 Gyr. It must be stressed that these numbers shouldnot be quoted as the absolute age uncertainties from our work.They only represent the internal precision with which we are
8. Ram´ırez et al.: Fundamental parameters of solar twins N ⊙ )05101520 N Fig. 10.
Histograms of stellar mass and age for our sample stars.The dashed lines correspond to the canonical solar values. l og R ′ H K Fig. 11.
Stellar age versus chromospheric activity index. Outlierstars are labeled with their HIP numbers. The gray bar at 4.5 Gyrrepresents the range covered by the 11-year solar cycle.able to find nearby Yonsei-Yale isochrone points. For our presentpurposes, this is certainly acceptable, as we are mainly interestedin the chronology of the sample and not necessarily the star’strue ages (i.e., relative ages rather than absolute ages).To test the internal precision of our derived stellar ages, weplot them against our measured chromospheric activity indiceslog R ′ HK in Figure 11. Stellar activity is predicted to decay withtime due to rotational braking (e.g., Skumanich 1972; Barnes2010), but plots of activity index versus stellar age typically havevery large scatter. The most likely explanation for this is that theactivity indices depend on the stars’ e ff ective temperatures. Inour case, the resulting relation is very tight (after excluding theoutliers; see below). This owes to the fact that these objects are all very similar one-solar-mass, solar-metallicity main-sequencestars.There are a few outliers in the log R ′ HK versus age plot ofFigure 11. For example, one star at age = R ′ HK value about 0.15 above that of all other coeval stars. This ob-ject, HIP 67620, is known to have an unresolved (for our spec-troscopic observations) faint companion, which is revealed byspeckle interferometry (Hartkopf et al. 2012). The other out-liers are also unusually high activity stars, but in the age rangebetween about 3 and 4 Gyr; they are HIP 19911, HIP 22395,HIP 29525, and HIP 43297.Figure 11 shows an overall decrease of stellar activity withincreasing age. The star-to-star scatter at a given age is mostlikely dominated by intrinsic changes in the activity of the starsand not due to observational errors. During the 11-year solar cy-cle, for example, the log R ′ HK index of the Sun varies from about − .
02 to − .
88 (Hall et al. 2009). This range is illustrated by thegray bar at age 4.5 Gyr in Figure 11. The solar twins of age closeto solar span a log R ′ HK range compatible with the solar data, sug-gesting that the activity levels of the present-day solar cycle aretypical of other Sun-like stars of solar age.The larger scatter seen in younger stars suggests that theyhave larger variations in their activity levels. On the other end,the very low log R ′ HK values of the oldest solar twins (age & R ′ HK ranges. Forexample, 18 Sco has a cycle of about 7 years (Hall et al. 2007).We will investigate thoroughly the age dependency of stellar ac-tivity of solar twins in a future publication.
5. Validation
The fundamental atmospheric parameters T e ff and log g can bedetermined using techniques which are independent of the ironline (spectroscopic) analysis described in the previous section.To be more precise, these alternative techniques are less depen-dent on the iron line analysis; the average [Fe / H] could still playa role as input parameter.As will be described below, T e ff can be measured using thestar’s photometric data or H α line profile. Also, log g can be es-timated using a direct measurement of the star’s absolute magni-tude, which requires a knowledge of its trigonometric parallax.The [Fe / H] value derived for each spectral line depends on theinput T e ff and log g . Thus, if they are di ff erent from the “spectro-scopic” values derived before, the slopes of the [Fe / H] versus χ and REW relations will no longer be zero. The same will be truefor the mean Fe i minus Fe ii iron abundance di ff erence.Determining T e ff and log g using other methods requires re-laxing the conditions of excitation and ionization equilibrium.However, one could derive a consistent v t value by forcing the[Fe / H] versus
REW slope to be zero. The resulting average[Fe / H] value will be di ff erent than the spectroscopic one, whichmay in turn have an impact on the alternative T e ff and log g val-ues. Therefore, strictly speaking, one must iterate until all pa-rameters are internally consistent.Finding consistent solutions for these alternative parameterswould be necessary if we were interested in using them in ourwork. As will be shown later, these parameters are not as inter-nally precise as those we inferred from the spectroscopic analy-
9. Ram´ırez et al.: Fundamental parameters of solar twins sis of the previous section. We will thus only use the latter in ourfuture works. In this section, we are only interested in calculat-ing these parameters given one di ff erent ingredient. In that way,we can better understand the sources of any important discrep-ancies. Therefore, in deriving T e ff or log g using other methods,we kept all other parameters constant and no attempt was madeto achieve self-consistent results using iterative procedures. One of the most reliable techniques for measuring with accu-racy a solar-type star’s e ff ective temperature is the so-called in-frared flux method (IRFM). First introduced by Blackwell et al.(1979), the IRFM uses as T e ff indicator the ratio of monochro-matic (infrared) to bolometric flux, which is independent on thestar’s angular diameter. Observations of that ratio based on ab-solutely calibrated photometry are compared to model atmo-sphere predictions to determine T e ff . The flux ratio is highlysensitive to T e ff and weakly dependent on log g or [Fe / H].In addition, systematic uncertainties due to model simplifica-tions are less important in the infrared. Modern implementationsof the IRFM (e.g., Alonso et al. 1996; Ram´ırez & Mel´endez2005; Gonz´alez Hern´andez & Bonifacio 2009; Casagrande et al.2010) have been very valuable for a large number of investiga-tions in stellar astrophysics.In this work, we used the implementation describedin Casagrande et al. (2010), which uses multiband optical(Johnson-Cousins) and infrared (2MASS) photometry to recon-struct the monochromatic (infrared) and bolometric flux. Theaccuracy of such implementation has been tested thoroughly(see Casagrande et al. 2014 for a summary). We used the ho-mogeneous set of BV ( RI ) C and JHK S photometry published inour earlier investigations of Sun-like stars (Ram´ırez et al. 2012;Casagrande et al. 2012). The overlap with this study is restrictedto 30 objects. The flux outside photometric bands is estimatedusing the Castelli & Kurucz (2004) theoretical model fluxes in-terpolated at the spectroscopic [Fe / H], log g , and (for only thefirst iteration) T e ff values of each star.While the IRFM is only mildly sensitive to the adopted[Fe / H] and log g , the spectroscopic T e ff is used only as an in-put parameter, and an iterative procedure is adopted to convergein T e ff (IRFM). We checked that convergence is reached indepen-dently on the input T e ff , be it spectroscopic or a random point inthe grid of synthetic fluxes. Errors in T e ff (IRFM) were computedas the sum in quadrature of the scatter in the three JHK S T e ff values and the error due to photometric errors, computed usingMonte Carlo experiments. A constant value of 20 K was addedlinearly to these errors to account for the uncertainty in the zeropoint of the IRFM T e ff scale. Casagrande et al. (2010) showedthat IRFM and direct, i.e., interferometric, T e ff values are o ff setby 18 K.The di ff erences between IRFM and spectroscopic e ff ectivetemperatures for the 30 stars in our sample with homogeneousand accurate photometric data are shown in Figure 12 as a func-tion of atmospheric parameters. There are no significant o ff setsor correlations. On average, ∆ T e ff = − ±
47 K (IRFM minusspectroscopic). The mean value of the errors in T e ff (IRFM) is52 K, which shows that the scatter in Figure 12 is fully explainedby the IRFM uncertainties.It is important to re-emphasize that the IRFM T e ff scale ofCasagrande et al. (2010) has been thoroughly tested, in partic-ular its absolute calibration. It has been shown to have a zeropoint that is accurately and precisely consistent with that whichcorresponds to the most reliable e ff ective temperatures available T eff (K)−200−1000100200 4.30 4.35 4.40 4.45 4.50 4.55 log g −200−1000100200 ∆ T e ff ( K , I R F M − s p e c . ) −0.15 −0.10 −0.05 0.00 0.05 0.10[Fe/H]−200−1000100200 Fig. 12.
