Masses and ages for metal-poor stars: a pilot program combining asteroseismology and high-resolution spectroscopic follow-up of RAVE halo stars
M. Valentini, C. Chiappini, D. Bossini, A. Miglio, G. R. Davies, B. Mosser, Y. P. Elsworth, S. Mathur, R. A. García, L. Girardi, T. S. Rodrigues, M. Steinmetz, A. Vallenari
AAstronomy & Astrophysics manuscript no. ValentiniMP c (cid:13)
ESO 2019May 29, 2019
Masses and ages for metal-poor stars
A pilot program combining asteroseismology and high-resolution spectroscopicfollow-up of RAVE halo stars (cid:63)
M. Valentini , C. Chiappini , D. Bossini , , A. Miglio , , G. R. Davies , , B. Mosser , Y. P. Elsworth , , S. Mathur , ,Rafael A. García , , L. Girardi , T. S. Rodrigues , M. Steinmetz , and A. Vallenari Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany Osservatorio Astronomico di Padova, INAF, Vicolo dell’Osservatorio 5, I-35122 Padova, Italy Instituto de Astrofísica e Ciˆ e ncias do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, 4150-762 Porto,Portugal School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark LESIA, Observatoire de Paris, PSL Research University, CNRS, Université Pierre et Marie Curie, Université Paris Diderot, 92195Meudon, France Departamento de Astrofísica, Universidad de La Laguna, E-38206 Tenerife, Spain Instituto de Astrofísica de Canarias, C / Vía Láctea s / n, La Laguna, E-38205 Tenerife, Spain IRFU, CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France AIM, CEA, CNRS, Université Paris-Saclay, Université Paris Diderot, Sorbonne Paris Cité, F-91191 Gif-sur-Yvette, FranceReceived ??? ??, ????; accepted ??? ??, ????
ABSTRACT
Context.
Very metal-poor halo stars are the best candidates for being among the oldest objects in our Galaxy. Samples of halo starswith age determination and detailed chemical composition measurements provide key information for constraining the nature of thefirst stellar generations and the nucleosynthesis in the metal-poor regime.
Aims.
Age estimates are very uncertain and are available for only a small number of metal-poor stars. Here we present the first resultsof a pilot program aimed at deriving precise masses, ages and chemical abundances for metal-poor halo giants using asteroseismology,and high-resolution spectroscopy.
Methods.
We obtained high-resolution UVES spectra for four metal-poor RAVE stars observed by the K2 satellite. Seismic dataobtained from K2 light curves helped improving spectroscopic temperatures, metallicities and individual chemical abundances. Massand ages were derived using the code PARAM, investigating the e ff ects of di ff erent assumptions (e.g. mass loss, [ α / Fe]-enhancement).Orbits were computed using Gaia DR2 data.
Results.
The stars are found to be normal metal-poor halo stars (i.e. non C-enhanced), with an abundance pattern typical of old stars(i.e. α and Eu-enhanced), and with masses in the 0.80-1.0 M (cid:12) range. The inferred model-dependent stellar ages are found to rangefrom 7.4 to 13.0 Gyr, with uncertainties of ∼ Kepler seismic data from APOGEE survey and a set of M4 stars.
Conclusions.
The present work shows that the combination of asteroseismology and high-resolution spectroscopy provides preciseages in the metal-poor regime. Most of the stars analysed in the present work (covering the metallicity range of [Fe / H] ∼ − − > > Key words.
Stars - fundamental parameters – Asteroseismology – Stars - abundances
1. Introduction
The Milky Way halo is a key component to understand the as-sembly history of our Galaxy. The halo is composed by stars thatwere accreted during mergers as well as stars that formed in-situ(e.g., Helmi et al. 1999, 2018), and is suggested to be one ofthe oldest component of our Galaxy, (e.g., Jofré & Weiss 2011;Kalirai 2012; Kilic et al. 2019). In addition, metal-poor halo gi-ant stars enshrine information on when star formation began, onthe nature of the first stellar generation and on the chemical en-richment time-scale in the Galactic halo (Cayrel et al. 2001; Chi-appini 2013; Frebel & Norris 2015). A comprehensive under-standing of the Galactic halo can be obtained only when combin-ing precise stellar chemical abundances, kinematics, and ages.While detailed chemical information can be obtained via high- resolution spectroscopic analysis and precise kinematics is beingprovided by astrometric missions like Gaia, the determination ofreliable stellar ages (i.e. ages that are precise and unbiased), isstill a challenging task, especially in the case of red giants.Before the confirmation of solar-like oscillations in red-giantstars (De Ridder et al. 2009), ages had been estimated only for alimited sample of nearby field stars, either by model-dependenttechniques such as isochrone fitting, or empirical methods suchas nucleo-cosmo-chronometry. The age determination via theclassic isochrone-fitting method has always been hampered bythe fact that in the red-giant locus the isochrones clump together,which leads to a large degeneracy. This degeneracy leads to ageuncertainties easily above 80% for the oldest stars (e.g., da Silvaet al. 2006; Feuillet et al. 2016). The few metal-poor field halostars with a better age determination than the isochrone fitting
Article number, page 1 of 24 a r X i v : . [ a s t r o - ph . S R ] M a y & A proofs: manuscript no. ValentiniMP uses the nucleo-cosmo-chronometry technique (mostly derivedusing the Th-232 and U-238 ratio), and these indicate old ages(Cayrel et al. 2001; Cowan et al. 2002; Hill et al. 2002; Sne-den et al. 2003; Ivans et al. 2006; Frebel et al. 2007; Hill et al.2017; Placco et al. 2017). These old ages seem to confirm theexpectations that metal-poor halo objects are among the oldestobjects in our Galaxy. Although the nucleo-cosmo-chronometrymethod is more precise than isochrone fitting in the case of redgiants, it is not a viable solution for all stars. The method re-quires high-resolution and high signal-to-noise (SNR) spectra inthe blue region of the spectrum (SNR >
300 at ∼
390 nm), andhigh r-process enhancement in order to allow for the presence ofstrong, and su ffi ciently measurable, U and Th lines.Asteroseismology of red giant stars has, in recent years,demonstrated to provide precise masses for such stars, and there-fore ages (Casagrande et al. 2016; Anders et al. 2017; SilvaAguirre et al. 2018). Solar-like oscillations are commonly sum-marised by two parameters: ∆ ν (average frequency separation)and ν max (frequency of maximum oscillation power). These twoquantities provide precise mass (precision of about 10%) andradius (precision of about 3%), using the so-called seismic scal-ing relations, and an additional information on stellar tempera-ture ( T e ff ) (Miglio et al. 2013; Casagrande et al. 2014; Pinson-neault et al. 2014). Since for red giants the stellar masses are agood proxy for stellar age, it is possible to determine a model-dependent age with a precision that can be better than 30% de-pending on the quality of the seismic information (Davies &Miglio 2016). More precise ages, error ∼ ff ect of mass-loss can be minimised by look-ing at stars in the low-RGB phase, where the e ff ect of mass lossare smaller compared to red-clump stars (Anders et al. 2017).The first study to determine masses for a sample of metal-poorhalo giants with both seismic information (from Kepler , Boruckiet al. 2010) and chemistry from high-resolution APOGEE (Ma-jewski et al. 2015) spectra, was the one of Epstein et al. (2014).The authors used scaling relations at face value and reportedmasses larger (M > (cid:12) ) than what would be expected for atypical old population. Similar results were obtained by Caseyet al. (2018), also using scaling relations for three metal-poorstars. These findings led to the need for further tests of the useof asteroseismology in the low metallicity regime. Miglio et al.(2016), analysed a group of red giants in the globular clusterM4 ([Fe / H] = − α / Fe] = ∆ ν scaling re-lation is taken into account for red giant branch (hereafter RGB)stars. The correction presented in Miglio et al. (2016) is a correc-tion theoretically motivated, based on the computation of radialmode frequencies of stellar modes. Wavelength [ ˚ A] N o r m a li z ed F l u x Fig. 1.
RAVE spectra of the 4 metal-poor stars presented in this paper.Spectra are normalised and corrected for radial velocity, the Fe con-tent labeled comes from the analysis of RAVE spectra using the samemethod as in Valentini et al. (2017).
In this work, we present a first set of four stars, identified asmetal poor ([Fe / H] ∼ − ff sets and uncertainties in-troduced by di ff erent seismic pipelines, erroneous assumptionsin temperature, [ α / Fe]-enhancements, and mass loss. Distancesand orbits of the stars are derived in Sec 5, using Gaia-DR2 par-allaxes and proper-motions. In Sec. 6 we discuss each of the fourRAVE stars in light of their chemistry, age and orbital properties.Sec. 7 summarises our conclusions and provide an outlook.
2. Observations
Targets analysed in this works belong to K2 mission campaigns1 and 3. The K2 Campaign 1 field (C1), centred at RA 11 h 35m 46 s DEC + ◦
25’ 00” (l = =+ − ◦
25’ 02” (l =
51, b = − In C1 and C3 K2 fields there are a total of 376 RAVE targets forwhich solar-like oscillations have been detected. Following the
Article number, page 2 of 24. Valentini et al.: Masses and ages for metal-poor stars t-SNE x dimension t - S N E y d i m e n s i o n dwarfsgiantsMetal-poor FGK-typeCaII emission A-typeM-type Fig. 2. t-SNE projection of ∼ joint spectroscopic and seismic analysis described in Valentiniet al. (2017) we identified four stars expected to have metallici-ties [Fe / H] ≤ − ∼ ff er of degeneracies and o ff -sets. Using the t-SNE projection (Matijeviˇc et al. (2017), we con-firmed that the four stars were, indeed, metal poor. The t-SNEprojection (van der Maaten & Hinton 2008) is an algorithm that,when applied to spectra, provides a low-dimensional projectionof the spectrum space and isolates objects that present similarmorphology. In our case, as visible in Fig. 2, metal-poor starsclump in the upper-left region of the projection. In the figure ∼ >
10 are projected, with theRAVE stars in K2 C1 and C3 represented as empty circles. Thefour stars that fall into the very metal-poor island (top right) arethe metal poor giants analysed in the present work.
