Rubidium abundances in solar metallicity stars
C. Abia, P. de Laverny, S. Korotin, A. Asensio-Ramos, A. Recio-Blanco, N. Prantzos
AAstronomy & Astrophysics manuscript no. rb © ESO 2021February 5, 2021
Rubidium abundances in solar metallicity stars
C. Abia , P. de Laverny , S. Korotin , A. Asensio Ramos , , A. Recio-Blanco , N.Prantzos Dpto. Física Teórica y del Cosmos. Universidad de Granada, E18071 Granada, Spaine-mail: [email protected] Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, France Crimean Astrophysical Observatory, Nauchny 298409, Republic of Crimea Instituto de Astrofísica de Canarias (IAC), Avda Vía Láctea S / N, 38200 La Laguna, Tenerife,Spain Departamento de Astrofísica, Universidad de La Laguna, 38205 La Laguna, Tenerife, Spain Institut d’Astrophysique de Paris, UMR7095 CNRS & Sorbonne Université, 98bis Bd. Arago,F-75104 Paris, FranceReceived; accepted
ABSTRACT
Context.
Rubidium is one of the few elements produced by the neutron capture s- and r-processesalmost in equally proportions. Recently, a Rb deficiency ([Rb / Fe] < .
0) by a factor of about twowith respect to the Sun has been found in M dwarfs of near solar metallicity. This contrastswith the close to solar [Sr,Zr / Fe] ratios derived in the same stars. This deficiency is di ffi cult tounderstand from both the observational and nucleosynthesis point of views. Aims.
To test the reliability of this Rb deficiency, we study the Rb and Zr abundances in a sampleof KM-type giant stars in a similar metallicity range extracted from the AMBRE Project.
Methods.
We use high resolution and high signal-to-noise spectra to derive Rb and Zr abun-dances in a sample of 54 bright giant stars with metallicity in the range − . (cid:46) [Fe / H] (cid:46) + . i at λ Results.
The LTE analysis also results in a Rb deficiency in giant stars although considerablylower than that obtained in M dwarfs. However, when NLTE corrections are done the [Rb / Fe]ratios are very close to solar (average − . ± .
09 dex) in the full metallicity range studied.This contrasts with the figure found in M dwarfs. The [Zr / Fe] ratios derived are in excellentagreement with those obtained in previous studies in FGK dwarf stars with a similar metallicity.We investigate the e ff ect of gravitational settling and magnetic activity as possible causes ofthe Rb deficiency found in M dwarfs. While, the former phenomenon has a negligible impactArticle number, page 1 of 23 a r X i v : . [ a s t r o - ph . S R ] F e b . Abia et al.: Rubidium abundances in solar metallicity starson the surface Rb abundance, the existence of an average magnetic field with intensity typicalof that observed in M dwarfs may result in systematic Rb abundance underestimations if theZeeman broadening is not considered in the spectral synthesis. This can explain the Rb deficiencyin M dwarfs, but not completely. On the other hand, the new [Rb / Fe] and [Rb / Zr] vs. [Fe / H]relationships can be explained when the Rb production by rotating massive stars and low-and-intermediate mass stars (these later also producing Zr) are considered, without the need of anydeviation from the standard s-process nucleosynthesis in AGB stars as suggested previously.
Key words. abundances – stars: abundances – stars: late type, nucleosynthesis, nuclear reactions
1. Introduction
The chemical evolution of the galaxies can be traced through abundance determinations in long-lived FGK dwarfs belonging to the di ff erent stellar populations. Theoretically, these stars preserveunaltered in their atmospheres the chemical composition of the original cloud from which theyformed. Nowadays a number of large spectroscopic surveys in the Milky Way devoted mainly tothe study of these stars like Gaia-ESO (Gilmore et al. 2012; Jackson et al. 2015), GALAH (DeSilva et al. 2015; Buder et al. 2018), AMBRE (de Laverny et al. 2013), APOGEE (Ahumada et al.2020) and others, are providing a huge quantity of spectroscopy data. Together with the accuratedistances and kinematic information determined by the Gaia mission (Gaia Collaboration et al.2018) followed by accurate stellar age estimations from large asteroseismic surveys (e.g. Miglioet al. 2020), these studies are revolutionising the current understanding of the Milky Way history.However, abundance analyses of FGK dwarfs do not always allow an easy determination of theabundances of some elements. This is the case for several heavy elements (A >
70) producedmainly by neutron capture reactions through the s- and r-processes in di ff erent astrophysical sce-narios (see e.g. Busso et al. 1999; Käppeler et al. 2011; Thielemann et al. 2017; Cowan et al. 2019).The universal low abundances of these elements and the physical parameters of the atmospheresof FGK dwarfs usually make their available spectroscopic lines very weak, which in addition areoften heavily blended, in particular in stars with near solar metallicity or higher (see e.g. Jofré et al.2019). This problem is worsened when medium resolution spectra are used ( R (cid:46) i lines at λλ ffi cult an accurate determination of the Rb abundance. In fact,a controversy on the photospheric Solar Rb abundance existed until recently (Goldberg et al. 1960;Lodders & Palme 2009; Asplund et al. 2009; Grevesse et al. 2015). To date, only two Rb abundancestudies FGK-type stars exist, namely those of Gratton & Sneden (1994) and Tomkin & Lambert Article number, page 2 of 23. Abia et al.: Rubidium abundances in solar metallicity stars (1999). These authors derived Rb abundances in a sample of metal-poor disc and halo stars and,considering the results in both studies together that the [Rb / Fe] versus [Fe / H] relationship behavesat low metallicity ([Fe / H] < − ) similarly as [Eu / Fe] does, that is, showing an approximatelyconstant [Rb / Fe] ratio as a typical r-process element. However, the behaviour of [Rb / Fe] at highermetallicities ([Fe / H] > − .