IRFM minus spectroscopic T e ff as a function of spectro-scopic parameters. The solid line is at zero.for restricted samples of calibrating stars, for example those withaccurate measurements of angular diameter or spectrophotome-try. The fact that the spectroscopic e ff ective temperatures of arepresentative group from our solar twin sample are on the samelevel as the most reliable IRFM T e ff values ensures that the T e ff scale adopted in this work has a zero point consistent with thebest direct T e ff determinations. H α line-winganalysis The wings of Balmer lines in cool dwarf stars have been shownto be highly sensitive to the e ff ective temperature while show-ing only a mild dependency on other stellar parameters suchas log g or [Fe / H] (e.g., Gehren 1981; Fuhrmann et al. 1993;Barklem et al. 2002). Since they form in deep layers of the stars’atmospheres, their modeling is expected to be largely insensitiveto non-LTE e ff ects (see, however, Barklem 2007), but dependenton the details of the treatment of convection (e.g., Ludwig et al.2009). These potential systematic uncertainties in the modelingof the Balmer lines will a ff ect our sample stars in a very similarmanner, which implies that we can determine a set of internallyprecise T e ff (H α ) values. We restrict our work to the Balmer H α line because it is the least a ff ected by overlapping atomic fea-tures and it is the most amenable to proper continuum normal-ization (see below).The H α line is very wide and it occupies nearly one-half ofone of the orders in our MIKE extracted spectra. The normal-ization procedure described in Section 3.2 does not result in aproperly normalized H α profile because the H α line wings arenot correctly disentangled from the local continuum. For echellespectra, a better continuum normalization can be done by inter-polating the shape of the continua and blaze functions of nearbyorders to the order containing the H α line. The details of this pro-cedure are described in Barklem et al. (2002). In this work, weemployed the six orders nearest to the H α order and normalizedthem using 10th order polynomials (only the half of each orderthat aligns with the position of the H α line was used). Then,
10. Ram´ırez et al.: Fundamental parameters of solar twins we fitted a 3rd order polynomial to the order-to-order contin-uum data for each pixel along the spatial axis. The value of thesepolynomials at the order where H α resides was then adopted asthe continuum for that order.To derive T e ff (H α ) we employed model fits to the observedH α lines using χ minimization. We adopted the theoretical gridof H α lines by Barklem et al. (2002) for this procedure. Sincereal spectra of Sun-like stars contain many weak atomic featureson top of the H α line, the χ was computed only in those smallspectral windows free from weak line contamination. The lat-ter have to exclude also the telluric lines present in our spectra.Since their position changes from star to star due to the di ff er-ences in radial velocity and epoch of observation, these cleanspectral windows are di ff erent for each spectrum. The internalprecision of our T e ff (H α ) values was estimated from the T e ff ver-sus χ relation as follows: σ ( T e ff ) = [2 / ( ∂ χ /∂ T ff )] / .We applied the technique described above to calculate thesolar T e ff (H α ). The average value from our three solar (asteroid)spectra is 5731 ±
21 K. Even though this value is inconsistentwith the nominal T ⊙ e ff = T e ff (H α ) derived by Barklem et al. (2002), whoemployed the very high quality ( R &
500 000, S / N & ff ective temperature isintrinsic to the adopted 1D-LTE modeling of the H α line and notdue to observational errors (Pereira et al. 2013). Given the sim-ilarity of our sample stars, and the fact that we are exploitingdi ff erential analysis, we can apply a constant o ff set of +
46 K toall our T e ff (H α ) as a first order correction.The +
46 K o ff set leads to a T ⊙ e ff (H α ) = T e ff (H α ) = ±
18 K (average of thefour 18 Sco spectra available). After applying the +
46 K correc-tion, this value becomes T e ff (H α ) = T e ff = ff erences between H α and spectro-scopic T e ff for our entire sample. The average di ff erence (H α minus spectroscopic) is ∆ T e ff = ±
30 K (after applying the +
46 K o ff set to the H α temperatures of all stars). The average in-ternal T e ff errors are only 23 K and 7 K for H α and spectroscopic T e ff , respectively. Thus, the expected scatter for these di ff erencesis 24 K, assuming no systematic trends, which do appear to exist.Figure 13 reveals a small trend with T e ff such that ∆ T e ff seems tobe slightly more positive for the cooler solar twins. These starshave stronger contaminant lines, which may lower the level ofthe H α line wing regions, leading to higher T e ff (H α ) values. Thecomplex ∆ T e ff versus log g trend is di ffi cult to understand, butit is clear that the agreement in T e ff values is excellent for solartwins of log g < . ∆ T e ff as a functionof χ , i.e., the χ value of the best-fit model. Lower χ val-ues imply a much better overall agreement between model andobservations. Systematically high T e ff (H α ) values are found for χ > ∆ T e ff = ±
