Non-LTE abundances of Mg and K in extremely metal-poor stars and the evolution of [O/Mg], [Na/Mg], [Al/Mg] and [K/Mg] in the Milky Way
S.M. Andrievsky, Monique Spite, S.A. Korotin, F. Spite, P. Bonifacio, R. Cayrel, P. François, V. Hill
aa r X i v : . [ a s t r o - ph . GA ] J a n c (cid:13) ESO 2018
Astronomy & Astrophysics
Non-LTE abundances of Mg and K in extremely metal-poor starsand the evolution of [O/Mg], [Na/Mg], [Al/Mg] and [K/Mg] in theMilky Way. ⋆ S.M. Andrievsky , , M. Spite , S.A. Korotin , F. Spite , P. Bonifacio , , , R. Cayrel , P. Franc¸ois , and V. Hill GEPI, Observatoire de Paris, CNRS, Universit´e Paris Diderot; F-92125 Meudon Cedex, France, e-mail : [email protected] Department of Astronomy and Astronomical Observatory, Odessa National University, Isaac Newton Institute of Chile, Odessabranch, Shevchenko Park, 65014 Odessa, Ukraine, e-mail : [email protected] CIFIST Marie Curie Excellence Team Istituto Nazionale di Astrofisica, Osservatorio Astronomico di Trieste, Via Tiepolo 11, I-34143 Trieste, Italy Observatoire de la Cote dAzur, CNRS UMR6202, BP4229, 06304 Nice Cedex4, France
ABSTRACT
Aims.
LTE abundances of light elements in extremely metal-poor (EMP) stars have been previously derived from high quality spectra.New derivations, free from the NLTE e ff ects, will better constrain the models of the Galactic chemical evolution and the yields of thevery first supernovae. Methods.
The NLTE profiles of the magnesium and potassium lines have been computed in a sample of 53 extremely metal-poor starswith a modified version of the program MULTI and adjusted to the observed lines in order to derive the abundances of these elements.
Results.
The NLTE corrections for magnesium and potassium are in good agreement with the works found in the literature. Theabundances are slightly changed, reaching a better precision: the scatter around the mean of the abundance ratios has decreased.Magnesium may be used with confidence as reference element. Together with previously determined NLTE abundances of sodiumand aluminum, the new ratios are displayed, for comparison, along the theoretical trends proposed by some models of the chemicalevolution of the Galaxy, using di ff erent models of supernovae. Key words.
Galaxy: abundances – Galaxy: halo – Galaxy: evolution – Stars: abundances – Stars: mixing – Stars: Supernovae
1. Introduction
In the frame of the ESO Large Program ”First stars, first nu-cleosynthesis” Cayrel et al. (2004) and Bonifacio et al. (2007,2009) have studied an homogeneous sample of extremely metal-poor giants and turno ff stars. For about fifty stars, most of themwith [Fe / H] < −
3, they determine the abundances of the ele-ments from C to Zn, especially of the light metals Na, Mg, Aland K, in the early Galaxy. These abundances are based on LTEcomputations of the equivalent widths or of the line profiles.After sodium and aluminum (Andrievsky et al., 2007, 2008)we present here non-LTE determinations of the magnesium andpotassium abundances by comparison of the observed and com-puted line profiles and we discuss the evolution of the abundanceratios [O / Mg], [Na / Mg], [Al / Mg] and [K / Mg] in the Galaxy.Recently, Takeda et al. (2009) have computed the non-LTE abun-dance of potassium in the same sample of EMP stars, based onthe equivalent widths of the potassium lines given in Cayrel etal. (2004). We compare our results with their determinations.In Cayrel et al. (2004) and Bonifacio et al. (2007, 2009), ironhad been first chosen as the main tracer of the chemical evolu-tion of the Galaxy. It had also been noted however,that iron isperhaps not the best choice since there are several processes thata ff ect the yield of iron : Si burning in massive SNe II, explo- ⋆ Based on observations obtained with the ESO Very Large Telescopeat Paranal Observatory (Large Programme ”First Stars”, ID 165.N-0276; P.I.: R. Cayrel. sive nucleosynthesis, mixing and fallback episodes and possi-ble late SN Ia contributions. Magnesium is, in principle, a betterchoice since this element is mainly formed in massive SNe, itsproduction is dominated by hydrostatic carbon burning, and it isless a ff ected by explosive burning and fallback (e. g. Woosley &Weaver, 1995). Among others, Shigeyama & Tsujimoto (1998)recommended Mg rather than Fe as a reference element, follow-ing the same logic.Cayrel et al. (2004) have recognised this too and have ac-cordingly used magnesium as a reference element to comparethe observed ratios [X / Mg] to the ejecta of the massive super-novae in the last part of the paper. But it appeared that unexpect-edly the relations [X / Mg] vs. [Mg / H] were more scattered thanthe corresponding relations [X / Fe] vs. [Fe / H]. Also, in Bonifacioet al. (2009), the mean value of [Mg / Fe] di ff ered significantly ingiant and turno ff stars. As a consequence we suspected that boththe unexpected behaviour of the scatter of the ratios [X / Mg] andthe di ff erent behaviour of dwarfs and giants could be due at leastpartly to the neglect of the departures from LTE.