Paula R T Coelho

Gustavo Bruzual

Stéphane Charlot

To use or not to use synthetic stellar spectra in population synthesis models?

Keywords: galaxies, stellar content -stars, atmospheres

Stellar population synthesis (SPS) models are invaluable to study star clusters and galaxies. They provide means to extract stellar masses, stellar ages, star formation histories, chemical enrichment and dust content of galaxies from their integrated spectral energy distributions, colours or spectra. As most models, they contain uncertainties which can hamper our ability to model and interpret observed spectra. This work aims at studying a specific source of model uncertainty: the choice of an empirical vs. a synthetic stellar spectral library. Empirical libraries suffer from limited coverage of parameter space, while synthetic libraries suffer from modelling inaccuracies. Given our current inability to have both ideal stellar-parameter coverage with ideal stellar spectra, what should one favour: better coverage of the parameters (synthetic library) or better spectra on a star-by-star basis (empirical library)? To study this question, we build a synthetic stellar library mimicking the coverage of an empirical library, and SPS models with different choices of stellar library tailored to these investigations. Through the comparison of model predictions and the spectral fitting of a sample of nearby galaxies, we learned that: predicted colours are more affected by the coverage effect than the choice of a synthetic vs. empirical library; the effects on predicted spectral indices are multiple and defy simple conclusions; derived galaxy ages are virtually unaffected by the choice of the library, but are underestimated when SPS models with limited parameter coverage are used; metallicities are robust against limited HRD coverage, but are underestimated when using synthetic libraries.

INTRODUCTION

Stellar population synthesis (SPS) models are among the most powerful tools developed over the last few decades in astrophysics. Originally based on the seminal work by Tinsley & Gunn (1976, see also Tinsley 1978), they are today the means through which we are able to model (and thus, interpret) the integrated properties of galaxies and unresolved star clusters. In the current era of large spectroscopic galaxy surveys, SPS models play a key role in inferring massive amounts of information about the origin and evolution of galaxies (see, e.g., Kauffmann et al. 2003;Tremonti et al. 2004;Gallazzi et al. 2005;da Cunha et al. 2008;Cid Fernandes et al. 2009;Conroy & Gunn 2010;Sodré et al. 2013;Chevallard & Charlot 2016, for examples of the use of SPS models in the interpretation of large samples of galaxies).

SPS models can be built in a variety of ways, but the E-mail: pcoelho@usp.br (PC) so-called Evolutionary Stellar Population Synthesis models are among the ones with more predictive and interpretative power, and have been used very frequently in the literature (e.g. Bruzual A. 1983;Arimoto & Yoshii 1986;Guiderdoni & Rocca-Volmerange 1987;Charlot & Bruzual 1991;Bruzual & Charlot 1993, 2003;Bressan et al. 1994;Fritzev. Alvensleben & Gerhard 1994;Worthey 1994;Vazdekis et al. 1996Vazdekis et al. , 2015;;Fioc & Rocca-Volmerange 1997, 2019;Kodama & Arimoto 1997;Maraston 1998Maraston , 2005;;Coelho et al. 2007;Leitherer et al. 1999;Conroy & Gunn 2010;Conroy & van Dokkum 2012). Such models are built upon a set of key ingredients, namely: (i) stellar evolutionary tracks or isochrones; (ii) stellar flux libraries; (iii) initial mass functions; and (iv) star formation histories (see e.g. the review by Conroy 2013).

A model can only be as good as its ingredients, and there are published studies devoted to the investigation of the uncertainties affecting SPS models (e.g. Charlot et al. 1996;Conroy et al. 2009;Percival & Salaris 2009). These studies have shown that limitations of SPS models can arise from uncertainties in both stellar evolution theory and stellar spectral libraries.

In this work, we take a new look at quantifying the uncertainties affecting SPS models by studying a particular source of error: the impact of choosing between an empirical (i.e. observational) or a theoretical library of individual stellar spectra to describe stellar fluxes. By 'stellar spectral library', we mean a compilation of homogeneous spectra (either observed or modelled), of which a plethora is available in the literature. 1 For stellar population studies, a library should ideally provide complete coverage of the Hertzsprung-Russell diagram (HRD hereafter), accurate and precise atmospheric parameters (effective temperature, T eff , surface gravity, log g, abundances, [Fe/H] and [Mg/Fe], rotation, micro-and macro-turbulent velocities, etc.), as well as a good compromise between wavelength coverage, spectral resolution and signal-to-noise ratio (SNR). Both empirical and theoretical spectral libraries have been largely used in the literature, each presenting advantages and disadvantages.

In a theoretical library (e.g., in recent years, Leitherer et al. 2010;Palacios et al. 2010;Sordo et al. 2010;Kirby 2011;de Laverny et al. 2012;Husser et al. 2013;Coelho 2014), a stellar spectrum has well-defined atmospheric parameters, does not suffer from low SNR or flux calibration problems, and covers a larger wavelength range at a higher spectral resolution than any empirical library. The drawback is that current limitations in our knowledge of the physics of stellar atmospheres and in the databases of atomic and molecular opacities make theoretical spectra suffer from limited ability to reproduce observations accurately (e.g. Bessell et al. 1998;Kučinskas et al. 2005;[START_REF] Kurucz | Radiative Transfer and Applications to Very Large Telescopes[END_REF]; Martins & Coelho 2007;Bertone et al. 2008;Coelho 2009;Plez 2011;Lebzelter et al. 2012b;Sansom et al. 2013;Coelho 2014;Knowles et al. 2019).

In an empirical library, in contrast, all spectral features are accurate (modulo any observational and data reduction problems). Several such libraries have been proposed with different coverages in wavelength, resolution and stellar parameters (e.g., in recent years, Ayres 2010;Blanco-Cuaresma et al. 2014;Chen et al. 2014;De Pascale et al. 2014;Lebzelter et al. 2012a;Liu et al. 2015;Villaume et al. 2017;Worley et al. 2012Worley et al. , 2016;;Luo et al. 2015;Yan et al. 2018). The strongest limitation of an empirical library is that it is virtually impossible to fully sample the parameter space -in terms of atmospheric parameters, including abundance ratios -needed to probe the full range of galaxy evolution studies: stellar populations exist in other galaxies, which are not represented by the stars we harbour in our Galaxy, such as young metal-poor stars expected to dominate the spectra of high-redshift galaxies (e.g., Stark 2016) and chemical mixtures different from those tracing the specific history of the solar neighbourhood. A classical example of the latter is the over-abundance of α-process over iron-peak elements in high-metallicity populations found in elliptical galaxies (e.g. Worthey et al. 1992;Thomas et al. 2005). Moreover, even to date, assigning atmospheric parameters to observed spectra remains challenging, to the point that different groups often derive different parameters for the same stars. This is a concern for the community, which triggered the creation of an IAU Working Group on Stellar Spectral Libraries.2 Meanwhile, impressive work is being achieved towards deriving accurate and precise parameters for stars, while exploring and understanding the sources of deviant parameter estimates (e.g. Gilmore et al. 2012;Smiljanic et al. 2014;Jofré et al. 2014Jofré et al. , 2015Jofré et al. , 2017, and references therein), and references therein).

SPS models incorporating stellar spectral libraries can be roughly classified into 4 types:

(i) models relying purely on empirical stellar libraries, which we refer to as semi-empirical SPS models3 (e.g., Maraston et al. 2009;Vazdekis et al. 2010Vazdekis et al. , 2016));

(ii) models relying purely on theoretical stellar libraries, which we refer to as fully-theoretical SPS models (e.g., Leitherer et al. 1999;Delgado et al. 2005;Maraston 2005;Coelho et al. 2007;Percival et al. 2009;[START_REF] Buzzoni | New Quests in Stellar Astrophysics. II. Ultraviolet Properties of Evolved Stellar Populations[END_REF]Lee et al. 2009;Leitherer et al. 2014);

(iii) models combining empirical and theoretical libraries to sample the parameter space and widen the wavelength coverage (e.g. Bruzual & Charlot 2003;Maraston & Strömbäck 2011);

(iv) models using an empirical library as a base (typically for solar abundances), from which predictions are computed differentially (often via theoretical spectra), which we refer to as differential SPS models [START_REF] Prugniel | Stellar Populations as Building Blocks of Galaxies[END_REF]Walcher et al. 2009;Conroy & van Dokkum 2012;Vazdekis et al. 2015).

Traditionally, the trend has been to prefer empirical libraries to study stellar absorption features in the spectra of old stellar populations (e.g. Vazdekis et al. 2016), while models for young and UV-bright stellar populations heavily rely on theoretical libraries (e.g. Leitherer et al. 2014). The recent work by Martins et al. (2019) probed different spectral libraries to reproduce the integrated spectra of Galactic star clusters, concluding that modern theoretical libraries are competitive also for modelling old populations.

Our focus in the present work is on the comparison between semi-empirical and fully-theoretical SPS models. In particular, we aim at investigating how the strengths and caveats of empirical versus theoretical libraries of stellar spectra impact the integrated properties of Simple Stellar Populations (SSPs). The questions we seek to answer are:

(i) How do the uncertainties identified in theoretical stellar libraries affect integrated colours and spectral indices of model stellar populations?

(ii) How does the non-ideal coverage of the HR diagram by empirical libraries affect the predictions of integrated properties of stellar populations?

(iii) How do random errors in the stellar atmospheric parameters translate into the models? (iv) To what extent does the choice of an empirical or a theoretical library affect age and metallicity estimates from integrated light of galaxies?

To address these questions, we compute SPS models for different choices of empirical and theoretical stellar libraries, isolating the effects introduced by the use of synthetic versus empirical spectra from those due to the HRD coverage. These SPS models are tailored to the specific tests performed in this paper and are not expected to be useful for the general user.

The structure of the paper is as follows: we start by detailing a new synthetic stellar library in Section 2; in Section 3 we describe the SPS models built to address the questions outlined above; Section 4 shows results from the model comparison. The discussion and conclusions follow in Sections 5 and 6. We provide ancillary information in an online appendix. All models computed for this work are available at http://specmodels.iag.usp.br.

SynCoMiL: A SYNTHETIC COUNTERPART TO THE MILES LIBRARY

For the present work we built a Synthetic Counterpart to the MILES Library (SynCoMiL hereafter), a theoretical spectral grid which mimics the MILES stellar library in terms of its wavelength and HRD coverage, and spectral resolution. MILES (Sánchez-Blázquez et al. 2006;Cenarro et al. 2007) is a carefully flux-calibrated empirical spectral library widely used in stellar population modelling (e.g. Vazdekis et al. 2010Vazdekis et al. , 2012Vazdekis et al. , 2015Vazdekis et al. , 2016;;Martín-Hernández et al. 2010;Maraston & Strömbäck 2011;Röck et al. 2016). It contains spectra for close to 1000 stars covering λλ 3540 -7410 Å at FWHM ∼ 2.5 Å spectral resolution (Falcón-Barroso et al. 2011). Atmospheric parameters for the stars in MILES were first compiled from the literature by Cenarro et al. (2007). Prugniel et al. (2011) and Sharma et al. (2016) re-derived these parameters, providing error estimates for the majority of the MILES stars. MILES was designed to have an optimal coverage of the HRD in terms of the effective temperature T eff , surface gravity log g, and metallicity [Fe/H] of the stars in the library. The [Fe/H] vs. [α/Fe] relation for the MILES stars, characterised by Milone et al. (2011), made the library particularly suitable for comparison with stellar spectral models, where both the abundance pattern and the global metallicity need to be defined. It is well known that atomic and molecular opacities play an essential role in stellar atmosphere models and corresponding synthetic spectra. An analysis of libraries from the literature shows different predictions for spectral indices, depending on the exact combination of opacities and grid (e.g. Martins & Coelho 2007). The authors illustrate a trend with T eff (hot stars are better reproduced on average than cool ones) and wavelength (redder spectral indices being on average better reproduced than bluer ones). The recent work by Knowles et al. (2019, see their fig. 16) shows that modern grids still show evidence for a light trend with wavelength, and their differential predictions also differ. Nonetheless, and even though improving the opacities is a slow and timeconsuming process, considerable progress has been achieved over time (e.g. Peterson & Kurucz 2015;[START_REF] Kurucz | [END_REF]Franchini et al. 2018). The recent work by Martins et al. (2019) compared the ability of different grids (both empirical and synthetic) in reproducing the integrated spectra of globular clusters. They show that current synthetic grids are competitive, despite still showing discrepancies when compared to observations. Martins & Coelho (2017) discuss current needs regarding synthetic libraries, in particular for applications to stellar population studies.