5) was poorly studied because of the issues commented above.An alternative to FGK dwarfs for Galactic chemical tagging are M dwarfs. Due to their ubiquityand very long main-sequence lifetimes, abundance determinations in M dwarfs are a powerful andcomplementary tool to study the formation and chemical enrichment of the Galaxy. Their potentialis only beginning to be explored (see e.g. Souto et al. 2020; Birky et al. 2020). Because of theirlow e ff ective temperature (T e ff (cid:46) i lines,which can be easily identified out of a forest of molecular absorptions (mainly TiO) even in metal-rich stars. Very recently Abia et al. (2020) (hereafter Paper I) derived Rb abundances for the firsttime in a sample of nearby M dwarfs in the metallicity range − . (cid:46) [Fe / H] (cid:46) + . / Fe] ratios derived by these authors were in excellent agreementwith those observed in FGK dwarfs of similar metallicity (e.g. Battistini & Bensby 2016; DelgadoMena et al. 2017), they found [Rb / Fe] ratios systematically lower than solar (i.e. [Rb / Fe] < . / Fe] ratios for [Fe / H] > . / or a deviation from the standard s-processnucleosynthesis scenario for Rb in AGB stars (Cristallo et al. 2009; Karakas et al. 2010; Cristalloet al. 2018), but no plausible solution was found . In Paper I, it was finally suggested that additionalRb abundance measurements in FGK dwarfs and giants of near solar metallicity, as well as a moredetailed evaluation of the impact of stellar activity on abundance determinations in M dwarfs, wereurgently needed to confirm or disprove these findings.In the present study, we derive Rb abundances from high-resolution spectra in a sample ofnearby and bright K and M stars located on the subgiant and giant branches with metallicities closeto solar. We also determine their Zr abundance - an element with predominantly main s-processorigin - as a cross check to the analysis. For that purpose, we use high signal-to-noise templatespectra of 54 giants provided by the AMBRE Project. Our aim is to study the reliability of the low Note that Gratton & Sneden (1994) derived upper limits for the Rb abundance in some of the stars in theirsample., one may concluded Here we follow the standard abundance notation, [X / H] = log (X / H) (cid:63) − log (X / H) (cid:12) , where X / H is theabundance by number of the element X, and log (cid:15) ( X ) ≡ log (X / H) + The [Rb / Fe] ratios derived by the Tomkin & Lambert (1999) in K dwarf stars, which have slightly largermasses than M dwarfs, apparently do not show any systematic di ff erence when compared with the ratiosderived in G dwarfs and giants in their stellar sample. Article number, page 3 of 23. Abia et al.: Rubidium abundances in solar metallicity stars [Rb / Fe] ratios found in the previous study on nearby M dwarfs of similar metallicity for a betterunderstanding of the evolution of the Rb abundance in the Galaxy, and to put constraints on therole played by the s- and r-processes in the galactic Rb budget.The structure of this paper is as follows: the observational material and analysis is presented inSec. 2, where the data acquisition is briefly described; we also discuss the atmospheric parametersused in this study, the line lists, and the derivation of the abundances from the spectra, togetherwith an evaluation of the observational and analysis uncertainties. In Sec. 3 the main results arepresented. The results are then compared with recent nucleosynthesis models through a state-of-the-art galactic chemical evolution model for the solar neighbourhood. We also briefly discussgravitational settling and magnetic activity as possible explanations of the Rb deficiency found inM dwarfs. Section 4 summarises the main conclusions of this study.
2. Observations and analysis
We have looked for ESO-archived UVES spectra collected with the RED860 setup (appropriatefor the observation of the Rb i lines around λλ ff ectivetemperature T e ff , the surface gravity (log g ) and the mean metallicity [M / H], adopted hereafter asan estimate of [Fe / H] and, the enhancement in α -elements with respect to iron ([ α / Fe]). A quality-flag of the stellar parametrisation, based on the computation of a χ between the observed andreconstructed spectra at the derived stellar parameters, has also been estimated.Within these parametrised AMBRE-UVES spectra, we selected only cool ( T e ff < < .
0) with SNR > ≤
1) werealso considered. With these criteria, an initial sample of 80 objects were selected. However, wefiltered again the sample excluding those objects with peculiar spectral types (e.g. R-stars, Ap-stars,symbiotics..), those belonging to stellar clusters, and those that might be placed in the asymptoticgiant branch (AGB) phase , all this according to the SIMBAD database. The final selected spectraset consisted in 54 giant stars of spectral types K and M with SNR > It is indeed very well known that AGB stars may show Rb enhancements produced by the in-situ operationof the main s-process (Abia et al. 2001; García-Hernández et al. 2006). Article number, page 4 of 23. Abia et al.: Rubidium abundances in solar metallicity stars
In a first step, we adopted the stellar parameters derived by Worley et al. (2016). We refer to thisstudy for a detailed description of the method. We also adopted initially for all the stars a micro-tubulence parameter ξ = . − , a typical value for giant stars. We build a model atmospherefor each star interpolating within the grid of MARCS model atmospheres by Gustafsson et al.(2008) for the corresponding stellar parameters. Then, a synthetic spectrum calculated in LTE withthe Turbospectrum v19.1 code (Plez 2012) was compared with the observed spectrum of each starin specific spectral ranges to check the validity of the stellar parameters. These ranges were aboutfifty angstroms centred at λλ ∼ λλ − λ λ i lines of interest here, but also several metallic andmolecular lines (TiO and CN). These metallic lines served as a check of the metallicity initiallyadopted in the atmosphere model, while molecular lines were used to estimate the C / O ratio, whichdetermines critically the shape of the spectrum for stars cooler than T e ff (cid:46) − , to account for the instrumental profile and macroturbulence. The atomic line list was takenfrom the VALD3 database adopting the corrections performed within the Gaia-ESO survey (Heiteret al. 2015b, 2020) in the wavelength ranges studied. Additional corrections to the log g f valuesof specific atomic lines were made from comparison of a synthetic spectrum with the observedspectrum of Arcturus (Hinkle et al. 1995). Molecular line lists were provided by B. Plez and theyinclude several C- and O-bearing molecules (CO, CH, CN, C , HCN, TiO, VO, H O) and a fewmetallic hydrides (FeH, MgH, CaH). As mentioned above, for the stars with T e ff (cid:46) / Oratio plays an important role in the shape of the spectrum and, in fact, determines the intensity ofa veil of TiO lines present in the spectral regions of the Rb i lines, which may depress significantlythe spectral pseudo-continuum there. To estimate this ratio we proceed as follow:i) We scaled the CNO abundances to the initial metallicity adopted since [C,N,O / Fe] ≈ . / Fe] ≈ − . / H] dex (see e.g. Edvardsson et al. 1993).According to Worley et al. (2016), the overwhelming majority of the stars studied here show no α -enhancement or very small ([ α / Fe] (cid:46) . α -enhancement within thisrange of values has no e ff ect on the analysis.ii) Then the carbon abundance was estimated using some weak CN lines in the λ C / C ratio,we adopted a C / C ∼
20 ratio (this value is typically observed in giant stars of near solar metal-licity after the first dredge-up, see e.g. Charbonnel (1994)) for all the stars, except for those forwhich measurements were available in the literature. Ideally, to determine the carbon abundancefrom CN lines, the N abundance should be known a priori from an independent spectral analysis These molecular line lists are publicly available at https: // nextcloud.lupm.in2p3.fr / s / r8pXijD39YLzw5T,where detailed bibliographic sources can be also found. Article number, page 5 of 23. Abia et al.: Rubidium abundances in solar metallicity stars (e.g. NH or N i lines), but unfortunately the available spectral region in our spectra do not containany such lines, nor there are accurate N abundance determinations available in literature for mostof the stars in our sample. Therefore, we adopted the N abundance scaled with the stellar metal-licity. Note however, that the CN lines used are not very sensitive to moderate variations of the Nabundance, in particular in stars with T e ff > ± . C / C value within 30%, have a minimal impactin the determination of Rb and Zr abundances.iii) With this carbon abundance, the oxygen abundance was estimated from fits to TiO linesmainly in the λ / O ratio was estimated, we determined again the carbon abundance from the λ / O from 0.05 to 0.1, dependingon the specific stellar parameters: in the cooler stars of the sample the uncertainty is lower since CNand TiO lines become more intense as the e ff ective temperature decreases and are more sensitiveto changes in the carbon or the oxygen abundance, respectively. Considering this uncertainty, mostof the C / O ratios derived are close to the photospheric solar value, (C / O) (cid:12) = . ± .
