The AMBRE Project: Spectrum normalisation influence on Mg abundances in the metal-rich Galactic disc
Pablo Santos-Peral, Alejandra Recio-Blanco, Patrick de Laverny, Emma Fernández-Alvar, Christophe Ordenovic
AAstronomy & Astrophysics manuscript no. Santos-Peral c (cid:13)
ESO 2020June 16, 2020
The AMBRE Project: Spectrum normalisation influence onMg abundances in the metal-rich Galactic disc
P. Santos-Peral , A. Recio-Blanco , P. de Laverny , E. Fernández-Alvar , and C. Ordenovic Laboratoire Lagrange (UMR7293), Université de Nice Sophia Antipolis, CNRS, Observatoire de la Côte d’Azur, BP 4229, F- 06304Nice Cedex 04, Francee-mail: [email protected]
Received January 17 2020 / Accepted June 2 2020
ABSTRACT
Context.
The abundance of α -elements provides an important fossil signature in Galactic archaeology to trace the chemical evolutionof the di ff erent disc populations. High-precision chemical abundances are crucial to improving our understanding of the chemody-namical properties present in the Galaxy. However, deriving precise abundance estimations in the metal-rich disc ([M / H] > Aims.
The aim of this paper is to analyse di ff erent error sources a ff ecting magnesium abundance estimations from optical spectra ofmetal-rich stars. Methods.
We derived Mg abundances for 87522 high-resolution spectra of 2210 solar neighbourhood stars from the AMBRE Project,and selected the 1172 best parametrised stars with more than four repeated spectra. For this purpose, the GAUGUIN automatedabundance estimation procedure was employed.
Results.
The normalisation procedure has a strong impact on the derived abundances, with a clear dependence on the stellar typeand the line intensity. For non-saturated lines, the optimal wavelength domain for the local continuum placement should be evaluatedusing a goodness-of-fit criterion, allowing mask-size dependence with the spectral type. Moreover, for strong saturated lines, apply-ing a narrow normalisation window reduces the parameter-dependent biases of the abundance estimate, increasing the line-to-lineabundance precision. In addition, working at large spectral resolutions always leads to better results than at lower ones. The resultingimprovement in the abundance precision makes it possible to observe both a clear thin-thick disc chemical distinction and a decreasingtrend in the magnesium abundance even at supersolar metallicities.
Conclusions.
In the era of precise kinematical and dynamical data, optimising the normalisation procedures implemented for largespectroscopic stellar surveys would provide a significant improvement to our understanding of the chemodynamical patterns of Galac-tic populations.
Key words.
Stars:abundances – The Galaxy: disc – Methods: data analysis
1. Introduction
Disentangling the chemodynamical signatures present in thedisc’s stellar populations is essential to unveiling the forma-tion and evolution of the Milky Way. Since the first thin-thickdisc identification (Yoshii 1982; Gilmore & Reid 1983), chemi-cal signatures (preserved in FGK-type stars’ atmospheres) havebeen suggested as the best criteria to di ff erenciate betweenGalactic stellar populations. Numerous studies (e.g. Adibekyanet al. 2012; Recio-Blanco et al. 2014; Bensby et al. 2014; Wo-jno et al. 2016; Ivanyuk et al. 2017; Buder et al. 2019; Haywoodet al. 2019; Hayden et al. 2020) have characterised these twoGalactic components in the solar neighbourhood.In particular, the α -elements abundance (e.g. O, Mg, Si,S, Ca, Ti) has been widely analysed to chemically disentan-gle the Galactic thin-thick disc populations (Fuhrmann 2011;Adibekyan et al. 2012; Recio-Blanco et al. 2014; Hayden et al.2017). The observed thick disc has been reported to be [ α / Fe]-enhanced relative to the thin disc for most metallicities, unveilingdistinct chemical evolution histories in both disc components.The abundance of [ α / Fe] is used as a good chronological proxy.This is due to the timescale delay between core-collapse su-pernovae (Type II SNe) of the most massive stars ( M (cid:38) (cid:12) ),which enrich the ISM with α -elements predominantly, and Type Ia SNe, which release mainly iron-peak elements (Matteucci &Greggio 1986). However, both high- and low- α sequences seemto overlap at supersolar metallicites, showing a flat trend formost α -process elements (not expected by chemical evolutionmodels) being impossible to chemically identify to which stel-lar population they belong. In addition, di ff erent features of thedisc [ α / Fe] abundances as the intermediate α populations at highmetallicities (Adibekyan et al. 2012; Mikolaitis et al. 2017) andthe gap between these stars and the high- α metal-poor popula-tion (Adibekyan et al. 2012; Gazzano et al. 2013), are still matterof debate.In the solar neighbourhood and beyond, several spectro-scopic stellar surveys have provided valuable chemical infor-mation and constraints, such as SEGUE (Yanny et al. 2009,R ∼ ∼ ∼ ∼ ∼ α / Fe] abun-dances at supersolar metallicities is a common feature of manydi ff erent studies. For instance, Anders et al. (2014) and Haydenet al. (2015) showed the [ α / Fe] vs [Fe / H] plane across the MilkyWay for a large sample of giant stars from APOGEE. They findthat both low- and high-[ α / Fe] sequences decrease with [Fe / H],
Article number, page 1 of 18 a r X i v : . [ a s t r o - ph . GA ] J un & A proofs: manuscript no. Santos-Peral merging and showing a flattened trend at supersolar metallicities.Recently, Buder et al. (2019) found similar signatures over thesample of dwarfs and turn-o ff stars from GALAH DR2, show-ing a remarkable agreement with the results of Adibekyan et al.(2012). Similarly, Mikolaitis et al. (2017) defined both Galacticdiscs chemically finding the flattening trend in the [Mg / Fe] ratiofor stars with metallicity [Fe / H] > -0.2 dex in a dwarf star samplefrom AMBRE data.Theoretically, two-infall chemical evolution models (Chiap-pini et al. 1997; Romano et al. 2010) predict a steeper slope inthe metal-rich regime ([Fe / H] > ff erent surveys(Kordopatis et al. 2015; Hayden et al. 2017; Feltzing et al. 2020).Updated chemical evolution models developed by Grisoni et al.(2017, 2018) conclude also that other mechanisms are needed,in addition to the inside-out formation scenario, to reproduce theflattened trend in the Galactic disc at supersolar metallicites.On the basis of these apparent discrepancies, the study ofchemical signatures requires the best possible precision and ac-curacy in the abundance measurement. Precise abundances aremandatory to detect stellar populations that di ff er in their el-emental abundances from each other (Lindegren & Feltzing2013). Magnesium is probably the most representative and com-monly used α -element (c.f. Carrera et al. 2019). It is known tohave a high number of measurable spectral lines in optical spec-tra. In addition, the ratio of the Mg abundance with respect toiron, [Mg / Fe], shows a large absolute separation of the Galacticthick-thin disc populations, along with a smaller scatter and ashallower trend with temperature and metallicity (Brewer et al.2016; Bergemann et al. 2017; Ivanyuk et al. 2017; Buder et al.2019), making this element possibly the best tracer.A detailed exploration of possible error sources is crucial tointerpreting the reality of the observed chemical signatures inthe Galactic stellar populations and the resulting implicationson chemodynamical relations (such as the contribution of radialmigration in the solar neighbourhood or the use of [Mg / Fe] asa good age proxy), which are mainly constrained by the abun-dance precision. The main issues concerning the determinationof high-precision abundances are characterised by the need forboth high signal-to-noise ratio (S / N) and spectral resolution, andpredominantly by the definition of continuum to normalise theobserved spectral data. The latter issue can be responsible forthe largest fraction of the uncertainty in the abundance estima-tions, which is still complex for cool metal-rich stars due to thehigh presence of blended and molecular lines (as reviewed byNissen & Gustafsson 2018; Jofré et al. 2019). In particular, thecontinuum normalisation is not fully optimised for di ff erent stel-lar types in large spectroscopic stellar surveys.In this paper, we present a detailed spectroscopic analysisof the Mg abundance estimation for a sample of 2210 FGK-type stars in the solar neighbourhood observed and parametrisedat high spectral resolution within the context of the AMBREProject (de Laverny et al. 2013). We point out that we refer to theobserved high- and low-[Mg / Fe] sequences as thick and thin discpopulations hereafter, although we have not applied any kine-matic selection to the sample. The paper is organised as follows.In Sect. 2, we introduce the observational data sample used inthis work. The automatic abundance estimation method is de-scribed in Sect. 3. We present the sources of error caused by the normalisation procedure in Sect. 4. In Sect 5, we show the finalderived [Mg / Fe] abundances of the sample. We conclude with asummary in Sect 6.