The four stars are in Gaia DR2 (Gaia Collaboration et al. 2016,2018). Parallaxes, proper motions and flags are listed in Table 1.The duplicated_source flag is listed as Dup.Star S1 (Epic ID: 201359581) has a duplicated_source flag = true, meaning that this source presented more than onedetection and only one entry was kept. This means that the starhad observational or processing problems, leading to possibleerroneous astrometric or photometric solution. This same starhas an astrometric_excess_sigma ≥ astrometric_excess_noise flag >
0, indicates large astro-metric errors and an untrustworthy solution. For this same star the Gaia DR2 radial velocity has an error of 5.17 km / s, hencelarger than the ∼ / s expected for a star of that temperatureand brightness.Star S2 (Epic ID: 205997746) has a Priam_flag indicatinga silver photometry quality and a lower quality in the tempera-ture, radius and luminosity solutions (while the rest of the starsin the sample have a better, golden , photometry quality).For S1 (201359581), we did not consider the ages andmasses derived by taking into account the Gaia DR2 informa-tion. In addition, we consider the solutions for S2 (205997746)of lower quality respect to the other 2 stars, S3 (206034668) andS4 (206443679). We will use the Gaia DR2 proper motions whencomputing orbits for our stars in Section 5, with the exception ofS1, for which we will use UCAC-5 (Zacharias et al. 2017) propermotions.Gaia DR2 parallax, (cid:36) , can be used for deriving the surfacegravity: log( g ) (cid:36) = log( g ) (cid:12) + (cid:32) T e ff T e ff , (cid:12) (cid:33) + log (cid:32) mm (cid:12) (cid:33) ++ . (cid:0) m V + − /(cid:36) ) − . E ( B − V )) + BC − M bol , (cid:12) (cid:1) (1)We derived log( g ) (cid:36) for the stars of our sample, assuming thebolometric correction (BC) as in Casagrande & VandenBerg(2018) and Casagrande & VandenBerg (2014), using Ks magni-tudes and assuming stellar masses of 0.9 M (cid:12) and spectroscopic(UVES) temperatures. Errors were calculated via propagation ofuncertainties and varying stellar masses from 0.8 to 2.2 M (cid:12) (atypical red giant star mass range). We also took into account thee ff ect of the di ff erent o ff sets in the (cid:36) , considering the zero pointcorrection (Lindegren et al. 2018) and the o ff set pointed out byZinn et al. (2018): thus we considered an o ff set e ff ect that varies (cid:36) within ( (cid:36) − (cid:36) + UVES high resolution spectra of our targets were collected inthe period 99D, using UVES-CD 3 set-up (Dekker et al. 2000),program ID: 099.D-0913(A). Spectra have a resolving powerof ∼ ∼
3. Data analysis
Very metal poor stars typically have large radial velocities thatinduce a Doppler shift of observed frequencies. Although small,this shift can be larger than the precision on asteroseismic fre-quencies. In this work we use the average seismic parameters ∆ ν and ν max . Because ∆ ν is a frequency di ff erence and becausethe precision on ν max is much lower than for individual modefrequencies the Doppler correction does not need to be appliedto asteroseismic average parameters (Davies et al. 2014).In order to quantify the impact of the di ff erent seismic inputson the estimates of the mass and age of our stars, we first consid-ered the ∆ ν and ν max measurements coming from four di ff erentseismic pipelines: – COR : It is the method adopted for CoRoT and Kepler stars(Mosser & Appourchaux 2009; Mosser et al. 2011). In a firststep, the average frequency separation ∆ ν , is measured from Article number, page 3 of 24 & A proofs: manuscript no. ValentiniMP S [ µ H z ] [ µ H z ] S [ µ H z ] [ µ H z ] S [ µ H z ] [ µ H z ] S [ µ H z ] [ µ H z ] COR GRD A2Z YE BM_N
Fig. 3. ∆ ν and ν max as measured by di ff erent pipelines. Each colour (blue, magenta, red and green) corresponds to a di ff erent pipeline (COR, GRD,A2Z and YE - see Appendix). The values plotted in black correspond to a further test using COR with inflated uncertainties (BM_N). Table 1.
Gaia DR2 data and seismic data for the 4 RAVE metal-poor stars studied here. In this work we adopted ∆ ν and ν max from COR pipelineand investigated the e ff ect of adopting errors computed considering the dispersion among four di ff erent seismic pipelines (COR, GRD, YE, A2Z),here identified as BM_N seismic values. S1 S2 S3 S4GAIA DR2 dataGaia source ID 3602288924850161792 2596851370212990720 600175713555136256 2622975976942392320 (cid:36) [mas] 0.4621 0.4764 0.6027 1.3793 (cid:36) error [mas] 0.0880 0.0543 0.0386 0.0434pmra [mas / yr] − − / yr] 0.1695 0.4889 0.0632 0.0791pmdec [mas / yr] − − − / yr] 0.0719 0.1795 0.0592 0.0713Dup. 1 0 0 0Astrom. exc. 0.1474; 8.895 0; 0 0; 0 0; 0Priam flag 100001 100002 100001 100001K2 dataEpicID 201359581 205997746 206034668 206443679Kp 10.96 12.46 11.65 12.15Campaign C1 C3 C3 C3 ∆ ν COR [ µ Hz] 2.79 ± ± ± ± ν maxCOR [ µ Hz] 20.20 ± ± ± ± ∆ ν BM_N [ µ Hz] 2.79 ± ± ± ± ν maxBM_N [ µ Hz] 20.20 ± ± ± ± Table 2.
Coordinates and set-up of the ESO-UVES observations of the stars. The SNR listed is the one calculated in the all spectral range.
ID RA DEC JD middle Set-up Exp. time SNR[deg] [deg] [s]S1 178.650541 − − − − – GRD : This pipeline is based on fitting a background modelto the data (Davies et al. 2016). The model is a model H(Kallinger et al. 2014), comprised of two Harvey profiles, a Gaussian oscillation envelope, and an instrumental noisebackground. For the estimate of ν max the central frequencyof the Gaussian component is considered. The median andthe standard deviations are used to summarise the normal-like posterior probability density for ν max . To estimate theaverage frequency separation a model was fitted to the powerspectrum (Davies & Miglio 2016). Article number, page 4 of 24. Valentini et al.: Masses and ages for metal-poor stars – YE : This is a three stages approach. First, a signal-to-noiseratio spectrum (SNR) in function of frequency is created bydividing the power spectrum by a heavily smoothed versionof the raw power spectrum. The second step consists in usinga combination of H0 and H1 hypothesis for detecting oscil-lation power in segments of the SNR spectrum. If a segmentshows detection of oscillations power, then ν max and ∆ ν aredetected as a third step (Hekker et al. 2010; Elsworth et al.2017). – A2Z : A first estimate of ∆ ν was done using the same methodas COR. ν max is measured by fitting a Gaussian on top of thebackground to the power spectrum. Then ∆ ν is recomputedfrom the power spectrum of the power spectrum and by con-sidering only the central orders of the spectrum centred onthe highest radial mode (Mathur et al. 2010, 2011). Di ff er-ently from the previous pipelines, this one measured a valuefor ∆ ν only for 2 of the 4 targets and provided significantlylarger error bars for ν max .We then checked that the di ff erent pipelines were in agree-ment for the four stars, as showed in Fig. 3. As we are deal-ing with a small number of stars and since the four pipelinesare in agreement, we can perform a star-by-star analysis of thegoodness of the seismic values. From a visual inspection, as vis-ible in Appendix A, it appears that: i) A2Z pipeline is provid-ing ∆ ν with very large uncertainties; ii) YE and GRD pipelinesprovide a ν max value that appears shifted respect to the expectedvalue, for star S1 and S2 respectively (see Appenfix Fig. A.1).As shown by previous works (e.g. Lillo-Box et al. 2014; PérezHernández et al. 2016), using individual frequencies for deriv-ing ∆ ν is more precise than the method presented above. Theindividual frequencies fitting exercise is di ffi cult to perform forK2 light-curves, because of the short duration of the K2 runs.For this reason the use of the universal pattern is preferred, as inMosser et al. (2011), which uses the detailed information of thewhole oscillation pattern (Mosser et al. 2011). This dedicatedanalysis provides refined values of the global seismic parame-ters, with smaller uncertainties. This choice is justified also bythe tests performed in Hekker et al. (2012). For these reasons wehave therefore adopted ∆ ν from the COR pipeline as our pre-ferred value.An additional test has been performed, for RGB stars in the α -rich APOGEE- Kepler (APOKASC Pinsonneault et al. 2018)sample: individual mode frequencies has been measured for ≈ ∆ ν measured fromindividual frequencies with the ∆ ν measured by COR pipelinehad been performed. A small ( (cid:46) ff erence between ∆ ν asdetermined by COR, and ∆ ν determined from individual radial-mode frequencies is found (Davies et al., in preparation), sup-porting our choice for COR values. This is also relevant becausethe ∆ ν determined from individual mode frequencies is closer tothe ∆ ν given in the stellar models adopted in PARAM, the toolused in this work for deriving mass, radii, and ages. We addition-ally considered the seismic values from GRD pipeline, which haserror bars in ∆ ν and ν max compatible with the COR pipeline andwith the data quality (see more details in Appendix A).For having a better comprehension of the impact of the useof a global error coming from considering all the pipelines wealso adopted a fifth set of ∆ ν and ν max (BM_N), where the ∆ ν and ν max are from the COR pipeline but with inflated errors that con-sider the dispersion of the pipelines respect to COR values: σ x , BM_N = σ x , COR + (cid:80) i = GRD , YE , A2Z ( x i − x COR ) ν max [ µ Hz] ∆ ν [ µ H z ] APOKASC201359581 (S1)205997746 (s2)206034668 (S3)206443679 (S4) 0.811.21.41.61.822.22.42.62.8
Mass[M sun ] Fig. 4. ∆ ν and ν max distribution of the 4 stars studied in this work. Onthe background the ∆ ν - ν max distribution distribution of the APOKASCsample, colour coded following the mass. where x =∆ ν or ν max . The adopted seismic values, COR andBM_N, are listed in Table 1 (the complete set of seismic valuesare in Appendix Table A.1) and a comparison of the di ff erentsets of ∆ ν and ν max is shown Fig. 3.We compared the ∆ ν and ν max of our sample with the ∆ ν and ν max distribution of the APOKASC sample. The high quality ofthe APOKASC sample makes it the perfect benchmark to pro-vide a first glance on the masses expected for our objects. Fig. 4shows that our four stars fall in the region where the less massivestars are located. The analysis of the RAVE spectra has been performed followingthe method described in Valentini et al. (2017, Sect. 4). We itera-tively derived atmospheric parameters by fixing the gravity to theseismic value, log( g ) S . As a starting point for deriving T e ff , weused the Infra-Red Flux Method (IRFM) temperature publishedin RAVE-DR5 (Kunder et al. 2017), allowing for variations aslarge as 250 K. This analysis was performed using the GAUFREpipeline (Valentini et al. 2013).The seismic gravity we used is defined as:log( g ) S = log( g ) (cid:12) + log (cid:32) ν max ν max , (cid:12) (cid:33) +
12 log (cid:32) T e ff T e ff , (cid:12) (cid:33) (3)with the adoption of the following solar values: ν max , (cid:12) = µ Hz, ∆ ν (cid:12) = µ Hz, log( g ) (cid:12) = T e ff , (cid:12) = α -enhanced with [ α / Fe] ∼ / Fe], [Si / Fe] and [Ti / Fe]are significantly discrepant for the di ff erent stars. Notice that the[Fe / H] values reported in Table 3 are not corrected for non-localthermodynamic equilibrium (NLTE) e ff ects. We will return tothis point when discussing the abundance ratios obtained fromhigh-resolution spectra. Article number, page 5 of 24 & A proofs: manuscript no. ValentiniMP
Table 3.