25 K. This star-to-star scatter is in ex-cellent agreement with the expected one if systematic trends donot exist. Although we were very careful in our continuum de-termination and the selection of clean spectral windows for the χ measurements, the spectra with χ > ∆ T e ff occurs in thestar with the worst χ . eff (K)−150−100−500501001504.1 4.2 4.3 4.4 4.5log g−150−100−50050100150 ∆ T e ff ( K , H α − s p e c . ) −150−100−50050100150 Fig. 13. H α minus spectroscopic T e ff as a function of T e ff , log g ,and χ of the best T e ff (H α ) model fit. The solid line is at zero.Small inconsistencies in the continuum determination, whichis already challenging for the H α line, and the impact of weakatomic lines contaminating the H α line wings are most likely re-sponsible for the barely noticeable di ff erences between H α andspectroscopic T e ff values of our solar twins. When we restrictthe comparison to those stars with the best H α line normaliza-tion, the average di ff erence (and star-to-star scatter) is perfectlyconsistent with zero within the expected internal errors. For nearby stars, the trigonometric parallaxes from
Hipparcos can be employed to calculate their absolute visual magnitudeswith high precision. The well-defined location of the stars onthe M V versus T e ff plane can then be used to calculate the stars’parameters by comparison with theoretical isochrones, as de-scribed in Section 4.5.To calculate absolute magnitudes we used previously mea-sured apparent magnitudes and trigonometric parallaxes. Theparallaxes we used are from the new reduction of the Hipparcos data by van Leeuwen (2007). Visual magnitudes were com-piled from various sources. First, we searched in the catalog byRam´ırez et al. (2012), which is the most recent and comprehen-sive homogeneous
U BV ( RI ) C photometric dataset for solar twinstars. If not available in that catalog, we searched for Johnson’s V magnitudes in the General Catalog of Photometric Data (GCPD)by Mermilliod et al. (1997). Then, we looked for ground-based V magnitudes listed in the Hipparcos catalog (i.e., not the trans-formed V T magnitudes, but previous ground measurements ofvisual magnitudes compiled by the Hipparcos team). For a fewstars we employed the V magnitudes listed in the Str¨omgren cat-alogs of the GCDP or V magnitudes calculated from Hipparcos’ V T values. We used the V magnitude errors reported in each ofthese sources, if available. Otherwise, we adopted the average ofthe errors reported, which is 0.012 mag.
11. Ram´ırez et al.: Fundamental parameters of solar twins l og g ( t r i g o n o m e t r i c ) Fig. 14.
Spectroscopic versus trigonometric surface gravity. Thesolid line corresponds to the 1:1 relation. Outlier stars are labeledwith their HIP numbers.On average, the trigonometric log g error of our sample starsis 0.035. The mean log g di ff erence ( ∆ (log g ), trigonometric mi-nus spectroscopic) for our sample stars is − . ± .
07. Given theformal errors in spectroscopic (0.019) and trigonometric (0.035)log g values, we would expect the 1 σ scatter of the log g dif-ferences to be lower (0.039). Figure 14 shows a comparison ofour spectroscopic and trigonometric log g values. There are afew outliers worth investigating. Six stars have ∆ (log g ) greaterthan 2 σ , where σ is the standard deviation of the full sample’s ∆ (log g ) distribution. We discuss them in turn.HIP 10175 and HIP 30158 have their V magnitudes takenfrom the GCDP. These magnitudes are flagged as AB, which rep-resents blended photometry, implying that their V magnitudesare contaminated by a cooler nearby companion (no other starin our sample has the same AB flag in the GCDP). HIP 10303is in a wide binary system and its parallax has a very large er-ror despite being a nearby system. The trigonometric log g ofthis star has an error of nearly 0.2. HIP 114615 is the most dis-tant and faintest star in our sample, which contributes to makingthe quality of both its spectroscopic and trigonometric log g val-ues significantly below average. HIP 83276 has been identifiedas a single-lined spectroscopic binary by Duquennoy & Mayor(1988), who suggests a companion cooler than a K4-type dwarf.These authors derived a photometric parallax of about 31 mas,which is well below the Hipparcos value (36 . ± . g by only 0.1. HIP 103983 isalso a binary. Tokovinin et al. (2013) have identified a sub-arcseccompanion which is a ff ecting either the primary star’s visualmagnitude or the system’s Hipparcos parallax (or both), lead-ing to an incorrect trigonometric log g . To confirm the latter, weestimated the age of the system using the Hipparcos log g in-stead of the spectroscopic value as was done in Section 4.5. Thisresults in ∼ R ′ HK = − .
84 is too high forthat age, but fully consistent with the solar log R ′ HK evolution forits “spectroscopic” age of about 2 Gyr, as shown in Figure 11.Excluding the six stars discussed above, ∆ (log g ) reduces to − . ± .
04. This di ff erence is in principle fully explained bythe formal errors. However, we note that ∆ (log g ) exhibits minortrends with log g and in particular the relative error in the stellar ∆ ( l og g ) t r i g . − s p ec . ∆ ( l og g ) t r i g . − s p ec . Fig. 15.
Trigonometric minus spectroscopic surface gravity dif-ference as a function of spectroscopic log g (top panel) and rela-tive parallax error (bottom panel). The solid line is at zero.parallax, as shown in Figure 15. No significant correlations werefound for any of the other stellar parameters. The bottom panelof Figure 15 shows that there is excellent agreement for δ ( π ) /π errors below 3 %, where π is the Hipparcos trigonometric paral-lax. Indeed, the mean ∆ (log g ) for those stars is − . ± . − . ± .
040 (excludingthe 6 stars discussed in the previous paragraph).Thus, we conclude that the higher uncertainty of the moredistant stars in our sample leads to a small systematic di ff erencebetween spectroscopic and trigonometric log g values. On theother hand, if we restrict the comparison to only the most pre-cise trigonometric log g determinations, the agreement with ourspectroscopic log g values is excellent.