2. The AMBRE:HARPS observational data sample
The AMBRE Project (de Laverny et al. 2013) is a collabora-tion between the Observatoire de la Côte d’Azur (OCA) andthe European Southern Observatory (ESO), of which the maingoal is to determine the stellar atmospheric parameters (T e f f ,log(g), [M / H], [ α / Fe]) of archived stellar spectra of the FEROS,HARPS, and UVES ESO spectrographs. The stellar parameterswere derived by the multi-linear regression algorithm MATISSE(MATrix Inversion for Spectrum SynthEsis, Recio-Blanco et al.2006), developed at OCA and used in the Gaia RVS analysispipeline (
Radial Velocity Spectrometer , see Recio-Blanco et al.2016), with the AMBRE grid of synthetic spectra (de Lavernyet al. 2012).For the present paper, we derived [Mg / Fe] abundances over asample of 87522 HARPS spectra , corresponding to 2210 stars.These spectra sample was selected according to the goodnessof fit between the synthetic and the observed spectrum, keepingthose that present a quality label of 0 or 1 (see Table 3 of De Pas-cale et al. 2014). The signal-to-noise ratio (S / N) distribution ofthe sample is shown in Fig. 1. We only considered the HARPSspectra sample due to the high spectral resolution (R ∼ ff erent spec-trographs included in the AMBRE Project. N u m b e r o f s p e c t r a Fig. 1.
Signal-to-noise ratio (S / N) for the spectra in our AM-BRE:HARPS sample.
The HARPS sample contains a large number of repeated ob-servations for some stars. A cross-match with the
Gaia
DR2 cat-alogue (Gaia Collaboration et al. 2018) allowed us to assign a
Gaia
ID to each spectrum, identifying the di ff erent spectra of thesame star. In order to be statistically significant and avoid spuri-ous e ff ects in single spectra, we analysed the stars with more thanfour observed spectra ( ≥ e f f > The AMBRE analysis of the HARPS spectra comprises the obser-vations collected from October 2003 to October 2010 with the HARPSspectrograph at the 3.6m telescope at the La Silla Paranal Observatory,ESO (Chile).Article number, page 2 of 18. Santos-Peral et al.: The AMBRE Project: Spectrum normalisation influence on Mg abundances in the metal-rich Galactic disc
Teff (K) N o r m a li z e d d i s t r i b u t i o n o f s t a r s T eff Teff = 18.6 K logg (dex) N o r m a li z e d d i s t r i b u t i o n o f s t a r s log g logg = 0.03 dex [ M / H ] (dex) N o r m a li z e d d i s t r i b u t i o n o f s t a r s [M/H] [ M / H ] = 0.01 dex Spectrum-to-spectrum dispersion (1172 stars)
Fig. 2.
Estimated dispersion of the selected stars ( ≥ ff ective temperature (left), the surface gravity (middle), and the globalmetallicity (right). l o g g ( d e x ) Clean sample 901 stars 105 stars -1.0 [M/H] -0.545005000550060006500 T eff (K)2345 l o g g ( d e x )
435 stars -0.5 < [M/H] 0.0 45005000550060006500 T eff (K) 345 stars[M/H] > 0.0
Fig. 3.
HR diagram (in metallicity bins) of the selected AM-BRE:HARPS stellar sample with FWHM
CCF ≤ − and more thanfour observed spectra ( ≥ star we excluded spectra whose atmospheric parameters di ff erby more than two sigma from the mean value of said star. Thisallows us to discard possible mismatches and avoid the propaga-tion of uncertainties on the atmospheric parameters to the stellarabundances. These di ff erent quality selections lead to a total of76502 spectra, corresponding to 1172 stars. The estimated dis-persion on the stellar atmospheric parameters from the di ff erentspectra of the same star are shown in Fig. 2. The average dis-persion on T e f f , log(g) and [M / H] are 18.6 K, 0.03 dex and 0.01dex, respectively.To avoid any possible source of uncertainties from line-broadening, we only kept spectra with FWHM
CCF ≤ − .As a consequence, the selected AMBRE:HARPS sample is re-stricted to the stellar atmospheric parameters shown in Fig. 3,mostly dwarf stars cooler than 6200K. Cross-correlation function between the observed spectra and the cor-responding templates used for the radial velocity estimation.
3. Method
From the high-resolution observational spectra sample describedin the previous section, we derived and analysed the [Mg / Fe]abundances using 9 Mg I spectral lines in the optical range auto-matically, via the optimisation method GAUGUIN (Bijaoui et al.2012; Guiglion et al. 2016; Recio-Blanco et al. 2016), and usinga reference synthetic spectra grid produced in the framework ofthe Gaia-ESO Survey (GES) project (Gilmore et al. 2012). GAU-GUIN was part of the analysis pipeline of GES for the GIRAFFEspectra (Recio-Blanco et al. 2014), and is also used for Gaia RVSspectra (Recio-Blanco et al. 2016).The atmospheric parameters (T e f f , log(g), [M / H], [ α / Fe])were used as an input (independently determined by the AM-BRE Project, as described above). A first global normalisationprocedure was iteratively attached to the parameter estimation.This iteration is described in Worley et al. (2012) and was per-formed by De Pascale et al. (2014). For the present abundanceanalysis, an initial global normalisation was applied, consider-ing a large wavelength domain of 70Å. In addition, a local nor-malisation around the considered spectral line was performed tooptimise the continuum placement. Di ff erent widths of the localnormalisation window were explored (c.f. Section 4). The localnormalisation is not iterative. The details regarding the normali-sation algorithm are described hereafter.Moreover, the radial velocity correction was performed us-ing the accurate estimated provided by the ESO:HARPS reduc-tion pipeline, except for a small proportion of the spectra withno HARPS radial velocity available, for which it was estimatedby the AMBRE analysis procedure with similar precision (seeWorley et al. 2012; De Pascale et al. 2014). The observed spectrum flux was normalised over a given wave-length interval centred on the analysed line. For this purpose,the observed spectrum (O) was compared to an interpolated syn-thetic one (S) with the same atmospheric parameters. First, themost appropriate pixels of the residual (R = S / O) were selectedusing an iterative procedure implementing a linear fit to R fol-lowed by a σ -clipping. The clipping values vary from the first tothe final iteration, starting with σ + − . and ending with σ + − . Then,a final residual was calculated (R f inal = S* norm / O* norm ), whereS* norm and O* norm are the synthetic and observed flux values Article number, page 3 of 18 & A proofs: manuscript no. Santos-Peral in the previously selected pixels, applying an additional 0.2 σ -clipping. Finally, the normalised spectrum was obtained after di-viding the observed spectrum by a linear function resulting bythe fit of R f inal . No convolution was carried out during the nor-malisation procedure, so the original spectral resolution is con-served. As an example, Fig. 4 shows the normalised observedsolar spectrum around the Mg line 5711.09 Å. Wavelength (Å) N o r m a li z e d f l u x Abund norm norm Mg I (5711.09 Å ) Fig. 4.