Radial velocity, atmospheric parameters and abundances of the metal-poor RAVE stars in K2 Campaigns 1 and 3, as derived from RAVEspectra. Temperature and abundances have been derived by fixing the gravity to the seismic value (following the method described in Valentiniet al. (2017)) and using RAVE spectra. Abundances were determined under LTE assumptions.
ID Vrad T e ff log( g ) [Fe / H] [M / H] [ α / Fe] [Mg / Fe] [Si / Fe] [Ti / Fe][km / s] [K] [dex] [dex] [dex] [dex] [dex] [dex] [dex]S1 77.14 ± ±
62 2.24 ± − ± − ± ± ± ± ± − ± ±
81 2.58 ± − ± − ± ± ± ± ±
93 2.57 ± − ± − ± ± ± ± ± − ± ±
90 3.17 ± − ± − ± ± − ± We analysed the high-resolution UVES spectra using theGAUFRE pipeline for retrieving T e ff , log( g ), and [Fe / H] iter-atively using the seismic information on log( g ), using Eq. 3.The analysis was performed with the GAUFRE moduleGAUFRE_EW, that derives atmospheric parameters via ionisa-tion and excitation equilibrium using the equivalent widths (EW)of FeI and FeII lines, MARCS model atmospheres (Gustafssonet al. 2008) and the silent version of MOOG 2017 . For sake ofcomparison we derived atmospheric parameters also using theclassical method (imposing excitation and ionisation equilibriumusing FeI and FeII lines), results are listed as T e ff , Cl and log( g ) Cl in Table 4.The error in T e ff was calculated considering the range of T e ff within the Fe I abundances were independent from theline excitation potential (slope equal to zero) and by varyinglog( g ) and v mic within errors. The error in log( g ) was calcu-lated via propagation of uncertainty when the adopted log( g ) wasderived using asteroseismology (Eq. 3). When log( g ) was mea-sured via the classic method (ionization equilibrium of Fe I andFe II), the uncertainty was derived by varying T e ff , v mic , and[Fe / H] by their uncertainty, since the values are interdependent.Abundances of di ff erent chemical elements were derivedusing MOOG 2017, in the updated version properly treatingRayleigh scattering (Sobeck et al. 2011) . For the abundancesanalysis an ad-hoc model atmosphere with the same atmosphericparameters found by GAUFRE, was created via interpolationusing MARCS models. The linelist was constructed using thelinelists in Roederer et al. (2014b), Hill et al. (2002), imple-mented, when necessary, with line parameters retrieved fromVALD DR4 database (Ryabchikova et al. 2015; Kupka et al.2000, 1999; Ryabchikova et al. 1997; Piskunov et al. 1995). TheC abundance was derived via fitting the A-X CH band-head at ∼ . As indicator of r-process enrichmentwe measured abundances of Eu and Gd. As s-process markerswe measured Sr and Ba.Final abundances are listed Table 5 (for more details see Ap-pendix B). The uncertainties on abundances provided in Table 5(and in B.1) were calculated considering: the internal error of Code available at: https://github.com/alexji/moog17scat Available at the website http://nlte.mpia.de/ the fit, the errors on T e ff and log( g ), and the error on contin-uum normalisation. The error on the fit is provided by MOOGitself. We computed the impact of T e ff and log( g ) uncertaintiesby creating di ff erent model atmospheres by varying atmosphericparameters within the errors. Error on continuum normalisationhas been taken into account by creating, for each stellar spec-trum, ten di ff erent continuum normalisations and then analysingthem. The error listed in Table 5 is the sum in quadrature of thesethree di ff erent errors. In Figure 5 we compare the abundance pat-tern of the four RAVE stars with that of CS 31082-001 (dottedgrey curve) which is considered to be a typical pure r-process en-riched star Spite et al. 2018. The abundances for CS 31082-001were taken from Roederer et al. 2014a.The four stars are clearly enhanced in core collapse (SN typeII) nucleosynthetic products (such as Mg, Si, and Eu), as onewould expected to be the case for old stars. However, the range in α -enhancement is very large, and it is not correlated with metal-licity. S1, S2 and S4 can be classified as r-I stars (i.e. stars with0.3 ≤ [Eu / Fe] ≤ / Eu] < , Christlieb et al. 2004), whileS3 is clearly Ba-enhanced. The low C-enhancement, and the low[Ba / Fe] ratios (with only the exceptional case of S3), suggestminor contribution from AGB-mass transfer (if any).The values obtained from our HR analysis for [Mg / Fe],[Si / Fe], and [Ti / Fe] can now be compared with those reportedin Table 3 obtained from the RAVE spectra. In most of the casesthe discrepancies are above the quoted error bars, and it is prob-ably due to the combination of the lower resolution and shorterspectral coverage of RAVE spectra, that leads to undetected lineblends and the presence of very few lines per element. The[ α / Fe] ratios coming from high-resolution UVES spectra showa large variation. Enhancements for S2 and S4 seem systemati-cally larger than the ones of S1 and S3.In Fig. 6 the atmospheric parameters in this work (fromRAVE and UVES spectra) are compared with the literaturevalues presented in RAVE-DR5 (calibrated values), RAVE-on(Casey et al. 2017, where the stellar parameters were obtainedby using a data-driven approach). It is worth noticing that theRAVE-on catalogue misplaced these red giants in metallicityand / or gravity. This misclassification might be due to the train-ing sample adopted in Casey et al. (2017), consisting mostly ofAPOGEE red giants, that are mostly metal rich. In Fig. 6 is vis-ible also that for the star 201359581 the temperature obtainedwith the Valentini et al. (2017) method is ∼
350 K higher thanthe one measured from the high-resolution spectrum. This is aconsequence of the fact that the starting T e ff adopted was er-roneous. For stars S2, S3 and S4, there is a good agreementbetween the temperatures estimated from the RAVE and high-resolution analysis spectra, upon the use of the seismic gravity.The agreement is also seen in metallicity, where the most dis-crepant case, S4, is our most metal-poor star for which the non-local thermodynamic equilibrium (NLTE) corrections are moreimportant (we took into account NLTE e ff ects, when analysing Article number, page 6 of 24. Valentini et al.: Masses and ages for metal-poor stars
Table 4.
Atmospheric parameters and radial velocities of the stars as obtained from Gaia-DR2 and from high-resolution UVES spectra. The lattervalues were obtained in two ways: using the classical analysis with MOOG and FeI-FeII equivalent widths (Cl.) or in an iterative way fixing thegravity to the seismic value (log( g ) S ). σ σ σ σ T e ff [K] 4987 + − + − + − + − v rad [km / s] 70.00 5.17 − − g ) (cid:36) [dex] 1.87 0.26 2.51 0.25 2.39 0.25 3.17 0.25Classical σ σ σ σ T e ff , Cl [K] 4936 63 4987 78 4890 85 5120 64log( g ) Cl [dex] 1.98 0.20 2.25 0.19 2.22 0.21 2.95 0.20With Seismo σ σ σ σ T e ff [K] 4850 43 5020 35 4995 25 5245 35log( g ) S [dex] 2.17 0.03 2.58 0.02 2.58 0.04 3.17 0.05vmic [km / s] 2.1 0.5 1.80 0.5 2.40 0.4 1.8 0.5v rad [km / s] 74.63 0.11 − − Table 5.
Summary of the abundances of the stars of this work. The solar composition adopted is listed in the last column, from Asplund et al.(2009). Values are corrected for NLTE e ff ects and in case of multiple ions (e.g. FeI and FeII), the mean has been considered. / H] NLTE − ± − ± − ± − ± / Fe] σ [X / Fe] σ [X / Fe] σ [X / Fe] σ log (cid:15) (cid:12) (X )[C / Fe] 0.30 0.15 -0.18 0.10 0.18 0.11 0.01 0.09 8.43[Na / Fe] 0.28 0.06 1.14 0.12 0.25 0.05 0.41 0.08 6.24[Mg / Fe] 0.45 0.11 0.63 0.05 0.27 0.15 0.72 0.10 7.60[Si / Fe] 0.75 0.07 0.61 0.04 0.62 0.10 0.81 0.10 7.51[Ca / Fe] 0.48 0.05 0.42 0.10 0.24 0.13 0.57 0.13 6.34[Sc / Fe] 0.32 0.11 0.00 0.14 0.12 0.11 0.34 0.14 3.15[Ti / Fe] 0.26 0.08 0.27 0.15 0.17 0.10 0.59 0.10 4.95[Cr / Fe] 0.01 0.22 0.05 0.11 − / Fe] 0.07 0.08 0.20 0.10 − / Fe] 0.32 0.10 0.17 0.09 − / Fe] − − − / Fe] 0.30 0.11 0.26 0.11 0.39 0.14 0.41 0.11 4.56[Sr / Fe] 0.10 0.08 − / Fe] 0.50 0.08 0.31 0.09 0.92 0.10 0.83 0.13 2.18[Eu / Fe] 0.80 0.07 0.41 0.08 0.03 0.08 0.79 0.08 0.52[Gd / Fe] 0.05 0.07 − i ) by combining the RAVE spectra with seismic grav-ities it is possible to reach precise stellar parameters, similar towhat is obtained from high-resolution spectra (see the agreementbetween the black dots (UVES) and red points (RAVE) for 3out of the 4 stars); ii ) the high-resolution analysis has confirmedthat one of the stars has metallicity [Fe / H] < −
2. The di ffi cultyin determining the metallicity of such metal-poor objects frommoderate resolution spectra covering a rather short wavelengthrange, not having the extra seismic information, is clearly illus-trated by the discrepant metallicities found by RAVE DR5 andRAVE-on, versus the good agreement with the value publishedin Valentini et al. (2017) upon the use of K2 information, wherethe temperatures and gravities are consistent.