04 (Lodders2019) or slightly lower, this later is that being expected after the operation of the first dredge-up(see Table 1).For most of the stars we find a nice agreement between observed and synthetic spectra in allthe spectral ranges mentioned above. This procedure served also as a test to validate the stellarparameters of the stars according to the estimations within the AMBRE Project. However, forsome stars, small discrepancies between observed and theoretical spectra were detected indicatingthat some stellar parameters derived in AMBRE may slightly depart from the ones fitting better theshorter wavelength ranges of the present study, in particular the T e ff . For these stars, we searchedin the most recent literature other estimations of the stellar parameters and tested them in thesame way as described above until an agreement between the observed and theoretical spectrumwas found. In average e ff ective temperatures finally adopted di ff ered from those in AMBRE by ∼ − ±
100 K in average, in the sense AMBRE minus this study. The mean di ff erence withthe e ff ective temperatures estimated from two-micron sky survey (2MASS ) colours is found tobe equal to 6 ±
100 K, in the same sense. The final di ff erences with respect to AMBRE were − . ± .
30 dex, and − . ± .
20 dex for log g and the average metallicity, respectively. We pointout that such departures are in agreement with the typical external errors reported by the AMBREProject. Moreover, it is important to note that the reported di ff erences in the parameters can also beexplained by the di ff erent line lists, analysis procedure and, spectral ranges considered in Worleyet al. (2016) and this study.The next step was to adjust the determination of the stellar (average) metallicity to our analysis.To do that we used a number of weak metallic lines available in the spectral ranges mentionedabove, in particular the Ti i lines at λλ ∼ . , . , .
23, and 8069.79 Å; the Fe i lines Article number, page 6 of 23. Abia et al.: Rubidium abundances in solar metallicity stars | Z r I | Z r I | Z r I | F e I | F e I C o I | N i I | R b I | F e I | F e I Fig. 1.
Comparison of the observed (black dots) and synthetic spectra for the M4.0 III star HD 145206 inthe spectral region around λλ λλ (cid:15) (Rb) = .
35 and 2.6 (top panel), or log (cid:15) (Zr) = . λλ at 7095.50, 7802.47, 7807.90, 7941.08, and 7945.84 Å; and the Ni i lines at 7788.93 and 7797.58Å. The weakness of these lines should minimise possible deviations from LTE. In addition, theirproximity to the heavy element (Rb and Zr) lines may reduce systematic e ff ects introduced by theuncertain location of the pseudocontinuum when deriving the elemental ratios with respect to the Article number, page 7 of 23. Abia et al.: Rubidium abundances in solar metallicity stars average metallicity ([X / M] ), since this uncertainty should cancel out. The theoretical fits to thesemetallic lines also served us to adjust the microturbulence parameter. In general our metallicitiesagree within the uncertainty ( ± .
15 dex) with those initially adopted. Nevertheless, when a di ff er-ence larger than 0 .
15 dex was found, we recalculated a model atmosphere with the new metallicityand repeated the derivation of the metallicity until convergence was reached. Table 1 summarisesthe final stellar parameters adopted; last column indicates the specific bibliographic source for eachstar. We note that the average metallicity [M / H] and microturbulence velocity shown may not matchwith the value given in the specific reference as discussed above.Finally, the abundances of Rb, and Zr were determined by spectral synthesis fits to the corre-sponding spectral features. For rubidium, we use the very well known resonance lines at λλ Rb / Rb = .
43 ratio (Lodders 2019).Unfortunately, the isotopic splitting is tiny and does not allow the derivation of this ratio from ourspectra. Concerning zirconium, our main abundance indicator was the Zr i line at λ λλ i λ λ i line (top panel)and the Zr i lines (bottom panel) in a representative star of the sample. Fits to some of the metalliclines used for the determination of the average metallicity are also shown. A small depression ofthe continuum mainly due to TiO molecule is particularly apparent in the spectral region of the Zr i lines. The two main sources of error in the abundances are observational (i.e. related with the SNR ofthe spectrum) and analysis errors caused by the uncertainties in the adopted model atmosphereparameters. The scatter of the abundances provided by individual lines of the same species is agood guide to measurement error. When it was possible ( ∼
70% of the stars), we found excellentagreement between the Zr abundances derived from the three lines, typically with a dispersionof less than 0.08 dex. This agreement contrasts with the di ff erences ( ≥ .
10 dex) found in theRb abundance derived from the two lines. In particular that derived from the Rb i Since for near-solar metallicity stars, it holds that [Ni / Fe] ≈ [Ti / Fe] ≈ .