Observed solar spectrum from HARPS (R = ∆ λ Abund ∼ ff erent local normalisation intervals of 1Å( ∆ λ ) and 4Å ( ∆ λ ) are shown with red and orange dashed vertical lines,respectively. The GAUGUIN code is a classical optimisation method basedon a local linearisation around a given set of parameters fromthe reference synthetic spectrum, via linear interpolation of thederivatives. The abundance estimate is performed consideringthe spectral flux in a predefined wavelength window, which isalways inside the defined local normalisation one. The abun-dance window ( ∆ λ Abund , c.f. Fig. 4) was set around 0.5Å for non-saturated lines, and 2.5Å for strong saturated ones (see classifi-cation in Sect 3.4 below, ∼ ff erent local continuum inter-vals, always larger than these abundance estimation windows, tostudy the normalisation influence on the derived abundances foreach type of line. It is worth noting that the local normalisationinterval is not always perfectly symmetric around the analysedline. For some cases, due to contiguous strong absorption linespresent on a particular side of the line, an asymmetric windowis chosen in order to maximise the number of pixels close to thecontinuum level (see Appendix A for further details). For thoseparticular configurations (only a few among the total analysedcases), the abundance window although included in the normal-isation interval would be o ff centre. The observed abundancetrends for these cases are consistent with the results obtainedfrom symmetrically selected windows.Once the observed spectrum is normalised, a new specific-reference synthetic spectra grid is interpolated at the input at-mospheric parameters in order to measure the abundance from the analysed spectral line. This grid now includes a large rangeof the element abundance dimension (A X ). For the α -elementsabundance determination, the grid covers di ff erent [ α / Fe] val-ues. A minimum quadratic distance is then calculated betweenthe reference grid and the observed spectrum , providing a firstguess of the abundance estimate (A ). Then, this first guess isoptimised via a Gauss-Newton algorithm, carrying out iterationsthrough linearisation around the new solutions. The algorithmstops when the relative di ff erence between two consecutive it-erations is less than ∆ A X / Fig. 5.
Example of the fit carried out by the optimisation code GAU-GUIN for the line 5711.09 Å of the observed solar spectrum. The nor-malised observed spectrum is shown with red open diamonds, while thesolution is indicated by blue crosses. The reference synthetic spectragrid is colour-coded according to [ α / Fe] value.
A high-resolution optical synthetic grid (4200-6900Å;R ∼ ≤ T e f f ≤ ≤ log(g) ≤ − (in stepsof 0.5 cm s − ), -3.5 ≤ [M / H] ≤ + α / Fe] is -0.4 ≤ [ α / Fe] ≤ / H] ≥ ≤ [ α / Fe] ≤ ≤ [M / H] < ≤ [ α / Fe] ≤ / H] < -0.5 dex), withsteps of 0.2 dex.This grid was computed in a similar way to the original AM-BRE grid (de Laverny et al. 2012), which was adopted for theparameter estimation. It does however contain some more recent Calculated over the wavelength domain, centred on the line, whereGAUGUIN derives the abundance: χ = (cid:80) Ni = (cid:2) O (cid:0) i (cid:1) − S (cid:0) i (cid:1)(cid:3) , where Oand S are the observed and the synthetic spectrum, respectively. ∆ A X = specificities. First, we adopted the Gaia-ESO Survey atomic andmolecular line lists (Heiter et al. 2015, 2019; submitted). Next,we considered more realistic values of the microturbulent ve-locity for the spectra computation by adopting a polynomial re-lation between V mic and the main atmospheric parameters (M.Bergemann, private communication). Finally, we always con-sidered perfectly consistent [ α / Fe] enrichments between the se-lected MARCS models and the calculated emerging spectra. Tobe in agreement with the observational spectra data set, we re-duced the resolution of the synthetic spectra to the observed re-solving power (R = The abundance analysis was performed using nine magnesiumspectral lines in the optical range shown in Table 1, adopting theatomic data of Heiter et al. (2015).
Mg I (Å):
Non-saturated lines:
Saturated lines:
Table 1.
Optical magnesium lines selected in the present analysis.
We performed an in-depth analysis of each line separatelyin order to test their reliability at di ff erent metallicity regimes.For a solar-type star, the selected lines could be classified in twocategories: non-saturated (4730.04, 5711.09, and triplet: 6318.7,6319.24, 6319.49 Å) and strong saturated lines (Mg Ib triplet:5167.3, 5172.7 & 5183.6, and the line 5528.4 Å). Both cases areillustrated in Fig. 6. The number of pixels available for stronglines are approximately five times higher than for non-saturatedlines. We only considered non-saturated lines for spectra withFWHM CCF ≤ − to avoid possible uncertainties from line-broadening (see Appendix B for further details).The selected lines in Table 1 have been widely used in theliterature to determine both [Mg / Fe] and [ α / Fe] abundances.Bergemann et al. (2014, 2017) analysed di ff erent approxima-tions for radiative transfer and spectral line formation in modelatmospheres, focused on their e ff ect on Mg abundance deter-mination using lines in the optical and infrared, among whichthere are four lines used in our analysis (5172, 5183, 5528, and5711Å). They find no significant di ff erences between 1D LTEand 1D NLTE abundances, and for the lines in common withours, they present a quite robust behaviour with respect to the full3D NLTE calculations in cool FGK stars. Small NLTE e ff ects onMg I line formation were also found by Zhao et al. (2016) andAlexeeva et al. (2018). In conclusion, 1D LTE Mg abundancesare accurate enough for our selected sample and computationallycheaper than applying NLTE corrections. The results and discus-sions presented in this paper are therefore based on 1D LTE Mgabundances.The methodology to calculate the final stellar [Mg / Fe] abun-dance from all the Mg lines information is described as follows.For a given spectrum, a weighted average of the individual linesresults was calculated following Adibekyan et al. (2016), wherethe distance from the median abundance was considered as aweight. This method allows us to avoid the combined randomuncertainties of the di ff erent lines, minimising the error when Wavelength (Å) N o r m a li z e d f l u x Mg I (6318.7, 6319.24 & 6319.49 Å ) Wavelength (Å) N o r m a li z e d f l u x Mg I (5183.6 Å ) Fig. 6.
Non-saturated triplet lines around 6319 Å (top) and the strongsaturated line 5183.6 Å (bottom), identified by green dashed verticallines, in the normalised observed solar spectrum. more lines are considered. Next, as at least four spectra wereavailable for each star in the sample, the final [Mg / Fe] abun-dance of each object was calculated from the median value ofthe repeats.
4. Optimising the spectral normalisation fordifferent stellar types
In large spectroscopic stellar surveys, an automatic adjustmentof the continuum is performed over the observed spectrum, gen-erally via few iterations, searching for possible line-free regions(Valenti & Piskunov 1996; Sousa et al. 2007; García Pérez et al.2016). Most of the spectral analysis pipelines for determiningchemical abundances and stellar atmospheric parameters carryout the same normalisation procedure for all stellar types, apply-ing a constant continuum interval around the considered spectralfeature. Mikolaitis et al. (2014) used a spectral fitting methodto correct the local continuum in regions of ±
5Å and ± ffi culty ofidentifying the continuum, which depends on the spectral type. Article number, page 5 of 18 & A proofs: manuscript no. Santos-Peral ( l o g ) MgI (4730.04 Å) [M/H] (dex) [ M g / F e ] ( d e x ) (1.35Å - 4.35Å) (1.35Å - 68Å) [M/H] (dex) [ M g / F e ] ( d e x )
544 stars norm norm
Fig. 7.
Analysis of the non-saturated line 4730.04 Å.
Left: comparison, averaged in metallicity bins of 0.1 dex, of the line χ fitting in logarithmicscale (top) and the derived abundance (bottom) values from di ff erent local normalisation intervals ( ∆ λ norm = Right: stellar abundance ratios[Mg / Fe] vs. [M / H] for the local normalisation window ∆ λ norm = ∆ λ norm = / Fe] abundance value per metallicity bin. The reduced number of stars is due to the cut in FWHM
CCF for thenon-saturated lines.