The computation of SynCoMiL is largely based on the work by Coelho (2014) 10) show trends with T eff and wavelength similar to the ones mentioned above. The ingredients for these models are summarised below, and we refer the reader to C14 for technical details.

(i) Opacity distribution functions (ODFs) were adopted from C14 for iron abundances [Fe/H] = -1.3, -1.0, -0.8, -0.5, and from [START_REF] Castelli | Modelling of Stellar Atmospheres[END_REF] 4 for [Fe/H] = -3.0, -2.5, -2.0, -1.5, -0.3, -0.2, -0.1, +0.0, +0.2, +0.3, +0.4, +0.5, +1.0. A new set of ODFs was computed with [Fe/H] = -0.5 and [α/Fe] = +0.2.

(ii) Model atmospheres were computed with ATLAS9 (Kurucz 1970;Sbordone et al. 2004) for stars with T eff ≥ 3500 K and the ODFs described above, adopting the atmospheric parameters of the MILES stars and the convergence criteria as in Mészáros et al. (2012); For stars with T eff < 3500 K we used existing MARCS atmosphere models5 (Gustafsson et al. 2008) to compute a small grid of cool stars. In all MARCS models we adopted the standard chemical composition class, with spherical model geometry for log g ≤ 1.5, and plane-parallel for log g ≥ 4.5.

(iii) Synthetic stellar spectra were computed with the SYNTHE code (Kurucz & Avrett 1981;Sbordone et al. 2004), based on the ATLAS9 and MARCS models. The opacities are as in C14 with one update, the inclusion of the molecular transition C 2 D-A from Brooke et al. (2013) 6 to correct for the problem identified by Knowles et al. (2019). For stars with T eff ≥ 3500 K the synthetic spectrum was computed based on the ATLAS9 models. Cooler star spectra were computed from the MARCS model grids, then interpolated to achieve the atmospheric parameters of SynCoMiL stars. Interpolation was performed linearly in θ = 5040/T eff , log g and [Fe/H], with the flux in logarithmic scale. We adopted this scheme after different tests comparing synthetic spectra with the interpolated ones.

(iv) The synthetic spectra were then corrected for the effect of predicted lines, interpolating linearly the coefficients listed in Table B1 of C14 to the exact atmospheric parameters of the SynCoMiL stars.

(v) The spectra were convolved, rebinned and trimmed to match the resolution, dispersion and wavelength range of MILES (Falcón-Barroso et al. 2011).

We adopt the MILES atmospheric stellar parameters Counts q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 3000 4000 5000 10000 15000 20000 30000 mainly from Prugniel et al. (2011), with the revision for cool stars provided by Sharma et al. (2016). For 26 stars we use the parameters from Cenarro et al. (2007), either because Prugniel et al. (2011) do not provide an independent determination, or because we concluded by visual comparison that the Cenarro et al. (2007) parameters permit a closer match between observed and model spectra. For stars HD001326B and HD199478 we modified slightly the reported parameters, as we could not obtain converged models for the nominal parameters. The changes in T eff and log g are nevertheless small -the smallest needed to achieve convergence -and are within the reported errors. We list in Table 1 the atmospheric parameters adopted for each star in MILES and SynCoMiL, along with their respective sources.

To mimic the abundance pattern of the MILES library, we follow table 7 of C14, based on the work by Milone et al. (2011).

SynCoMiL spectra were compared with the empirical ones from MILES both visually and quantitatively. Quantitative differences between model and observations were obtained via a χ 2 metrics

χ 2 = λ f syn λ -f obs λ 2 σ 2 λ , (1)
and a median deviation ∆ defined as where f syn λ and f obs λ are the synthetic and observed fluxes at a given λ, respectively. The standard deviation σ λ appearing in Eq. (1) was estimated for each star as follows. P. Sánchez-Blázquez (priv. comm.) kindly provided us with the error spectra for each star in MILES, which was used in turn to compute the signal-to-noise ratio SNR(λ) for each star. Since very deviant values of SNR were obtained for some of the stars, we chose to use the median[SNR(λ)] of the distribution of SNR at each λ as a fiducial value to compute σ λ = f obs λ /median [SNR(λ)]. This fiducial SNR(λ) ranges from ≈ 8 to ≈ 190 over the MILES wavelength range.

∆ = median | f syn λ -f obs λ | f obs λ , (2)
Fig. 1 shows the resulting distributions of χ 2 and ∆, as well as the corresponding values for each star plotted vs. T eff . We found that T eff is the only atmospheric parameter which correlates with the metrics in Eqs. 1 and 2. The patterns in Fig. 1 are in agreement with previous work: the larger values of χ 2 and ∆ for cool stars are in agreement with, e.g., Martins & Coelho (2007) and C14, and the larger values for T eff 7000K are consistent with the larger errors in T eff for these stars reported by Prugniel et al. (2011). The red symbols in 1 correspond to 71 stars which we opted not to use in the remaining of this work (e.g., bottom panel in Fig. 2). Spectra in MILES which are not suitable for stellar population modelling have been identified previously in the literature (e.g., Prugniel et al. 2011;Barber et al. 2014, R. Peletier, priv. comm.). In the present work, a star is not used in the SPS models if any of the conditions below applies.

(i) The observed spectrum shows:

• emission lines, • excessive noise or corrupted pixels, • distortions in the continuum, • E(B -V) > 0.3, as inferred by Prugniel et al. (2011),

• peculiar spectral features (e.g. HD0554967 ).

(ii) χ 2 and T eff fulfill any of:

• T eff < 4000 K and χ 2 > 1,
• 4000 ≤ T eff ≤ 7000K and χ 2 > 0.05, • T eff > 7000 K and χ 2 > 0.15.

(iii) ∆ and T eff fulfill any of:

• T eff < 4000K and ∆ > 0.4, • T eff ≥ 4000K and ∆ > 0.1.
Table 2 lists the discarded stars. Most of the discarded stars satisfy more than one of these criteria. Stars which fall into the quantitative cuts listed above show strong continuum mismatches between model and observations. We hypothesise that these are due to either large errors in T eff , 1 and2.

or problems with flux calibration, reddening, or star identification. The results of Prugniel et al. (2011) and Martins et al. (2019) also show evidence of residual flux calibration problems in MILES. For illustration purposes, in Fig. 2 we compare model and observed spectra for three stars. Isochrones for ages 0.1, 1 and 10 Gyr are plotted as black lines.

The chemical mixtures are indicated in each panel (see Table 3).

METHODOLOGY

To address the questions outlined in Section 1, we compute four different sets of SPS models in which all the ingredients are the same except for the choice of the stellar flux library. The SPS models are computed using the galaxev code (Bruzual & Charlot 2003, and recent updates). This is a flexible code which provides SPS models for a variety of stellar evolutionary tracks, stellar spectral libraries, chemical abundances, initial mass functions, and star formation histories, and probes ideal towards our goal of computing models which differ only in the stellar spectral library. We adopt the PARSEC stellar evolutionary tracks (Bressan et al. 2012;Chen et al. 2015) to describe the evolution of stellar populations of the five metallicities listed in Table 3. From the evolutionary tracks the galaxev code builds isochrones for the required age and metallicity.

Fig. 3 shows three isochrones for each stellar metallic-ity in We consider four different sets of SPS models8 for each mixture in Table 3, denoted sps-m, sps-s, sps-c and sps-r, which differ only in the stellar spectral library, as follows:

sps-m: the empirical MILES library. sps-s: the synthetic SynCoMiL library. sps-c: the synthetic C14 library9 . sps-r: 10 realisations of sps-s (details below).

To each star along an isochrone, the galaxev code assigns a spectrum drawn from the selected library. The stellar spectrum is assigned on the basis of the proximity of the stellar parameters of the library stars to the corresponding parameters of the problem star in the HRD, interpolating between neighbouring spectra when required. For the sps-c models, each problem star in the isochrone is bracketed by four C14 stellar models (see Fig. 3), characterized each by (θ, log g), where θ= 5040/T eff . In this case, we interpolate the stellar models logarithmically in flux, first in θ at constant log g and then in log g. This interpolation scheme is possible only in very few instances when using the MILES library in the sps-m models. In some cases, we can interpolate in T eff two MILES spectra of the required log g, but in most cases we use the MILES spectrum closest in (T eff , log g) to the problem star on the isochrone.

For the sps-s models, we use the same spectral assignment as in the sps-m models, but draw the corresponding stellar spectra from the SynCoMiL instead of the MILES library.

For the sps-r models, we modify the stellar parameters of each SynCoMiL star by adding to each parameter a Gaussian random error. Then we replace each star in the sps-s models with the star with closest parameters in the modified table. This exercise is repeated 10 times for each set of SPS models listed in Table 3. We adopt errors for T eff and log g as compiled by C14 (see her table 5): for T eff the error ranges from 120 K for cool stars to 3000 K for hot stars; for log g the errors range from 0.1 to 0.3 depending on T eff . For [Fe/H] we adopt conservative errors of 0.15 (e.g., Soubiran et al. 1998).

RESULTS

The different SPS models described in Section 3 were compared to each other in two ways: (1) via direct modelmodel comparisons (Section 4.1), and (2) using the models to derive stellar population parameters via spectral fits to a sample of galaxy spectra (Section 4.2).

Model -model comparisons

From the direct comparison of the colours and spectral line indices predicted by the different models we aim at understanding the following three effects: Synthetic effect: comparing the predictions of the sps-m and sps-s models we can assess the consequences of using theoretical instead of empirical stellar spectra for a fixed coverage of the HRD.

Coverage effect: comparing the predictions of the sps-s and sps-c models we can isolate the consequences of limited vs. complete HRD spectral coverage on the observables.

Random error effect: comparing the sps-r and sps-s models, we can assess the effects of random errors in the stellar atmospheric parameters on the model predictions.

Broad-band colors

For each set of models, we compute 5 colours, ug, ur, gr, gi, and ri, using the SDSS ugri filter response functions (Doi et al. 2010) 10 . For each age and metallicity of the SPS models we compute the following colour differences in direct relation to the effects listed above:

∆colour Synthetic = c sps-m -c sps-s , (3a)
∆colour Coverage = c sps-c -c sps-s , (3b)
∆colour RanError = c sps-r -c sps-s , ( 3c
)
where c is a colour. Results are shown in Figs. 4, 5 and 6, and listed in Table 4. Fig. 4 shows the distributions of ∆colour for the different colours (rows) and effects (columns). We notice that the distributions are not always symmetric, and that they are typically broader for the coverage effect than for the synthetic and randomised-parameter effects. These results are 10 The MILES spectra extend from 3540 to 7410 Å and do not cover the full widths of the u and i bands. The u band extends from 2980 to 4130 Å, with λ eff (u) = 3560 Å inside the MILES range, while the i band extends from 6430 to 8630 Å, with λ eff (i) = 7500 Å not far from the MILES edge. The stellar flux is considered to be zero for λ < 3540 Å and λ > 7410 Å when computing the u and i magnitudes. Given that all our SPS models cover the same wavelength range as the MILES library, we consider that the use of the u and i bands is still useful and informative. illustrated in a condensed manner as a boxplot in Fig. 5, indicating the corresponding median and interquartile range (IQR) 11 given in Table 4. In Fig. 6, we show ∆colour as a function of stellar population age for the different colours and effects. A large variance in colours involving the u band arises at ages younger than 1 Gyr, especially at low metallicity, which is not surprising given the limited number of hot metal poor stars in empirical libraries. In summary, the coverage effect dominates the systematics and variance in ∆colour. The most affected colours are those involving the u band, and the largest ∆colour is ∆(ur) Coverage = 0.06.