0, in the following we refer indis-tinctly to [M / H] or [Fe / H] as the stellar metallicity. Article number, page 8 of 23. Abia et al.: Rubidium abundances in solar metallicity stars from their analyses in similar stars than here. Thus, we also decide to exclude the λ i linefrom the analysis in this study. We note that a nice agreement between the Rb abundance derivedfrom the two lines was found in Paper I: typically we found a dispersion of only ± .
02 dex betweenthe abundances derived from the two Rb lines (see Table 2 in Paper I.) Since the stars studied hereare systematically hotter than the M dwarfs in Paper I, and that e ff ect of telluric lines is very smallat the location of this line, we guess that this discrepancy might be caused by an unknown blendwith an atomic line with a moderate excitation energy. A detailed study on the formation of theseRb lines in stars of di ff erent spectral types is required to enlight this long standing problem.The error caused by uncertainties in the adopted stellar parameters can be estimated by mod-ifying them by the quoted errors in the analysis of a typical star in the sample and checking thee ff ect on the abundance derived for each species. To do this we have adopted the uncertaintiesestimated in the AMBRE project (Worley et al. 2016), since for most of the stars we adopted thestellar parameters derived in this survey (see Table 1), namely: ±
100 K in T e ff , ± . ± . − in ξ , ±
5% in C / O, and ± .
15 dex in [Fe / H]. For a typical giant star in the sample withparameters T e ff / log g / [Fe / H] = / . / .
0, we found that the abundances derived are mostlya ff ected by the uncertainty in T e ff : ± .
07 and ± .
14 dex for Rb, and Zr, respectively. Uncertain-ties in the gravity, metallicity, microtubulence and the C / O ratio are relatively low for Rb, namely: ∓ . , ∓ . , ∓ .
05 and ∓ .
04 dex, respectively, while they are rather significant for Zr: ∓ .
10 and ∓ .
15 dex for gravity and metallicity, respectively. However, the above quoted uncertainties in themicroturbulence and C / O have almost no e ff ect on the Zr abundance. Adding these uncertaintiestogether quadratically, we estimated a total uncertainty in [X / H] of ± .
15 dex for Rb, and ± . ± .
04 dex) around the meanabundance value when more than one line was used. Nevertheless, the abundance of these elementsrelative to average metallicity, [X / Fe], holds the most interest. This ratio is more or less sensitive tothe uncertainties in the atmospheric parameters depending on whether changes in the stellar param-eters a ff ect the heavy element abundance and metallicity in the same or opposite sense. In our case,we estimated total uncertainties of ± .
12 dex and ± .
20 dex for the [Rb / Fe] and [Zr / Fe] ratios,respectively. Certainly the internal (relative) errors within the sample studied would be smaller.On the other hand, the structure of the atom of Rb is very similar to that of other alkalineelements, such as Na and K. It is very well known that the resonant lines of these alkaline elementsare a ff ected by deviations from LTE (Bruls et al. 1992). Recently Korotin (2020) (see also PaperI) has estimated the LTE deviations in the formation of the Rb lines as a function of the e ff ectivetemperature, gravity, metallicity, microturbulence and [Rb / Fe] ratios in dwarf and giant stars. Thisstudy shows that the NLTE corrections (in the sense ∆ NLTE = N NLTE − N LTE abundances) vary in anon trivial way depending on the stellar parameters. Here, we have estimated NLTE corrections tothe Rb abundances derived from the λ Article number, page 9 of 23. Abia et al.: Rubidium abundances in solar metallicity stars
Fig. 2. [Rb / Fe] vs. [Fe / H] diagram for M-dwarfs studied in Paper I (top panel, black dots, LTE abundances)and for KM-type giants (blue dots) in this study in LTE (middle panel) and NLTE (bottom panel). The greydots with error bars in the three panels are the [Rb / Fe] ratios derived in halo and disc giant and dwarf stars byGratton & Sneden (1994) and Tomkin & Lambert (1999). A typical error bar in the [Rb / Fe] ratios in Paper Iand this study is shown in the bottom left corner of each panel. Upper limits in the Rb abundances are omittedin the figure. In the bottom panel, solid curves are theoretical GCE predictions by Prantzos et al. (2018, 2020):Black line includes the contributions from LIMS and RM stars, and the r-process, while magenta line includeonly LIMS (see text for details). or negative depending on the stellar parameters, and may reach up to − .
15 dex for stars with T e ff ∼ / Fe] > . . We refer to Korotin (2020) for a detailed discussion on thistopic. It is worth noting that the Solar NLTE Rb abundance found in this paper is 2.35, which isin excellent agreement with that found in meteorites (Lodders 2019). Unfortunately there is a verylimited information in the literature concerning the NLTE corrections for the LTE Zr abundancederived from di ff erent lines, although it appears that for solar metallicity stars they may be small(see Velichko et al. 2010). In Paper I we showed that the average NLTE Rb abundance corrections in M dwarfs is ∼ − .
15 dex.However, the [Rb / Fe] ratios derived remain equal respect to the LTE analysis since the NLTE corrections arealmost compensated by the Solar NLTE abundance, which is 0.12 dex (2.35) lower than the LTE value (2.47).Article number, page 10 of 23. Abia et al.: Rubidium abundances in solar metallicity stars
3. Results and discussion
Table 1 shows the final Rb and Zr abundances derived in our stars. When more than one Zr linewas used the abundance quoted is the average value.Figure 2 shows the observed [Rb / Fe] vs. [Fe / H] relationship obtained in our stars (middle andbottom panels, blue dots) compared with that obtained in M dwarfs in Paper I (top panel, blackdots). In the three panels we have also included the [Rb / Fe] ratios obtained by Gratton & Sne-den (1994) and Tomkin & Lambert (1999) (grey dots) in metal-poor GK dwarfs and giants . First,focusing on the LTE Rb abundances (middle panel), it is apparent that the [Rb / Fe] vs. [Fe / H] rela-tion derived is nearly flat in the full metallicity range studied (excluding the moderate metal-poorgiant HD 1638, see Table 1), showing a small deficiency with respect to the solar value: average[Rb / Fe] = − . ± .
11 dex, which is compatible with [Rb / Fe] ≈ . / Fe] with metallicity were obtained (see top panel inFig. 2). This is even more evident when NLTE Rb abundances are considered (bottom panel, bluedots). Furthermore, in this case the dispersion of the [Rb / Fe] at a given [Fe / H] diminishes signifi-cantly around the solar value (average [Rb / Fe] = − . ± .