6. Conclusions
We presented here the largest sample of solar twins (88 stars)analyzed homogeneously using high resolution, high signal-to-noise ratio spectra. Precise stellar parameters ( T e ff , log g , [Fe / H], v t ) were obtained from a di ff erential spectroscopic analysis rela-tive to the Sun, which was observed using reflected light of as-teroids, employing the same instrumentation and setup. We alsomeasured stellar activity from the Ca ii H and K lines.Our stellar parameters have been validated using e ff ectivetemperatures from the infrared flux method and from fits ofH α line profiles, and with surface gravities determined using Hipparcos parallaxes. There is an excellent agreement with theindependent determinations after their less precise cases are ex-cluded from the comparisons, suggesting that systematic errorsare negligible and that we can achieve the highest precision usingthe di ff erential spectroscopic equilibrium, with e ff ective temper-atures determined to better than about 10 K, log g with a preci-sion of about 0.02 dex, and [Fe / H] to better than about 0.01 dex.The precise atmospheric parameters ( T e ff , log g , [Fe / H])were used to determine isochrone masses and ages, taking theerror bars in the determination of the stellar parameters into ac-count. The masses are within about 5 % of the solar mass, andthere is a range in ages of about 0.5–10 Gyr. Our sample is idealto test di ff erent aspects of the main-sequence evolution of the
12. Ram´ırez et al.: Fundamental parameters of solar twins
Sun, such as the evolution of surface lithium abundance withage (Baumann et al. 2010; Monroe et al. 2013; Mel´endez et al.2014b) or the decay of stellar activity.Although the goal of this work was to present our “SolarTwin Planet Search” project and to provide the stellar parame-ters for our sample stars to use in future publications, two impor-tant scientific results were obtained while preparing this “inputcatalog”: – i) The formal errors in stellar parameters derived from strictdi ff erential analysis are excellent indicators of the actual un-certainty of those measurements. In other words, systematicerrors in the derivation of fundamental atmospheric param-eters using only the iron lines are negligible when studyingsolar twin stars. This had been assumed in our previous work(and similar works by other groups), but it has only now beendemonstrated. – ii) A very tight log R ′ HK versus age relation is found for oursample of solar twin stars thanks to the high precision of ourrelative stellar ages. This trend can be employed to quanti-tatively constrain evolutionary models of stellar activity androtation. The fact that the solar cycle fits this trend and itsdispersion very well shows that the sample size is appropri-ate to take variations in the log R ′ HK index due to the stars’activity cycles into account, although that will be further im-proved once our multi-epoch HARPS data are analyzed in asimilar way.The stellar parameters ( T e ff , log g , [Fe / H], v t ) and fundamen-tal properties (mass, age, stellar activity) determined here willbe employed in a subsequent series of papers aiming to obtain athigh precision the detailed chemical composition of solar twinsand to characterize the stars’ planetary systems from our dedi-cated solar twin planet search. Furthermore, our sample will bealso useful for other applications related to stellar astrophysics,such as constraining non-standard stellar models and studyingthe chemical evolution of our Galaxy. Acknowledgements.
I.R. acknowledges past support from NASA’s SaganFellowship Program to conduct the MIKE / Magellan observations presented inthis paper. J.M. would like to acknowledge support from FAPESP (2012 / / References
Allende Prieto, C., Barklem, P. S., Lambert, D. L., & Cunha, K. 2004, A&A,420, 183Alonso, A., Arribas, S., & Martinez-Roger, C. 1996, A&AS, 117, 227Anders, E. & Grevesse, N. 1989, Geochim. Cosmochim. Acta, 53, 197Asplund, M. 2005, ARA&A, 43, 481Barklem, P. S. 2007, A&A, 466, 327Barklem, P. S., Stempels, H. C., Allende Prieto, C., et al. 2002, A&A, 385, 951Barnes, S. A. 2010, ApJ, 722, 222Baumann, P., Ram´ırez, I., Mel´endez, J., Asplund, M., & Lind, K. 2010, A&A,519, A87Bensby, T., Feltzing, S., & Oey, M. S. 2014, A&A, 562, A71Bernstein, R., Shectman, S. A., Gunnels, S. M., Mochnacki, S., & Athey,A. E. 2003, in Society of Photo-Optical Instrumentation Engineers (SPIE)Conference Series, ed. M. Iye & A. F. M. Moorwood, Vol. 4841, 1694–1704Blackwell, D. E., Shallis, M. J., & Selby, M. J. 1979, MNRAS, 188, 847Casagrande, L., Portinari, L., Glass, I. S., et al. 2014, MNRAS, 439, 2060Casagrande, L., Ram´ırez, I., Mel´endez, J., & Asplund, M. 2012, ApJ, 761, 16Casagrande, L., Ram´ırez, I., Mel´endez, J., Bessell, M., & Asplund, M. 2010,A&A, 512, 54Casagrande, L., Sch¨onrich, R., Asplund, M., et al. 2011, A&A, 530, A138 