4. Mass and age determination
Mass determinations have been performed using two di ff erentmethods: i) a direct method, using scaling relations, and ii) aBayesian fitting using the PARAM code (Rodrigues et al. 2017).Masses derived using scaling relation di ff er from the ones fromPARAM (see discussion in Rodrigues et al. 2017). We now il- lustrate this di ff erence for the case of our four metal-poor stars.The resulting masses from the two methods are summarized inTable 6. Mass estimate using scaling relations:
For our computations using the scaling relations we adopt as in-put ∆ ν and ν max from the COR pipeline and the T e ff measuredfrom the UVES spectra. The scaling relations are in the form: MM (cid:12) (cid:39) (cid:32) ν max ν max , (cid:12) (cid:33) (cid:32) ∆ ν ∆ ν (cid:12) (cid:33) − (cid:32) T e ff T e ff , (cid:12) (cid:33) / (4) RR (cid:12) (cid:39) (cid:32) ν max ν max , (cid:12) (cid:33) (cid:32) ∆ ν ∆ ν (cid:12) (cid:33) − (cid:32) T e ff T e ff , (cid:12) (cid:33) / (5)were the solar values adopted are the same ones listed in Sec-tion 2, and ∆ ν = µ Hz.The uncertainties on the masses and radii are calculated us-ing propagation of uncertainties, under the assumption of uncor-related errors. .
Article number, page 7 of 24 & A proofs: manuscript no. ValentiniMP Z [ X / F e ] [ de x ] -1-0.500.511.5 C Na Mg Si Ca Sc Ti Cr Mn Fe Ni Cu Zn Sr Ba Eu Gd Fig. 5.
Chemical abundance pattern [X / Fe] for the four metal-poor stars studied in this work. As a reference, the abundances pattern of the r-processenriched star CS 31082-001 are plotted as a dark grey line (abundances from Roederer et al. (2014a)).
Fig. 6.
Atmospheric parameters of the sample of metal-poor stars, as taken from literature and this work: RAVE spectra and seismic parameters(red squares), RAVE-DR5 (blue triangles), RAVE-on (cyan triangles) and ESO high-resolution spectra and seismic parameters (black circles).
Mass estimate using PARAM:
For deriving ages and masses via Bayesian inference we adoptedthe latest version of the PARAM code. The new version of thecode uses ∆ ν that has been computed along MESA evolution-ary tracks, plus ν max computed using the scaling relation. Thefollowing modifications were implemented with respect to theversion described in Rodrigues et al. (2017), namely: i ) we ex-tended the grid towards the metal poor end, down to [Fe / H] = − / H] = − − ii ) we took α -elements enrichment into ac-count, by converting the observed chemical composition into asolar-scaled equivalent metallicity. We investigated the solutionsprovided by PARAM when setting an upper limit to the age at14 Gyr and without age upper limit (the latter helps in under-standing the shape of the PDF of mass and age). PARAM provides also an estimate for stellar distance and lu-minosity, L (listed in Table 7). The luminosities provided byPARAM were used to construct Fig. 7, where we placed ourstars in the temperature-luminosity diagram. The figure showsa set of MESA evolutionary tracks for masses 0.8 and 1.0 M (cid:12) ,at two di ff erent metallicities Z = = ν max - T e ff (middle panel) and ∆ ν - T e ff planes. The stars ofour sample are most likely low-luminosity RGB stars which arenot expected to undergo significant mass loss. The evolution-ary state of star S1 (201359581), on the other hand, is more un-certain, since it is locate close to the RGB bump (dashed line),following also Fig. 1 of Khan et al. (2018), it can be core-Heburning, RGB, early AGB. The evolutionary status of this starbecomes relevant when it comes to discussing the reliability ofage estimates, since stars in the red-clump or early AGB phasessu ff er of significant mass loss, that hampers the mass (and hence Article number, page 8 of 24. Valentini et al.: Masses and ages for metal-poor stars age) determination. Finally, since our stars are well located be-low the bump (with a flag on S1 that is an borderline case), weconsider their abundances not a ff ected by extra-mixing processthat happens at the bump and early AGB stage.Because the adopted MESA stellar tracks in Rodrigues et al.(2017) assume the Grevesse & Noels (1993) solar mixture forthe metals, we adopt the α -enhancement correction to convert[Fe / H] into [M / H] by using the formula from Salaris et al.(1993), updated using the relative mass fraction of elements fromOPAL tables :[M / H] chem = [Fe / H] + log (cid:16) C × [ α/ Fe] + (1 − C ) (cid:17) (6)where C = α -enhanced. We tested the e ff ectiveness of this assumption by com-paring two PARSEC track sets (from MS to RGB tip), which arealso provided for α -enhanced cases. In Appendix C) we compareone track computed for [ α / Fe] =+ / H] = − / H] = − ff ect respect to the typical age un-certainty. We derived mass and ages by adopting first the atmo-spheric parameters derived from RAVE spectra and then for theatmospheric parameters obtained from UVES spectra. We alsocomputed mass and ages using the di ff erent seismic inputs dis-cussed in Section 2 (COR and BM_N). This strategy allows usto see the impact of di ff erent precision in the atmospheric pa-rameters and seismic parameters. Results are summarised in Ap-pendix Table E.1. Results obtained with the high-resolution inputfor temperature, metallicity, and an averaged [ α / Fe] (computedas ([Mg / Fe] + [Si / Fe] + [Ca / Fe]) /
3) are in Fig. 8 and in AppendixFig. E.2. In these figures it is visible that the PDF of masses andages obtained with the seismic values with BM_N seismic valuesare broad and, in the case of 205997746, double peaked. This isa consequence of the inflated error in BM_N, caused by blindlycombining all the spectroscopic pipelines. This shows that, whendealing with a detailed analysis of individual stars, a star-by-starapproach for testing the performances of each seismic pipelineis a necessary step for increasing the precision of mass and agedetermination.Our adopted final values of stellar mass and radius, derivedusing COR seismic input and UVES spectra, are shown in Tab. 6,where we also show, for comparison, the results obtained di-rectly from the scaling relations. The mass and ages of PARAMare obtained adopting a mass-loss value derived from Reimers(1975) law with an e ffi ciency parameter of η = ∆ ν (see Miglio et al. (2016)),that leads to a more accurate mass estimation for red giants.In PARAM this correction is not necessary. The code can, in https://opalopacity.llnl.gov/pub/opal/type1data/GN93/ascii/GN93hz L / L s un ν m a x [ µ H z ] T eff [K] ∆ ν [ µ H z ] M=0.8 M sun
Z=0.00060M=0.8 M sun
Z=0.00197M=1.0 M sun
Z=0.00060M=1.0 M sun
Z=0.00197bump
Fig. 7.
Top panel: Position in the temperature - luminosity diagram ofthe four RAVE stars of this work (nomenclature following Table 1).Evolutionary tracks at masses M = (cid:12) , at two di ff erentmetallicities (Z = ν max diagram of the four RAVE stars of thiswork, same tracks as top panel. Bottom panel: Position in the temper-ature - ∆ ν diagram of the four RAVE stars of this work, same tracksas top panel. Error bars of the plotted quantities are of the size of thepoints. fact, derive the theoretical ∆ ν directly by interpolation, since thisquantity has been estimated along each evolutionary track. PARAM
In the work of Rodrigues et al. (2017) the adoption of the in-trinsic stellar luminosity, L , derived using Gaia parallaxes, leadsto a significant improvement into the mass and age determina-tion (from an error of 5% in mass and 19% in age to 3% and10% respectively). These estimates were based on high-quality Kepler seismic data and very precise atmospheric parameters. Inaddition, the uncertainties on luminosity were assumed to be 3%,from Gaia end-of-the-mission performances. Gaia DR2 does notstill reach this precision and o ff sets in (cid:36) have to be taken intoaccount. Nevertheless we calculated mass, radius and age usingthe additional information on L , calculated from parallax andfind out the shape of the PDFs were a ff ected, suggesting sometension with the input luminosities.Instead of using the luminosities tabulated in Gaia DR2, weconsidered the weighted mean of the L calculated from K s , I, and Article number, page 9 of 24 & A proofs: manuscript no. ValentiniMP
Table 6.
Seismic mass and radius calculated using scaling relations ( T e ff measured from UVES spectra), and mass, radius, and age derived usingPARAM, for the 4 metal-poor RAVE stars in K2 Campaigns 1 and 3. The last column lists the stellar radius provided by Gaia DR2. ID M scaling R scaling M PARAM R PARAM
Age
PARAM R GaiaDR2 this work [M (cid:12) ] [R (cid:12) ] [M (cid:12) ] [R (cid:12) ] [Gyr]S1 1.18 ± ± + . − . + . − . + . − . + . − . S2 1.12 ± ± + . − . + . − . + . − . + . − . S3 0.87 ± ± + . − . + . − . + . − . + . − . S4 1.01 ± ± + . − . + . − . + . − . + . − . S1 S2 S3 S4 M a ss [ M s un ] A ge [ g y r ] M a ss [ M s un ] BMN COR COR T eff +100K COR T eff -100K
S1 S2 S3 S4 A ge [ g y r ] Fig. 8.
Left column: violin plot of the PDFs of mass (top) and age (bottom). The right magenta shaded PDF is derived using the seismic parametersfrom BM_N seismic set of parameters, with the new errors that take into account dispersion between pipelines, the PDFs on the left of the violinare calculated using seismic parameters from COR pipeline (black line, gray shaded) and varying the T e ff of +
100 K (dashed blue line) or − T e ff of −
100 and +
100 K respectively.
V magnitudes, considering BC provided by Casagrande & Van-denBerg (2014) and Casagrande & VandenBerg (2018) and thereddening derived from Schlegel et al. (1998) maps. Errors on L were calculated via error propagation, with the error on BC cal-culated via Monte-Carlo simulation of 100 points for each star.Luminosities are listed in Table 7 and show ∼
15% uncertain-ties, and not the 3% end of mission expectation. We thus optedfor not using luminosities as an extra constraint in our calcula-tions of mass and radius.