09 dex). As a consequence the [Rb / Fe]ratio behaves very similarly to that observed for [Eu / Fe] (Battistini & Bensby 2016; Delgado Menaet al. 2017; Forsberg et al. 2019) – Eu being an almost pure r-process element – at least up to[Fe / H] ∼ − . / Fe] ratio for [Fe / H] (cid:46) − . / Fe] ≈ . / Fe] vs. [Fe / H] seemstotally flat at [Fe / H] > .
0, however the [Eu / Fe] ratios apparently become negative for metallicitylarger than solar (see e.g. Battistini & Bensby 2016). This would imply that at this metallicity Rbhas di ff erent contributing sources than Eu; more Rb abundance determinations at metallicity largerthan solar are needed to confirm this figure.Figure 2 (bottom panel) compares the observed relationship with model predictions from agalactic chemical evolution (GCE) model of Prantzos et al. (2018, 2020), which includes Rb con-tributions from low-and-intermediate mass stars (LIMS), rotating massive stars (RMS) and the r-process (black continuous line). Note taht the GCE model from Prantzos et al. (2018) used here isa one-zone model tailored for the solar neighborhood. It is meant to reproduce the evolution of thechemical composition of the local gas, reaching a final metallicity (at age 0 Gy) of [Fe / H] ∼ + . The [Rb / Fe] ratios in these studies have been scaled to the Solar LTE Rb abundance adopted here. For thetypical atmosphere parameters in their stellar sample, NLTE corrections for these stars are within 0.07-0.10dex (negative), however the corresponding [Rb / Fe] ratios would change only slightly due again to the lowerNLTE Solar Rb abundance. Article number, page 11 of 23. Abia et al.: Rubidium abundances in solar metallicity stars di ff erent chemical evolution history and reached supersolar metallicities early on) and they havemigrated at ∼ ∼ ffi cient for our discussion, as far aswe do not enter the super-solar metallicity regime . According to this GCE model, the productionof Rb through the weak s-process in RMS is critical to account for the observed relationship, inparticular at solar metallicity. Note that the contribution only by LIMS through the main s-process(magenta line in Fig. 2) is clearly not enough, as expected according the ∼
50% s- and r-processorigin for the bulk Rb abundance observed in the Solar System (see Prantzos et al. (2018, 2020) fora detailed discussion on the stellar yields adopted). The [Rb / Fe] vs. [Fe / H] relationship obtainedis now nicely reproduced without invoking any non-standard nucleosynthesis process for Rb formetallicities close to solar in contrast to our suggestion in Paper I.Figure 3 shows the [Zr / Fe] vs. [Fe / H] relationship derived in our stars (middle panel, bluedots) compared with the relation obtained in the most recent similar analyses in GK dwarfs byBattistini & Bensby (2016) and Delgado Mena et al. (2017) (grey dots in top and middle panels).We compare also with the results obtained in Paper I for Zr (top panel, black dots) in M dwarfs.From this figure, it is evident that the [Zr / Fe] vs [Fe / H] behaviour obtained here is almost identicalto that for M dwarfs in the metallicity range studied, and both indistinguishable from that derived inGK dwarfs. We note a slight tendency for [Zr / Fe] to decrease with metallicity, even for [Fe / H] > / Fe] vs. [Fe / H] relationship is also nicely accounted by theGCE model of Prantzos et al. (2018) when all the contributing sources for Zr are considered (blackcurve in Fig. 3). Again LIMS are not su ffi cient (magenta curve in Fig. 3) to adjust the observedtrend, although their contribution at [Fe / H] ∼ . ∼
82% s-process contribution to the abundance of this element in the SolarSystem (see e.g. Prantzos et al. 2020). Recently it has been reported a possible increasing trend ofthe [Zr / Fe] ratio (and of other s-elements; Y, Ba, La, Ce) with age in supersolar metallicity starsbelonging to young open cluster (see e.g. Maiorca et al. 2012; Mishenina et al. 2015; Magrini et al.2018). Our GCE predictions cannot reproduce this apparent increase of the [Zr / Fe] ratio at veryyoung age. It has been argue that the i-process and / or a non standard s-process nucleosythesis inlow-mass AGB stars, might explain this observational trend (see references in the studies above).In any case, if we plot [Zr / Fe] vs. time according to our GCE model, we obtain an almost flat curvefrom 12.5 to 0 Gy age around [Zr / Fe] ∼ .
0, which is fully compatible with the observational resultsby Magrini et al. (2018) (see their Fig. 9) obtained for the stars belonging to the thin disk (from theirkinematic properties, we deduce that the overwhelming majority of the stars studied here belong A note of caution here: if some nucleosynthesis e ff ect depends on metallicity (e.g. secondary elements froms-process) then the e ff ect should show up clearly as function of metallicity, independently of the stellar age.Article number, page 12 of 23. Abia et al.: Rubidium abundances in solar metallicity stars Fig. 3.
Top and middle panels: same as Fig. 2 but for LTE [Zr / Fe] vs. [Fe / H] for M dwarfs studied in PaperI (top panel, black dots) and for KM-type giants (blue dots) in this study (middle panel). Grey dots are the[Zr / Fe] ratios derived by Battistini & Bensby (2016) and Delgado Mena et al. (2017), both in thin and thickdisc dwarf stars. Bottom panel: [Rb / Zr] vs. [Fe / H] for the stars in this study (blue dots) when using NLTE Rbabundances. Grey dots correspond to the giants and dwarfs stars analysed in common by Gratton & Sneden(1994), Tomkin & Lambert (1999), and Mishenina et al. (2019). A typical error bar in the abundance ratiosis shown in the bottom left corner of each panel. For the data in the literature (grey dots) the error bars havebeen omitted for clarity. Upper limits in the Zr abundance have been also omitted. Continuous solid lines inmiddle and bottom panels are the GCE predictions as in Fig. 2. to the thin disk). However, this apparent increase of the [X / Fe] ratios of s-elements in young opencluster is still rather controversial: at least, as far as the [Ba / Fe] ratio concerns, this trend has beenshown to be correlated with the stellar activity of young stars and to not be nucleosynthetic in origin(see Reddy & Lambert 2017), putting serious doubts on the reliability of this increasing trend withage. In fact, we already addressed this issue in Paper I (at the end of Section 3) when discussing theobserved trend of increasing [Rb / Fe] vs. [Fe / H] in metal-rich stars, trend which we discard now inthis study.Finally, the bottom panel in Figure 3 shows the [Rb / Zr] ratios derived here against [Fe / H].This figure should be compared with the equivalent Fig. 8 in Paper I for M dwarfs. Similarlyto that figure in Paper I, Fig. 3 shows that as metallicity increases, the [Rb / Zr] diminishes andcluster around [Rb / Zr] ∼ . / H] ∼ .