- In Sect. 2 we present the characteristics of the atomic modelsused for the non-LTE computations.- In Sect. 3 are presented the main parameters of the analysis.- In Sect. 4 we discuss the ratios [Mg / Fe] and [K / Fe] in the earlyGalaxy, and we compare the ratios [O / Mg], [Na / Mg], [Al / Mg]and [K / Mg] at low metallicity to the predictions of the ejectaof supernovae / hypernovae. Finally for a complete halo-disk pic-ture we have also added the NLTE determinations of the abun- Andrievsky: Relative abundances of light metals in EMP stars dances of Na, Mg, Al and K in the disk from the ”Gehren team”(Gehren et al. 2004, 2006, Mashonkina et al. 2008, and Zhang etal. 2006), to study the evolution of these ratios in the Galaxy andto compare this to the predictions of the models of the chemicalevolution of the Galaxy.
Fig. 1.
Profile fitting of the magnesium lines in the solar spec-trum.
Fig. 2.
Profile fitting of the potassium lines in thesolar spectrum.
2. Atomic models and NLTE calculations
The atomic model of magnesium used in this work is essen-tially the same as the onedescribed in Mishenina et al. (2004).This model consists of 84 levels of Mg i , 12 levels of Mg ii andthe ground level of Mg iii (Martin & Zalubas, 1980, Biemont& Brault 1986). Within the described system the transitions be-tween the 59 first levels of Mg i and the ground level of Mg ii have been considered. The detailed structure of the multipletswas ignored and each LS multiplet was considered as a sin-gle term. The fine structure was taken into account only for the3s3p P level (more details in Mishenina et al. 2004). Our model of the K i atom is based on the model of Bruls etal. (1992). In our implementation we considered in detail all thetransitions between the first 20 levels of the K i and the groundlevel of the K ii . For the level 4p2P we took into account thefine splitting. The other levels were considered as single levels.Fifteen additional levels of K i and 7 levels of K ii were usedto allow the conservation of the number of particles. The levelenergies are taken from Sugar & Corliss (1985). The oscillatorstrengths of the bound-bound transitions are takenfrom Wiese etal. (1969) as well as Biemont & Grevesse (1973). For the res-onance transitions we used data from Morton (1991). The totalnumber of bound-bound transitions considered in detail is 62.Photoionization cross-sections from the ground level ofpotassium were reported by Rahman-Attia et al. (1986). For p-levels we took ionization cross-sections published by Aymar etal. (1976). For 2S, 2D, 2F levels the cross-sections calculatedwith the help of quantum defect method (Hofsaess, 1979) wereused. For the other levels, we used the hydrogen-like approxima-tion. The electron collisional rates were estimated with the helpof the Van Regemorter (1962) formula, while Allen’s (1973) for-mula was used for forbidden transitions. The collisional ioniza-tion from the ground level was described using the correspond-ing formula from Sobelman et al. (1981). For the other levels weused Seaton’s (1962) formula. To take into account collisions ofpotassium atoms with hydrogen atoms we applied the formula ofSteenbock & Holweger (1984) with a correcting factor equal to0.05. A similar correcting factor was used by Zhang et al. (2006).The principal di ff erence between the LTE and NLTE-basedabundances is caused by an over-recombination on the first levelof the K i atom in the atmospheres of the late-type stars. Thisleads to an increase of the equivalent widths of the K i ff ect is given inIvanova & Shymansky (2000). To verify our adopted atomic models of magnesium and potas-sium we have carried out the computation of the NLTE syntheticprofiles of several magnesium and potassium lines. The SolarFlux Atlas of Kurucz (1984) in the visual and infra red rangewas used for this purpose.The NLTE profiles have been determined with the help ofthe modified ”MULTI” code of Carlsson (1986). The modifica-tions are described in Korotin et al. (1999), they include opac-ity sources from ATLAS9 (Kurucz 1992). The Kurucz’s (1996) ndrievsky: Relative abundances of light metals in EMP stars 3 model of the solar atmosphere has been used in these computa-tions.The damping constants have been taken from the ViennaAtomic Line Data Base (VALD, Piskunov et al., 1995). The cor-rection ∆ logC found by Mishenina et al. (2004) has been ap-plied for the computation of the magnesium lines. The NLTEprofiles of the Mg I lines computed with log(Mg / H) = . / H) ⊙ = .