Castelli, F. & Kurucz, R. L. 2004, arXiv / / NSpectroscopy on Stellar Physics, ed. G. Cayrel de Strobel & M. Spite (KluwerAcademic Publishers, Dordrecht), 345Cayrel de Strobel, G. 1996, A&A Rev., 7, 243Chambers, J. E. 2010, ApJ, 724, 92Cincunegui, C., D´ıaz, R. F., & Mauas, P. J. D. 2007, A&A, 469, 309da Silva, L., Girardi, L., Pasquini, L., et al. 2006, A&A, 458, 609Dumusque, X., Udry, S., Lovis, C., Santos, N. C., & Monteiro, M. J. P. F. G.2011, A&A, 525, A140Duncan, D. K., Vaughan, A. H., Wilson, O. C., et al. 1991, ApJS, 76, 383Duquennoy, A. & Mayor, M. 1988, A&A, 195, 129Epstein, C. R., Johnson, J. A., Dong, S., et al. 2010, ApJ, 709, 447Fuhrmann, K., Axer, M., & Gehren, T. 1993, A&A, 271, 451Gehren, T. 1981, A&A, 100, 97Ghezzi, L., Cunha, K., Smith, V. V., et al. 2010, ApJ, 720, 1290Gonzalez, G. 1997, MNRAS, 285, 403Gonzalez, G. 2011, MNRAS, 416, L80Gonzalez, G., Carlson, M. K., & Tobin, R. W. 2010, MNRAS, 407, 314Gonz´alez Hern´andez, J. I. & Bonifacio, P. 2009, A&A, 497, 497Gonz´alez Hern´andez, J. I., Delgado-Mena, E., Sousa, S. G., et al. 2013, A&A,552, A6Gonz´alez Hern´andez, J. I., Israelian, G., Santos, N. C., et al. 2010, ApJ, 720,1592Gray, R. O., Corbally, C. J., Garrison, R. F., et al. 2006, AJ, 132, 161Gustafsson, B., Edvardsson, B., Eriksson, K., et al. 2008, A&A, 486, 951Hall, J. C., Henry, G. W., & Lockwood, G. W. 2007, AJ, 133, 2206Hall, J. C., Henry, G. W., Lockwood, G. W., Ski ff , B. A., & Saar, S. H. 2009,AJ, 138, 312Hartkopf, W. I., Tokovinin, A., & Mason, B. D. 2012, AJ, 143, 42Henry, T. J., Soderblom, D. R., Donahue, R. A., & Baliunas, S. L. 1996, AJ, 111,439Jenkins, J. S., Jones, H. R. A., Tinney, C. G., et al. 2006, MNRAS, 372, 163Jenkins, J. S., Murgas, F., Rojo, P., et al. 2011, A&A, 531, A8Jørgensen, B. R. & Lindegren, L. 2005, A&A, 436, 127Kim, Y., Demarque, P., Yi, S. K., & Alexander, D. R. 2002, ApJS, 143, 499Kurucz, R. L., Furenlid, I., Brault, J., & Testerman, L. 1984, Solar flux atlas from296 to 1300 nm (National Solar Observatory Atlas, Sunspot, New Mexico:National Solar Observatory, 1984)Lachaume, R., Dominik, C., Lanz, T., & Habing, H. J. 1999, A&A, 348, 897Laws, C. & Gonzalez, G. 2001, ApJ, 553, 405Lovis, C., Dumusque, X., Santos, N. C., et al. 2011, arXiv / ff en, M., & Bonifacio, P. 2009, A&A, 502, L1Mayor, M., Pepe, F., Queloz, D., et al. 2003, The Messenger, 114, 20Mel´endez, J., Asplund, M., Gustafsson, B., & Yong, D. 2009, ApJ, 704, L66Mel´endez, J., Bergemann, M., Cohen, J. G., et al. 2012, A&A, 543, A29Mel´endez, J. & Ram´ırez, I. 2007, ApJ, 669, L89Mel´endez, J., Ram´ırez, I., Karakas, A. I., et al. 2014a, ApJ, 791, 14Mel´endez, J., Schirbel, L., Monroe, T. R., et al. 2014b, A&A, 567, L3Mel´endez, J., Schuster, W. J., Silva, J. S., et al. 2010, A&A, 522, A98Mermilliod, J., Mermilliod, M., & Hauck, B. 1997, A&AS, 124, 349Monroe, T. R., Mel´endez, J., Ram´ırez, I., et al. 2013, ApJ, 774, L32Nidever, D. L., Marcy, G. W., Butler, R. P., Fischer, D. A., & Vogt, S. S. 2002,ApJS, 141, 503Pereira, T. M. D., Asplund, M., Collet, R., et al. 2013, A&A, 554, A118Perryman, M. A. C., Lindegren, L., Kovalevsky, J., et al. 1997, A&A, 323, L49Pont, F. & Eyer, L. 2004, MNRAS, 351, 487Porto de Mello, G. F. & da Silva, L. 1997, ApJ, 482, L89Ram´ırez, I., Allende Prieto, C., & Lambert, D. L. 2013, ApJ, 764, 78Ram´ırez, I., Asplund, M., Baumann, P., Mel´endez, J., & Bensby, T. 2010, A&A,521, A33Ram´ırez, I. & Mel´endez, J. 2005, ApJ, 626, 446Ram´ırez, I., Mel´endez, J., & Asplund, M. 2009, A&A, 508, L17Ram´ırez, I., Mel´endez, J., Cornejo, D., Roederer, I. U., & Fish, J. R. 2011, ApJ,740, 76Ram´ırez, I., Michel, R., Sefako, R., et al. 2012, ApJ, 752, 5Santos, N. C., Israelian, G., & Mayor, M. 2004, A&A, 415, 1153Schuler, S. C., Cunha, K., Smith, V. V., et al. 2011a, ApJ, 737, L32Schuler, S. C., Flateau, D., Cunha, K., et al. 2011b, ApJ, 732, 55Skumanich, A. 1972, ApJ, 171, 565Sneden, C. A. 1973, PhD thesis, The University of Texas at AustinSousa, S. G., Santos, N. C., Mayor, M., et al. 2008, A&A, 487, 373Stefanik, R. P., Latham, D. W., & Torres, G. 1999, in Astronomical Society of thePacific Conference Series, Vol. 185, IAU Colloq. 170: Precise Stellar RadialVelocities, ed. J. B. Hearnshaw & C. D. Scarfe, 354Tokovinin, A., Hartung, M., & Hayward, T. L. 2013, AJ, 146, 8Tucci Maia, M., Mel´endez, J., & Ram´ırez, I. 2014, ApJ, 790, L25
13. Ram´ırez et al.: Fundamental parameters of solar twins
Udry, S., Mayor, M., & Queloz, D. 1999, in Astronomical Society of thePacific Conference Series, Vol. 185, IAU Colloq. 170: Precise Stellar RadialVelocities, ed. J. B. Hearnshaw & C. D. Scarfe, 367Valenti, J. A. & Fischer, D. A. 2005, ApJS, 159, 141van Leeuwen, F. 2007, A&A, 474, 653Wright, J. T., Marcy, G. W., Butler, R. P., & Vogt, S. S. 2004, ApJS, 152, 261Yi, S., Demarque, P., Kim, Y., et al. 2001, ApJS, 136, 417
14. Ram´ırez et al.: Fundamental parameters of solar twins
Table 2.