0, although with a much less dispersion
Article number, page 13 of 23. Abia et al.: Rubidium abundances in solar metallicity stars than that obtained in Paper I. This dispersion is consistent with the uncertainties in the presentanalysis. The decrease in the [Rb / Zr] ratio for increasing metallicity is clearly due to the increasingrelevance of the contribution of low-mass stars in the production of Rb and Zr through the mains-process, for which the C( α, n ) O is the main neutron source. When this neutron source is atwork, [Rb / Zr] < . / Fe] ratios at metallicity close to solar, can be understood within our currentunderstanding of the Rb and Zr production in rotating massive and low-and-intermediate mas starsthrough the weak and main s-process nucleosynthesis, respectively.
Why M dwarfs with near solar metallicity apparently show Rb deficiencies with respect to the Solarvalue? Is this finding real? In Paper I we discussed various issues that might account for this (NLTEe ff ects, stellar activity, or an anomalous Rb abundance in the Solar System), but no satisfactoryexplanation was found. Here we address again this issue discussing the impact of gravitationalsettling and the existence of a magnetic field of moderate intensity in the surface of M dwarfs. Comparison of evolutionary tracks (Bressan et al. 2012; Tang et al. 2014; Bara ff e et al. 2015) forM dwarfs of 0 . − . (cid:12) and Z ∼ Z (cid:12) in the T e ff − log g diagram shows that the M dwarfs studiedin Paper I have ages ∼ ff erent masses and metallicities becomerather degenerate in age for ages larger than ∼ T e ff and log g uncertainties, make di ffi cult an accurate age estimate. In any case, and depending on the specificstellar mass and metallicity, for such old ages the surface chemical composition of these stars mayhave been altered due to gravitational settling, with di ff erential depletion for some metals. In fact, itis very well known that the current surface chemical composition of the Sun is di ff erent from that inthe proto-solar nebulae 4.56 Gyr ago (Lodders 2003). In particular, Piersanti et al. (2007) showedthat the proto-solar Rb abundance was a ∼
8% higher than the present Solar photospheric valuedue to the operation of gravitational settling. For stellar masses lower than the Sun and Z ∼ Z (cid:12) ,larger surface Rb depletion would occur at an age ∼ ff ectin a similar way to the neighbouring elements Sr, Y and Zr, thus no relative e ff ect between Rb andthese elements would be expected . This is at odd with that observed in Paper I where no hint forany Sr and / or Zr depletion was found. Furthermore, we note that stars in the mass range 0 . − . Note that the isotope Rb would be depleted in a larger factor ( ∼ / ∼ . × yr) into Sr. However, the abundance of this isotope represents only ∼
27% of the total Rbabundance. Article number, page 14 of 23. Abia et al.: Rubidium abundances in solar metallicity stars
Fig. 4.
Comparison of the observed spectrum (black dots) at the location of the λ i line for theM dwarfs G244-77 (non-active, left panel) and OT Ser (active, right panel) studied in Paper I, with syntheticspectra (continuous and dashed lines) computed with di ff erent average magnetic field intensities in the lineof sight and Rb abundances (as labelled). Only the Rb i line is included in the spectral synthesis (see text fordetails). M (cid:12) have about ∼ . (cid:12) in their convective envelope near the turn-o ff at solar metallicity. This actsas a good bu ff er to changes in the surface composition keeping everything near the surface nicelystirred up: i.e. the thickness of the convective envelope of a typical M dwarf at solar metallicityshould prevent any changes by gravitational settling from being significant. One has to conclude,therefore, that gravitational settling is probably not the cause of the observed Rb deficiency in Mdwarfs. On the other hand, in Paper I we qualitatively discussed the e ff ect of magnetic fields in the profileof the spectral lines with large Landé factors (as the Rb resonance lines) in active M dwarfs. The af-fected lines appear shallower and broader, and this may a ff ect the abundance determination. In fact,in Paper I we identified three stars (J11201–104, OT Ser, and J18174 + α -emission as a proxy for activity indicator. For instance, Schweitzer et al.(2019) derived an average field intensity (cid:104) B (cid:105) ∼ / Fe] < − .
30 dex) in the stellar sample. Here we address this issue more quantitatively.The existence of strong magnetic fields in M dwarfs is known since Saar & Linsky (1985) basedon the analysis of high resolution spectroscopy infrared spectra. Several recent studies report field
Article number, page 15 of 23. Abia et al.: Rubidium abundances in solar metallicity stars strength measurements in the range from 0.8 to 7.3 kG (see e.g. Shulyak et al. 2019), althoughthe spectroscopic requirements for detecting subtle signatures of the Zeeman broadening may besatisfied for only a small number of the brightest active M dwarfs. Furthermore, interpretation ofthese signatures became ambiguous as soon as the stellar rotational velocity exceeded ∼ − since line profile details are washed out by the rotational Doppler broadening. This made itimpossible to probe magnetic fields in faster rotating and, presumably, most magnetically activeM dwarfs. A detailed discussion on the e ff ects of magnetic fields in the spectrum of M dwarfs isobviously beyond the scope of this study. Our aim here is only to quantify how the Rb abundancederived may be a ff ected by the presence of an average magnetic field in a typical M dwarf, evenin those which are considered as non active where no Zeeman broadening is seen on the profile ofthe spectroscopic lines that potentially could be a ff ected. An excellent review on magnetic fieldsin M dwarfs together with the observational techniques used for its determination can be found inKochukhov (2020).The synthesis of the Rb i lines under the presence of a magnetic field needs to be done underthe intermediate Paschen-Back e ff ect using the proper hyperfine and Zeeman e ff ective Hamiltoni-ans (see, e.g., Asensio Ramos et al. 2007). The proximity of the hyperfine energy levels producesinterferences among the magnetic sublevels when a magnetic field is present, so that one needs toresort to the diagonalisation of the full Hamiltonian for computing the wavelength shift of everymagnetic component on the Zeeman pattern. The synthesis is done by solving the polarised ra-diative transfer equation for the Stokes vector ( I , Q , U , V ) using the DELOPAR method (TrujilloBueno 2003). The emission vector and the propagation matrix is computed under the assumptionof LTE using the expressions found in Section 9.1 of Landi Degl’Innocenti & Landolfi (2004) fordi ff erent orientations of the magnetic field vector. Rubidium contains two main isotopes with non-negligible abundance (see above). Both isotopes have di ff erent nuclear spins ( Rb has I = / Rb has I = /
2) and the isotopic shifts of their energy levels is smaller than the widthof the line, so that both need to be considered as blends when computing the opacities. The lineat λ S / − P / . Theisotopic shifts δ = E − E , i.e., the energy di ff erence for a given level between the level for Rb and Rb are: δ ( S / ) = .