For better understanding the systematics that may a ff ect the agedetermination using PARAM we performed several tests underdi ff erent assumptions: – We determined ages and masses for each set of seismic pa-rameters provided by di ff erent pipelines. – We used atmospheric parameters from RAVE and UVESspectra. – For each set of seismic parameters, when using atmosphericparameters derived from RAVE spectra, we considered fivedi ff erent [ α / Fe] abundances: 0.0, 0.1, 0.2, 0.3, 0.4 dex. Sincethe low resolution and the limited wavelength interval of Codes available at https://github.com/casaluca/bolometric-corrections
RAVE may a ff ect the measured alpha content of the stars,we wanted to quantify the impact of a erroneous [ α / Fe]. – Two di ff erent mass loss e ffi ciency parameters were consid-ered, η = – We varied the T e ff of ± ff ect of a di ff erence in temperature that may exist betweendi ff erent methods for measuring it. – We tested the impact of the precision on T e ff , by adoptingas input error a value two times the spectroscopic value. Re-sulting masses and ages are listed in Appendix Table E.1, inthe rows labeled as ”COR σ Te ff ”. – We tested the introduction of an upper limit on the age. Re-sulting masses and ages are listed in Appendix Table E.1, inthe rows labeled as ”COR agelim ”.It is worth to remember that the e ff ects of these tests dependon the position of the star on the HR diagram, and on its evo-lutionary stage. Each locus of the HR diagram is populated bydi ff erent tracks and with di ff erent levels of crowdedness.The variation on α content has no significant e ff ect, provid-ing a mass spread on average of 0.01 M (cid:12) and of 0.3 Gyr in age(see Appendix Figs. D.1 and D.2). As a general behaviour, whenthe α enrichment increases the mass slightly decreases and theage increases.The underestimation of T e ff of 100 K leads to a variationin mass and age on average of −
10% and +
30% respectively.
Article number, page 10 of 24. Valentini et al.: Masses and ages for metal-poor stars
Table 7.
Seismic distances and luminosities calculated using scaling relations, PARAM, distances obtained from Gaia parallaxes (both using theclassical 1 / (cid:36) and Bailer-Jones et al. (2018)), distance calculated using StarHorse (Queiroz et al. 2018a), and luminosity provided by Gaia DR2. Forcalculating L from (cid:36) GaiaDR2 we used the bolometric corrections of Casagrande & VandenBerg (2018). Stars are identified using the nomenclaturein Table 3.
ID Dist scaling
Dist
PARAM
Dist (cid:36)
GaiaDR2
Dist
S H
Dist (cid:36)
GaiaDR2 B − J L PARAM L (cid:36) B − J L GaiaDR2 [pc] [pc] [pc] [pc] [pc] [L (cid:12) ] [L (cid:12) ] [L (cid:12) ]S1 * 1634 ±
322 1536 + − + − + − + − + . − . ± + . − . S2 2094 ±
546 1879 + − + − + − + − + . − . ± + . − . S3 1378 ±
355 1446 + − + − + − + − + . − . ± + . − . S4 675 ±
187 706 + − + − + − + − + . − . ± + . − . (*) Gaia DR2 values for S1 (201359581) are flagged for duplicity and astrometric noise (see Table 1). For this reason distance and luminosityobtained using Gaia (cid:36) are not reliable. As expected, when temperature increases the mass increases andthe age decreases, the contrary happens when the temperaturedecreases. This e ff ect is more visible for the most metal poorand hottest stars.The adoption of an inflated error on T e ff , two times the nom-inal spectroscopic error, lead to no sensible change in the massand age determination. When adopting a seismically determined T e ff , we are taking advantage of using a T e ff that is consistentwith the seismic parameters themselves. In the case of an inac-curate T e ff , as for S1 using RAVE spectra, the solution is mis-leading and PARAM shows tensions in the posterior PDFs (seeAppendix Fig. E.1).The adoption of a mass-loss parameter η = η = ff ect of mass loss is more significant for redclump stars than for RGB stars. Three of the four stars studiedhere are consistent with the RGB classification (see Fig. 7), soour results appear consistent with their findings.Setting a uniform prior on age with an upper limit has a con-sequence on the shapes of the PDFs of ages. This is the reasonwhy, in some cases, for the oldest stars of the sample, the PDFof the age appears truncated at the upper limit, as visible in Ap-pendix Fig. E.2. Although not considering an upper limit on theage at 14 Gyr would not represent the information that we haveabout the age of the Universe, removing the age limit allowsthe PDF to extend to older ages, so we can better understand itsshape and therefore the goodness of the age determination (e.g.multiple peaked PDF). As visible in Appendix Fig. E.2 and listedin Appendix Table E.1, the removal or adoption of an upper agelimit has little consequence on the resulting mass and ages. We compare the masses of our stars with the masses previouslydetermined in the literature for metal-poor field giants in theAPOKASC sample (Epstein et al. 2014) and for giants in theglobular cluster M4 (Miglio et al. 2016) also using asteroseismicinformation. We also recomputed masses and ages for the twoliterature samples using PARAM in the same set-up used for theRAVE metal-poor stars analysed in this work.
The APOKASC metal-poor giants
For the APOKASC targets of Epstein et al. (2014) we adoptedatmospheric parameters and their uncertainties from APOGEE- DR14 (Abolfathi et al. 2018) together with ∆ ν and ν max ob-tained by the COR pipeline from Kepler light-curves (this choiceis needed for granting homogeneity in our sample). The atmo-spheric parameters of APOGEE-DR14 di ff er from those adoptedby Epstein et al. (2014), since that work used previous ASPCAPreleases. The input parameters we used in PARAM are given inTable 8, where the metallicities [M / H] are computed with Eq. 6to take into account the [ α / Fe]-enhancement. The PARAM codeprovided mass and age for each star of the Epstein et al. (2014)work. We did not considered the results for star E14-S5, sincethe resulting a-posteriori T e ff , ν max , and ∆ ν were not in agree-ment with the input values (see Appendix E for an example), in-dicating the presence of erroneous input parameters. The masseswe obtain are now smaller with respect to the original values ofEpstein et al. (2014) who reported masses obtained using scalingrelations. The new masses are also in agreement with the masseswe obtained for the four RAVE stars (see Fig. 10 upper panel).The di ff erences in masses between the Epstein et al. (2014) es-timates and ours are consistent with the fact that the scaling re-lation masses are systematically larger than the ones computedby PARAM for RGB stars (as previously discussed, see Table 6).The two samples together provide a better coverage of the metal-poor [Fe / H] regime. Masses of the Epstein et al. (2014) samplehave been already recomputed by Sharma et al. (2016), Pinson-neault et al. (2018), and Yu et al. (2018), taking into account ∆ ν corrections derived from stellar models. In Fig.9, we com-pared the masses of the Kepler metal-poor stars of Epstein et al.(2014), with those computed in this work, Pinsonneault et al.(2018), and Yu et al. (2018) ones (the lattest considerig the valuecorresponding to their evolutionary status). Masses agree withinerrors. On the other hand, Yu et al. (2018) masses are in generalalways larger than those we computed in this work, resultinginto smaller ages. This might be the result of the di ff erent set ofatmospheric parameters adopted by the authors. The red giants in the M4 globular cluster
We also provide a similar comparison for seven M4 stars pre-viously studied by Miglio et al. (2016) for which K2 seismicinformation were available. This sample is an ideal benchmarkfor testing our method, since for globular clusters a reliable andprecise age can be measured. In this case the temperature wasobtained from (B–V) colour (corrected) as in Casagrande & Van-denBerg (2014), assuming a temperature uncertainty of 100 K.The input parameters adopted in this case are summarised in Ta-ble 9. Our masses and ages determinations are consistent withthe original values of Miglio et al. (2016) who, despite of us-ing the scaling relations, took the necessary correction for RGB
Article number, page 11 of 24 & A proofs: manuscript no. ValentiniMP
Epstein et al. 2014 stars
E14-S1 E14-S2 E14-S3 E14-S4 E14-S5 E14-S6 E14-S7 E14-S8 E14-S9 M a ss [ M s un ] Fig. 9.
Mass and age comparison for the 9 stars presented in Epsteinet al. (2014) (blue diamonds) with the values derived in this work (redcircles), in Pinsonneault et al. (2018) (green triangles) and Yu et al.(2018) (magenta triangles). Stars are indexed as in Table 8 stars into account. With the exception of one outlier (M4-S6), thestars provide an age for the globular cluster of ∼ ± ∼ ± ± ∼ Kepler , but also from the K2 less preciselight curves.
5. Distances and orbits
In this section we compute distances and orbits for the RAVEstars studied in this work. As a sanity check, we first comparedistances estimates coming from five di ff erent methods, namely: – scaling relation; – PARAM distances derived using UVES atmospheric param-eters and the COR seismic values; – direct GAIA-DR2 parallax; – with the StarHorse pipeline (Queiroz et al. 2018b), usingphotometry and Gaia DR2 data, assuming a parallax zero-point correction of 0.52 mas (Zinn et al. 2018); – distances provided by Bailer-Jones et al. (2018).Distances using scaling relations were derived using the ex-pression of Miglio et al. (2013), using the reddening as measuredfrom Schlegel et al. (1998):log d = + . T e ff T e ff , (cid:12) + log ν max ν max , (cid:12) − ∆ ν ∆ ν (cid:12) + . m bol − M bol , (cid:12) )(7)where d is in parsec, m bol is the apparent bolometric magnitudeof the star, and M bol , (cid:12) the absolute solar bolometric magnitude. Bolometric corrections were adopted from Casagrande & Van-denBerg (2018). Errors are calculated using propagation of un-certainty. Distances calculated using the di ff erent methods listedabove are summarised in Table 7.The di ff erent distances are in broad agreement. In particu-lar, SH distances assuming a parallax zero point of − . We adopted a Galactic potential (MWpotential2014)and a solar radius of 8.3 kpc. We adopted PARAM distancesand, when available, Gaia proper motions (see Tables 1 and 7).In the case of 201359581 (S1) we adopted PARAM distancesand UCAC 5 (Zacharias et al. 2017) proper motions, since theGaia astrometric solution is not reliable. Errors on orbit parame-ters were calculated via Monte-Carlo approach, simulating 1,000stars per object with velocity, distance and proper motions vary-ing within errors. Results are summarised in Table 11.Three out of four stars are on very eccentric orbits, attaininglarge distances, typical of what is expected for halo stars. Fig-ure 11 shows that 3 of the four studies stars occupied the halolocus in the Toomre diagram, whereas 206443679 (S4, our mostmetal poor star and the star with the less eccentric orbit) seemsto be more consistent with a thick disk kinematics.