Spectral indices

The spectral indices listed in Table 5 were measured in all SPS models. We define ∆idx as the index difference between 11 IQR is equal to the difference between the 75th and 25th percentiles. For a normal distribution, IQR = 1.35 × σ. Trager et al. (1998) Fe4383, Ca4455, Fe4531, Fe4668, H β , Fe5015, Mg1, Mg2, Mgb, Fe5270, Fe5335, Fe5406, Fe5709, Fe5782, NaD, TiO1, TiO2 two sets of models:

∆idx Synthetic = I sps-m -I sps-s , ( 4a
)
∆idx Coverage = I sps-c -I sps-s , (4b)
∆idx RanError = I sps-r -I sps-s , ( 4c
)
where I is any spectral index. We measure ∆idx for all ages and metallicities. Results are shown in Figs. 7 -11, and listed in Table 6. Fig. 7 shows the distributions of ∆idx for each index. The impact of the three effects on the indices is complex and defies simple conclusions. In all cases, the effect of the random errors on the atmospheric parameters is the least important. The indices for which the synthetic effect is most prominent are: CaHK, Fe4668, Fe5270, Fe5709 and NaD. The impact of HRD coverage in the indices is not negligible and dominates over the synthetic effect in the case of, e.g., H8, B4000, and G4300. For many indices the synthetic and coverage effects are comparable and may introduce different In Figs. 8, 9 and 10 we plot the indices computed from sps-m, sps-c and sps-r against those of sps-s models, respectively. The dependence with the age of the population is apparent: as expected, the largest deviations from the 1-to-1 line occur for the old population in the case of the synthetic effect, and for the young population in the case of the coverage effect. In these plots we can locate opacity related problems, e.g., Fe4668 (see discussion in Knowles et al. 2019), or the high sensitivity to HRD coverage of the Balmer line indices. The effect of randomising the stellar parameters is to increase the dispersion of the data points but they do not deviate significantly from the 1-to-1 line except for young populations: most likely this is induced by the coverage effect due to the scarcity of hot stars in the HRD.

The boxplot in Fig. 11 is convenient to easily rank the sensitivity of each index to the effect being explored. To facilitate visualisation, ∆idx has been scaled to its standard score (or z-value), defined as:

z = x -µ σ , ( 5
)
where x is the raw ∆idx value, µ is the mean value of x for the population, and σ its standard deviation. In each panel (top: synthetic effect; middle: coverage effect; bottom: randomised parameters) the indices are sorted in increasing order of ∆idx.

Deviations from the zero-line indicate systematic effects and the size of the box indicates the IQR. The further away from the zero-line the midline of a box is, the more the index is affected by systematics. In summary, the consequences of the synthetic and the coverage effects on the indices are multiple and difficult to summarise in simple terms. The outcome of randomising the stellar parameters is small compared to the other effects.

Spectral fitting of galaxies

The model -model comparisons of the previous section illustrate interesting differences between the sets of SPS models, but cannot be easily translated into the question that matters the most: how does the adoption of different spectral libraries change the age and metallicity of galaxies derived from their integrated light?

To address this question, we use the sps-m, sps-s, and sps-c models to derive stellar population parameters from the spectra of ∼1000 nearby galaxies (0.04 < z < 0.06). We use the sample of Gadotti (2009) which encompasses galaxies of different morphology: ellipticals, spirals (with classical or pseudo-bulges, with and without bars), and bulgeless discs. The spectra were obtained from the SDSS database (Abazajian et al. 2004) and processed as in Coelho & Gadotti (2011). We use the Starlight spectral fitting code (Cid Fernandes et al. 2005) to infer the stellar population parameters, processing the sample three times, once for each set of SPS models. We refer the reader to the quoted work for details on the sample and technique.

We show in Fig. 12 the results for two parameters related to the fit-quality and three parameters related to the stellar population. The parameters related to the fit-quality are χ 2 (as in equation 1) and an average relative deviation adev, defined as

adev = 1 N λ | f model λ -f obs λ | f obs λ , ( 6
)
where N is the number of wavelength points in the spectrum, f model λ is the model spectrum fitted by Starlight, and f obs λ is the observed galaxy spectrum.

The synthetic effect can be inspected in the left hand side column of Fig. 12, which compares the results from spsm (y-axis) vs. those from sps-s (x-axis). We highlight that spectral fits performed with sps-s models tend to have larger χ 2 and adev than those obtained with sps-m models, even though there are no noticeable differences in the retrieved values of A V and log (age). The values of [Fe/H] obtained with the sps-s models are systematically lower than those obtained with the sps-m models. The differences in [Fe/H] correlate with [Fe/H], lower metallicities showing larger differences.

The coverage effect can be inspected in the right hand side column of Fig. 12, which shows the results from spsc (y-axis) vs. results from sps-s (x-axis) models. We notice that spectral fits performed with the sps-s and sps-c models have similar adev, but χ 2 is slightly larger for the sps-c fits. There are no noticeable differences in the retrieved values of Av. Whereas the values of log(age) obtained from the sps-c models are larger than for the sps-s models, there are no systematic differences in the retrieved mean [Fe/H], even though there are some outliers from the 1-to-1 line, which remain to be investigated.

0.5 1.0 -2 0 2 -4 -2 0 2 -1 0 1 2 -0.04 -0.02 0.00 -1 0 1 -5.0 -2.5 0.0 2.5 -4 -2 0 2 -2 -1 0 1 -1.0 -0.5 0.0 0.5 1.0 -4 -2 0 2-5.0 -2.
Table 7 shows the median residuals and IQRs for the parameters obtained from sps-m vs. sps-s fits (synthetic effect), and sps-c vs.s sps-s fits (coverage effect). In all cases, the systematic differences are inside the IQR ranges. We note that the median residuals on [Fe/H] and log(age) are of the same order of the IQR for the synthetic effect and the coverage effect, respectively.

DISCUSSION

Semi-empirical vs. theoretical SPS models

How do uncertainties in theoretical stellar libraries affect integrated colours and line indices measured in SPS models?

Several works in the literature compare synthetic stellar spectra to empirical ones on a star-by-star basis (e.g. In the range 3525 to 6300 Å, a theoretical library outperformed the empirical ones in 70% of their tests, essentially because the shape of the continuum is more in agreement with the observations in the theoretical case.

Our results add more information to the theoretical vs. empirical library debate. The SPS models built in this work are largely based on the theoretical library by C14. Her fig. 10 illustrates the systematic differences between synthetic spectra for given T eff and log g, and MILES spectra averaged over all stars in the library with the same atmospheric parameters (within uncertainties). The two main possible reasons for these differences are: either they result from abundance patterns unaccounted for in the synthetic grid (such as variations of C and N due to dredge-up in giants stars), or they reflect true deficiencies in the spectral modelling, related to either the physics of the stellar atmosphere or to the adopted atomic opacities. In the present analysis we assume that all differences are due to the opacities.

In Section 4.1, colours and spectral indices from the sps-m and sps-s models were compared to quantify how the inaccuracies in the opacities translate into the integrated light of the stellar population. The results from Table 4 show that the systematic effect on broad-band colours ranges from -0.002 in u-g to -0.018 in u-r. The IQR of the distributions range from 0.017 in gr to 0.059 in ur. For comparison, the reported accuracy (global rms dispersion) of the flux calibration for the MILES library is 0.013 mag in B -V.

Comparing the spectral indices we get a closer view of the role played by the opacities. Figs. 7, 8 and 11 show a complex and index-dependent behaviour. One may argue that the best performance of the sps-s models occurs for the indices H10, B4000, Hδ F , CN 2 , G4300, Hγ F , Fe4383, Hβ, Mg b and Fe5782, whereas the indices that deserve most attention from modellers are Fe5270, Fe5015, CaHK, Fe5709, Fe4383 and Fe4668 (the latter had already been pointed out by Knowles et al. 2019).

It is unclear to what extent the results presented here can be safely applied to other theoretical libraries. Given that the broad-band colours depend mostly on averaged opacities and on the physics of the stellar atmosphere, we expect the results for the colours to be similar for other modern libraries of statistical fluxes (e.g. Gustafsson et al. 2008;[START_REF] Castelli | Modelling of Stellar Atmospheres[END_REF], or in high-resolution spectral libraries as long as the effect of predicted lines has been taken into account (see discussion in section 3 of C14). On the other hand, the results for the spectral indices depend on the details of the specific opacities, and it is less likely that they can be reliably adopted for other synthetic libraries. As such, the reader should see our results on the spectral indices as guidelines for the use of the C14 library.

Synthetic effect

Coverage effect

Randomised pars

The effect of the HRD coverage

How does the non-ideal or poor coverage of the HRD by empirical libraries affect the predictions of SPS models?

Empirical libraries cannot cover the HRD homogeneously and completely due to observational constrains. We do not harbour in our Galaxy massive metal-poor stars, which are likely to be present in high redshift galaxies, nor can we cover the abundance patterns of galaxies with diverse star formation and chemical enrichment histories. By construction, with semi-empirical SPS models we can reproduce to a better degree the properties of populations similar to the solar neighbourhood than others.

Vazdekis et al. ( 2010) discuss this issue in the context of three empirical libraries MILES, STELIB (Le Borgne et al. 2003), and Lick/IDS (Worthey et al. 1994). They define the quality parameter Q n to quantify the reliability of their semiempirical SPS models as a function of age, metallicity and IMF (see their Section 3.2). The authors conclude that the minimum age at which a model is reliable ranges from 60 Myr around solar metallicity to 10 Gyr in the most metalpoor regime, with a varying degree of quality Q n .

Here we retake this discussion comparing our sps-s and sps-c models: the first mimics the HRD coverage of an empirical library, and the second covers the HRD completely and homogeneously for populations older than 30 Myr (cf. Fig. 3). Differences found in this experiment will be due to the incomplete HRD coverage of the empirical library, since SynCoMiL and C14 share the same codes and opacities.

The effects that the different HRD coverage have on colours can be seen in Figs. 4, 5 and 6, and are summarised in Table 4. For all colours, except ri, the coverage effect introduces systematic differences and variances larger than the synthetic effect. The largest difference occurs in ur, with a systematic value of -0.061 and IQR of 0.085. The effect is largest in the most metal-poor regime, in accordance with the results of Vazdekis et al. (2010). This is expected since the coverage of the HRD is poorest at the lowest metallicities.

The effects on spectral indices are shown in Figs. 7, 9, and 11, and are difficult to generalise. Some indices seem to be little affected (at least in comparison to the other effects) such as Fe5709 and Fe5782, while in other cases, such as B4000, the difference is prominent. Fig. 11 shows that the most affected indices are, at one extreme, B4000 and Mg1 (sps-s models, on average, underestimate the indices), and, at the other extreme, Hδ and Hγ (sps-s models, on average, overestimate the indices).

Errors in the atmospheric parameters

How do errors in the stellar atmospheric parameters translate into SPS models?

Percival & Salaris ( 2009) performed an interesting investigation on the possible impact of systematic uncertainties in the atmospheric parameters on the integrated spectra of stellar populations. These authors simulated a systematic difference between the T eff scale of the isochrones and that of the stellar flux libraries, and considered errors within the typical offsets found in the literature (100 K in T eff , 0.25 in log g and 0.15 in [Fe/H]). Their results raised a caution, by showing that small systematic differences between the atmospheric parameter scales can mimic non-solar abundance ratios or multiple populations in the analysis of integrated spectra. If this result is confirmed, much of what the community is concluding in terms of abundance patterns in galaxies can be an artefact, due to offsets between parameter scales and not truly a tracer of different chemical evolution.

At the suggestion of the referee, we compare our results to Percival & Salaris (2009). See their tables 1 and 2, where these authors show the impact of their tests on Lick indices for 2 choices of SSPs. In Table 8, we list ∆idx and IQR(∆idx) from our experiments for the same choices of age, metallicity and indices as in Percival & Salaris (2009). The effect of random errors on the stellar parameters is typically smaller than the effect introduced by adding a systematic difference of 100 K in the T eff scale, and of comparable magnitude to the effect of adding systematic differences in log g and [Fe/H] of 0.25 and 0.15, respectively. The exact reason why a systematic difference in the T eff scale has a larger impact than adding random errors to the stellar parameters is difficult to trace. We can hypothesise that random errors tend to cancel out, while a systematic difference in the T eff scale is equivalent to selecting a younger (hotter) or older (cooler) isochrone when building an SSP model without changing the selection of stellar spectra.

In any case, a look at table 3 of Percival & Salaris (2009) shows that the deviations introduced by tampering with the atmospheric parameters is comparable to (or larger than) typical observational errors on the spectral indices. As such, these effects cannot be safely neglected. Here we complement this investigation with the sps-r models, simulating the effect of random rather than systematic variations in the atmospheric parameters. Our tests reveal that both in colours (Figs. 5 and6, Table 4) and spectral indices (Fig. 7 and 11), the effect of randomising the atmospheric parameters is small compared to the other effects. We conclude then that random errors in the stellar parameters (within the uncertainties adopted here, see Section 3) are not a major source of concern for current SPS models.