Cool metal-rich stars are a particularly di ffi cult case due to thepresence of blended and molecular lines. For instance, in the caseof the APOGEE survey, Holtzman et al. (2015) remark how chal-lenging it is to identify a true continuum in the observed spectraof these stellar types, leading to a ’pseudo-continuum’ normali-sation. Similarly, after an analysis of systematic errors using sixdi ff erent methods, Jofré et al. (2017) concluded that the defini-tion of continuum may be responsible for the largest fraction ofthe uncertainty in abundance estimations.The automated abundance estimation code GAUGUIN is notan exception on the continuum placement performance. As de-scribed in Sect 3.2, it carries out an iterative procedure over alocal window around the analysed line. For that reason, we stud-ied the normalisation influence on the derived abundances ap-plying (for each Mg I line; see Table 1) di ff erent local contin-uum intervals (from narrow, ∆ λ norm ∼ ∆ λ norm ∼ χ ) between the interpolated synthetic spectrum (with thecorresponding atmospheric parameters of the star) and the nor-malised observed one. This was performed over the abundanceestimation window, as it is constant for each line (c.f. blue linesin Fig. 4 and the corresponding fit in Fig. 5).As described in detail hereafter, our analysis reveals that thewidth of the local normalisation interval can have an importantimpact on the derived abundances. In fact, the optimal widthof the normalisation window depends clearly on the stellar type(T e f f , log g, [M / H]). As a consequence, if a constant wavelengthinterval is chosen, independently of the stellar parameters, di ff er-ent biases appear depending on the e ff ective temperature, the sur-face gravity, and the global metallicity, especially in the metal-rich regime ([M / H] ≥ We use the following nomenclature:[M / H] (cid:46) - 0.2 dex (metal-poor); T ef f < / H] > - 0.2 dex (metal-rich); T ef f (cid:38) As expected, the environment and the intensity of the spec-tral line drastically influence the selection of the appropriate nor-malisation interval where the continuum placement should bedefined for each case. In the following, we summarise the re-sults of our study for the two characteristic cases mentioned inTable 1 and illustrated in Fig. 6 for the normalised observed solarspectrum.
Figure 7 shows, for the non-saturated line 4730.04 Å, the di ff er-ence in the line χ fitting in logarithmic scale (top-left panel)and the corresponding derived abundance values (bottom-leftpanel) between di ff erent local normalisation intervals. The re-sulting comparison reveals a more precise fit applying the nar-rowest interval ( ∆ χ <
0) for all the metallicities. We find thatthis improvement of the fit has a larger impact on the derivedabundances for the metal-rich stars, leading to lower [Mg / Fe]abundances at supersolar metallicities, with di ff erences as highas ∼ / H] = + / Fe] vs. [M / H] plane, highlights the influence of the nor-malisation procedure on the behaviour of the α -elements in themetal-rich regime of the disc.Figure 8 illustrates the e ff ect of di ff erent normalisation win-dows in the flux of the Mg line at 4730.04 Å, for a particularmetal-rich star ([M / H] = + ff erences observed inFig. 7. The use of a larger normalisation interval can drop artifi-cially the observed flux, leading to higher abundance estimates.More di ffi cult pseudo-continuum placements due to contiguousabsorption lines can explain this continuum drop, and the poorergoodness-of-fit values observed in Fig. 7.As for the 4730.04 Å line, the weak triplet lines around6319Å (left panel in Fig. 6) are better fitted by applying a narrownormalisation interval. For the Mg line 5711.09 Å (see Fig. 4),which is stronger than the other non-saturated lines, the optimal Article number, page 6 of 18. Santos-Peral et al.: The AMBRE Project: Spectrum normalisation influence on Mg abundances in the metal-rich Galactic disc
Wavelength (Å) N o r m a li z e d f l u x = 1.35 Å [Mg/Fe] = -0.22 dex = 4.35 Å [Mg/Fe] = -0.20 dex = 68 Å [Mg/Fe] = -0.02 dex Mg I (4730.04 Å) - [M/H] = +0.31 dex
Fig. 8.
Normalised observed spectrum of a particular metal-rich star([M / H] = + ff erent line profile depending on the ap-plied local continuum intervals ( ∆ λ norm = / Fe] abundance for each case. local normalisation window is larger for cool metal-rich stars,for which the line is more intense although still not saturated.In conclusion, for non-saturated lines, there is generallyenough continuum information around and close to the line. Asa consequence, it is convenient to optimise the normalisation in-terval, close to the considered spectral feature.
For strong saturated lines like the Mg Ib triplet (5167.3, 5172.7,and 5183.6 Å) and the line 5528.4 Å, no pixels are availableclose to the continuum level for most of the stellar types (seebottom panel in Fig. 6) in the analysed region, and a pseudo-continuum normalisation has to be performed for the automaticfit, including part of the line wings.However, two main di ffi culties a ff ect the procedure. On theone hand, due to the line saturation, only the wings are sensi-tive to the abundance. As a consequence, an important degener-acy between the continuum placement and the derived [Mg / Fe]abundance appears. In other words, large changes in the contin-uum placement, like those induced by the use of di ff erent nor-malisation windows, can be compensated by a change in theabundance without degrading the line fitting quality. Figure 9 il-lustrates, for the di ff erent local normalisation intervals analysedaround the 5183.6Å line, the comparison of the line χ fittingvalues (top panel), and the corresponding derived abundance val-ues (bottom panel). A negligible di ff erence in the goodness offit from the studied continuum intervals is observed, although,as shown below, it corresponds to notorious di ff erences in theabundance estimations. Therefore, the χ quality criterion, reli-able to carry out an appropriate normalisation interval selectionfor the non-saturated lines (Sect. 4.1), is usually not discriminat-ing enough in saturated lines.On the other hand, the larger the local normalisation window,the larger the dependencies of the abundance results on the pa-rameters and, as a consequence, the larger the dispersion on the[Mg / Fe] abundance with respect to [M / H]. This is illustrated inFig. 10, where the resulting [Mg / Fe] vs. [M / H] abundances areshown for the same line and most representative normalisationintervals of Fig. 9, colour-coded with the star’s e ff ective tem- [M/H] (dex) ( l o g ) MgI (5183.6 Å) (log ) (6Å - 10Å) (log ) (6Å - 13Å) (log ) (6Å - 15Å) (log ) (6Å - 23Å) (log ) (6Å - 70Å) 1.0 0.8 0.6 0.4 0.2 0.0 0.2 0.4 [M/H] (dex) [ M g / F e ] ( d e x ) [Mg/Fe] (6Å - 10Å) [Mg/Fe] (6Å - 13Å) [Mg/Fe] (6Å - 15Å) [Mg/Fe] (6Å - 23Å) [Mg/Fe] (6Å - 70Å) Fig. 9.
Analysis of strong saturated line 5183.6 Å.
Top: comparison, av-eraged in metallicity bins of 0.1 dex, of the line χ fitting values (in log-arithmic scale) for di ff erent local normalisation intervals ( ∆ λ norm ∼ Bottom: same analysis comparing the derivedabundance values. perature and surface gravity. Clearly, the results obtained withthe largest normalisation window (left panels) have a significantT e f f dependence and even a log g dependence, inducing a higherdispersion. Those e ff ects are alleviated when the normalisationwindow is narrowed to 10Å (middle panels), and they practicallydisappear for the narrowest window of 6Å (right panels). In ad-dition, broader windows tend to have lower [Mg / Fe] values forcooler and higher gravity stars. These trends do not disappeareven if an iterative procedure involving local normalisation andabundance estimation is implemented. In addition, the parameterdependence is also observed when larger normalisation intervalsare explored (going beyond the MgI triplet wings, up to ∆ λ norm ∼ e f f = e f f = + α / Fe] abundance. The bluesynthetic spectra consider all the absorption sources (atomic andmolecular lines), while the red ones present only the Mg linesabsorption source for comparison purposes. As illustrated in theright panel, the pseudo-continuum level is essentially driven bythe Mg line absorption. As a consequence, when no pixels atthe continuum are available (e.g. cool and metal-rich stars), the
Article number, page 7 of 18 & A proofs: manuscript no. Santos-Peral [ M g / F e ] ( d e x )
901 stars norm Å norm Å MgI (5183.6 Å) norm Å [M/H] (dex) [ M g / F e ] ( d e x )
901 stars norm Å [M/H] (dex) norm Å [M/H] (dex) norm Å T e ff ( K ) l o g g ( d e x ) Fig. 10.