58. Thepotassium lines are also well reproduced by our calculations(see Fig. 2) with a potassium abundance log(K / H) ⊙ = .
11, ingood agreement with the value adopted by Zhang et al. (2006),and very close to the meteoritic potassium abundance (Lodders,2003).
3. Analysis of the star sample
The sample of stars and the observational data are the same asdiscussed in Cayrel et al. (2004). The observations were per-formed with the high resolution spectrograph UVES at the VLT(Dekker et al., 2000). The resolving power in the region of themagnesium lines is R ≈ ,
000 and it is R ≈ ,
000 in the re-gion of the potassium lines. The S / N ratio is generally ≈ / pix with about 5 pixels per resolution element. In this region of thepotassium lines, residual fringes limit the precision of the mea-surements and in most of the stars a line with an equivalent widthless than 3 mÅ cannot be detected.The spectra have been reduced using the UVES context(Ballester et al. 2000). The parameters of the atmosphere of the stars T e ff , log g , v t and[Fe / H] are given in Table 1, and are quoted from the LTE analy-ses of Cayrel et al. (2004) and Bonifacio et al. (2007, 2009). An”m” in the last column of the table means that the atmosphere ofthe star (giant) has been found ”mixed” with the deep hydrogenburning layer by Spite et al. (2005, 2006a). For the determinationof the relative LTE and NLTE abundances, we adopted in this ta-ble the solar values log(Mg / H) ⊙ = .
58 and log(K / H) ⊙ = . As a comparison, we give in Table 1 new abundances of magne-sium and potassium computed with the LTE hypothesis. Thesenew determinations have been obtained by fitting the syntheticspectra with the observed profiles.For the abundance of potassium the result is sometimesslightly di ff erent from the value published in Cayrel et al. (2004)because, for example, a di ff erent position of the continuum hasbeen adopted.However, the di ff erence is larger for magnesium. In Cayrelet al. (2004) the equivalent widths of magnesium lines in giantshave been often underestimated: the lines are often strong andthe wings had been neglected. This error has been corrected inBonifacio et al. (2009). The correction is negligible for the mostmagnesium-poor giants, but in in the other (less Mg-poor) gi-ants, the di ff erence is about 0.15 dex. To compute NLTE profiles of the magnesium and potassiumlines, we have used Kurucz’s models (ATLAS9) without over-shooting (Kurucz 1993). We have checked on some typical starsthat the use of MARCS models (Gustafsson et al., 2008) as inCayrel et al. (2004) would not make a significant di ff erence.The NLTE corrections depend on the e ff ective temperatureand gravity of the model, as well as on the element abundanceitself. The latter circumstance strongly suggests that the abun-dances must be derived individually for each star using com-plete NLTE computation. The use of published NLTE correc-tions as a function T e ff and log g can introduce some errors inthe derived abundances if the abundances are di ff erent. For ex-ample in metal-poor stars in the range − . < [Fe / H] < − . / H] < − .
0) the potassium line is very weak (the equiva-lent width of the 7699 Å line is always less than 25 mÅ andoften less than 10 mÅ); the line is thus formed rather deeplyin the atmosphere where collisions are important and finallythe NLTE correction at these metallicities is small. As a con-sequence, the use of a uniform NLTE correction (computed byIvanova & Shymansky for a metallicity of -2.0), has led Cayrelet al. (2004) to underestimate the potassium abundance at verylow metallicity. λ R E L A T I VE FL U X (A) BS 16968-61 λ (A) BS 16968-61 λ R E L A T I VE FL U X (A) HD186478 λ (A) HD186478
Fig. 3.
Magnesium. Profile fitting for two metal-poor starswith di ff erent e ff ective temperature, with similar metallicity:[Fe / H] ≈ − .
8. One is a turno ff star (BS 16968-61), the other agiant (HD 186478). The Mg abundance was varied by 0.10 dex(dotted lines).The profile fitting for two metal-poor stars is displayed inFig. 3 and 4. The NLTE magnesium and potassium abundancesin our program stars are listed in Table 1. In this table, we givealso as a comparison the abundance of these elements computed Andrievsky: Relative abundances of light metals in EMP stars
Table 1.