35 MHz, and δ ( P / ) = .
31 MHz, respectively (Aldridgeet al. 2011). The hyperfine e ff ective Hamiltonian was parametrised in terms of the magnetic-dipoleand electric-quadrupole hyperfine structure constants. Since the e ff ect of the electric-quadrupoleconstant is almost negligible, we only use the magnetic-dipole constant. We adopted the follow-ing values for Rb: A ( S / ) = .
341 MHz, A ( P / ) = . A ( P / ) = . Rb we use: A ( S / ) = .
910 MHz, A ( P / ) = .
721 MHz and A ( P / ) = . g ( S / ) = g ( P / ) = / g ( P / ) = . Article number, page 16 of 23. Abia et al.: Rubidium abundances in solar metallicity stars
Figure 4 compares the observed spectrum of a non active M dwarf (G244-77, left panel) andan active one (OT Ser, right panel) (see Schweitzer et al. 2019) - both stars studied in Paper I -at the position of the Rb i λ ff erent Rbabundances and average magnetic field intensities in the line of sight computed as described above.Only the Rb i line has been included in the spectral synthesis. For the active star OT Ser (rightpanel), synthetic spectra were convolved with a rotational profile (together with the instrumentalprofile) since this star shows v sin i > − (Reiners et al. 2018). From Figure 4 it can be clearlyappreciated that the profile of the Rb i line in OT Ser is much broader and shallower than in theno-active star G244-77 (left panel), considering that both stars have very similar stellar parameters(see Table 1 in Paper I). This is due to the combined e ff ect of rotation and a strong magnetic fieldin OT Ser. For a given Rb abundance (2.6) and assuming an average field (cid:104) B (cid:105) =
0, the computedsynthetic spectrum clearly fails to fit the wings of the line despite it does fit the core; while whenan average field similar to that observed ( ∼ − ff erence in the Rb abundance between both cases: fromthe figure it comes o ff that this di ff erence may be up to 0 . − . weak magnetic field ( ∼ ff erence up to ∼ . ff ected byan average weak magnetic field and, as a consequence, Rb abundances may be underestimated. Theexact amount of this e ff ect would depend on the orientation of the average magnetic field along theline of sight, which is rather di ffi cult to discern observationally. Fig. 4 shows the case of maximume ff ect occurring when the magnetic field is parallel to the line of sight: the larger inclinations, thedeeper becomes the core of the 7800 Å line so that the abundance di ff erence with respect to theabsence of magnetic field is reduced correspondingly. Then, for an expected uniform distribution ofmagnetic field inclinations respect to the line of sight in a given sample of observed M dwarfs withdi ff erent levels of activity, one would expect a uniform distribution of Rb abundance corrections,which would be within the range ∼ . − . ffi culty to explain the Rb deficiency found,although would not fully solve the issue. Obviously, magnetic fields also exist at the surface ofKM-type giants (see e.g. Aurière et al. 2015) but their intensity is much smaller (a few tenths ofGauss) than those observed in M dwarfs and, therefore, its e ff ect would be negligible. Article number, page 17 of 23. Abia et al.: Rubidium abundances in solar metallicity stars
4. Conclusions
We have compiled a sample of 54 bright K- and M-type giant stars with metallicity close to solar.New Rb and Zr abundances are derived from the high-resolution, high-SNR spectra parametrisedby Worley et al. (2016) within the AMBRE Project. Our aim is to test the reliability of the Rb defi-ciency recently found in a sample of M dwarfs in a similar metallicity range by Abia et al. (2020)(Paper I). Based on the observational data analysed, our main conclusions can be summarised asfollows.1. The LTE [Rb / Fe] ratios derived in our sample stars show in average a slight deficiency withrespect to the solar value, [Rb / Fe] ≈ − . ± .
11 dex, nevertheless smaller than that found in PaperI. However, when a NLTE analysis is done, this deficiency disappears and the [Rb / Fe] ratio clustersaround the solar value with a small dispersion, [Rb / Fe] ≈ − . ± .
09 dex. This contrasts with theresults in M dwarfs for Rb in Paper I.2. The [Zr / Fe] ratios derived are very similar to the most recent determinations in FGK dwarfsof similar metallicity, which support our analysis for Rb.3. As a consequence, the [Rb / Fe] and [Rb / Zr] vs. [Fe / H] relationships obtained in the metallic-ity range studied can be explained through a chemical evolution model for the solar neighbourhoodwhen the Rb production by rotating massive stars and low-and-intermediate mass (AGB) stars(these later also producing Zr), are considered according to the yields from Limongi & Chie ffi (2018) and Cristallo et al. (2015), respectively, without the need of any deviation from the standards-process nucleosynthesis in AGB stars, contrarily to what was suggested in Paper I.4. We explore if gravitational settling and magnetic activity may be the cause of the Rb defi-ciency previously reported for M dwarfs. While the first phenomenon would have little impact onthe surface Rb abundance in these stars, we show that when the Zeeman broadening is included inthe spectral synthesis for the typical average magnetic field intensity observed in M dwarfs, the Rbabundances derived may increase significantly. This can explain, but not totally, the discrepancybetween the Rb abundances derived in solar metallicity M dwarfs and KM-type giants.We conclude then that, although abundance analysis in M dwarfs well illustrates its value forGalactic chemical evolution studies, attention has to be paid when deriving elemental abundancesfrom spectral atomic lines formed in the upper layers of their atmospheres, whether a ff ected ornot by magnetic activity. This will be important, for instance, for future spectroscopic follow-upobservations of the PLATO mission, among others. More generally, the complexity of the physicalprocesses influencing Rb abundance estimates illustrated here shows the importance of carefullyconsidering all the stellar physical properties in any spectral analysis. This is particularly true forlarge scale surveys dealing with a variety of stellar types. Acknowledgements.