Comparison of stellar abundance ratios [Mg / Fe] vs. [M / H] derived for the strong saturated line 5183.6 Å, colour-coded by stellar e ff ectivetemperature (top row) and surface gravity (bottom row), after carrying out the continuum placement in three di ff erent local normalisation intervalsaround the line. Left: ∆ λ norm ∼ Middle: ∆ λ norm ∼ Right: ∆ λ norm ∼ ∼ twice the FWHM of the line in solar-type stars). Wavelength (Å) N o r m a li z e d f l u x T eff = 6000 K ; log g = 4.5 dex ; [M/H] = +0.25 dex ; [alpha/Fe] = 0.0 dex Wavelength (Å) N o r m a li z e d f l u x T eff = 5000 K ; log g = 4.5 dex ; [M/H] = +0.25 dex ; [alpha/Fe] = 0.0 dex Å Å Å Å Fig. 11.
Comparison of synthetic spectra around the saturated line 5183.6 Å (black solid vertical line), considering all the absorption lines (bluespectra) and only the Mg line absorption (red spectra). The black and red dashed vertical lines present the limits of the 6Å and 15Å normalisationwindows, respectively. Left: hot star (T ef f = ef f = = / H] = + α / Fe] = first Mg abundance guess has a strong influence in the pseudo-continuum placement. In our procedure, the normalisation step,taking as a reference a synthetic spectrum with the star’s atmo-spheric parameters, assumes as a first guess that [Mg / Fe] is equalto the input [ α / Fe] parameter (see Sect. 3.1). To explore the dependence of the normalisation, and there-fore of the resulting [Mg / Fe] estimates, on the initial abundanceguess, we artificially substracted 0.2 dex to the correspond-ing [ α / Fe] initial value of each star ([ α / Fe] (cid:63) input = [ α / Fe] input -0.2 dex) without modifying the observed spectra sample, sim-
Article number, page 8 of 18. Santos-Peral et al.: The AMBRE Project: Spectrum normalisation influence on Mg abundances in the metal-rich Galactic disc
Effective temperature (K) [ M g / F e ] ( d e x ) [Mg/Fe] = [Mg/Fe] [ alpha / Fe ] INPUT - [Mg/Fe] [ alpha / Fe ] INPUT dex *MgI (5183.6 Å) ; [M/H] > + 0.2 dex
Narrow interval ( 6 Å )Larger interval ( 15 Å ) 1.00.80.60.40.20.00.20.4 [M/H] (dex) [ M g / F e ] ( d e x ) [Mg/Fe] = [Mg/Fe] [ alpha / Fe ] INPUT - [Mg/Fe] [ alpha / Fe ] INPUT dex *MgI (5183.6 Å) ; T eff < 5400 K
Narrow interval ( 6 Å )Larger interval ( 15 Å ) Fig. 12.
Analysis of saturated line 5183.6 Å. Comparison of the derived [Mg / Fe] abundances per spectrum after introducing a bias in the input[ α / Fe] value ([ α / Fe] (cid:63) = [ α / Fe] - 0.2 dex) to simulate a [ α / Fe]-[Mg / Fe] shift. The black and red lines correspond to the normalisation windows of6Å and 15Å, respectively.
Left: temperature dependence for the metal-rich sample ([M / H] (cid:38) + Right: metallicity dependence for thecool sample (T ef f (cid:46) [M/H] (dex) [ M g / F e ] ( d e x ) norm Å
244 stars [M/H] (dex) T e ff ( K ) l o g g ( d e x ) MgI (5183.6 Å) - Cases without pseudo-continuum ( 5500 T eff ) Fig. 13.
Stellar abundance ratios [Mg / Fe] vs. [M / H], including only cases without pseudo-continuum, for the large normalisation window of 15Åaround the strong line 5183.6 Å, colour-coded by stellar e ff ective temperature (left panel) and surface gravity (right panel). ulating a di ff erence between the [ α / Fe] and the [Mg / Fe] abun-dance. Figure 12 shows the di ff erence in the resulting [Mg / Fe]estimate for two local normalisation windows of 6 and 15 Åaround the saturated line 5183.6 Å (illustrated in Fig. 11). Onthe left panel, the temperature dependence of the di ff erencesis plotted only for the metal-rich sample. On the right panel,the metallicity dependence of the di ff erences is only plotted forthe cool sample. This allows us to isolate the impact of the[ α / Fe]-[Mg / Fe] bias for the typical cases of spectra with pseudo-continuum. The normalisation procedure is independent on theinitial [ α / Fe] when the derived [Mg / Fe] abundance has not beenshifted ( ∆ [Mg / Fe] measured = / Fe]abundance depends highly on the assumed parameters (temper-ature on the right panel and metallicity on the left one). In-deed, as the number of pixels at the real continuum used to nor-malise varies from nearly 100% (hot, metal-poor stars) to 0%(cool, metal-rich stars), the parameter dependence of the resultwill vary from no impact ( ∆ [Mg / Fe] measured =
0) to an almostcompletely dependent situation ( ∆ [Mg / Fe] measured = + α / Fe].Therefore, almost no parameter dependence is observed arounda ∆ [Mg / Fe] measured =+ / Fe] abundances, isalways present but constant with the stellar atmospheric param-eters if the narrow normalisation interval is applied around thestrong saturated lines. This is not the case for the 15Å window,for which this induced bias is partially corrected but only to anextent that depends on the stellar parameters.The application of a large local continuum interval is onlyconvenient for the stellar types with pixels reaching the contin-uum level. In those cases, as described before, the normalisationprocedure is independent on the initial guess of the [ α / Fe] value.In our sample, this condition only occurs for stars with 5500 ≤ T e f f ≤ ≤ log g ≤ / Fe] vs. [M / H] for these stars, using the large normalisationwindow (15Å), is shown in Fig. 13. It can be appreciated that thethin and thick disc sequences clearly separate up to a metallicityof ∼ + Article number, page 9 of 18 & A proofs: manuscript no. Santos-Peral stellar types (right panels of Fig. 10). We therefore conclude thatour procedure, through narrow normalisation windows using theglobal [ α / Fe] as an initial abundance guess, is a reliable way ofusing these strong saturated lines.In conclusion, the dispersion on the [Mg / Fe] abundance es-timation from strong saturated lines, with respect to [M / H], isdominated by the induced bias in the continuum-level estima-tion for the stellar types where a pseudo-continuum evaluationaround the line is performed. The application of larger normal-isation windows results in a parameter dependence of the ob-tained abundance and a larger line-to-line dispersion, each sat-urated line having its own level of continuum misplacement fora given star. The amplitude of this continuum placement erroris smaller applying a narrower normalisation interval, thereforeimproving the abundance estimation precision. The strong linkof the narrow normalisation window to the initial [ α / Fe] guessthrough the pseudo-continuum reduces the atmospheric parame-ter dependence.