Adopted model and potassium abundance for our sample of stars. In the last column the letter m indicates that the gianthas been found “mixed” (see text). T e ff log v t LTE NLTE NLTE NLTE LTE NLTE NLTE NLTEstar (K) g (kms − ) [Fe / H] ǫ (Mg) ǫ (Mg) [Mg / H] [Mg / Fe] ǫ (K) ǫ (K) [K / H] [K / Fe] Rem
GIANTS
01 HD 2796 4950 1.5 2.1 -2.47 5.54 5.74 -1.84 0.63 3.25 2.90 -2.22 0.25 m02 HD 122563 4600 1.1 2.0 -2.82 5.29 5.39 -2.19 0.63 2.78 2.57 -2.55 0.27 m03 HD 186478 4700 1.3 2.0 -2.59 5.55 5.72 -1.86 0.73 3.10 2.85 -2.27 0.32 m04 BD + TURNOFF independently with the LTE approximation (and without anycorrection). The potassium abundance can be computed only ingiant stars, the lines are not visible in the turno ff stars. ndrievsky: Relative abundances of light metals in EMP stars 5 λ R E L A T I VE FL U X (A) CS 22953-003 λ (A) HD 122563
Fig. 4.
Potassium. Profile fitting for two metal-poor giants, bothwith [Fe / H] ≈ − . ff erent e ff ective temperature. Thebest-fit K abundance was varied by 0.05 dex.
4. Discussion
As recalled in Cayrel et al. (2004), Mg is formed during hy-drostatic carbon burning and explosive neon burning, K duringexplosive oxygen burning; their abundances are therefore relatedto the importance of both the hydrostatic and explosive phases.In Fig. 5 we compare the LTE abundances of magnesium inour sample of EMP dwarfs and giants (Bonifacio et al., 2009)with the new NLTE determinations. The carbon-rich and pecu-liar star CS 22949-037 has been discarded.
Fig. 5. [Mg / Fe] vs. [Fe / H] in the early Galaxy. Open circles (redand blue) stand for ”mixed” and ”unmixed” giants (see Spite etal. 2005, 2006a, 2006b), black filled symbols for turno ff stars. Fig. 6. [K / Fe] vs. [Fe / H] in the early Galaxy. Open circles (redand blue) stand for ”mixed” and ”unmixed” giants respectively(see Spite et al. 2005, 2006a). The potassium abundance cannotbe measured in the turno ff stars, the lines are too weak.The trend of the [Mg / Fe] ratio vs. metallicity at low metal-licity is not changed, it remains a plateau. But the scatter of[Mg / Fe] is smaller when NLTE e ff ects are taken into account:0.13 from NLTE computations and 0.16 from LTE computation.The di ff erence between dwarfs and giants is strongly reducedand is not significant any more. The mean value of [Mg / Fe] inthe interval − < [Fe / H] < − . + + / Fe] is now similarto the mean value of [O / Fe] previously deduced (Cayrel et al.2004) from the forbidden oxygen line (not sensitive to NLTEe ff ects).For the determination of the mean value of the ratios[Mg / Fe], their trend and their scatter around the trend, thecarbon-rich star CS 22949-037 (showing also strong abundanceanomalies of light elements) has been discarded. The star hasbeen as well excluded from all computations and / or figures re-lated to Mg abundances.When NLTE is taken into account, the values of the abun-dance ratios [K / Fe] are slightly decreased. The scatter of [K / Fe]is also slightly smaller. The mean value of [K / Fe] in the interval − < [Fe / H] < − . + ff erences between the two determinations reflectthe fact that we have determined the potassium abundance bya direct fit of the profiles whereas Takeda et al. have used theequivalent widths given in Cayrel et al. (2004).We have estimated star by star the error on [K / Fe] in our sam-ple of stars. This error is dominated by the measurement error(equivalent width or profile) and it increases significantly whenthe metallicity decreases: at low metallicity the potassium lines
Andrievsky: Relative abundances of light metals in EMP stars becomes very weak (less than 10 mÅ and often less than 5 mÅ)in a region where the S / N ratio is only about 100 and where theposition of the continuum is not very precise because of residualfringes. In consequence, as shown in our Fig. 6 we do not con-firm the suggestion of Takeda et al. (2009) of ”a marginal signof decline toward a further lower [Fe / H]”.It is interesting to note that the K-rich star CS 30325-94(LTE, see Cayrel et al. 2004) remains K-rich (and with a smallerror) in the NLTE analysis (see Fig. 6) and it is also Sc-rich. Inthe stellar sample of Zhang & Zhao (2005), the most potassium-rich star HD 195636 (with [Fe / H] = –3.3, and [K / Fe] =+ Oxygen:The magnesium abundances listed in Table 1 can be used as anormalization factor for other elements. It is interesting to com-pute the ratio [O / Mg] using this new NLTE value of the mag-nesium abundance : since the abundance of oxygen has beendetermined from the forbidden oxygen line, is free from NLTEe ff ects. The corresponding