We acknowledge financial support from the Agencia Estatal de Investigación of the Spanish Ministeriode Ciencia e Innovación through the FEDER founds projects PGC2018-095317-B-C21 and PGC2018-102108-B-I00. Thefrench coauthors of this article acknowledge financial support from the ANR 14-CE33-014-01 and the "Programme Nationalde Physique Stellaire" (PNPS) of CNRS / INSU co-funded by CEA and CNES. SK acknowledge financial support from theRFBR and Republic of Crimea, project 20-42-910007. We would like to thanks to L. Piersanti and O. Straniero for thediscussion on the gravitational settling. Finally, part of the AMBRE parametrisation has been performed with the high-performance computing facility SIGAMM, hosted by OCA.
Article number, page 18 of 23. Abia et al.: Rubidium abundances in solar metallicity stars
Table 1.
Stellar parameters and abundances derived in the sample of stars a . Star T e ff (K) log g [M / H] ξ (km s − ) C / O log (cid:15) (Rb)
LTE ∆ NLTE (dex) log (cid:15) (Zr) Reference b HD 1638 4138 1.25 − .
64 1.8 0.36 2.07 0.06 1.85 1HD 5544 4443 2.20 0 .
05 1.5 0.61 2.30 − − − − − .
45 1.8 0.53 1.78 0.05 2.30 2HD 29139 3814 1.00 − .
03 1.9 0.59 2.30 − − .
10 1.5 0.55 2.27 − − − .
10 1.7 0.54 2.20 − − − − .
26 1.8 0.59 2.30 0.03 2.20 3HD 78479 4418 2.20 0.35 1.7 0.54 2.80 − − − − − .
40 1.7 0.54 1.93 − − − .
04 1.4 0.59 2.13 0.07 2.67 5HD 95849 4472 1.17 0.18 2.1 0.63 2.57 0.02 2.74 4HD 102212 3812 0.86 − .
10 2.0 0.30 2.15 0.01 ... 1HD 102780 3900 1.60 − .
11 1.6 0.58 2.07 0.07 2.55 3HD 107446 4100 1.24 0.10 1.5 0.55 2.55 − − − .
40 1.8 0.49 2.05 0.05 2.45 7HD 121416 4576 2.07 0.35 1.7 0.53 2.80 − − − − − − − .
03 1.7 0.54 2.40 − − < − .
10 1.6 0.49 < − − − .
21 1.9 0.53 2.23 − − .
12 1.9 0.42 2.40 − − .
15 2.0 0.57 2.15 0.08 2.45 1HD 157244 4233 1.17 0.02 2.2 0.58 2.25 0.12 2.50 1HD 167006 3600 1.00 − .
10 2.0 0.53 2.15 0.02 < − .
25 1.7 0.58 2.17 0.04 2.50 4HD 169191 4283 1.88 − .
03 1.4 0.57 2.35 − − − .
10 1.7 0.58 2.35 − − .
12 2.0 0.45 2.45 0.01 2.55 1HD 199642 3912 0.71 0.00 1.6 0.50 2.43 − − − − − − − − Notes. ( a ) Abundances of Rb and Zr are given on the scale log N (H) ≡ ( b ) Reference for the stellar pa-rameters: (1) AMBRE Worley et al. (2016); (2) Heiter et al. (2015a); (3) Koleva & Vazdekis (2012); (4) Luck(2015); (5) McDonald et al. (2012); (6) Jönsson et al. (2017); (7) Meléndez et al. (2008); (8) Park et al. (2013);(9) Alves et al. (2015); (10) Kordopatis et al. (2013). Article number, page 19 of 23. Abia et al.: Rubidium abundances in solar metallicity stars
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List of Objects ‘HD 145206’ on page 7‘HD 1638’ on page 19‘HD 5544’ on page 19‘HD 11643’ on page 19‘HD 12642’ on page 19‘HD 17361’ on page 19‘HD 18884’ on page 19‘HD 29139’ on page 19‘HD 31421’ on page 19‘HD 61603’ on page 19‘HD 65354’ on page 19‘HD 71160’ on page 19‘HD 72505’ on page 19‘HD 74088’ on page 19‘HD 78479’ on page 19‘HD 79349’ on page 19‘HD 81797’ on page 19‘HD 83240’ on page 19‘HD 90862’ on page 19‘HD 93813’ on page 19‘HD 95208’ on page 19‘HD 95849’ on page 19‘HD 102212’ on page 19‘HD 102780’ on page 19‘HD 107446’ on page 19‘HD 111464’ on page 19‘HD 119971’ on page 19‘HD 121416’ on page 19‘HD 124186’ on page 19‘HD 128688’ on page 19‘HD 132345’ on page 19‘HD 138716’ on page 19‘HD 140573’ on page 19‘HD 143107’ on page 19‘HD 145206’ on page 19‘HD 146051’ on page 19‘HD 148291’ on page 19
Article number, page 22 of 23. Abia et al.: Rubidium abundances in solar metallicity stars ‘HD 148513’ on page 19‘HD 149161’ on page 19‘HD 149447’ on page 19‘HD 152786’ on page 19‘HD 157244’ on page 19‘HD 167006’ on page 19‘HD 167818’ on page 19‘HD 169191’ on page 19‘HD 169916’ on page 19‘HD 190421’ on page 19‘HD 198357’ on page 19‘HD 199642’ on page 19‘HD 202320’ on page 19‘HD 203638’ on page 19‘HD 210066’ on page 19‘HD 219215’ on page 19‘HD 320868’ on page 19‘2MASS J15023844-4156105’ on page 19‘HD 148513’ on page 19‘HD 149161’ on page 19‘HD 149447’ on page 19‘HD 152786’ on page 19‘HD 157244’ on page 19‘HD 167006’ on page 19‘HD 167818’ on page 19‘HD 169191’ on page 19‘HD 169916’ on page 19‘HD 190421’ on page 19‘HD 198357’ on page 19‘HD 199642’ on page 19‘HD 202320’ on page 19‘HD 203638’ on page 19‘HD 210066’ on page 19‘HD 219215’ on page 19‘HD 320868’ on page 19‘2MASS J15023844-4156105’ on page 19