The previous sections allow us to conclude that: (i) for weaknon-saturated lines, the optimal wavelength domain for the localcontinuum placement has to be evaluated using a goodness-of-fit criterion, allowing a wavelength dependence with the spectraltype. Generally, narrow normalisation windows between 1 and2 Å provide the best line fittings (around two to four times theFWHM of each line in a solar-type star); (ii) for strong satu-rated lines, a narrow normalisation window allows us to reduceparameter-dependent biases of the abundance estimate, improv-ing the precision (around two to four times the FWHM of eachline in a solar-type star).To evaluate the improvement in precision of the abundanceresults with our optimised procedure, we analysed the internalerror estimation. Figure 14 shows the cumulative distributionof the line-to-line scatter per spectrum of the derived [Mg / Fe]abundances for non-saturated (top panel) and strong saturatedlines (bottom panel) separately. For non-saturated lines, the im-provement in precision is confirmed after the optimisation basedon the goodness of fit (blue curve), and applying narrow nor-malisation windows around each line ( ∆ λ norm ∼ CCF (seeSect. 3.4). For strong saturated lines, the application of a nar-row normalisation interval ( ∆ λ norm ∼ ff erent strengths are considered. We compare resultsfor the normalisation windows used in the literature (red) and forour optimised normalisation procedure (blue). In the top panel,we can see the analysis over the whole spectra sample for whichall the Mg lines are considered. In addition, 40 % of the sample [ Mg / Fe ] (dex)0.00.20.40.60.81.0 C u m u l a t i v e D i s t . F un c t i o n ( o f s p e c t r a )
545 starsLine-to-line scatter (4730.04, 5711.09, triplet 6319 Å)
Narrow interval 1-2 Å norm fit0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 [ Mg / Fe ] (dex)0.00.20.40.60.81.0 C u m u l a t i v e D i s t . F un c t i o n ( o f s p e c t r a )
901 starsLine-to-line scatter (5167.3, 5172.7, 5183.6, 5528.4 Å)
Narrow interval 3 - 6 Å norm
15 ÅBest fit Fig. 14.
Cumulative distribution function of the line-to-line scatter es-timation of the derived [Mg / Fe] abundances per spectrum, for weaknon-saturated Mg lines (top; 4730.04, 5711.09, 6318.7, 6319.24, and6319.49Å) and strong saturated ones (bottom; 5167.3, 5172.7, 5183.6,and 5528.4 Å) separately. The blue curve describes the values that cor-respond to the normalisation interval that presents the lowest χ fittingvalue, the red one corresponds to the continuum placement performancein the typical wavelength interval used in previous works in the litera-ture, and the black curve corresponds to a narrower local normalisationinterval around each line as proposed in this work. presents a scatter smaller than 0.05 dex choosing our best valuein each case, while this is only the case for 20 % of the samplewith the classical normalisation windows. This improvement inprecision is even more significant if we focus the analysis on themetal-rich part ([M / H] > τ Cet) from Jofréet al. (2015) in our sample, finding an excellent agreement withan overall average di ff erence of 0.01 dex. We also tested the de-rived abundances for those stars applying the normalisation win-dows used in the literature, finding an average di ff erence withinone sigma error from the optimised value. In other words, ournormalisation procedure improves the abundance estimation pre-cision, preserving its accuracy. Article number, page 10 of 18. Santos-Peral et al.: The AMBRE Project: Spectrum normalisation influence on Mg abundances in the metal-rich Galactic disc [ Mg / Fe ] (dex) C u m u l a t i v e D i s t . F un c t i o n ( o f s p e c t r a ) Best normalization interval weak strong
15 Å545 stars 20%
Line-to-line scatter (all Mg lines) [ Mg / Fe ] (dex) C u m u l a t i v e D i s t . F un c t i o n ( o f s p e c t r a ) Best normalization interval weak strong
15 Å149 stars 35% [M/H] > 0.0 dex
Fig. 15. Top: cumulative distribution function of the line-to-line scatterestimation of the derived [Mg / Fe] abundance ratio for the spectra sam-ple for which all the Mg lines are taken into account.
Bottom: same butfor the metal-rich sample ([M / H] >
5. Disentangling the thin and the thick discpopulations
In this section, we summarise the final derived [Mg / Fe] abun-dances of our AMBRE:HARPS stellar sample (901 stars, seeFig. 3).The results for each Mg I line are presented separately inFig. 16. The four saturated lines (MgIb triplet: 5167.3, 5172.7& 5183.6, and 5528.4 Å) and the intermediate-strength line5711.09Å seem to reproduce the thin-thick disc sequences moreprecisely, also showing a decreasing trend in [Mg / Fe] even atsupersolar metallicities. This is in agreement with the analy-sis of NLTE e ff ects on Mg abundances done by Bergemannet al. (2017), where they highlight the robust behaviour of thestrong lines 5172, 5183, 5528, and 5711 Å. The higher disper-sion present on the abundance results for the weak non-saturatedlines with respect to the strong saturated ones is due to di ff er-ent factors. On the one hand, for certain stellar types (towardshot metal-poor stars) and for lower Mg abundances (in termsof [Mg / H]), weak lines are closer to the spectral noise level.On the other hand, although saturated lines are less sensitive,pixel per pixel, to abundance variations (therefore presenting smaller flux variations per pixel), they span larger wavelengthdomains than non-saturated lines. As a consequence, the cumu-lative quantity of information on the abundance through all theconsidered pixels is very significant for strong lines, favouringa higher precision. This is confirmed by the study of the inter-nal errors, through simulated noised theoretical spectra (see Ap-pendix C). However, a high spectral resolution is required, evenat high signal-to-noise values, to compensate the limited sensi-tivity of the lines to the abundance (c.f. Fig. C.1).Figure 17 illustrates the final stellar abundance ratios[Mg / Fe] relative to [M / H] for our selected stellar sample (leftpanel), along with their estimated dispersion from the repeatedobserved spectra (right panel). The chemical distinction betweenthe Galactic thin-thick disc populations is clearly observed, andthe trend in [Mg / Fe] abundances at high metallicity ([M / H] > / Fe]-enhanced disc stellar population, first observed by Adibekyanet al. (2012) and later confirmed by Mikolaitis et al. (2017), stillseems to be present in Fig. 16 & Fig. 17 around [M / H] ≈ -0.3dex and [Mg / Fe] ≈ + ff erent trend at high metal-licities. However, as described before, Mikolaitis et al. (2017)did not optimise the continuum normalisation for di ff erent stel-lar types, applying a constant local interval depending on the in-tensity of the line. On the other side, the agreement of our resultswith those of Fuhrmann et al. (2017) is higher. Nevertheless, theslope of the low-alpha sequence in Fuhrmann et al. (2017) seemsless pronounced than in our work. Fuhrmann et al. (2017) usedthe Mg I abundance estimate from weak lines as the input pa-rameter to the Mg Ib lines (strong saturated). This first-guessabundance could have an important influence on the pseudo-continuum estimate, and therefore in the derived [Mg / Fe] abun-dance, for saturated lines. For cool or metal-rich dwarf stars, theimpact of this first guess in the derived Mg Ib abundances couldbe stronger than for the other stars in the sample. As a conse-quence, possible parameter-dependencies in the results could re-main.Finally, we checked the consistency of our first-guess as-sumptions by comparing (on the left panel of Fig. 18) our initialabundance guess, coming from the [ α / Fe], and our final derived[Mg / Fe] abundances. The very good agreement between bothquantities confirms the consistency of the procedure. In addition,the right panel of Fig. 18 compares our initial guess with othersuggested initial input in the literature, the abundance result fromthe weak lines (4730.04 and 5711.09 Å) used by Fuhrmann et al.(2017). There is a very good agreement between our initial guess(the global [ α / Fe]) and the [Mg / Fe] from the weak lines, withonly a few cool stars with [ α / Fe] around 0.1 dex with lower[Mg / Fe] weaklines values. Those few cases correspond to cool starswith supersolar metallicities. This suggests that the two weaklines could su ff er from blends in the very crowded spectra, af-fecting the continuum placement and therefore the abundanceestimate. As we can indeed see in Fig. 16, the results of the twoweak lines are more dispersed. On the other hand, the global[ α / Fe] parameter value was derived considering the completeHARPS wavelength domain (De Pascale et al. 2014). Therefore,it is also less a ff ected by continuum placement problems. For thisreason, we believe that the global [ α / Fe] determined by the AM-BRE pipeline, although very similar to the results of the weaklines, is a more precise initial guess for our application.