6. Summary of the properties of the four metal-poorRAVE stars
In this section we give a brief summary of the main properties ofeach of the four RAVE stars, by combining all the informationwe obtained: chemistry, ages and masses, and kinematics.
This object is the only star of the sample where the temperaturederived from the high-resolution spectrum is 380 K lower thanthe T e ff derived from the lower resolution RAVE spectrum andthe T e ff derived from the IRFM. We already noticed in Valentiniet al. (2017) that the IRFM tends to overestimate temperatures at T e ff > T e ff derived fromhigh-resolution spectroscopy brings the age back into agreementwith the expectation of this very metal-poor star being old. Thisis the star with the lower value of ∆ ν and ν max , and, lookingat its position in the HR diagram, Fig. 7, it is the only objectthat could be confused with a red-clump star, which would thencontribute to more uncertain estimates of mass and radius, andtherefore age (mostly due to mass loss). The PDF of the age hasa complex profile, multi-peaked. Among the four stars, this isthe object with the largest [C / Fe] ratio (around 0.30 dex). Thestar has both a high Ba and Eu also a [Eu / Ba] ratio of 0.3 ± / s) in radial velocity and the big er-ror ( > / s) associated to Gaia radial velocity suggest that thisobject can be a binary star. Due to the flags in the astrometricsolutions, the orbital parameters obtained for this star are larger,since we adopted the less precise proper motions from UCAC-5catalogue (Zacharias et al. 2017). The star has an highly eccen- Code available at http://github.com/jobovy/galpy .Article number, page 12 of 24. Valentini et al.: Masses and ages for metal-poor stars [Fe/H] [dex] -2.6 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 M a ss [ M s un ] Epstein 2014Epstein PARAMRAVE-MP (this work)M4 PARAM [Fe/H] [dex] -2.6 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 A ge [ G y r ] Fig. 10.
Mass and ages of red giant branch stars in the metal-poor regime for a) four metal-poor RAVE stars with K2 seismic oscillationspresented in this work (red diamonds) ; b) nine APOKASC the objects from Epstein et al. (2014) (original values as empty black circles; our newdetermination using PARAM and APOGEE-DR14 atmospheric parameters and abundances are shown as filled red circles), and c) seven stars inM4 from Miglio et al. (2016) recomputed with PARAM in this work (yellow triangles). tric orbit and, looking at the Toomroe diagram in Fig. 11, it canbe classified as an Halo star.
The star is not C enhanced, it is below the RGB bump, see Fig. 7.The star appears enhanced in Na: [Na / Fe] =+ / Fe] = / Fe] > Looking at the HR diagram in Fig. 7, the star is located be-low the bump. It is alpha-enhanced and it does not show C-enhancement. This star is the richest star in Ba of our sample, while [Eu / Fe] is almost solar (r-poor). The low C-abundanceand the absence of v rad variation that might indicate binarity,suggest that the star is not Ba-enriched via mass transfer froma more massive companion while in AGB phase. If we use theelement ratios as a diagnostic we find [Eu / Ba] = − ± / Ba] = − . ± .
15. Following (Spite et al. 2018, Fig. 4), theseratios put the star outside the correlation of [Eu / Ba] and [Ba / Fe],suggesting an origin from an environment with di ff erent chem-ical history than the Galactic Halo. When looking at mass andage of 201034668, PARAM provides di ff erent results depend-ing on the seismic pipeline adopted. COR seismic values pro-vided a double-peaked age PDF, with no probability that the staris younger than 4 Gyr, when GRD seismic values lead to olderage. In all the cases the age PDF extends beyond 30 Gyrs (ortruncated when the age prior is adopted, as visible from Fig. E.2.The star seems to have a slightly retrograde orbit: in the Toom-roe diagram the star is beyond the −
220 km / s (the slightly ret-rograde orbit is maintained also when integrating the orbit us-ing Gaia-DR2 distances). This star has an angular velocity ofv φ mean = − / s and it is on a highly energetic orbit, look-ing at the lower panel of Fig. 11. The Ba and Eu enrichment,combined with the retrograde orbit, suggests that this star might Article number, page 13 of 24 & A proofs: manuscript no. ValentiniMP
Table 8.
Input atmospheric parameters for the Epstein et al. (2014) stars and PARAM results of mass and age. [M / H] was computed using theEquation 6. Atmospheric parameters and [Fe / H] come from APOGEE DR14. Seismic ∆ ν and ν max are derived using COR pipeline (source:APOKASC catalogue 4.4.2). ID KIC ID ∆ ν ν max [M / H] T e ff [Fe / H] Age Mass[ µ Hz] [ µ Hz] [dex] [K] [dex] [Gyr] [M (cid:12) ]E14-S1 7191496 2.45 ± ± − ± ± − ± + . − . + . − . E14-S2 12017985 2.64 ± ± − ± ± − ± + . − . + . − . E14-S3 8017159 0.69 ± ± − ± ± − ± + . − . + . − . E14-S4 11563791 5.06 ± ± − ± ± − ± + . − . + . − . E14-S5* 11181828 4.14 ± ± − ± ± − ± + . − . + . − . E14-S6 5858947 14.54 ± ± − ± ± − ± + . − . + . − . E14-S7 7019157 3.49 ± ± − ± ± − ± + . − . + . − . E14-S8 4345370 4.09 ± ± − ± ± − ± + . − . + . − . E14-S9 7265189 8.57 ± ± − ± ± − ± + . − . + . − . (*) Star E4-S5 presented tensions between input parameters and output parameters (similar to the case presented in Appendix E. Forthis reason, we disregarded this result, even if we report the result in this table. ). Table 9.
Input atmospheric parameters for the stars analysed in the M4 globular cluster Miglio et al. (2016) adopted in PARAM and resulting massand age. [M / H] has been computed using the Equation 6 ([Fe / H] = − α / Fe] =+ ID ∆ ν σ ∆ ν ν max σν max [M / H] σ [M / H] T e ff σ T e ff Age Mass[ µ Hz] [ µ Hz] [ µ Hz] [ µ Hz] [dex] [dex] [K] [K] [Gyr] [M (cid:12) ]M4-S1 1.83 0.02 11.1 0.4 -0.80 0.13 4585 100 15.09 + . − . + . − . M4-S2 2.55 0.04 17.2 0.7 -0.80 0.13 4715 100 12.11 + . − . + . − . M4-S3 2.62 0.04 17.7 0.7 -0.80 0.13 4710 100 13.05 + . − . + . − . M4-S4 2.64 0.02 18.5 0.7 -0.80 0.13 4715 100 8.38 + . − . + . − . M4-S5 4.14 0.02 32.5 1.3 -0.80 0.13 4847 100 12.07 + . − . + . − . M4-S6 4.30 0.02 32.9 1.3 -0.80 0.13 4842 100 22.79 + . − . + . − . M4-S7 4.30 0.02 34.3 1.4 -0.80 0.13 4805 100 12.26 + . − . + . − . Table 10.
Reddening values for each stars as calculated from Schlegelet al. (1998), PARAM and COR seismic values, StarHorse Queirozet al. (2018a) (spectroscopic atmospheric parameters and Gaia paral-laxes) and Green et al. (2018).
Star Av
Schl . Av PARAM Av StarHorse Av Green2018 [mag] [mag] [mag] [mag]S1 0.079 0.506 + . − . + . − . ± + . − . + . − . ± + . − . + . − . ± + . − . + . − . ± The star is well located below the RGB bump. The alpha-enrichment, the high Eu-content ([Eu / Fe] = / Fe] = / Fe] = / Ba] = − / H] = -2.2 dex is indicative of a halo / accreted origin. This star could haveacquired the presently observed orbit in two ways:1. Keeping in mind its age of 9-10 Gyr, it could have belongedto Milky Way’s last massive merger. It can be seen in Fig.1of Helmi et al. (2018) that this region of the Toomre diagramis degenerate with respect to accreted and in-situ born popu-lation. This requires an in-plane accretion, which can resultfrom massive mergers being dragged into the disk mid-planeby dynamical friction (Read et al. 2009).2. The inner halo has long been known to acquire angular mo-mentum from the bar, causing it to slows down, as seen in N-body simulations bar as (e.g. Athanassoula 2003; Minchevet al. 2012). With a guiding radius of 7 kpc, this star mayhave therefore gained rotational support from the bar.
7. Conclusions
As part of a pilot program aimed at obtaining precise stellar pa-rameters and ages for very metal-poor stars with available seis-mic information, we here determined mass and ages for a sam-ple of 4 RAVE metal-poor stars. We also characterized the starsby combining the information on age, with their chemical pro-file (form high-resolution UVES spectra, covering di ff erent pro-duction channels) and their kinematics. Our analysis took ad-vantage of the seismic information derived from K2 light curves(Campaigns 1 and 3): asteroseismology was first involved in thespectroscopic analysis and then in the mass and age determi-nation using a Bayesian approach. We provided a full analysis Article number, page 14 of 24. Valentini et al.: Masses and ages for metal-poor stars
Table 11.
Adopted proper motions for the orbit integration, plus orbit parameters of the stars in this work. Distance has been derived by PARAM,using BM seismic parameters (see Table 6); radial velocity has been measured from ESO spectra via cross-correlation (see Table B.1)and proper-motions were taken from GAIA-DR2 catalogue (UCAC-5 for S1, due to the flags in Gaia DR2 catalogue). Orbits have been integrated using Galpyv.1.4.0 using
MWpotential2014 potential.
ID PMRA PMDE U V W Rmin Rmax ecc Zmaxmas / yr mas / yr km / s km / s km / s kpc kpc kpcS1 − σ = − σ = − + . − . − + . − . − + . − . + . − . − . − . + . − . + . − . S2 16.79 σ = − σ = − + . − . − + . − . + . − . + . − . − . − . + . − . + . − . S3 − σ = − σ = + . − . − + . − . − + . − . + . − . − . − . + . − . + . − . S4 32.43 σ = σ = − + . − . − + . − . − + . − . + . − . − . − . + . − . + . − . V [km/s] -300 -250 -200 -150 -100 -50 0 ( U + W ) / [ k m / s ] S1: 201359581S2: 205997746S3: 206034668S4: 206443679
ThinDiscThickDiscHalo
Lz [Kpc*km/s] E [ ( k m / s ) ] -50-45-40-35-30-25-20-15 S1: 201359581S2: 205997746S3: 206034668S4: 206443679
Fig. 11.