Inferring stellar-population parameters from integrated light

To what extent does the choice of an empirical or a theoretical library in the SPS model affect age, metallicity and reddening estimates from integrated light?

Possibly, the most important result of the experiments performed in this work is to estimate to what extent stellar population parameters -age, metallicity, reddening -derived from SPS models vary if we adopt in the model an empirical or a theoretical library. Given our current inability to have both complete coverage of the HRD with high quality stellar spectra, what should one favour: complete coverage of the HRD (theoretical library) or accurate spectra on a star-by-star basis (empirical library)?

There are several ways proposed in the literature to derive the stellar population parameters from integrated light, but for the purpose of the present paper we choose to investigate results obtained from spectral fitting. To that end we adopt the widely used code Starlight (Cid Fernandes et al. 2005) to fit a sample of nearby galaxies (Gadotti 2009;Coelho & Gadotti 2011). In Section 4.1 we show that the synthetic and coverage effect impact both colours and spectral features. A code such as Starlight, which fits the continuum and the spectral features together, is a good option to evaluate in a global manner how the stellar library of choice will influence the derived galaxy properties.

Results are shown in Fig. 12 and summarised in Table 7. The first noticeable feature is that the use of synthetic spectra tends to increase χ 2 and adev for the fit, i.e., the fits tend to be statistically worse. This is not surprising, and reminds us that atomic and molecular opacities still need improvement. Nevertheless, and to some extent a surprising result, there are no important differences in the reddening or the ages derived using sps-m and sps-s models. There is only a hint that for intermediate ages (9 log(age) 9.5), the values obtained with sps-s are slightly lower than for sps-m.

On the other hand, the effect of HRD coverage on inferred ages is more significant: the use of models with non-optimal HRD coverage underestimates virtually all ages, the effect being more pronounced for log(age) ∼ 9.0. The effects on the derived metallicities are shown in the bottom panels of Fig. 12. sps-s models recover lower metallicites than sps-m models, with a median difference of 0.13. This result is consistent with the top-panel of Fig. 11, which shows more indices below the zero-line than around or above it. This is also in agreements with results from the literature that show that in general synthetic stellar spectra are stronger-lined than observed stellar spectra (e.g. Martins & Coelho 2007;Coelho 2014). There is an indication that the difference is stronger towards lower-metallicities, but the origin of this tendency is unclear. Having a complete coverage of the HRD does not seem to affect the derived mean metallicities, although the dispersion increases.

CONCLUSIONS

It has been traditionally accepted that SPS models tailored to study young populations favour the use of theoretical stellar libraries, due to their better HRD and wavelength coverage, while models targeting intermediate and old populations favour empirical stellar libraries, whose detailed spectral features are more reliable than in synthetic spectra.

In this paper we perform experiments with especially built SPS models to investigate and quantify the impact of the choice of stellar library type on: (i) the predicted colours and magnitudes of evolving simple stellar populations, and (ii) the inferred age, metallicity and redenning of a galaxy from spectral fits to its integrated spectrum.

We build a new synthetic stellar library which mimics the HRD coverage of a widely used empirical library (Section 2). During this exercise we identified 71 MILES stars (Table 2) whose spectra we consider not suitable for stellar population modelling, and we recommend not to use these spectra in SPS models.

We build SPS models using different stellar libraries (Section 3). We name synthetic effect the differences introduced in the SPS model predictions by using a theoretical vs. an empirical library, for identical HRD coverage. Analogously, we name coverage effect the differences introduced in the SPS models by using libraries with a limited vs. a complete HRD coverage. The results of our tests are given in Section 4, and further discussed in Section 5. The lessons learned are as follows.

In the majority of the cases the coverage effect is responsible for the larger deviations in the predicted colours, especially those involving the u band, for which the lack of hot stars in the empirical library is more noticeable.

For spectral indices, the coverage and synthetic effects are comparable for most features in the wavelength range considered. Some indices are more sensitive to the synthetic effect (e.g. CaHK, Ca4227, Fe4668, Fe5270), indicating spectral regions that deserve more attention from the modellers to improve the theoretical grids. Other indices are more sensitive to the coverage effect (H8, B4000, G4300), and we warn users of semi-empirical SPS models to take the predictions for these indices with caution.

We test the effects that random errors in the atmospheric parameters of the stars have on the SPS model predictions, and conclude that, for the typical errors in atmospheric parameters adopted in our experiments, this effect is minor in comparison to the other effects.

We use different SPS models to infer the stellar population parameters of a sample of nearby galaxies by spectral fitting. The synthetic effect is null for the mean lightweighted log(age) of the galaxies, but metallicity is underestimated by an average of ∼ 0.13. The coverage effect results in galaxy ages being underestimated (for all ages but more strongly around log(age) ∼ 9), but has little impact on the inferred metallicities other than increasing the dispersion. The inferred reddening is virtually unaffected by either effect.

Strictly speaking, our results are valid for the specific HRD coverage of the MILES library and the synthetic grid of C14. Nonetheless, we believe that our conclusions on the coverage effect will not change much in the near future, given that MILES already has an optimal coverage of the HRD for solar neighbourhood stars. More stars from different populations (LMC, SMC, galactic bulge) need to be introduced in the library to possibly produce a significant change, at the expense of lowering the spectral resolution and/or the SNR, due to current observational constraints. We expect that the synthetic effect on optical colours will be similar for most modern theoretical libraries currently in use. The effect on the spectral indices is more sensitive to the specific choice of the synthetic grid and atomic and molecular opacities.

Overall, we conclude that in several instances a sparse coverage of the HRD can introduce larger errors than the inaccuracies of the synthetic spectra. As such, one has to decide with care which kind of SPS models -semi-empirical or fully theoretical -to favour, depending on the application. As of now, SPS models built on current theoretical grids of synthetic spectra are very competitive, for all ages. tion, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The SDSS Web Site is http://www.sdss.org/.

The This paper has been typeset from a T E X/L A T E X file prepared by the author.

Figure 1 .

 1 Figure 1. Top panels: The χ 2 and ∆ metrics as a function of T eff for the SynCoMiL stars. Red crosses indicate stars which have not been used in the SPS models (see text in Section 2). The smooth line corresponds to a LOESS (locally estimated scatter plot smoothing) regression to the points, plotted to aid the eye. Bottom panels: Distribution of χ 2 and ∆ values for the SynCoMiL library.

Figure 2 .

 2 Figure 2. Comparison of MILES and SynCoMiL spectra for 3 stars in the MILES library. (top) star 149, HD027371, T eff = 4995 K, log g = 2.76, [Fe/H] = 0.15, (middle) star 581, HD143807, T eff = 10727 K, log g = 3.84, [Fe/H] = -0.01, and (bottom) star 104, HD018391, T eff = 5750 K, log g = 1.20, [Fe/H] = -0.13. The indicated atmospheric parameters are taken from Prugniel et al. (2011). MILES spectra are shown in gray and Syn-CoMiL spectra are shown in red. Fluxes have been normalised to ∫ 7410 3540 F λ dλ = 1. The top and middle panels show SynCoMiL stars around the 25th and 50th percentiles of the ∆ distribution in Fig. 1. The bottom panel shows a 'peculiar' case, identified as a Cepheid variable by Prugniel et al. (2011), discarded from the remaining of the present work. See Section 2 and Tables1 and 2.

Figure 3 .

 3 Figure 3. Coverage of the stellar flux libraries in the log g vs. T eff diagram. Red symbols indicate the MILES (and Syn-CoMiL) stars, and the blue symbols represent the stars from C14. Isochrones for ages 0.1, 1 and 10 Gyr are plotted as black lines. The chemical mixtures are indicated in each panel (see Table3).

Figure 4 .Figure 5 .

 45 Figure 4. Density plots showing the distributions of colour differences (∆colour, defined in Section 4.1.1) for the different combinations of SDSS-based colours (in rows) and the model effects (in columns). Colours indicate the metallicities Z, as indicated in the label.

Figure 6 .

 6 Figure 6. ∆colour differences for the three effects (columns) described in Section 4.1, plotted as a function of stellar population age (in yr). Different colours are shown in rows, and different metallicities are identified as indicated in the label.

Figure 8 .

 8 Figure 8. Spectral indices predicted by sps-m (y-axis) vs. sps-s (x-axis) models. The points are colour-coded by the age of the population, as indicated by the auxiliary axis.

Figure 9 .

 9 Figure 9. Spectral indices predicted by sps-c (y-axis) vs. sps-s (x-axis) models. The points are colour-coded by the age of the population, as indicated by the auxiliary axis.

Figure 10 .

 10 Figure 10. Spectral indices predicted by sps-r (y-axis) vs. sps-s (x-axis) models. The points are colour-coded by the age of the population, as indicated by the auxiliary axis.

Figure 12 .

 12 Figure12. Results from the spectral fitting of a sample of nearby galaxies. The left-side column shows the results obtained from sps-m (y-axis) vs. sps-s (x-axis) models. The right-side column shows the results obtained from sps-c (y-axis) vs. sps-s (x-axis) models. The different parameters inferred are given in rows: χ 2 , adev (Eq. 6), reddening Av, light-weighted log(age), and light-weighted [Fe/H]. The smooth line corresponds to a LOESS (locally estimated scatterplot smoothing) regression to the points and is shown to guide the eye.

  (C14 hereafter). Comparisons with MILES library stars discussed in C14 (see her table 6 and fig.

Table 1 .

 1 Atmospheric

		parameters used as input values in the
	computation of SynCoMiL (abridged; the full table is available
	as supplementary online material; see Table A1). Unlisted MILES
	stars are not used in the SPS models in this work and are reported
	separately in Table 2 (see Section 2).
	MILES ID Star	T eff	log g	[Fe/H] Notes
	001	HD224930	5411	4.19	-0.78 b
	002	HD225212	4117	0.68	0.14 c
	012	HD001326b	3571	4.81	-0.57 d
	096	HD016901	5345	0.85	0.00 a
	149	HD027371	4995	2.76	0.15 b
	581	HD143807	10727	3.84	-0.01 b
	Atmospheric parameters adopted from: a Cenarro et al. (2007);
	b Prugniel et al. (2011); c Sharma et al. (2016); d Used different
	parameters than proposed in the literature to ensure model
	convergence.

Table 2 .

 2 MILES stars unsuitable for SPS modelling (abridged; the full table is available as supplementary online material; see Table A2). Prugniel et al. (2011); c Sharma et al. (2016); d same as a but unknown [Fe/H] assumed to be solar. Star discarded due to: 1 Excessive noise or corrupted spectrum; 2 Visible continuum distortions; 3 Visible emission lines; 4 Peculiar features; 5 E(B -V ) > 0.3 from Prugniel et al. (2011); 6 Removed by cut in χ 2 ; 7 Removed by cut in ∆ (Section 2).

	MILES ID Star	T eff	log g	[Fe/H] Notes
	029	HD004395	5444	3.43	-0.27 b, 1, 6
	044	HD006474	6781	0.49	0.26 b, 6, 7
	045	HD006497	4401	2.55	0.00 c, 1, 6
	104	HD018391	5750	1.20	-0.13 b, 5, 6, 7
	140	HD281679	8542	2.50	-1.43 a, 6
	204	HD041117 20000	2.40	-0.12 b, 3
	212	HD043042	6480	4.18	0.06 b, 2
	246	HD055496	4858	2.05	-1.48 b, 4
	780	HD199478 11200	1.90	0.00 d, 3, 6
	Atmospheric parameters adopted from: a Cenarro et al. (2007);

b

Table 3 .

 3 Metallicity regimes explored in the present work

	Bin	Isochrone Z	[Fe/H] range	# MILES stars	C14 a mix
	Sub Solar 3	0.0002	< -1.3	86	m20p04
	Sub Solar 2	0.004	[-1.3, -0.6]	144	m10p04
	Sub Solar 1	0.008	[-0.6, -0.1]	262	m05p02
	Solar	0.017	[-0.1, +0.1]	224	p00p00
	Super Solar 1	0.030	> +0.1	198	p02p00
	a Extended for the present work by adding the mixtures
	([Fe/H], [α/Fe]): (-2.0, 0.4) and (-0.5, 0.2), corresponding to
	Z = 0.0002 and 0.008.