Sample of solar twin starsHIP HD V UT of observation JD RV log R ′ HK (mag) (Y-M-D / H:M:S) (days) (km s − )1954 2071 7.27 2011-01-03 / . ± . − . / . ± . − . / − . ± . − . / . ± . − . / . ± . − . / − . ± . − . / − . ± . − . / . ± . − . / . ± . − . / − . ± . − . / . ± . − . / . ± . − . / − . ± . − . / . ± . − . / . ± . − . / . ± . − . / − . ± . − . / − . ± . − . / . ± . − . / . ± . − . / − . ± . − . / . ± . − . / − . ± . − . / . ± . − . / . ± . − . / . ± . − . / . ± . − . / . ± . − . / . ± . − . / . ± . − . / . ± . − . / . ± . − . / . ± . − . / . ± . − . / . ± . − . / . ± . − . / . ± . − . / . ± . − . / . ± . − . / − . ± . − . / − . ± . − . / − . ± . − . / . ± . − . / . ± . − . / − . ± . − . / . ± . − . / . ± . − . / . ± . − . / . ± . − . / . ± . − . / − . ± . − . / . ± . − . / . ± . − . / − . ± . − . / . ± . − . / . ± . − . / . ± . − . / . ± . − . / − . ± . − . / − . ± . − . / . ± . − . / − . ± . − . / − . ± . − . / . ± . − . / . ± . − . / . ± . − .
962 15. Ram´ırez et al.: Fundamental parameters of solar twins
Table 2. continued.HIP HD V UT of observation RJD RV log R ′ HK (mag) (Y-M-D / H:M:S) (days) (km s − )83276 153631 7.13 2012-04-30 / . ± . − . / − . ± . − . / . ± . − . / . ± . − . / . ± . − . / − . ± . − . / . ± . − . / − . ± . − . / − . ± . − . / − . ± . − . / . ± . − . / . ± . − . / . ± . − . / . ± . − . / . ± . − . / − . ± . − . / − . ± . − . / . ± . − . / . ± . − . / . ± . − . / − . ± . − . / − . ± . − . Table 3.
Iron line listWavelength Species χ log( g f ) EW ⊙ (Å) (eV) (mÅ)4389.25 26.0 0.05 − .
58 73 . ± . − .
44 40 . ± . − .
15 72 . ± . − .
61 59 . ± . − .
73 67 . ± . − .
13 36 . ± . − .
69 27 . ± . − .
56 74 . ± . − .
08 102 . ± . − .
23 90 . ± . − .
14 99 . ± . − .
79 74 . ± . − .
99 87 . ± . − .
96 67 . ± . − .
94 66 . ± . − .
59 30 . ± . − .
89 62 . ± . − .
74 63 . ± . − .
51 62 . ± . − .
67 33 . ± . − .
63 32 . ± . − .
57 78 . ± . − .
23 34 . ± . − .
19 14 . ± . − .
36 98 . ± . − .
09 53 . ± . − .
27 51 . ± . − .
77 78 . ± . − .
75 19 . ± . − .
75 60 . ± . − .
16 86 . ± . − .
36 39 . ± . − .
20 58 . ± . − .
30 60 . ± . − .
44 22 . ± . − .
53 27 . ± . − .
62 35 . ± . − .
95 55 . ± . − .
23 41 . ± . − .
48 23 . ± . − .
17 89 . ± . − .
07 77 . ± . − .
55 52 . ± . − .
21 70 . ± . − .
06 85 . ± . − .
43 22 . ± . − .
09 65 . ± . − .
40 74 . ± . − .
53 119 . ± . − .
02 47 . ± . − .
57 36 . ± . − .
30 31 . ± . − .
81 38 . ± . − .
28 51 . ± . − .
46 45 . ± . − .
88 69 . ± . − .
62 48 . ± . − .
42 74 . ± . − .
52 83 . ± . − .
43 90 . ± . − .
10 30 . ± . − .
22 85 . ± . − .
29 50 . ± . − .
55 87 . ± . − .
70 25 . ± . − .
43 77 . ± . Table 3. continued.Wavelength Species χ log( g f ) EW ⊙ (Å) (eV) (mÅ)6380.74 26.0 4.19 − .
32 53 . ± . − .
03 17 . ± . − .
01 113 . ± . − .
70 46 . ± . − .
39 85 . ± . − .
97 45 . ± . − .
34 15 . ± . − .
02 38 . ± . − .
98 47 . ± . − .
88 16 . ± . − .
40 21 . ± . − .
19 18 . ± . − .
03 47 . ± . − .
47 27 . ± . − .
79 12 . ± . − .
62 75 . ± . − .
33 13 . ± . − .
11 35 . ± . − .
99 51 . ± . − .
69 17 . ± . − .
35 30 . ± . − .
83 62 . ± . − .
94 52 . ± . − .
88 84 . ± . − .
62 44 . ± . − .
66 79 . ± . − .
52 87 . ± . − .
95 64 . ± . − .
21 54 . ± . − .
73 36 . ± . − .
22 83 . ± . − .
18 84 . ± . − .
13 45 . ± . − .
25 41 . ± . − .
58 28 . ± . − .
22 41 . ± . − .
83 21 . ± . − .
75 36 . ± . − .
38 53 . ± . − .
11 19 . ± . − .
75 40 . ± . − .
57 42 . ± . − .
05 65 . ± . − .
39 14 . ± . . R a m ´ ı r eze t a l . : F und a m e n t a l p a r a m e t e r s o f s o l a r t w i n s Table 4.
Stellar parametersHIP HD T e ff σ ( T e ff ) log g σ (log g ) [Fe / H] σ ([Fe / H]) v t σ ( v t ) M σ ( M ) τ τ − σ τ + σ (K) (K) ([cgs]) ([cgs]) (dex) (dex) (km s − ) (km s − ) ( M ⊙ ) ( M ⊙ ) (Gyr) (Gyr) (Gyr)1954 2071 5717 5 4.46 0.02 − .
068 0.006 0.96 0.02 0.974 0.007 4.7 3.9 5.73203 3821A 5850 10 4.52 0.02 − .