Article number, page 11 of 18 & A proofs: manuscript no. Santos-Peral [ M g / F e ] ( d e x )
545 stars MgI (4730.04 Å)
Non-saturated lines [ M g / F e ] ( d e x ) MgI (5711.09 Å) [ M g / F e ] ( d e x ) MgI (6318.7 Å) [ M g / F e ] ( d e x ) MgI (6319.24 Å) [ M g / F e ] ( d e x ) MgI (6319.49 Å) [ M g / F e ] ( d e x )
901 stars MgI (5167.3 Å)
Strong saturated lines [ M g / F e ] ( d e x ) MgI (5172.7 Å) [ M g / F e ] ( d e x ) MgI (5183.6 Å) [ M g / F e ] ( d e x ) MgI (5528.4 Å)
Fig. 16.
Most precise stellar abundance ratios [Mg / Fe] vs. [M / H] following the optimal method for each Mg I spectral line separately.
Left: non-saturated lines: 4730.04, 5711.09, 6318.7, 6319.24, and 6319.49 Å.
Right: strong saturated lines: 5167.3, 5172.7, 5183.6, and 5528.4 Å (from topto bottom).
Our analysis allows a remarkable improvement with regardto previous e ff orts to chemically disentangle the Galactic thin-thick disc populations, and emphasises the importance of thenormalisation procedure to properly interpret the chemical evo-lution of the disc. In conclusion, the feasibility of an opti-mal treatment on strong saturated lines to derive precise non-parameter-dependent abundances represents a major advance-ment. It will allow us to appropriately study the chemical sig-natures in the Galactic stellar populations and the resulting im-plications on chemodynamical relations, such as the abundanceratio [Mg / Fe] as a good age proxy, or the contribution of radialmigration in the solar neighbourhood (Santos-Peral, in prep.).
6. Conclusions
We carried out a detailed spectroscopic analysis of the Mg abun-dance estimation over a sample of 2210 FGK-type stars in thesolar neighbourhood observed and parametrised at high spec-tral resolution (R = ≥ ff erent stellar populations and nine Mg I spectral lines in Article number, page 12 of 18. Santos-Peral et al.: The AMBRE Project: Spectrum normalisation influence on Mg abundances in the metal-rich Galactic disc [M/H] (dex) [ M g / F e ] ( d e x ) All Mg lines901 starsMost precise derived abundances [ Mg / Fe ] stellar abundances (dex) N o r m a li z e d d i s t r i b u t i o n ( o f s t a r s ) [ Mg / Fe ] stellar abundancesSpectrum-to-spectrum dispersion Fig. 17. Left: stellar abundance ratios [Mg / Fe] vs. [M / H] considering the abundance information from all the studied Mg I spectral lines.
Right: estimated dispersion of the final stellar sample ( ≥ / Fe] abundances. [alpha/Fe] (dex) [ M g / F e ] ( d e x ) y = x
901 starsAll Mg lines [Mg/Fe] derived abundances vs. Initial [alpha/Fe] T e ff ( K ) [alpha/Fe] (dex) [ M g / F e ] ( d e x ) y = x
545 starsWeak Mg lines (4730&5711) [Mg/Fe] derived abundances vs. Initial [alpha/Fe] T e ff ( K ) Fig. 18.
Derived stellar abundance ratios [Mg / Fe] vs. initial stellar parameter [ α / Fe], colour-coded by stellar e ff ective temperature. Left: consider-ing the abundance information from all the studied Mg I spectral lines.
Right: considering only the weak non-saturated lines 4730.04 & 5711.09Å (used in Fuhrmann et al. 2017, as the input parameter to the strong saturated lines). the optical range, we observed di ff erent behaviours dependingon the stellar type and the intensity of the line.The normalisation procedure has an important impact on thederived abundances, with a strong dependence on the stellar pa-rameters (T e f f , log g, [M / H]). Contrary to what is currently donein large spectroscopic surveys, the continuum placement proce-dure therefore has to be optimised for each stellar type and eachspectral line. As expected, the intensity of the spectral lines hasa drastic influence in the optimal width of the normalisation in-terval: – Non-saturated lines: the optimal wavelength domain forthe local continuum placement could be evaluated using agoodness-of-fit criterion, allowing a wavelength dependencewith the spectral type. It is generally convenient to opti-mise the normalisation window close to the considered line(around two to four times their FWHM). For strong (al-though not saturated) lines like 5711.09 Å, a larger intervalcould be necessary when dealing with cool metal-rich stars([M / H] > -0.2 dex ; T e f f < – Saturated lines: no pixels are available at the continuumlevel for most of the stellar types in the analysed region, and apseudo-continuum normalisation has to be performed for theautomatic fit. The level of the pseudo-continuum depends onthe Mg abundance itself, which is at first assumed to be equalto the global α -element abundance (or to another first-guessabundance). The induced bias in the Mg estimate is only par-tially corrected by the Mg line fitting due to a degeneracy be-tween the fitting quality and the continuum placement (as theline is saturated, only the wings profile changes). In addition,the bias correction depends on the pseudo-continuum levelitself. In this situation, one possibility consists in reducingthe analysis of the saturated lines to the stellar types present-ing continuum in the spectra (hot metal-poor stars). Alterna-tively, we have demonstrated that using a narrow normalisa-tion window (around two to four times the FWHM of eachline in a solar-type star) drastically reduces the parameter-dependence of the abundance estimate, increasing the line-to-line precision. This relies on the assumption that the Mg Article number, page 13 of 18 & A proofs: manuscript no. Santos-Peral abundance behaviour is not very di ff erent from that of theglobal [ α / Fe] abundance.The final derived stellar abundance ratios [Mg / Fe], relative to[M / H], present a clear chemical distinction between the Galacticthin-thick disc populations and a decreasing trend in [Mg / Fe]abundances even at supersolar metallicities ([M / H] > ff er-ent Galactic populations. The improvement in chemical abun-dance precision is strongly required in the present era of precisekinematical and dynamical data driven by the Gaia mission. Acknowledgements.
We would like to thank Nils Ryde and Mathias Schultheisfor very useful suggestions and discussions. We thank the anonymous refereefor his / her constructive comments, making a considerable contribution to theimprovement of the paper. The authors thank M. Bergemann for providing herrelation between the microturbulent velocity and the atmospheric parametersadopted for the spectra grid computation. This work is part of the PhD the-sis project within the framework of "International Grants Programme" of theInstituto de Astrofísica de Canarias (IAC). P.S would like to thank the Cen-tre National de Recherche Scientifique (CNRS) for the financial support. Partof this work was supported by the "Programme National de Physique Stel-laire" (PNPS) of CNRS / INSU co-funded by CEA and CNES. A.R.B., P.dL. andE.F.A. acknowledge financial support from the ANR 14-CE33-014-01. E.F.A.also acknowledge partial support from the ANR 18-CE31-0017. This workhas made use of data from the European Space Agency (ESA) mission
Gaia ( ), processed by the Gaia
Data Process-ing and Analysis Consortium (DPAC, ). Funding for the DPAC has been provided by na-tional institutions, in particular the institutions participating in the
Gaia
Multi-lateral Agreement. Most of the calculations have been performed with the high-performance computing facility SIGAMM, hosted by OCA.
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Appendix A: Analysed local normalisation intervals Di ff erent local continuum intervals were defined around eachMg I spectral line to explore their impact in the abundance anal-ysis. By a spectral visualisation for di ff erent stellar types, the se-lection of the normalisation windows was adjusted to avoid thepresence of strong absorption lines in the limits of the spannedregion and chosen to have enough continuum points at the endsof the intervals. Figure A.1 shows, for the observed solar spec-trum, the di ff erent local normalisation intervals, along with theabundance estimation window, applied around each Mg line in-dividually. In addition to the wavelength intervals plotted in thisfigure, we also tested a very large wavelength range around eachanalysed line of ∆ λ ∼
70 Å. The complete list of the definednormalisation windows around each line is shown in Table A.1.