Table 3

 3

	, together with the coverage in the HRD of
	the MILES, SynCoMiL, and C14 libraries. This coverage
	is complete for C14 but very sparse for MILES. The sparse
	coverage of the HRD by the MILES and other empirical li-
	braries is what forces us to supplement these libraries with
	synthetic stellar spectra in the Bruzual & Charlot (2003,
	and recent updates) models. One of the goals of the present
	paper is to quantify the effects on the SPS models of assign-
	ing stellar spectra with (T eff , log g, [Fe/H]) relatively far from
	the true values.

Table 4 .

 4 Median and IQR values of ∆colour in magnitude units.

		Synthetic	Coverage	Random error
	Colour	effect (sps-m -sps-s)	effect (sps-c -sps-s)	effect (sps-r -sps-s)
		Median	IQR Median	IQR Median	IQR
	u -g	-0.002 0.043	-0.038 0.068	0.003 0.021
	u -r	-0.018 0.059	-0.061 0.085	0.001 0.031
	g -r	-0.017 0.017	-0.018 0.043	0.001 0.011
	g -i	-0.009 0.035	-0.017 0.062	-0.001 0.020
	r -i	0.007 0.019	-0.003 0.017	-0.001 0.009

Table 5 .

 5 Spectral indices measured in the present work.

	Indices	Reference
	H10, H9, H8	Marcillac et al. (2006)
	HK	Brodie & Hanes (1986)
	B4000	Kauffmann et al. (2003)
	HδA, HδF, HγA, HγF	Worthey & Ottaviani (1997)
	CN1, CN2, Ca4227, G4300,

Table 6 .

 6 Median and IQR values of ∆idx.

		Synthetic	Coverage	Random error
	Index	effect (sps-m -sps-s)	effect (sps-c -sps-s)	effect (sps-r -sps-s)
		Median	IQR	Median	IQR	Median	IQR
	H103798	-0.093	0.365	0.116	0.399	0.005	0.081
	H93835	-0.154	0.997	0.088	0.730	0.017	0.151
	H83889	0.046	0.472	0.068	1.095	0.003	0.159
	CaHK	-0.018	0.018	0.000	0.020	0.001	0.006
	B4000	0.014	0.027	-0.038	0.071	0.002	0.019
	HδA	0.138	1.068	0.520	1.467	-0.006	0.250
	HδF	0.052	0.568	0.242	0.903	-0.003	0.134
	HγA	0.458	1.285	0.653	1.820	-0.010	0.308
	HγF	-0.058	0.473	0.478	0.977	-0.003	0.148
	CN1	0.009	0.016	-0.006	0.024	0.000	0.005
	CN2	0.005	0.010	-0.006	0.017	0.000	0.004
	Ca4227	-0.104	0.257	-0.052	0.070	0.001	0.037
	G4300	0.014	0.439	-0.225	0.647	0.025	0.163
	Fe4383	-0.288	0.450	-0.150	0.624	0.003	0.144
	Ca4455	-0.071	0.072	-0.057	0.227	0.002	0.045
	Fe4531	-0.181	0.370	-0.109	0.143	0.012	0.080
	Fe4668	0.409	1.204	-0.150	0.622	0.011	0.081
	Hβ	0.074	0.550	0.146	0.661	0.003	0.095
	Fe5015	-0.378	0.631	0.019	0.462	0.034	0.138
	Mg1	-0.006	0.015	-0.009	0.013	0.000	0.003
	Mg2	-0.016	0.021	-0.011	0.012	-0.000	0.007
	Mgb	-0.026	0.091	-0.112	0.184	-0.001	0.101
	Fe5270	-0.294	0.248	-0.109	0.155	0.008	0.079
	Fe5335	-0.131	0.179	-0.123	0.153	0.008	0.086
	Fe5406	-0.101	0.179	-0.074	0.113	0.004	0.056
	Fe5709	-0.114	0.162	-0.011	0.080	0.005	0.040
	Fe5782	0.031	0.090	-0.025	0.056	0.003	0.032
	NaD	0.084	0.393	-0.163	0.151	-0.001	0.102
	TiO1	0.003	0.004	0.000	0.005	0.000	0.003
	TiO2	-0.004	0.007	0.001	0.008	-0.000	0.005

systematic effects. Table

6

lists the median and IQR values of ∆idx for each index and effect.

Table 7 .

 7 Median residuals and IQR for spectral fits

		Synthetic effect Coverage effect
	Parameter	(sps-m -sps-s)	(sps-c -sps-s)
		median	IQR median	IQR
	χ 2	-0.05	0.13	0.04	0.06
	adev	-0.16	0.29	0.09	0.10
	A V	0.00	0.04	0.01	0.05
	mean log (age)	0.00	0.12	0.11	0.14
	mean [Fe/H]	0.13	0.13	-0.01	0.12
	Martins & Coelho 2007; Bertone et al. 2008). Recent work

by

Martins et al. (2019)

provides insight into how synthetic vs. empirical spectra compare at the level of the integrated properties of stellar populations. These authors model integrated spectra of clusters combining CMDs and stellar libraries from different sources. Their conclusions depend on the wavelength range. From 3900 to 6300 Å, or when considering specific spectral features, empirical libraries do better.

Table 8 .

 8 ∆idx and IQR(∆idx) for Lick indices (Z = 0.017)

		Age = 4 Gyr	Age = 14 Gyr
	Index	∆idx IQR(∆idx)	∆idx IQR(∆idx)
	H δ F	0.101	0.071	0.041	0.059
	H γ F	0.131	0.086	0.090	0.196
	CN1	-0.003	0.007	0.002	0.006
	CN2	-0.002	0.008	0.006	0.005
	Ca4227 -0.040	0.137	0.082	0.370
	G4300	0.019	0.025	0.114	0.147
	Fe4383	-0.166	0.316	0.174	0.264
	Ca4455 -0.038	0.069	0.047	0.043
	Fe4531	-0.004	0.087	0.051	0.033
	H β	0.045	0.035	0.012	0.085
	Fe5015	0.025	0.163	0.164	0.182
	Mg1	-0.001	0.009	-0.002	0.018
	Mg2	-0.004	0.014	0.005	0.031
	Mgb	-0.154	0.121	0.153	0.387
	Fe5270	-0.037	0.141	0.085	0.119
	Fe5335	-0.018	0.140	0.054	0.227
	Fe5406	-0.021	0.125	0.034	0.130
	Fe5709	0.005	0.066	0.035	0.006
	Fe5782	0.009	0.061	0.017	0.059
	NaD	-0.009	0.137	0.001	0.445
	TiO1	0.001	0.004	-0.001	0.006
	TiO2	0.001	0.004	0.000	0.007

Table A1 :

 A1 SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington. Atmospheric parameters used as input values in the computation of SynCoMiL (Section 2). References for the source of the stellar parameters are given in column (f): a Cenarro et al. (2007); b Prugniel et al. (2011); c Sharma et al. (2016); d Computed with different parameters than proposed in the literature to ensure model convergence. Stars with MILES ID not listed in this table were not used in the SPS models of this work and are reported separately in Table A2.