plots are shown in Fig. 7.Sodium:As found in Andrievsky et al. (2007), the ”mixed” stars areoften enriched in sodium. This reflects an internal mixing insidethese giant stars. Therefore the mixed stars should not be usedto determine the ratio [Na / Mg] in the early Galaxy. Note thatthe star CS 22952-15 (a mixed star with [Fe / H] = –3.43) is verysodium-rich, but its ratio [Al / Fe] is normal (see Andrievsky etal., 2008). However its ratio [Al / Mg] is also rather high. Theexplanation is that this mixed star is Na-rich and Mg-poor.Mean value and scatter:Since the abundances of O, Na, Al and K relative to Mg arerather flat in their central part, we can define a mean value in thiscentral interval, say − . < [Fe / H] < − .
5. The mean values ofthese flat parts are :[O / Mg] ≈ .
1, [Na / Mg] ≈ − .
8, [Al / Mg] ≈ − . / Mg] ≈ − . − . < [Fe / H] < − . σ [O / Fe] = .
18 but σ [O / Mg] = . σ [Na / Fe] = .
12 but σ [Na / Mg] = . σ [Al / Fe] = . , σ [Al / Mg] = . σ [K / Fe] = . σ [K / Mg] = . ff erently); the scatter of [Na / Mg] and [K / Mg]would then be smaller than the scatter of [Na / Fe] and [K / Fe], butthe observations show the contrary.
Fig. 7.
Abundance of O, Na, Al, and K relative to Mg in theearly Galaxy. The abundances of all these elements have beencomputed taking into account the NLTE e ff ect. Since the mea-sured oxygen lines are forbidden lines they are free from NLTEe ff ects. It is interesting to compare the abundance ratios [O / Mg],[Na / Mg], [Al / Mg] and [K / Mg] to the predictions of the ejectaof metal-poor supernovae or hypernovae. In Fig. 8 the observedratios are compared to the predictions of Woosley & Weaver(1995), of Heger & Woosley (2008, 2002), of Chie ffi & Limongi(2003), and Kobayashi et al. for supernovae and hypernovae(Kobayashi et al., 2006). Fig. 8.
Comparison of the new abundance ratios to the predic-tions of supernovae or hypernovae.The quantity of potassium ejected is generally underesti-mated by the models of supernovae. The best agreement isobtained by the predictions of Heger & Woosley (2008) withthe hypotheses B and D (see the paper), although the abun-dance of sodium and aluminum are in this case a little overes-timated. The ratio Al / Mg is also well represented in the modelof Chie ffi & Limongi (2003). Unfortunately there are no pre-dictions for the abundance of O, Na and K in this model. Themodels of Kobayashi et al. (2006) (supernovae and hypernovaewith Z = ndrievsky: Relative abundances of light metals in EMP stars 7 of O, Na, Mg and Al, but here again the production of potassiumis strongly underestimated. In Fig. 9 we present the variation of [O / Mg], [Na / Mg], [Al / Mg]and [K / Mg] in the Galaxy as a function of [Mg / H] where Na, Al,Mg and K have been computed taking into account the NLTEe ff ects (the oxygen abundance deduced from forbidden lines isnot a ff ected by departure from LTE).As already noted, [Mg / H] should be a better index of time,since magnesium is only formed in massive SN II with a shortlifetime, unlike iron formed in SN II or SN I of various masses.We have added in the figure the determinations of Gehren etal. (2004, 2006), of Mashonkina et al. (2008), and Zhang et al.(2006) in the Galactic disk and halo. All these determinationshave been done including the NLTE e ff ects on the line profiles.As seen in Fig. 9, the abundance ratios [Na / Mg], [Al / Mg]and [K / Mg] in the Galaxy decrease with [Mg / H] from [Mg / H] = / H] = –2, then are almost constant between [Mg / H] = –2 and [Mg / H] = –2.8, and finally, at lower metallicity, the ratios[Na / Mg], [Al / Mg], and [K / Mg] and maybe also [O / Mg] seem toincrease when [Mg / H] decreases. (The error on [O / Mg] in thetwo most magnesium-poor stars is large and thus this tendencyis not firmly established for oxygen.)In Fig. 9 the evolutions of the abundance ratios [O / Mg],[Na / Mg], [Al / Mg] and [K / Mg] in the Galaxy are also drawn,following Kobayashi et al. (2006), Franc¸ois et al. (2004) and forNa and Al, Goswami & Prantzos (2000).Kobayashi et al. use new nucleosynthesis yields calculated,from Z = = Z ⊙ , for supernovae and hypernovae. Withthese new yields, the general trend of O, Na and Al is ratherwell reproduced, but not the behaviour of potassium. The under-production of potassium in the models of supernovae has alreaybeen pointed out by Samland (1998). To solve this problem aswell as the underproduction of Si and Sc, Umeda & Nomoto(2005) have proposed to introduce a model of supernova wherethe density is assumed to be reduced (during the explosive burn-ing) to increase the freezeout.The predictions of Franc¸ois et al. (2004) are based on theyields of Woosley & Weaver (1995). For a better fit of the ob-servations they had to systematically increase the productionof K by a factor of 8. In the computations of Kobayashi et al.(2006) the ratio [O / Mg] remains stable at very low metalliciticty.Contrary to that, Fanc¸ois et al. (2004) predict an increase of[O / Mg] when the metallicity decreases for [Mg / H] < − .