Appendix B: Sensitivity to spectral line-broadening
The AMBRE Project provides the FWHM of the cross-correlation function between the observed spectra and the corre-sponding templates used for the radial velocity estimation. ThisFWHM
CCF can be used to study the sensitivity of the abundanceprecision to the line-broadening sources as stellar rotation andmacroturbulence.Figure B.1 shows the [Mg / Fe] vs. [M / H] abundances derivedusing two di ff erent spectral lines (see Sect 3.4): a saturated one(5172.7Å, left panel) and a non-saturated one (5711.09Å, rightpanel). For each line, the continuum placement has been per-formed over a local window of the same width. We concludethat the dispersion on the [Mg / Fe] abundance measurement, withrespect to [M / H], is dominated by the spectral line-broadeningfor non-saturated lines, although not for strong saturated lines.This is expected since the larger natural broadening of stronglines makes them less sensitive to the line-broadening. Simi-larly, high-resolution spectra are more sensitive to this e ff ect thanlow-resolution data. This result highlights the relevance of a cor-rect treatment when using weak non-saturated lines. Otherwise,choosing stronger lines or restricting the analysis to cool stars(for which the v sin (i) is lower) would minimise the e ff ects.We only kept spectra with FWHM CCF ≤ − for strongsaturated lines, but only spectra with FWHM CCF ≤ − fornon-saturated lines. As we do not have any v sin (i) determina-tions for these stars, we applied this cut based on the minimisa-tion of the observed dispersion from each particular line. Appendix C: Effect of the spectral resolution on theabundance estimation for saturated lines
We implemented a test with theoretical spectra to evaluate theinternal error sources in our method of [Mg / Fe] estimation, con-centrating on the strong lines of the MgIb triplet (5167.3, 5172.7,5183.6 Å). This error assessment leaves out the error sources re-stricted to real data, like the uncertainties in the line-broadeningor the continuum normalisation, described in the body of the pa-per. In particular, the theoretical internal error analysis allows usto identify possible internal biases.We built statistically significant sets of interpolated spectrafrom the high-resolution synthetic spectra grid, convolving to sixdi ff erent spectral resolutions, in the range from R ∼ ∼ =
10, 25, 50, 75, and 100). We defined fourdi ff erent stellar types; – cool dwarf (4000 ≤ T e f f ≤ ≤ log(g) ≤ − ) – turn-o ff (5800 ≤ T e f f ≤ ≤ log(g) ≤ − ) – solar-type (5500 ≤ T e f f ≤ ≤ log(g) ≤ − ) – red clump (4000 ≤ T e f f ≤ ≤ log(g) ≤ − ).For each case, at a given spectral resolution, we generated250000 spectra (50000 per bin of S / N) for three di ff erent bins ofmetallicity: -1.0 ≤ [M / H] ≤ -0.5, -0.2 ≤ [M / H] ≤ + + ≤ [M / H] ≤ + / Fe] estimate (among the three MgIb lines) are given as afunction of the SNR and for di ff erent resolutions. The three pan-els correspond to the three metallicity intervals. In Fig. C.2, theabundance error is shown for the four considered stellar types(cool dwarf, turn-o ff , solar-type and red clump) at solar metal-licity and changing the spectral resolution from 2000 (left) to20000 (right).These two figures illustrate that the abundance estimationprecision depends principally on the spectral resolution and sec-ondly on the target’s e ff ective temperature and metallicity. Onthe one hand, despite the fact that the considered lines are verylarge, the uncertainty increases critically when the spectral reso-lution is degradated. Although, as expected, this e ff ect is moresignificant at low signal-to-noise values, increasing the SNRdoes not always compensate a resolution loss. In addition, evenat high signal to noise, significant dependences of the uncer-tainty with the stellar type appear, if the spectral resolution isnot high enough. In fact, the abundance uncertainties observedat low resolution are more dependent on the stellar type thanthose obtained at high resolution. This highlights the importanceof working at high resolution for spectroscopic surveys target-ing a variety of stellar types and metallicity ranges, in orderto achieve more precise and homogeneous results, even whenstrong lines are used. Moreover, the pseudo-continuum is ex-pected to become more significant (fewer pixels close to the con-tinuum level) at lower spectral resolutions.These results are in agreement with the analysis of Nissen &Gustafsson (2018) regarding high-precision stellar abundances,underlining the relevance of carefully balancing the need for alarge sample of stars against the spectral resolution and the S / Nnecessary to achieve a good precision in abundances.
Article number, page 15 of 18 & A proofs: manuscript no. Santos-Peral N o r m a li z e d f l u x MgI (4730.04 Å) N o r m a li z e d f l u x MgI (5711.09 Å) N o r m a li z e d f l u x MgI (triplet around 6319 Å) N o r m a li z e d f l u x MgIb (5167.3) N o r m a li z e d f l u x MgIb (5172.7) N o r m a li z e d f l u x MgIb (5183.6) N o r m a li z e d f l u x
12 3 4
MgI (5528.4 Å)
Fig. A.1.
Observed solar spectrum from HARPS around each Mg I spectral line. The abundance estimation window is delimited by blue verticallines ( ∆ λ Abund ∼ ∆ λ Abund ∼ ff erent local normalisation intervals applied inthe analysis are shown with red dashed vertical lines. Left: non-saturated lines: 4730.04, 5711.09, 6318.7, 6319.24, and 6319.49 Å.
Right: strongsaturated lines: 5167.3, 5172.7, 5183.6, and 5528.4 Å (from top to bottom).Article number, page 16 of 18. Santos-Peral et al.: The AMBRE Project: Spectrum normalisation influence on Mg abundances in the metal-rich Galactic disc
Normalisation windows ( Å )4730.04 5167.3 5172.7 5183.6 5528.4 5711.09 6319 triplet [4729.5,4730.6] [5166.0,5168.5] [5170.8,5175.0] [5180.3,5185.7] [5527.6,5529.5] [5710.7,5711.5] [6318.3,6319.8][4728.2,4732.6] [5162.5,5168.5] [5169.5,5176.3] [5177.6,5188.0] [5527.1,5529.5] [5710.5,5711.6] [6318.3,6320.2][5159.5,5168.5] [5169.5,5181.5] [5177.6,5191.0] [5525.7,5530.4] [5709.8,5713.4] [6316.0,6321.9][5156.5,5168.5] [5174.0,5197.0] [5522.7,5532.4] [5709.8,5714.4][5151.5,5168.5] [5709.8,5717.4][5148.5,5168.5][4696 - 4764] [5140 - 5210] [5140 - 5210] [5140 - 5210] [5492 - 5564] [5676 - 5746] [6284 - 6354] Table A.1.
List of the selected local normalisation intervals around each Mg I spectral line. [ M g / F e ] G A U G U I N MgI (5172.7 Å) 901 stars norm F W H M CC F ( k m s ) [ M g / F e ] G A U G U I N MgI (5711.09 Å) norm F W H M CC F ( k m s ) Fig. B.1.
Abundance ratio [Mg / Fe] as a function of [M / H], colour-coded by the FWHM
CCF of the cross-correlation function. Both panels containthe same number of stars. Strong saturated lines (left, with less dispersed sequences) are less sensitive to spectral line-broadening than non-saturatedlines (right). The [Mg / Fe] abundances were derived by performing the continuum placement around a local wavelength interval of 5Å.
Fig. C.1.
Internal error, in the MgIb triplet lines, given as the standard deviation of the mean of the abundances di ff erence ([Mg / Fe] measured -[Mg / Fe] input ) obtained from all measurements at a certain S / N and spectral resolution R, for a particular stellar type from the metal-poor (left) tothe metal-rich (right) regime. Article number, page 17 of 18 & A proofs: manuscript no. Santos-Peral
Fig. C.2.
Same as Fig. C.1 for di ff erent stellar types at low (left: R = ==