	APPENDIX A: ONLINE-ONLY MATERIAL Table A1: continued. Table A1: continued. Table A1: continued. Table A1: continued. Table A1: continued. Table A1: continued. Table A1: continued. Table A1: continued. Table A1: continued. Table A1: continued. Table A1: continued. Table A1: continued. Table A1: continued. Table A1: continued. Table A1: continued. Table A2: continued.
	MILES ID MILES ID MILES ID MILES ID MILES ID MILES ID MILES ID MILES ID MILES ID MILES ID MILES ID MILES ID MILES ID MILES ID MILES ID MILES ID Star	Star Star Star Star Star Star Star Star Star Star Star Star Star Star Star	T eff log g [Fe/H] Reference T eff log g [Fe/H] Reference T eff log g [Fe/H] Reference T eff log g [Fe/H] Reference T eff log g [Fe/H] Reference T eff log g [Fe/H] Reference T eff log g [Fe/H] Reference T eff log g [Fe/H] Reference T eff log g [Fe/H] Reference T eff log g [Fe/H] Reference T eff log g [Fe/H] Reference T eff log g [Fe/H] Reference T eff log g [Fe/H] Reference T eff log g [Fe/H] Reference T eff log g [Fe/H] Reference T eff log g [Fe/H] Reference Removed by
	(a)	(a) (a) (a) (a) (a) (a) (a) (a) (a) (a) (a) (a) (a) (a) (a)	(b)	(b) (b) (b) (b) (b) (b) (b) (b) (b) (b) (b) (b) (b) (b) (b)	(c)	(d)	(c) (c) (c) (c) (c) (c) (c) (c) (c) (c) (c) (c) (c) (c) (c)	(d) (d) (d) (d) (d) (d) (d) (d) (d) (d) (d) (d) (d) (d) (d) (e)	(e) (e) (e) (e) (e) (e) (e) (e) (e) (e) (e) (e) (e) (e) (e) (f)	(f) (f) (f) (f) (f) (f) (f) (f) (f) (f) (f) (f) (f) (f) (f) (g)
	834	53 118 178 242 304 364 424 485 545 603 663 724 790 858 923	HD007351 HD021581 HD035179 HD054605 HD072660 HD085235 HD103578 HD120136 HD136064 HD149009 HD165634 HD185144 HD201891 HD218235 M3 IV-25 HD213307	7800	3619 4825 4942 6268 9290 8769 8509 6386 6083 3862 4907 5293 5881 6463 4442 2.00	0.36 2.00 2.48 0.97 3.39 3.69 3.80 4.15 3.94 1.20 2.31 4.56 4.18 4.06 1.02 0.20	-0.35 -1.70 -0.60 0.10 -0.20 -0.23 -0.19 0.24 0.03 0.09 -0.14 -0.12 -1.05 0.23 -1.50 b	c a c a b b b b b c b b b b c 6, 7
	836	54 119 179 243 305 366 425 486 546 604 664 725 791 859 924	HD007374 BD+660268 HD035369 BD+371665 HD073471 HD085503 HD103877 HD121130 HD135482 HD148898 HD166620 HD338529 HD201889 HD218329 M3 III-28 HD213470 8943	12247 5300 4915 5128 4495 4425 7170 3543 4530 9141 4968 6178 5762 3796 4306 1.36	4.16 4.20 2.49 3.50 2.13 2.56 3.76 0.85 2.32 3.85 4.55 3.95 4.13 1.46 0.74 0.11	0.16 -2.00 -0.24 -0.65 0.10 0.27 0.65 -0.02 -0.04 0.38 -0.18 -2.09 -0.74 0.19 -1.50 b	b b b b c c b c c b b b b c c 5, 6, 7
	838	55 120 180 244 306 367 426 487 547 605 665 726 792 860 925	HD007595 HD022049 HD035296 HD054810 HD072905 HD085773 HD103932 HD120933 HD135722 HD149121 HD166161 HD184499 HD202109 HD218502 M3 398 G156-031	2805	4327 5115 6171 4726 5919 4345 4431 3594 4850 11099 5201 5743 4925 6167 4580 5.13	1.82 4.72 4.31 2.58 4.47 0.66 4.55 1.05 2.39 3.89 2.33 4.07 2.39 4.11 1.15 -0.04	-0.68 0.05 0.01 -0.33 0.01 -2.48 0.06 -0.15 -0.39 0.03 -1.25 -0.54 -0.23 -1.75 -1.50 c	3	c b b c b c c c b b b b b b c
	842	56 121 182 245 307 368 427 488 548 606 666 727 793 861 926	HD007672 HD022484 HD036003 HD054719 HD073898 HD086986 HD104307 HD121370 HD135485 HD149161 HD166285 HD184786 HD202447 HD218640 M5 III-03 BD+394926	7261	4939 5987 4378 4405 4912 8000 4423 5967 15500 3915 6389 3454 6277 5799 4174 0.85	2.78 4.07 4.58 2.14 2.30 2.55 2.24 3.78 4.00 1.64 4.10 0.35 4.01 3.26 0.51 -2.52	-0.42 -0.05 -0.15 0.13 -0.56 -1.70 -0.07 0.28 0.50 -0.26 -0.06 0.03 0.26 0.36 -1.29 a	7	b b c c b b c b b c b c b b c
	853	57 122 183 247 308 369 428 489 549 607 667 728 794 862 928	HD008724 HD021910 HD036395 HD055693 HD073665 HD087141 HD104304 HD121299 HD136726 BD+093223 HD166460 HD184406 HD202671 HD218804 M5 II-76 HD216916 21500	4792 4798 3579 5773 5024 6359 5485 4695 4176 5200 4478 4428 14353 6493 5974 3.75	1.76 2.48 4.72 4.16 2.70 3.90 4.23 2.58 1.85 2.00 2.19 2.71 3.25 4.17 2.44 -0.12	-1.63 -0.45 -0.05 0.25 0.21 0.09 0.30 0.10 -0.09 -2.31 -0.05 0.03 0.36 -0.13 -1.11 b	c c c b b b b c c b c c b b a 1, 6
	865	58 123 184 248 309 370 429 490 550 608 668 729 795 863 930	HD008829 HD022879 HD037160 HD055575 HD073394 HD087140 HD104833 HD121258 HD136202 HD149382 HD167105 HD185351 HD203638 HD218857 M5 IV-19 HD219116	4790	7129 5870 4754 5811 4612 5092 7588 6570 6139 35500 9000 5045 4553 5057 4251 1.79	4.10 4.23 2.64 4.19 1.48 2.48 3.51 4.00 4.00 5.70 2.36 3.27 2.48 2.43 0.90 -0.79	-0.17 -0.80 -0.64 -0.38 -1.49 -1.70 0.49 -0.92 0.05 -1.30 -1.50 0.08 0.12 -1.93 -1.29 b	7	b b c b c b b a b b b b c b c
	873	59 124 185 249 310 371 430 491 551 609 669 730 796 864 933	HD009138 HD023249 HD037792 HD056274 HD074000 HD087737 HD105262 BD+342476 HD137071 HD149661 HD167006 HD185657 HD204041 HD219134 M4 LEE-2303 HD219978 3910	4041 5020 6509 5769 6178 10958 8500 6200 3929 5281 3597 4813 8737 4759 6748 0.19	1.89 3.73 4.17 4.40 4.03 2.11 1.50 3.96 1.10 4.59 1.12 2.51 4.45 4.63 2.51 0.18	-0.50 0.08 -0.54 -0.53 -1.85 0.11 -1.87 -2.05 0.06 0.13 -0.16 -0.19 -0.44 0.04 -1.19 c	5	c b b b b b b b c b c c b c a
	MILES ID Star 60 HD009356 125 HD023261 186 HD037536 250 HD056577 311 HD073593 372 HD087822 431 HD105452 492 HD122106 552 HD136834 610 HD150012 670 HD167768 732 HD185859 798 HD204155 866 BD+384955 934 M13 A-171 884 BD+195116B 3259	T eff log g [Fe/H] Reference 6800 4.24 -0.80 b 5165 4.56 0.24 b 3775 0.22 0.14 c 3904 0.48 0.12 c 4815 2.82 -0.17 c 6573 4.06 0.10 b 7041 4.13 -0.19 b 6321 3.84 0.16 b 4856 4.50 0.23 c 6651 3.96 0.13 b 4953 2.29 -0.69 b 26200 3.05 -0.09 b 5718 3.93 -0.69 b 5270 3.50 -2.23 b 4266 1.35 -0.80 c 4.82 -0.26 c 3
	890	(a) 61 126 187 253 312 373 432 493 553 611 671 733 799 867 935	(b) HD009562 HD023194 HD037828 HD057264 HD074011 HD088230 HD105546 HD122563 HD137391 HD150177 HD169027 HD186408 HD204613 HD219449 M13 B-786 G171-010	2894	(c) 5766 8031 4505 4599 5795 4017 5131 4618 7186 6190 11030 5731 5718 4666 4114 5.04	(d) 3.89 4.00 1.36 2.41 4.08 4.67 2.36 1.32 3.93 4.08 3.89 4.15 3.88 2.52 0.43 0.09	(e) 0.14 -0.17 -1.41 -0.40 -0.56 -0.01 -1.46 -2.67 0.10 -0.58 -0.08 0.08 -0.38 0.00 -1.53 c	3	(f) b b c c b c b c b b b b b c c
	892	1 63 127 188 254 313 374 433 494 554 612 672 734 800 868 936	HD224930 HD009826 HD023439a HD037394 HD058207 HD074395 HD088446 HD105740 HD122742 HD137759 HD150281 HD168322 HD186427 HD205021 HD219623 M92 IV-114 HD223385 10023	5411 6139 5181 5279 4806 5546 5848 4791 5485 4459 5164 4745 5648 25500 6138 4726 1.59	4.19 4.06 4.47 4.60 2.55 1.41 3.89 2.78 4.35 2.43 4.54 2.33 4.18 3.70 4.24 1.44 0.29	-0.78 0.11 -0.90 0.20 -0.11 0.09 -0.51 -0.54 0.03 0.08 0.14 -0.51 0.03 -0.10 0.07 -2.31 b	3	b b b b c b b c b c b c b b b c
	915	2 65 128 189 255 314 375 434 495 555 613 673 735 801 869 937	HD225212 HD010380 HD023439b HD037984 HD058551 BD+251981 HD088725 HD106038 HD123299 HD137471 HD150453 HD167665 HD188119 HD204381 HD219617 M92 III-13 M79 153 4269	4117 4154 4786 4445 6306 6668 5647 6014 10371 3793 6589 6125 4904 5081 5941 4226 0.77	0.68 1.85 4.63 2.15 4.27 4.28 4.24 4.18 3.95 1.13 4.07 4.15 2.34 2.76 4.12 0.38 -1.60	0.14 -0.24 -1.09 -0.52 -0.42 -1.20 -0.64 -1.25 -0.19 -0.04 -0.24 -0.16 -0.49 -0.09 -1.36 -2.31 c	1	c c c c b b b b b c b b b b b c
	916	3 66 129 190 257 315 377 435 496 556 614 674 737 802 870 938	HD225239 HD010307 HD023607 HD038392 HD059374 HD074442 HD088737 CD-2809374 HD122956 HD137510 HD151203 HD168720 HD187879 HD204754 HD219615 HD170764 M79 160 4264	5559 5875 7586 4941 5873 4689 6106 4995 4734 5872 3570 3788 21004 12610 4890 5802 0.67	3.72 4.28 3.97 4.75 4.21 2.49 3.89 3.11 1.59 3.90 0.91 1.45 3.14 4.20 2.42 0.99 -1.60	-0.51 0.06 -0.03 -0.02 -0.82 -0.03 0.20 -0.76 -1.68 0.30 0.03 -0.08 0.05 0.30 -0.57 0.17 c	b b b c b c b b c b c c b b b b 1, 7
	927	4 67 130 191 258 316 378 436 497 557 615 675 738 803 871 939	HD000004 HD010700 HD023841 HD038393 BD+241676 HD074377 HD088986 HD106516 HD123657 HD137704 HD151217 HD168723 HD187691 HD204543 HD219734 HD170820 M5 II-51 5718	6779 5348 4306 6316 6230 4674 5766 6207 3408 4044 3878 4923 6099 4590 3665 4499 1.98	3.87 4.39 2.05 4.23 3.81 4.47 4.04 4.25 0.66 1.74 1.59 3.0 4.12 1.17 0.99 1.44 -1.29	0.21 -0.46 -0.66 -0.09 -2.55 -0.37 0.04 -0.69 -0.05 -0.47 0.05 -0.22 0.14 -1.97 -0.04 0.03 c	b b c b b b b b c c c b b c c c 6, 7
	929	5 69 131 192 259 317 379 437 498 558 616 676 739 804 872 940	HD000249 HD010780 HD023924 HD038007 HD059984 HD074721 HD089010 HD107113 HD123821 HD137909 HD152601 HD168608 HD187921 HD204587 HD219916 NGC6791-R4 M5 II-53 9441	4731 5406 7776 5705 5973 8900 5642 6543 4900 8466 4661 5580 5502 4111 5070 3382 2.43	2.83 4.63 3.94 3.98 4.07 3.38 3.80 4.19 2.28 4.06 2.67 1.00 0.68 4.61 2.84 0.20 -1.11	-0.31 0.15 0.07 -0.31 -0.68 -1.32 0.00 -0.42 -0.13 0.96 0.10 0.03 0.10 -0.11 -0.04 0.42 a	c b b b b b b b b b c b b c b c 1, 6
	931	6 70 132 193 260 318 380 438 499 559 617 677 741 805 874 941	HD000319 HD010975 HD024616 HD038545 HD059881 BD-122669 HD089254 HD107213 HD124186 HD138290 HD152781 HD170693 HD188650 HD205435 HD220009 NGC6791-R5 M5 IV-86 5576	8641 4843 5014 8673 7623 6800 7166 6209 4384 6822 4969 4396 5764 5069 4296 3193 2.44	4.29 2.44 3.16 3.68 3.64 4.10 3.83 4.00 2.56 4.14 3.55 2.1 2.90 2.86 1.90 1.12 -1.11	-0.35 -0.23 -0.71 -0.48 0.15 -1.50 0.31 0.24 0.27 -0.10 0.08 -0.49 -0.40 -0.12 -0.80 0.42 a	b c b b b b b b c b b c a b c c 1, 6