5. Themeasurement of [O / Mg] in the two most metal-poor stars in theFig. 9 is unfortunately too uncertain (one is clearly an upperlimit) to enable to choose one of the two models.For Na and Al we give the predictions of Goswami &Prantzos (2000), and of Cescutti et al. (private communication).These predictions are, as in Franc¸ois et al. (2004), based on theyields of Woosley & Weaver (1995) but the yields of low massand intermediate mass stars have been adjusted. Like Kobayashiet al. (2006), they predict a decrease of [Na / Mg] and [Al / Mg]when [Mg / H] decreases, but the agreement with the observationsis better when the model of Kobayashi et al. is adopted.
5. Conclusion
The spectra of the EMP stars, (programme First Stars) analysedpreviously (Cayrel et al. 2004) in LTE have been reanalysed herefor Mg and K, taking into account the departures of LTE.
Fig. 9.
Variation of [O / Mg], [Na / Mg], [Al / Mg], [K / Mg] vs.[Mg / H] in the Galaxy. The red and blue open circles repre-sent our measurements for mixed and unmixed giants (see theelectronic version of A&A for a color version of this figure),the large black dots represent the turno ff stars of our sampleand the small black dots are from Gehren et al. (2004, 2006),Mashonkina et al. (2008), and Zhang et al. (2006), for the diskand halo stars. The thin solid line is the prediction of Franc¸ois etal. (2004) for O and K and of Cescutti et al. (private communica-tion) for Na and Mg. The dashed dotted lines are the predicitionsof Goswami & Prantzos (2000) for Na and Al. These predictionsare based (with occasional adjustments) on the models of super-novae ejecta of Woosley & Weaver (1995). The thick solid linesare the predictions of Kobayashi et al. (2006) based (without ad-justments) on new models of supernovae and hypernovae.Abundances of Mg and K:The NLTE correction for magnesium is in accord with thecorrection computed by Gehren and collaborators (2004, 2006)in less metal-poor stars. The Mg abundance in the giants is raisedby a factor of about 2 and the NLTE abundance of Mg is the Andrievsky: Relative abundances of light metals in EMP stars same in giants and in dwarfs. The O / Mg ratio is nearly solar (theprecision of the O abundance is however rather low).The NLTE abundance of potassium, computed by adjuste-ment of observed and computed profiles, has been compared tothe work of Takeda et al. (2009). The agreement is generallyvery good. When di ff erences do occur, they arise from the factthat Takeda et al. used the equivalent widths given in Cayrel et al.(2004) while we fitted the computed profiles directly to the ob-served spectra. (There are sometimes slight di ff erences in the po-sition of the continuum.) The NLTE correction for the potassiumlines is smaller in the more metal-poor stars, (as already notedby Takeda et al., 2009). In Cayrel et al. (2004), the potassiumabundance had been roughly corrected for NLTE (by applyinguniformly a correction of –0.35dex) : the potassium abundancesin this paper have therefore been underestimated (especially forthose stars that are strongly metal-poor).Scatters:The scatters of [Mg / Fe] and [K / Fe] are found smaller in thepresent work, where departures from LTE are taken into account.The NLTE abundance trends are therefore better defined than theprevious LTE trends.The [Mg / H] should be a better reference element than Fe, buteven whith the new NLTE determinations, the scatter of [O / Mg],[Na / Mg] and [K / Mg] remains (slightly) larger than the scatter of[O / Fe], [Na / Fe] and [K / Fe]. This fact is surprising, iron beingformed in processes quite di ff erent from those (mainly hydro-static) supposed to be forming O, Mg, Na and K. An exceptionis Al : the scatter is the same for [Al / Mg] and [Al / Fe].Trends:The shapes of the new trends (versus both Fe or Mg) areslightly di ff erent from the LTE trends found previously (Cayrelet al., 2004). For example, the slope of the [K / Fe] ratio ver-sus [Fe / H], which was slightly positive, becomes slightly neg-ative (Fig. 6). Also, the NLTE values of [Na / Mg], [Al / Mg] and[K / Mg] show at low metallicity (for [Mg / H] < − .