Top panel: Toomroe diagram of the RAVE stars of this paper.Indicative limits for the thin and thick disk are plotted. Bottom panel:Orbit energy vs Lz plot of the stars. (stellar parameters, chemistry and ages) using both intermediate-resolution spectra (RAVE, R = = g ), T e ff ) pair, isadopted, as described in Valentini et al. (2017).In addition we provide a comparison of log( g ) derived us-ing three di ff erent methods: a) from the classical spectroscopicanalysis, b) from Gaia DR2 parallaxes (Eq. 1), c) from aster- oseismology (Eq. 3). The three estimated values are in agree-ment within errors and seismic log( g ) demonstrated to be reli-able even at low metallicities, with the advantage of providingthe most precise measurement. At low metallicities the classicallog( g ) derived via ionisation equilibrium is a ff ected by NLTEe ff ects, that may hamper the correct estimate of gravity and tem-perature. The log( g ) (cid:36) , even if it has a large uncertainty due tothe mass assumption, can be used as a good prior for spectro-scopic analysis of red giant spectra, in particular of spectra withknown T e ff -log( g ) degeneracies (as in RAVE) when no seismicinformation is available.The more precise and self-consistent stellar parameters ob-tained for the four RAVE stars, when combined with ∆ ν and ν max estimated from di ff erent seismic pipelines, deliver massesand ages with 9% and 30-35% uncertainties, respectively. Agesfor field red giants of this precision opens new perspectives tothe field of Galactic Archaeology (Miglio et al. 2017, see also).Along this work we also investigated the impact of di ff erent as-sumptions on the above uncertainties. The main conclusions canbe summarised as follows: – Impact of spectral resolution / short-wavelength interval:masses and ages were obtained from RAVE and UVES spec-tra using the same strategy of iterating on the best (log g ,Te ff ) pair using as prior the seismic gravity and the IRFMtemperatures. In the case of the RAVE spectra the known de-generacies lead to large uncertainties in mass and age. In onecase, when the IRFM T e ff was inaccurate by ∼
250 K (i.e.outside the flexibility range in temperature during the iter-ation) an erroneous age determination occurs. However, inthis case, the posteriors of temperature, mass, and age arein tension with those of ∆ ν and ν max . This already tends toindicate an erroneous determination on one of the input pa-rameters, and thus potentially leading to an erroneous agedetermination (this case is well illustrated by that specificexample). – Impact of the di ff erent seismic pipelines: the adoption of dif-ferent seismic pipelines has made clear the important impactthe uncertainties on ∆ ν and ν max estimates can have on theresulting masses and ages. However, also in this case, it ispossible to select those seismic estimates that seem in betteragreement with the quality of the light curves available, mak-ing sure that only the best seismic parameters are used. Inthis work we favoured the seismic method providing the low-est spread when compared to other methods (Pinsonneaultet al. 2018, Fig. 10). – The impact of surface temperature scale: a shift of − T e ff leads to a mass underestimation of ∼
10% and, as conse-quence, a stellar age that is older by ∼
30% (if temperaturesare overestimate the e ff ect works in the opposite direction.); Article number, page 15 of 24 & A proofs: manuscript no. ValentiniMP – The impact of [ α / Fe] ratios: In this case the impact is lessimportant than the ones discussed above (being only of a few% in age). In the case of the RAVE spectra, where the [ α / Fe]has larger uncertainties, we have computed ages and massesfor di ff erent [ α / Fe] ratios and the e ff ects were minor. – The impact of mass-loss: as pointed out in Anders et al.(2017) and Casagrande et al. (2016), the impact of mass-lossbecomes important in the RC phase. Our stars are compati-ble with being RGB where the mass-loss impact is expectedto be minor (as also shown by the computation made in thepresent work). – The impact of an accretion event: the seismic age measure-ment relies on the fact that the age of a red giant is propor-tional to the time spent on the MS, and therefore its mass.Any mass accretion event hampers this assumption (rejuve-nating the star). Radial velocity variations (due to binarity)or chemical hints of mass transfer (mostly C or s-process el-ements contribution due to AGB-mass transfer) must raisea flag regarding the accuracy of the ages measured with as-teroseismology. For three stars of our sample we have notfind any clear sign of radial velocity variability, nor any clearchemical signature of mass transfer from a companion, andtherefore we consider our ages reliable.This pilot project shows that it is possible to use astero-seismology for determining precise and consistent masses andages of metal-poor field giants. Together with nucleo-cosmo-chronometry, seismology provide the only way to estimate agesof distant field stars. However, this important new tool needskey steps to be followed, which are i ) a consistent spectroscopicanalysis which delivers not only detailed abundances, but also aconsistent (log( g ), Te ff ) pair; ii ) a careful and critical use of theseismic inputs, and iii ) an analysis of the posterior distributionsof all output parameters to look for tensions with the seismic in-put which might be indicative of erroneous parameter estimates.The use of seismic log( g ) and a temperature prior in an itera-tive way (see Valentini et al. and references therein), is thus acritical step in the analysis. This important step assures that theatmospheric parameters used for deriving mass and age with as-teroseismology is consistent with the seismic inputs used in thecode, also o ff ering a new way to provide more reliable surfacetemperatures.In the near future the impact of the Gaia data should becomeimportant thanks to a better understanding of the parallax o ff setsand also in terms of narrowing the current posterior age distribu-tions (see Rodrigues et al. 2017, discussion). For now, Gaia DR2data are already useful to better define the orbits of the studiedstars.Our strategy will enable a more serious program towards de-termining ages for giant halo field stars, that is complementaryto nucleo-cosmo-chronometry, but with two advantages whichare: it applies to all stars, and not necessarily only to thosestrongly r-process enhanced, and it provides ages with smalleruncertainties. Detailed abundance measurements are also nec-essary to gauge possible e ff ects of mass-accretion which wouldsystematically shift the seismic ages. Finally, the results of thispilot program pave the path for a more extensive study of metalpoor stars with asteroseismology, delivering samples with ageestimates to a ∼
30% precision, hence superior to all what is cur-rently available for field metal-poor distant stars in terms of agedeterminations. It seems not unrealistic to imagine that in thenear future we will be able to add the age dimension in the chem-ical diagrams of the metal poor universe (e.g. Cescutti & Chiap-pini 2014, Sakari et al. 2018, Spite et al. 2018), thus contributing enormously to our understanding of the first phases of the galaxyassembly and early nucleosynthesis.
Acknowledgements.
MV and CC acknowledge the DFG project number283705981: “Analysing the chemical fingerprints left by the first stars: chemi-cal abundances in the oldest stars”. DB is supported in the form of work contractFCT / MCTES through national funds and by FEDER through COMPETE2020 inconnection to these grants: UID / FIS / / / FIS-AST / / ).This work has made use of the VALD database, operated at Uppsala Univer-sity, the Institute of Astronomy RAS in Moscow, and the University of Vi-enna. Based on data obtained from ESO-UVES instrument under proposal ID:099.D-0913(A). Funding for RAVE has been provided by: the Australian As-tronomical Observatory; the Leibniz-Institut fuer Astrophysik Potsdam (AIP);the Australian National University; the Australian Research Council; the FrenchNational Research Agency; the German Research Foundation (SPP 1177 andSFB 881); the European Research Council (ERC-StG 240271 Galactica); theIstituto Nazionale di Astrofisica at Padova; The Johns Hopkins University; theNational Science Foundation of the USA (AST-0908326); the W. M. Keck foun-dation; the Macquarie University; the Netherlands Research School for Astron-omy; the Natural Sciences and Engineering Research Council of Canada; theSlovenian Research Agency; the Swiss National Science Foundation; the Sci-ence & Technology Facilities Council of the UK; Opticon; Strasbourg Obser-vatory; and the Universities of Groningen, Heidelberg and Sydney. The RAVEweb site is at: . This work has made use ofdata from the European Space Agency (ESA) mission Gaia ( ), processed by the Gaia
Data Processing and Anal-ysis Consortium (DPAC, ). Funding for the DPAC has been provided by national institutions,in particular the institutions participating in the
Gaia
Multilateral Agreement.We finally acknowledge the anonymous referee for the useful remarks.
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Normalized power spectrum of the RAVE stars (original: or-ange line, smoothed: blue). ν max values from the di ff erent pipelines areplotted: GRD (green), COR (red), YE (purple), and A2Z (brown). Appendix A: The selection of ∆ ν and ν max For the four RAVE metal-poor stars analysed in the present workwe obtained ∆ ν and ν max from four di ff erent pipelines. We de-cided to select the best ∆ ν and ν max pair by looking at the per-formances of the four pipelines for each object. When looking atthe power spectrum, see Fig. A.1, it is visible that the uncertaintyon the A2Z results is clearly too large in at least two instances.This is probably connected with the method and it’s sensitivityto poorly sampled data. For this reason we will decide we do notfavour the A2Z results for the ν max .For better understanding the ∆ ν results, SNR spectra havebeen created (Fig. A.2), then SNR spectra have been analysed asa function of frequency mod ∆ ν divided by ∆ ν (one realizationper each pipeline). The same analysis has been performed using ∆ ν + eDnu. If the uncertainty is sensible (i.e., not too large) wemight expect to still see repeated structure. If e ∆ ν is too large therepeated structure goes away.This check led to the following conclusions regarding ∆ ν : – – = – – =
0, 2 and plenty of otherrepeated structure. Every pipeline agrees for this star.This is probably a result of the di ff erent method used andthe degree to which the pipelines are set-up to be conservative.With only 4 stars we do not have the benefit of a large sampleto cope with, having uncertainties that are too large. From thetests above we concluded that BM and GRD have the lowest andprobably the most realistic uncertainties for these 4 stars (thisconclusion does not necessarily hold for other stars). We there-fore move forward with the analysis by using only the GRD andBM results. For the future works we will keep considering re-sults from di ff erent pipelines, performing this analysis for everytarget. Table A.1. ∆ ν and ν max as measured by the four di ff erent pipelines. CORID ν max e ν max ∆ ν e ∆ ν [ µ Hz] [ µ Hz] [ µ Hz] [ µ Hz]S1 20.2 0.3 2.79 0.06S2 51.2 1.1 5.76 0.06S3 41.8 2.2 5.26 0.10S4 190.0 8.0 16.05 0.06GRDID ν max e ν max ∆ ν e ∆ ν [ µ Hz] [ µ Hz] [ µ Hz] [ µ Hz]S1 19.7 0.8 2.75 0.16S2 50.0 0.8 5.80 0.09S3 42.0 1.3 5.13 0.10S4 188.5 2.3 16.15 0.08YEID ν max e ν max ∆ ν e ∆ ν [ µ Hz] [ µ Hz] [ µ Hz] [ µ Hz]S1 20.2 0.5 2.75 0.07S2* 50.5 0.9 5.72 0.07S3 43.8 1.1 5.06 0.21S4 188.2 2.2 16.16 0.11A2ZID ν max e ν max ∆ ν e ∆ ν [ µ Hz] [ µ Hz] [ µ Hz] [ µ Hz]S1 20.8 1.01 – –S2 51.1 2.46 5.69 0.15S3 42.3 4.8 – –S4 189.4 24.23 16.07 0.05 (*) For S2 the YE pipeline found that the ∆ ν value is sensitive to therange in the spectrum used. A central value is sprovided. S1 S2S3 S4
Fig. A.2.