	932	7 71 133 194 261 319 381 439 500 560 618 679 742 806 875 942	HD000400 HD011257 HD024341 HD038751 HD060219 HD074462 HD089449 BD+172473 HD124292 HD138481 HD153286 HD170737 HD188510 HD205153 HD220575 NGC6791-R16 M5 IV-87 5965	6190 7103 5405 4776 5900 4747 6467 5283 5398 3898 7534 5093 5539 6005 12241 3890 3.80	4.15 4.08 3.71 2.71 1.83 1.83 4.11 3.37 4.35 1.25 3.75 3.36 4.28 4.02 4.09 1.81 -1.11	-0.22 -0.27 -0.62 0.11 -0.49 -1.40 0.11 -1.04 -0.11 -0.07 0.49 -0.77 -1.43 0.07 0.27 0.42 b	b b b c a c b b b c b b b b b c 1, 6
	950	8 72 134 195 262 320 382 440 502 561 619 681 743 807 876 943	HD000245 HD011397 HD024421 HD038656 HD060179 HD075318 HD089484 BD+312360 HD124850 HD139669 HD153882 HD171391 HD188512 HD205512 BD+592723 NGC6791-R19 M71 KC-147 4819	5749 5526 6168 4943 9550 5432 4381 4716 6207 3930 9999 5150 5082 4703 5987 3904 2.57	4.13 4.24 4.20 2.55 3.83 4.48 1.79 2.44 3.86 1.44 3.50 2.89 3.48 2.57 3.98 1.95 -0.84	-0.57 -0.58 -0.29 -0.15 -0.13 -0.13 -0.50 -0.79 -0.06 0.12 0.61 0.04 -0.22 0.03 -1.89 0.42 b	b b b b b b c c b c b b b c b c 1, 7
	957	9 73 135 196 263 321 383 441 503 562 620 682 745 808 877 944	HD000448 HD011964 HD024451 HD039364 LHS1930 HD075691 HD089707 HD108177 HD125184 HD138776 HD154733 HD171443 HD188947 HD206078 HD220825 M71 A9 M71 1-63	4706	4770 5272 4418 4660 5420 4299 5937 6278 5536 5524 4227 4220 4828 4741 10228 4404 1.62	2.61 3.85 4.57 2.46 4.33 2.10 4.25 4.19 3.85 3.99 2.20 2.04 2.62 2.54 3.71 1.41 -0.78	0.02 0.05 -0.09 -0.74 -1.11 -0.16 -0.47 -1.41 0.24 0.35 -0.09 -0.10 0.06 -0.59 0.78 -0.78 c	c b c c b c b b b b c c b c b c 6, 7
	961	10 75 136 197 264 322 384 442 504 563 621 683 746 809 878 945	BD+130013 HD012438 HD025329 HD039853 HD060522 HD075732 HD089744 HD108564 HD125451 HD138764 HD155763 HD171496 HD189005 HD206165 HD220933 M71 1-109 M71 1-09 4784	5000 4937 4964 3858 3834 5260 6169 4634 6700 14054 12500 4933 5080 19300 10515 4759 2.01	3.00 2.35 4.60 1.58 1.54 4.35 3.93 4.67 4.12 3.88 3.50 2.29 2.32 2.65 3.72 2.33 -0.78	-0.75 -0.73 -1.58 -0.61 -0.02 0.43 0.18 -1.00 0.01 0.08 -0.11 -0.73 -0.26 -0.27 -0.06 -0.78 c	b b c c c b b c b b b c b b b c 6, 7
	963	11 76 137 198 265 323 385 443 505 564 622 684 747 810 879 946	HD000886 HD013043 HD025532 HD039833 HD061064 HD076151 HD089995 HD108915 BD+012916 HD139195 HD155358 HD171999 HD189558 HD206952 HD220954 M71 1-95 M71 1-34 5114	20454 5823 5600 5869 6646 5748 6472 5037 4375 4946 5888 5276 5770 4643 4784 4570 2.35	3.79 4.11 2.50 4.39 3.69 4.42 4.08 3.32 0.77 2.64 4.09 4.35 3.92 2.61 2.61 1.63 -0.84	-0.03 0.06 -1.35 0.18 0.27 0.15 -0.24 -0.10 -1.86 -0.13 -0.63 0.27 -1.04 0.15 0.06 -0.78 b	b b b b b b b b c b b b b c c c 1, 7
	967	12 77 138 199 266 324 386 444 506 565 623 685 748 811 880 947	HD001326b BD+290366 HD025673 HD039801 BD-011792 HD076292 HD089822b HD109443 HD126141 HD139641 HD155078 HD172380 HD189849 HD206453 HD221170 M71 1-107 M71 1-77 4261	3571 5666 5112 3666 5131 6958 10182 6758 6699 4945 6508 3364 7804 5026 4608 4848 1.87	4.81 4.25 4.54 0.20 3.38 3.88 3.85 4.17 4.14 2.82 4.00 0.42 3.89 2.34 1.29 2.07 -0.22	-0.57 -0.95 -0.40 0.07 -0.81 0.16 0.07 -0.60 -0.05 -0.51 0.03 -0.06 -0.01 -0.41 -2.05 -0.84 c	7	d b b c b b b b b b b c b b c b
	970	13 78 139 200 267 325 387 445 507 566 625 686 749 812 881 948	HD001461 HD013267 HD026297 HD039970 HD061606 HD076932 HD090508 HD109871 HD126053 HD139446 HD156026 HD172103 HD190360 HD207130 HD221148 M71 1-75 M71 X	3980	5666 15500 4497 12006 4890 5908 5776 3979 5598 5065 4381 6815 5468 4741 4588 4809 1.43	4.21 2.57 1.11 2.13 4.67 4.09 4.31 1.77 4.22 2.65 4.66 4.01 4.11 2.65 3.19 2.52 -0.84	0.19 -0.10 -1.79 0.19 0.05 -0.82 -0.30 -0.15 -0.37 -0.27 -0.28 0.03 0.21 0.08 0.34 -0.78 b	1	b b c b b b b b b b c b b c c c
		14 79 141 201 268 326 388 446 509 567 626 687 750 813 882 949		HD001918 HD013555 HD026322 HD040657 HD061772 HD076780 HD237903 HD109995 HD126218 HD140160 HD157373 HD172365 HD190404 HD206826 HD221345 M71 1-73		4888 6515 7008 4264 4096 5704 4106 8550 5137 9557 6552 5886 5008 6490 4662 4800	2.44 4.07 3.94 1.81 1.46 4.28 4.64 2.39 2.70 3.66 4.18 1.28 4.51 4.09 2.33 2.22	-0.40 -0.16 0.13 -0.73 -0.04 0.18 -0.16 -1.66 0.24 0.35 -0.43 0.05 -0.58 -0.11 -0.34 -0.78		b b b c c b c b b b b b b b c c
		15 80 143 202 269 327 389 447 510 568 627 688 752 816 883 951		HD002628 HD013520 HD284248 HD250792 HD061603 BD-052678 HD091347 HD110014 HD126660 HD140283 HD157214 HD172958 HD190178 HD207076 HD221377 M71 1-71		7335 4023 6113 5554 3953 5492 5887 4425 6293 5687 5621 11464 6263 3022 6553 4397	3.95 1.61 4.14 4.33 1.43 3.85 4.26 2.34 4.13 3.55 4.05 3.97 4.05 0.74 4.20 1.80	-0.09 -0.27 -1.55 -1.01 0.19 -2.02 -0.44 0.25 0.02 -2.53 -0.41 0.02 -0.66 -0.12 -0.60 -0.78		b c b b c b b c b a b b b c b c
		16 81 144 203 270 328 390 448 511 569 628 689 753 817 885 952		HD002665 BD-010306 BD-060855 HD041312 HD061935 HD076910 HD091889 HD110379 HD126614 BD+053080 HD157089 HD173524 HD190390 HD207330 HD221756 M71 KC-263	4986 5723 5442 4044 4802 6397 6109 6857 5399 5034 5792 11323 6440 20815 8833 4883	2.28 4.28 4.60 1.77 2.57 4.23 4.16 4.17 4.02 4.46 4.05 3.93 1.55 3.69 4.21 2.61	-1.96 -0.89 -0.69 -0.75 -0.06 -0.51 -0.21 -0.19 0.52 -0.44 -0.57 0.10 -1.05 0.04 -0.64 -0.84		b b b c c b b b b b b b a b b a
		17 82 145 205 271 329 391 449 512 570 629 690 754 818 886 953		HD002796 HD013783 HD026965 HD251611 HD061913 BD-032525 HD092523 HD110897 HD126778 HD141004 HD157910 HD173740 HD191026 HD207222 HD221830 M71 1-87		4837 5516 5114 5382 3568 5869 4112 5851 4832 5823 5227 3311 5177 9230 5719 4988	1.78 4.37 4.41 3.40 0.55 4.09 1.77 4.28 2.41 4.10 2.58 5.01 3.81 4.01 4.09 2.19	-2.23 -0.49 -0.26 -1.44 0.06 -1.60 -0.43 -0.53 -0.52 -0.03 -0.07 -0.34 0.08 -0.36 -0.40 -0.84		b b b b c b c b b b b c b b b b
		18 83 146 206 272 331 392 450 513 571 630 691 755 821 887 954		HD002857 HD014221 HD285690 HD041692 BD+002058a HD077338 HD093329 HD110885 HD126681 HD141714 HD157881 HD172816 HD191046 HD208906 HD222404 M71 1-66	8000 6619 4971 14800 6096 5300 8400 5545 5577 5332 4023 3318 4438 6048 4758 4250	2.70 4.07 4.70 3.30 4.17 4.30 3.10 2.99 4.25 3.22 4.64 0.72 1.67 4.27 3.16 1.65	-1.50 -0.17 0.18 -0.01 -1.22 0.36 -1.20 -1.06 -1.12 -0.20 -0.01 -0.14 -0.75 -0.68 0.10 -0.78		b b c b b b b b b b c c c b c c
		19 84 147 207 273 332 393 451 514 572 631 692 756 822 888 955		HD003008 HD014802 HD027126 HD041636 HD062345 HD077236 HD093487 HD112028 HD127243 HD141851 HD157856 HD173093 HD192907 HD209369 HD222368 M71 1-65		4364 5777 5425 4688 5029 4343 5215 9443 4903 8246 6523 6373 10444 6632 6231 4664	0.68 3.89 4.14 2.42 2.61 1.89 2.41 2.88 2.27 3.89 4.04 4.11 3.97 4.06 4.14 1.98	-1.83 -0.07 -0.38 -0.29 -0.01 -0.89 -1.06 -0.39 -0.78 -2.00 -0.07 0.00 -0.18 -0.04 -0.08 -0.78		c b b c b c b b b a b b b b b c
		20 85 148 208 274 333 394 452 515 573 632 693 757 823 889 956		HD003369 HD014829 HD027295 HD042182 HD062301 HD078541 HD094028 HD111631 HD127334 HD142373 HD157919 HD173648 HD345957 HD209459 HD222451 M71 1-64		16005 8750 11034 5041 5933 3917 6076 3908 5579 5783 6826 7914 5988 11015 6698 4504	3.71 3.15 3.99 4.63 4.12 1.45 4.23 4.67 4.10 3.93 3.61 3.70 4.06 3.99 4.07 1.64	0.04 -1.57 -0.11 0.13 -0.62 -0.37 -1.30 0.02 0.20 -0.54 0.29 0.38 -1.20 -0.07 0.10 -0.78		b b b b b c b c b b b b b b b c
		21 86 149 209 275 334 395 453 516 574 633 694 759 824 891 958		HD003360 HD014938 HD027371 HD041597 HD062721 HD078234 BD-103166 HD111786 BD+182890 HD142575 BD+233130 HD173650 HD192640 HD209975 HD223047 M71 1-21	20375 6275 4995 4607 3913 6976 5329 8080 5024 6779 5017 11832 8774 32983 5002 4486	3.80 4.22 2.76 2.01 1.81 4.04 4.38 3.88 2.31 4.23 2.31 3.71 4.42 3.40 1.26 1.40	-0.04 -0.25 0.15 -0.54 -0.36 -0.06 0.42 -1.50 -1.54 -0.70 -2.45 0.64 -0.80 0.06 0.04 -0.78		b b b c c b b b b b b b b b b c
		22 88 150 211 276 335 396 454 517 575 634 695 760 825 893 959		HD003567 HD015798 HD027771 HD042543 HD063302 HD078558 HD095128 HD111980 HD128167 HD142908 HD159332 HD173667 HD192909 HD210295 HD223524 M71 1-37		6094 6527 5285 3707 4264 5651 5852 5876 6777 7038 6298 6458 3942 4864 4560 4576	4.18 4.07 4.59 0.17 0.12 4.06 4.24 4.04 4.18 3.98 4.01 4.04 0.91 2.30 2.41 2.12	-1.14 -0.12 0.27 0.18 0.12 -0.45 0.02 -1.02 -0.39 -0.02 -0.10 0.01 -0.02 -1.26 0.02 -0.78		b b b c c b b b b b b b c c c c
		23 89 151 213 277 336 397 455 518 576 635 696 761 826 894 960		HD003546 HD016031 HD027819 HD043318 HD063352 HD078209 HD095578 HD112127 HD128429 HD142860 HD159307 HD175305 HD193281 HD210424 HD223640 M71 1-41		4945 6039 7871 6330 4149 7519 3849 4384 6427 6309 6395 5036 8597 12771 12429 5020	2.36 4.09 3.89 4.04 1.71 3.77 1.26 2.46 4.22 4.18 4.19 2.51 4.11 4.21 3.93 2.26	-0.66 -1.63 -0.06 -0.07 -0.60 0.55 -0.01 0.22 -0.08 -0.16 -0.54 -1.44 -0.37 0.22 0.73 -0.84		b b b b c b c c b b b b b b b b