5) an increasewhen [Mg / H] decreases.Comparison with models:There is some agreement with the models of galactic evo-lution. The trends of [O / Mg], [Na / Mg], [Al / Mg] with [Mg / H]in the Galaxy are rather well represented by the model ofKobayashi et al. (2006). However their model underestimatesthe production of potassium.Finally the precision currently reached in the measurementof high resolution high signal to noise spectra, obviously de-serves careful analyses, using accurate atomic parameters, NLTEcomputations, and even, in a near future, 3D stellar atmospheremodels.
Acknowledgements.
SMA kindly acknowledges the support and hospitality ofthe Paris-Meudon Observatory. P.B. acknowledges financial support from EUcontract MEXT-CT-2004-014265(CIFIST). M. S., R. C., F. S., P. B., V. H., P. F.acknowledge the support of CNRS (PNG and PNPS).
References
Allen C.W. 1973, Astrophysical Quantities (London: Athlone Press)Andrievsky S.M., Spite M., Korotin S.A., Spite F., Bonifacio P., Cayrel R., HillV., Franc¸ois P. 2007, A&A 464, 1081Andrievsky S.M., Spite M., Korotin S.A., Spite F., Bonifacio P., Cayrel R., HillV., Franc¸ois P. 2008, A&A 481, 481Aymar M., Luc-Koenig E., Combet Farnoux F. 1976, JPhB 9, 1279Ballester P., Modigliani A., Boitiquin O., Cristiani S., Hanuschik R. et al. 2000,ESO Messenger 101, 31Biemont E., Grevesse N. 1973, ADNDT 12, 217Biemont E., Brault J.W. 1986, Phys. Scr., 34, 751Bonifacio, P., Molaro, P., Sivarani, T., et al. 2007, A&A, 462, 851 ( “First StarsVII” ) Bonifacio, P., Spite M., Cayrel R., Hill V., et al. 2009 accepted to A&A(arXiv0903.4174).Bruls J.H., Rutten R.J., Shchukina N. 1992, A&A 265, 237Carlsson M. 1986, Uppsala Obs. Rep. 33Cayrel R., Depagne E., Spite M., Hill V., Spite F., Franc¸ois P., Plez B., BeersT.C., Primas F., Andersen J., Barbuy B., Bonifacio P., Molaro P., Nordstr¨omB. 2004, A&A 416, 1117 ( “First Stars V” )Chie ffi A., Limongi M. 2003 in the ESO astrophysics symposia: From Twilightto Highlight: The physics of Supernovae, ed. W. Hillebrandt & B.Leibundgut, p. 367Chen Y.Q., Nissen P.E., Zhao G., Zhang H.W., Benoni T. 2000, A&AS 141, 491Dekker H., D’Odorico S., Kaufer A., et al. 2000 in Optical and IR TelescopesInstrumentation and Detectors, eds I. Masanori & A.F. Morwood Proc. SPIE4008, 534Drawin H.-W. 1961, ZPhy 164, 513Drawin H.-W. 1968, ZPhy 211, 404Franc¸ois P, Matteucci F., Cayrel R., Spite M., Spite F., Chiappini C. 2004, A&A421, 613Gehren T., Liang Y.C., Shi J.R.et al. 2004, A&A 413, 1045Gehren T., Shi J.R., Zhang H.W. et al. 2006, A&A 451, 1065Goswami A., Prantzos N. 2000, A&A 359, 191Gratton R.G., Sneden C. 1987, A&A 178, 179Grevesse N., Sauval A. J., 2000, in Origin of Elements in the SolarSystem, Implications of Post-1957 Observations, Proceedings of theInternational Symposium., Edited by O. Manuel, Boston / Dordrecht: KluwerAcademic / Plenum Publishers, p.261Gustafsson B., Edvardsson B., Eriksson K., Jørgensen U. G., Nordlund A., PlezB. 