SNR spectra of the RAVE metal-poor stars of this work.
Appendix B: Analysis of UVES spectraAppendix C: Tests on alpha-enhancement and T e ff shifts In the present work we use PARAM which uses a set of MESAmodels, not α -enhanced. The e ff ect of the α -enhancement istaking into account by adopting the Salaris formula in Equa-tion 6. We tested this assumption using PARSEC models, forwhich alpha-enhanced computations are available. In Fig. C.1we compare two sets of PARSEC tracks, covering MS to RGBtip phases. One set (plotted in red) is a set of tracks for 0.7, 1.0and 1.3 M (cid:12) at [Fe / H] = − .
16 dex and [ α/ Fe] = . / H] = − .
86 dex (fol-
Article number, page 18 of 24. Valentini et al.: Masses and ages for metal-poor stars
Table B.1.
Chemical abundances derived for the metal-poor stars presented in this work. Values were derived from UVES spectra via equivalentwidth measurement (ew) or line fitting (f) using the atmospheric parameters derived using the seismic log( g ). − − − − − − − -1 0 1 2 3 4 log L age ( G y r) Fig. C.1.
PARSEC tracks at [Fe / H] = − α/ Fe] = / H] = − (cid:12) . lowing Equation 6). The maximum deviation between the twoset of tracks reaches the maximum in the RGB phase. Since thedi ff erence is negligible respect to the typical errors we have onage, we adopted the Salaris et al. (1993) correction in our com-putations. Appendix D: Masses and ages using RAVEatmospheric parameters and metallicities
We derived ages and masses for the four RAVE metal poor starsusing the atmospheric parameters derived from RAVE spectra T eff [K] age [ G y r ] Fig. C.2.
Same PARSEC tracks of Fig. C.1 but with temperature on theabscissa. using the seismic log( g ). RAVE spectra cover a small spectralrange (8420-8780Å) at intermediate resolution (R = ff er of o ff sets and inaccuracies. Forthis reason we computed ages and masses for five di ff erent α enhancements. Two di ff erent mass-loss approximations ( η = T e ff of ±
100 K (see Fig. D.3) us-ing COR seismic parameters.
Article number, page 19 of 24 & A proofs: manuscript no. ValentiniMP
From Fig. D.1, D.2 and D.3 it is possible to see the e ff ect ofthe di ff erent α -enhancement and mass-loss assumptions, and thee ff ects of shifts in T e ff . Appendix E: PARAM tensions and additionalresults
S1 is an exemplary case of how an erroneus temperature determi-nation leads to misleading age and mass values using PARAM.In the case of RAVE spectra the spectroscopically determined T e ff is 300 K higher than the temperature derived from the high-resolution spectrum. However, as visible in Fig. E.1, the erroneus T e ff lead to tensions between the a-posteriori and the input val-ues of ∆ ν , ν max and T e ff , and to asymmetric PDFs. This does nothappen when adopting the atmospheric parameters coming fromhigh-resolution spectroscopy. Appendix F: M4 PARAM results in detail
The globular cluster M4 is the ideal testing ground for investi-gating the accuracy of our stellar age and mass determinationrespect to other classic techniques. The cluster had been well in-vestigated in literature, and its age has been determined usingboth CMD fitting (e.g., Miglio et al. 2016) and the white dwarfscooling sequence (Hansen et al. 2004): both techniques agree onan age of ∼
13 Gyr with an error of 0.7 Gyr. The work of Miglioet al. (2016) determined also a typical mass of the stars in theRGB: M
RGB = (cid:12) , with an error of 0.05 M (cid:12) .In Fig.F.1 we report the individual mass and ages PDFs asdetermined using PARAM and we compare them with the liter-ature results for M4. Our values are in a very good agreementwith literature values, with the exception of star M4-S4, a prob-able red clump star. Article number, page 20 of 24. Valentini et al.: Masses and ages for metal-poor stars
StarS1 S2 S3 S4 M a ss η =0.2 [ α /Fe]=0.0[ α /Fe]=0.1[ α /Fe]=0.2[ α /Fe]=0.3[ α /Fe]=0.4 StarS1 S2 S3 S4 A ge M a ss η =0.4 StarS1 S2 S3 S4 A ge Fig. D.1.
Mass and ages of the five stars,determined using di ff erent [ α / Fe] (0.0, 0.1, 0.2, 0.3, 0.4 dex respectively) and two di ff erent η parameters(0.2 and 0.4) for the mass loss. COR seismic parameters and spectroscopic parameters derived from RAVE spectra and asteroseismology. Star
S1 S2 S3 S4 M a ss η =0.2 [ α /Fe]=0.0[ α /Fe]=0.1[ α /Fe]=0.2[ α /Fe]=0.3[ α /Fe]=0.4 Star
S1 S2 S3 S4 A ge Star
S1 S2 S3 S4 M a ss η =0.4 Star
S1 S2 S3 S4 A ge Fig. D.2.
Mass and ages of the five stars,determined using di ff erent [ α / Fe] (0.0, 0.1, 0.2, 0.3, 0.4 dex respectively) and two di ff erent η parameters(0.2 and 0.4) for the mass loss. GRD seismic parameters and spectroscopic parameters derived from RAVE spectra and asteroseismology.Article number, page 21 of 24 & A proofs: manuscript no. ValentiniMP M a ss [ M s un ] A ge [ G y r ] M a ss [ M s un ] A ge [ G y r ] M a ss [ M s un ] A ge [ G y r ] [ α /Fe] [dex] M a ss [ M s un ] [ α /Fe] [dex] A ge [ G y r ] Fig. D.3.
Mass and ages of the 5 stars,determined using di ff erent [ α / Fe] (0.0, 0.1, 0.2, 0.3, 0.4 dex respectively in blue, magenta, red, green andblack) and varying the T e ff of ±
100 K in each α assumption (triangle up for temperature increased, triangle down for decreased). BM_N (CORwith new errors) seismic parameters and spectroscopic parameters derived from RAVE spectra and asteroseismology. ν max [ ν Hz] P D F PDFinputoutput ∆ ν [ ν Hz] P D F Teff ν max [ ν Hz]
18 19 20 21 22 P D F PDFinputoutput ∆ ν [ ν Hz] P D F Teff
Fig. E.1.
Left column: a posteriori ∆ ν , ν max , and T e ff of S1 using RAVE atmospheric parameters. PDF for ∆ ν and ν max are showed as well. Rightcolumn: a posteriori ∆ ν (and its PDF), ν max (and its PDF), and T e ff of S1 using atmospheric parameters derived from UVES spectrum.Article number, page 22 of 24. Valentini et al.: Masses and ages for metal-poor stars M a ss [ M s un ] A ge [ G y r ] PDF COR no age upper limitPDF COR with age upper limitPDF COR no age upper limitPDF COR with age upper limit
Fig. E.2.
Violin plot of the PDFs of mass (top) and age (bottom) with input seismic parameters given by the COR pipeline with and without upperage limit (cyan and white shade respectively). The mode of each pdf, with the errorbar representing the lower and upper 68th percentile of thePDF, is also indicated.
Table E.1.
Ages and masses of the four RAVE stars as derived by PARAM, using COR seismic pipeline and stellar parameters obtained fromdi ff erent spectra, RAVE and ESO-UVES (after adopting the strategy of using seismic gravities to find a more self-consistent surface temperature).For the PARAM results obtained from RAVE spectra, we listed the values corresponding to an α enhancement closer to the measured one.Maximum and minimum error values of age and mass (measured on the 68 percentile of the PDF) are listed in superscript and subscript respectively.COR σ Te ff and COR agelim rows list the mass and age determined by doubling the error on T e ff and adding the upper limit on age (13.96 Gyr)respectively. Star Seismic RAVE UVES UVES + GAIAID Pipeline Age Mass Age Mass Age Mass[Gyr] [M (cid:12) ] [Gyr] [M (cid:12) ] [Gyr] [M (cid:12) ]S1 COR 1.77 + . − . + . − . + . − . + . − . + . − . + . − . COR σ Te ff + . − . + . − . COR agelim . + . − . + . − . + . − . + . − . BM_N 25.58 + . − . + . − . S2 COR 7.64 + . − . + . − . + . − . + . − . + . − . + . − . COR σ Te ff + . − . + . − . COR agelim . + . − . + . − . + . − . + . − . BM_N 7.84 + . − . + . − . S3 COR 12.95 + . − . + . − . + . − . + . − . + . − . + . − . COR σ Te ff – – 13.13 + . − . + . − . COR agelim . + . − . + . − . + . − . + . − . BM_N 15.98 + . − . + . − . S4 COR 10.03 + . − . + . − . + . − . + . − . + . − . + . − . COR σ Te ff – – 9.04 + . − . + . − . COR agelim . + . − . + . − . + . − . + . − . BM_N 9.72 + . − . + . − . Article number, page 23 of 24 & A proofs: manuscript no. ValentiniMP
Mass [M sun ] S t a r M4-S1M4-S2M4-S3M4-S4M4-S5M4-S6M4-S7
Mass [M sun ] Age [Gyr]
10 20 30 40 50 S t a r M4-S1M4-S2M4-S3M4-S4M4-S5M4-S6M4-S7
Age [Gyr]
M4-S1M4-S2M4-S3M4-S4M4-S5M4-S6M4-S7literature