087 0.008 1.16 0.02 1.034 0.008 0.8 0.3 1.64909 6204 5854 10 4.50 0.02 0 .
028 0.008 1.12 0.02 1.052 0.007 1.2 0.0 2.05301 6718 5728 5 4.42 0.02 − .
064 0.004 0.97 0.01 0.967 0.005 6.4 5.7 7.06407 8291 5764 8 4.52 0.01 − .
068 0.007 0.97 0.02 1.005 0.005 0.9 0.6 1.97585 9986 5831 5 4.43 0.01 0 .
095 0.005 1.02 0.01 1.060 0.002 3.3 2.7 3.78507 11195 5725 6 4.49 0.02 − .
096 0.006 0.99 0.02 0.978 0.007 3.6 2.7 4.59349 12264 5810 8 4.50 0.02 0 .
009 0.007 1.07 0.02 1.038 0.010 0.5 0.3 1.910175 13357 5738 7 4.51 0.01 − .
007 0.005 0.96 0.01 1.011 0.005 2.0 1.0 2.610303 13612B 5725 4 4.40 0.01 0 .
106 0.004 0.98 0.01 1.029 0.003 5.3 4.6 5.711915 16008 5760 4 4.46 0.01 − .
059 0.004 0.97 0.01 0.993 0.005 4.0 3.4 4.614501 19467 5728 7 4.29 0.02 − .
133 0.005 1.03 0.01 0.951 0.004 9.9 9.5 10.314614 19518 5784 9 4.42 0.03 − .
099 0.008 1.03 0.02 0.976 0.008 6.1 4.8 6.914623 19632 5769 13 4.52 0.02 0 .
106 0.010 1.15 0.02 1.051 0.008 1.1 0.5 1.815527 20782 5785 5 4.32 0.01 − .
051 0.005 1.05 0.01 0.993 0.005 7.8 7.5 8.118844 25874 5736 5 4.36 0.02 0 .
016 0.004 0.99 0.01 0.989 0.003 7.3 6.9 7.719911 26990 5764 12 4.47 0.04 − .
070 0.011 1.02 0.03 0.987 0.012 4.0 2.4 5.521079 28904 5846 11 4.50 0.03 − .
070 0.008 1.09 0.02 1.026 0.009 0.8 0.4 2.422263 30495 5840 8 4.50 0.02 0 .
030 0.007 1.08 0.02 1.053 0.007 0.5 0.2 1.622395 30774 5789 8 4.43 0.02 0 .
084 0.008 1.11 0.02 1.033 0.006 4.0 3.1 4.725670 36152 5771 5 4.44 0.02 0 .
057 0.005 1.00 0.01 1.025 0.005 4.5 3.4 4.928066 39881 5733 5 4.29 0.01 − .
128 0.004 1.05 0.01 0.959 0.003 9.7 9.4 10.029432 42618 5758 5 4.44 0.01 − .
096 0.005 1.01 0.01 0.974 0.007 5.4 4.6 6.029525 42807 5737 7 4.49 0.02 − .
022 0.007 1.12 0.02 0.997 0.007 2.9 1.8 4.030037 45021 5668 5 4.42 0.01 − .
011 0.004 0.94 0.01 0.961 0.004 6.7 6.1 7.330158 44665 5702 5 4.46 0.02 0 .
003 0.006 0.94 0.02 0.988 0.008 4.5 3.4 5.430344 44821 5750 9 4.50 0.02 0 .
063 0.007 1.09 0.02 1.026 0.005 1.2 0.8 2.430476 45289 5710 5 4.26 0.01 − .
022 0.004 1.03 0.01 0.980 0.002 9.5 9.3 9.830502 45346 5721 6 4.41 0.02 − .
076 0.006 0.98 0.02 0.960 0.003 6.8 6.1 7.533094 50806 5662 7 4.16 0.02 0 .
043 0.005 1.13 0.01 1.005 0.007 9.9 9.6 10.234511 54351 5819 6 4.47 0.02 − .
103 0.006 1.03 0.02 1.005 0.007 3.2 2.5 4.136512 59711 5737 4 4.41 0.01 − .
117 0.004 0.99 0.01 0.957 0.004 6.8 6.4 7.436515 59967 5847 12 4.54 0.02 − .
021 0.009 1.17 0.02 1.046 0.006 0.6 0.0 1.138072 63487 5849 8 4.49 0.02 0 .
058 0.007 1.14 0.02 1.059 0.005 0.9 0.5 1.940133 68168 5755 4 4.37 0.01 0 .
128 0.004 1.01 0.01 1.050 0.003 5.1 4.8 5.441317 71334 5700 5 4.38 0.01 − .
068 0.004 0.96 0.01 0.958 0.004 8.0 7.6 8.542333 73350 5848 8 4.50 0.02 0 .
138 0.008 1.16 0.02 1.086 0.005 1.0 0.4 1.543297 75302 5702 5 4.46 0.01 0 .
083 0.006 0.99 0.02 1.011 0.004 3.5 3.0 4.444713 78429 5768 6 4.28 0.01 0 .
088 0.005 1.06 0.01 1.039 0.003 7.3 7.0 7.644935 78534 5782 5 4.37 0.01 0 .
058 0.005 1.04 0.01 1.020 0.001 6.1 5.6 6.544997 78660 5731 5 4.47 0.02 − .
023 0.005 0.95 0.01 0.995 0.008 3.7 2.8 4.749756 88072 5795 4 4.42 0.01 0 .
043 0.004 1.01 0.01 1.022 0.004 4.6 4.0 5.054102 96116 5820 9 4.51 0.02 − .
014 0.007 1.02 0.02 1.035 0.007 0.5 0.3 1.754287 96423 5727 4 4.36 0.01 0 .
118 0.004 1.01 0.01 1.035 0.005 6.0 5.6 6.354582 97037 5875 7 4.27 0.02 − .
080 0.005 1.17 0.01 1.032 0.006 7.1 6.8 7.455409 98649 5700 6 4.40 0.02 − .
080 0.006 0.94 0.02 0.950 0.001 7.9 7.1 8.462039 110537 5753 6 4.35 0.02 0 .
088 0.005 1.05 0.01 1.028 0.004 6.3 5.9 6.864150 114174 5747 6 4.39 0.02 0 .