2008, A&A 486, 951Heger A., Woosley S.E. 2002, ApJ 567, 532Heger A., Woosley S.E. 2008, arXiv 0803.3161 (submitted to ApJ)Hofsaess D. 1979, ADNDT 24, 285Ivanova D.V., Shymansky V.V. 2000, ARep 44, 376Kobayashi C., Tsujimoto T., Nomoto K., Hachisu I., and Kato M. 1998, ApJ503,L155Kobayashi C., Umeda H., Nomoto K., Tominaga N., and Ohkubo T. 2006, ApJ653,1145Korotin S.A., Andrievsky S.M., Luck R.E. 1999, A&A 351, 168Kurucz R.L. 1992, The Stellar Population of Galaxies, ed. B. Barbuy, A. Renzini,IAU Symp. 149, 225Kurucz, R. 1993, ATLAS9 Stellar atmospher Programsand 2km / s grid CD-ROMNo. 13 Cambridge, Mass.: SAO, 1993, 13Kurucz R.L. 1996, Model Atmospheres and Spectrum Synthesis, ed. S.J.Adelman, F. Kupka, W.W. Weiss, San Francisco, ASP Conf. Ser. 108, 2Kurucz R.L., Furenlid I., Brault J., Testerman L., 1984, Solar Flux Atlas from296 to 1300 nm, New Mexico, National Solar ObservatoryLodders, K. 2003, ApJ, 591, 1220Martin W.C., Zalubas, R. 1980, J. Phys. Chem. Ref. Data, 9, 1Mashonkina L., Zhao G., Gehren T., Aoki W., Bergemann M., Noguchi K., ShiJ. R., Takada-Hidai M., Zhang H. W. 2008, A&A 478, 529Matteucci F. 2008, ArXiv 0804.1492v1Miles B.M., Wise W.L. 1969, ADNDT 1, 1Mishenina T.V., Soubiran C., Kovtyukh V.V., Korotin S.A. 2004, A&A 418, 551Morton D.C. 1991 Ap.J.Suppl. 77, 119Nomoto K., Hashimoto M., Tsujimoto T., Thielemann F.-K., Kishimoto N.,Kubo Y., Nakasato N. 1997, Nucl. Phys. A, 616, 79Peart B., Underwood J.R.A., Dolder K. 1989, JPhB 22, 1679Piskunov N.E., Kupka F., Ryabchikova T.A., Weiss W.W., Je ff ery C.S. 1995,A&AS 112, 525-535Rahman-Attia, M., Jaouen, M., Laplanche, G., Rachman, A. 1986 J.Phys.B 19,897Rutten R.J. 1978, SoPh 56, 237Samland M. 1998, ApJ 496, 155Shigeyama T., Tsujimoto T. 1998, ApJ 507, L135Shimanskaya N. N., Mashonkina L. I., Sakhibullin N. A. 2000, ARep, 44, 530Schoening T., Butler K. 1998, A&AS 128, 581Seaton M.J. 1962, Proc. Phys. Soc. 79, 1105Sobelman I.I., Vainshtein L.A., Yukov E. 1981, Excitation of Atoms andBroadening of Spectral Lines, Springer Ser. in Chem. Phys., Berlin,SpringerSpite M., Cayrel R., Plez B., et al. 2005, A&A 430, 655 ( “First Stars VI” )Spite M., Cayrel R., Hill V., et al. 2006, A&A 455, 291 ( “First Stars IX” )Spite M., Cayrel R., Spite F., et al. 2006, in : Chemical abundances and mixingin stars in the Milky Way and its satellites, Proc. ESO-Arcetri Workshop,eds. S. Randich & L. Pasquini, p. 200, SpringerSteenbock W., Holweger H. 1984, A&A 130, 319Sugar J., Corliss C.H. 1985, J.PhChRD, 14-2Takeda Y., Kaneko H., Matsumoto N., Oshino S., Ito H., Shibuya T. 2009, inpress at PASJ (arXiv0902.4504) ndrievsky: Relative abundances of light metals in EMP stars 9ndrievsky: Relative abundances of light metals in EMP stars 9