030 0.007 1.00 0.02 0.991 0.004 6.4 5.7 7.0 . R a m ´ ı r eze t a l . : F und a m e n t a l p a r a m e t e r s o f s o l a r t w i n s Table 4. continued.HIP HD T e ff σ ( T e ff ) log g σ (log g ) [Fe / H] σ ([Fe / H]) v t σ ( v t ) M σ ( M ) τ τ − σ τ + σ (K) (K) ([cgs]) ([cgs]) (dex) (dex) (km s − ) (km s − ) ( M ⊙ ) ( M ⊙ ) (Gyr) (Gyr) (Gyr)64673 115031 5918 8 4.35 0.02 − .
030 0.007 1.21 0.02 1.048 0.007 5.4 4.7 5.764713 115169 5767 8 4.46 0.02 − .
067 0.007 1.00 0.02 0.989 0.009 4.0 3.0 5.265708 117126 5755 6 4.25 0.02 − .
066 0.006 1.09 0.01 0.987 0.005 9.2 8.9 9.567620 120690 5670 9 4.41 0.03 − .
018 0.009 1.01 0.03 0.954 0.006 7.5 6.2 8.368468 122194 5845 6 4.37 0.02 0 .
054 0.005 1.13 0.01 1.040 0.002 5.2 4.7 5.669645 124523 5743 6 4.44 0.02 − .
045 0.006 0.99 0.02 0.981 0.008 5.2 4.3 6.072043 129814 5842 8 4.35 0.02 − .
034 0.007 1.12 0.02 1.015 0.006 6.4 5.9 6.873241 131923 5669 8 4.27 0.02 0 .
082 0.007 1.01 0.02 0.991 0.004 9.3 8.9 9.673815 133600 5788 6 4.37 0.02 0 .
004 0.005 1.05 0.01 1.003 0.005 6.5 6.0 6.974389 134664 5844 5 4.49 0.01 0 .
077 0.004 1.07 0.01 1.065 0.005 0.9 0.7 1.774432 135101 5684 8 4.25 0.02 0 .
037 0.007 1.09 0.02 0.986 0.005 9.6 9.3 9.976114 138573 5733 6 4.42 0.02 − .
037 0.006 0.97 0.02 0.977 0.007 6.1 5.2 6.877052 140538 5683 5 4.48 0.02 0 .
036 0.006 0.96 0.02 0.993 0.007 3.2 2.4 4.377883 142331 5690 6 4.40 0.02 − .
006 0.006 0.99 0.02 0.969 0.003 7.1 6.4 7.879578 145825 5820 5 4.47 0.01 0 .
057 0.005 1.04 0.01 1.052 0.007 2.3 1.4 2.879672 146233 5814 3 4.45 0.01 0 .
056 0.003 1.02 0.01 1.045 0.005 3.0 2.4 3.379715 145927 5803 6 4.38 0.02 − .
041 0.005 1.09 0.01 0.998 0.004 6.4 5.9 6.881746 150248 5715 5 4.40 0.02 − .
086 0.004 0.99 0.01 0.960 0.002 7.6 6.8 8.083276 153631 5885 8 4.22 0.02 − .
089 0.006 1.23 0.01 1.038 0.008 7.4 7.1 7.785042 157347 5694 5 4.41 0.02 0 .
015 0.004 1.00 0.01 0.975 0.005 6.7 5.9 7.287769 163441 5807 6 4.40 0.02 0 .
041 0.006 1.05 0.01 1.024 0.005 5.2 4.3 5.789650 167060 5841 5 4.44 0.02 − .
037 0.005 1.08 0.01 1.026 0.006 3.8 3.0 4.495962 183658 5806 5 4.44 0.02 0 .
023 0.005 1.04 0.01 1.024 0.007 4.2 3.1 4.796160 183579 5781 8 4.50 0.02 − .
053 0.007 0.96 0.02 1.009 0.007 2.4 1.3 3.0101905 196390 5890 6 4.47 0.02 0 .
057 0.006 1.07 0.02 1.072 0.008 1.1 0.8 2.3102040 197076A 5838 6 4.48 0.02 − .
093 0.006 1.05 0.02 1.018 0.008 2.9 1.7 3.5102152 197027 5718 5 4.40 0.02 − .
020 0.005 0.95 0.01 0.972 0.004 6.7 6.0 7.4103983 200565 5752 10 4.51 0.02 − .
048 0.008 0.96 0.02 1.000 0.008 1.9 1.0 2.8104045 200633 5831 6 4.47 0.02 0 .
045 0.005 1.00 0.01 1.045 0.007 2.5 1.4 3.1105184 202628 5833 11 4.54 0.02 − .
002 0.009 0.99 0.02 1.045 0.008 0.3 0.2 0.7108158 207700 5687 7 4.34 0.02 0 .
050 0.007 0.97 0.02 0.980 0.003 8.3 7.8 8.7108468 208704 5829 7 4.33 0.02 − .
111 0.006 1.16 0.01 0.990 0.003 7.5 7.1 7.9108996 209562 5847 17 4.53 0.03 0 .
064 0.013 1.11 0.03 1.060 0.009 1.0 0.0 1.7109110 209779 5787 17 4.50 0.04 0 .
035 0.014 1.06 0.03 1.026 0.011 1.8 1.0 3.4109821 210918 5746 7 4.31 0.02 − .
115 0.005 1.06 0.01 0.960 0.003 9.2 8.8 9.6114615 219057 5816 9 4.52 0.02 − .
077 0.008 1.04 0.02 1.022 0.008 0.5 0.2 1.6115577 220507 5699 9 4.25 0.03 0 .
036 0.008 1.12 0.02 0.989 0.006 9.5 9.1 9.8116906 222582 5792 6 4.37 0.02 0 .
010 0.005 1.05 0.01 1.003 0.005 6.5 6.0 6.8117367 223238 5871 8 4.32 0.02 0 .
044 0.007 1.15 0.02 1.050 0.007 5.9 5.5 6.3118115 224383 5808 7 4.28 0.02 − .
017 0.006 1.12 0.01 1.013 0.005 7.7 7.3 8.0017 0.006 1.12 0.01 1.013 0.005 7.7 7.3 8.0