		24 90 152 214 278 337 398 456 519 577 636 697 762 827 895 962		HD003574 HD016234 HD028305 BD+371458 BD-182065 HD078737 HD095735 HD112413 HD128801 HD142703 HD159482 HD173819 HD194598 HD210745 HD224458 M71 1-39	4019 6225 4964 5450 4878 6550 3454 12303 10200 6903 5740 4392 6090 4286 4809 5020	1.13 4.18 2.72 3.38 2.43 4.19 4.78 4.09 3.50 4.32 4.11 -0.25 4.24 0.65 2.27 2.26	0.01 -0.19 0.20 -2.12 -0.71 -0.46 -0.27 0.90 -1.40 -1.10 -0.75 -0.67 -1.04 0.11 -0.44 -0.84		c b b b c b c b b b b c b c c b
		25 91 153 215 279 338 399 457 520 578 637 698 763 828 896 964		HD003651 HD016232 HD285773 HD043380 HD064332 HD078732 BD+442051a HD113092 CD-2610417 HD143459 HD160933 HD174567 HD194943 HD210595 BD+612575 M71 1-53	5211 6314 5348 4521 3515 4939 3628 4269 4625 10498 5770 10256 6971 6639 6222 4167	4.48 4.29 4.56 2.40 0.19 2.27 4.87 1.47 4.62 4.00 3.79 3.95 4.04 4.11 1.97 1.51	0.21 0.11 0.25 -0.05 -0.11 -0.07 -0.48 -0.81 -0.21 -0.39 -0.31 -0.07 -0.01 -0.47 0.35 -0.84		b b b c c b c c c b b b b b a a
		26 92 154 216 280 339 400 458 521 579 638 699 764 829 897 965		HD003795 HD016673 HD028946 HD044007 HD064090 HD079211 HD096360 HD113022 HD128959 HD143761 HD160762 HD174912 HD196502 HD210705 NGC288-77 M71 KC-169	5345 6260 5314 4987 5405 3846 3471 6491 5857 5752 17678 5936 9417 6939 4238 5083	3.72 4.30 4.55 2.33 4.19 4.63 0.80 4.09 3.84 4.13 3.69 4.34 3.58 4.16 1.12 2.22	-0.63 0.00 -0.10 -1.53 -1.65 -0.17 0.00 0.11 -0.51 -0.26 0.02 -0.45 0.74 -0.18 -1.32 -0.84		b b b b b c c b b b b b b b c b
		27 93 155 217 281 340 401 460 522 580 639 700 765 830 898 966		HD003883 HD016784 HD028978 HD043378 HD063791 HD079452 BD+362165 HD114038 HD129174 MS1558.4-2232 HD160693 HD175225 HD195633 HD211075 HD020902 M71 A2	7616 5782 8864 9284 4822 4982 6144 4567 12052 4250 5691 5286 6119 4318 6690 4679	3.81 4.08 3.42 4.05 1.94 2.31 4.18 2.33 3.99 3.50 4.07 3.70 4.09 1.84 1.31 2.21	0.68 -0.68 -0.26 -0.27 -1.62 -0.79 -1.45 -0.02 0.18 0.10 -0.56 0.20 -0.52 -0.42 -0.05 -0.84		b b b b c b b c b a b b b c b b
		28 94 156 218 282 341 402 461 523 581 640 701 766 831 899 968		HD004307 BD+460610 HD029065 HD043947 HD064606 HD079765 HD097560 HD114330 HD130095 HD143807 HD161074 HD174959 HD195838 HD212454 Mel22 0296 M71 1-78	5773 5889 4034 5983 5302 7146 5328 9570 8900 10727 3949 14681 6152 14466 5196 3955	3.97 4.13 1.69 4.28 4.42 4.11 2.69 3.95 3.35 3.84 1.86 4.00 4.08 3.33 4.25 1.48	-0.24 -0.86 -0.35 -0.27 -0.76 -0.26 -1.04 -0.13 -1.70 -0.01 -0.14 -0.80 0.00 0.35 -0.03 -0.78		b b c b b b b b b b c a b b b c
		30 95 157 219 283 342 403 462 524 582 641 702 767 832 900 969		HD004539 G004-036 HD029139 HD044030 HD064488 HD079633 HD097633 HD114606 HD130322 HD144172 HD161149 HD174704 HD196544 HD212943 Mel22 2462 M71 S		25000 6073 3851 4026 8837 7223 9201 5584 5391 6432 7015 7193 8678 4634 5219 4244	5.40 4.20 1.62 1.75 3.65 4.06 3.68 4.15 4.52 4.14 3.70 3.63 3.80 2.62 4.47 1.28	0.00 -1.66 -0.13 -0.51 -0.36 -0.26 -0.16 -0.53 0.12 -0.38 0.33 0.79 -0.12 -0.31 -0.03 -0.78		b b c c b b b b b b b b b c b c
		31 96 158 222 284 343 404 463 525 583 642 703 768 833 901 971		HD004628 HD016901 BD+501021 HD045282 HD065228 HD080390 HD097907 HD114710 HD130817 HD144872 HD161096 HD175535 HD196755 HD213119 HD025825 M71 I	4964 5345 5081 5309 5861 3366 4307 5994 6749 4785 4497 5197 5582 3914 6005 4222	4.65 0.85 4.48 3.19 1.24 0.53 2.16 4.35 4.14 4.76 2.49 2.85 3.64 1.42 4.38 1.43	-0.23 0.00 -0.65 -1.42 0.06 -0.10 -0.19 0.05 -0.29 -0.29 0.20 -0.07 -0.02 -0.14 0.13 -0.78		b a b b b c c b b c c b b c b c
		32 97 159 223 285 344 405 464 526 584 644 704 769 835 902 972		HD004656 HD017081 BD+450983 HD045829 HD065583 HD081009 HD097916 HD114642 HD130705 HD144585 HD161227 HD175588 HD197177 HD213042 HD026736 NGC7789-329(491)	3934 12722 5155 4499 5281 8829 6478 6491 4375 5767 7320 3484 4964 4505 5772 4527	1.67 4.20 4.45 0.56 4.33 3.79 4.28 4.04 2.56 4.09 3.72 0.47 1.92 4.49 4.39 2.14	-0.13 0.28 -0.22 0.11 -0.65 0.84 -0.73 -0.04 0.34 0.29 0.38 -0.14 -0.03 0.12 0.13 -0.13		c b b c b b b b c b b c b c b a
		33 98 160 224 286 345 406 465 527 585 645 705 770 837 903 973		HD004744 HD017361 HD030743 HD046341 HD065714 HD081029 HD097855 HD114946 HD130694 HD144608 HD161695 HD175865 HD197572 HD214080 HD284253 NGC7789-468(589)	4590 4630 6484 5835 4983 6714 6416 4999 4093 5363 11506 3316 5188 23445 5283 4167	2.32 2.53 4.16 4.28 2.50 4.14 4.18 3.12 1.74 2.62 2.23 0.36 0.83 3.28 4.47 1.75	-0.74 0.02 -0.34 -0.66 0.18 -0.08 -0.39 -0.36 -0.77 0.03 0.11 0.06 0.15 0.04 0.13 0.01		c c b b b b b b c b b c b b b c
		34 99 161 225 287 346 407 466 528 586 646 706 771 839 904 974		HD004906 HD017491 HD030504 HD047205 HD065953 HD081192 HD098468 HD115383 HD131430 HD145148 HD161797 HD175640 HD197461 HD214567 HD027383 NGC7789-342(502) 10968 5157 3258 4022 4728 3986 4745 4528 6047 4287 4868 5454 12077 7334 4997 6091	3.58 0.65 1.75 3.10 1.73 2.57 2.06 4.24 2.19 3.65 3.82 3.94 4.02 2.62 4.34 3.85	-0.66 -0.15 -0.50 0.19 -0.34 -0.76 -0.36 0.17 0.09 0.10 0.22 0.17 -0.07 -0.23 0.13 -0.13		b c c c c c b b c b b b b b b b
		35 100 162 226 288 348 408 467 529 587 647 707 772 840 905 975		HD005268 HD017382 HD030649 HD046703 HD065900 BD+092190 HD098553 HD115589 HD132142 HD145675 HD161817 HD178089 HD198149 HD214714 HD027524 NGC7789-353(509)	4904 5339 5791 6250 9235 6270 5832 5227 5163 5270 7636 6722 4970 5224 6580 4538	2.35 4.64 4.21 1.00 3.69 4.11 4.27 4.39 4.38 4.31 2.93 4.07 3.29 2.03 4.14 2.30	-0.57 0.17 -0.48 -1.50 -0.16 -2.86 -0.44 0.28 -0.37 0.48 -0.95 -0.09 -0.19 -0.67 0.13 0.01		b b b b b a b b b b a b b b b c
		36 101 163 227 289 349 409 468 530 588 648 708 773 841 906 976		HD005384 HD017548 HD031128 HD047914 HD066141 HD082074 HD099109 HD115617 HD131918 HD145250 HD162211 HD175892 HD197989 HD214994 HD027561 NGC7789-415(550)	3933 6013 5949 3938 4265 5090 5242 5539 4118 4530 4486 8705 4728 9373 6682 3815	1.79 4.20 4.18 1.79 1.98 3.21 4.29 4.35 1.56 2.28 2.45 4.11 2.44 3.73 4.14 1.16	0.18 -0.53 -1.45 0.04 -0.51 -0.43 0.40 0.02 -0.10 -0.33 -0.06 -0.29 -0.20 -0.14 0.13 0.01		c b b c c b b b c c c b c b b c
		37 102 164 228 290 350 410 469 531 589 649 709 775 843 907 977		HD005395 HD017378 HD030959 HD048329 HD066573 HD082590 HD233832 HD115659 HD131976 HD145976 BD+203603 HD176301 HD198183 HD215648 HD027962 NGC7789-461(583)	4845 8477 3562 4496 5680 6669 4970 5104 3541 6927 6115 12667 15630 6243 8809 4123	2.45 1.25 0.37 0.75 4.26 4.22 4.49 2.64 4.72 4.08 4.10 4.18 3.81 4.03 3.80 1.75	-0.43 0.00 -0.09 0.08 -0.58 -0.81 -0.59 0.04 -0.14 -0.02 -2.10 0.18 0.05 -0.21 0.13 0.01		c b c c b b b b c b b b b b b c
		38 103 165 229 291 351 411 470 532 590 650 710 776 844 908 978		HD005780 HD018191 HD030834 HD048433 HD067523 HD082734 HD099648 HD116114 HD131977 HD146051 HD164058 HD176232 HD198001 HD216228 HD028483 NGC7789-501(614)	3917 3199 4194 4464 6810 4906 4977 8226 4501 3779 3963 8743 9266 4745 6455 4057	1.64 0.78 1.61 2.01 3.59 2.56 2.24 4.10 4.59 1.46 1.51 4.47 4.00 2.49 4.25 1.69	-0.71 -0.05 -0.35 -0.22 0.60 0.20 -0.03 0.67 -0.05 -0.15 0.07 0.53 -0.32 -0.03 0.13 0.01		c c c c b c b b c c c b b c b c
		39 105 166 230 292 352 412 471 533 591 651 711 777 845 909 979		HD005916 HD018907 HD031295 BD+151305 HD067228 HD082210 HD099747 HD116316 HD132345 HD147379b HD163990 HD176437 BD+044551 HD216174 HD028546 NGC7789-575(671)	4954 5069 8822 4901 5732 5445 6738 6487 4403 3873 3318 11226 6089 4371 7490 4547	2.31 3.43 4.11 4.66 3.84 3.64 4.19 4.26 2.54 4.68 0.48 4.11 4.21 1.82 3.85 2.18	-0.75 -0.65 -0.73 0.11 0.12 -0.10 -0.46 -0.51 0.31 0.06 -0.04 0.09 -1.26 -0.61 0.13 0.01		b b b b b b b b c c c b b c b c
		40 106 167 231 293 353 413 472 534 592 652 712 778 846 910 980		HD006186 HD019445 HD031767 HD048565 BD+800245 HD082885 HD099998 HD116544 HD132475 HD146624 HD163993 HD177463 HD198478 HD216131 HD029375 NGC7789-637(723)	4865 5900 4367 6030 5509 5520 3979 4417 5823 9125 5091 4611 16500 4999 7240 4857	2.36 4.20 1.50 3.94 3.74 4.41 1.53 3.31 3.93 3.99 2.87 2.30 2.17 2.70 3.93 2.54	-0.35 -2.07 -0.02 -0.63 -1.85 0.40 -0.37 0.15 -1.37 -0.27 0.09 -0.23 -0.21 -0.07 0.13 0.01		b b c b b b c c b b b c b b b c
		41 108 168 232 294 354 414 473 535 593 653 713 779 847 911 981		HD006203 HD019373 HD032147 HD048682 HD068284 HD083212 HD100906 HD117200 HD132933 HD147923 HD164136 HD180711 HD199191 HD216143 HD030034 NGC7789-765(804)	4506 5947 4650 6088 5945 4472 5042 6843 3797 4787 7140 4837 4696 4638 7446 4397	2.20 4.15 4.58 4.28 3.97 0.99 2.31 4.02 1.30 4.76 3.87 2.49 2.53 1.38 3.91 2.07	-0.41 0.11 0.16 0.11 -0.52 -1.64 -0.46 0.03 -0.71 -0.28 0.00 -0.18 -0.70 -2.09 0.13 0.01		c b c b b c b b c c b b c c b c
		42 109 169 233 295 355 415 474 536 594 654 714 781 848 912 982		HD006268 HD019994 HD032655 HD049161 HD069267 HD081817 HD101227 HD117176 HD133124 BD-114126 HD164349 HD179761 HD199799 HD216219 HD030210 NGC7789-859(853)	4571 6051 7114 4168 4068 4168 5534 5467 4006 4702 4594 12746 3387 5637 7694 4666	1.13 4.02 3.47 1.82 1.49 1.40 4.52 3.86 1.76 4.62 1.74 4.22 0.12 3.10 3.66 2.53	-2.63 0.16 0.23 0.17 -0.19 0.15 -0.32 -0.10 -0.01 0.00 -0.01 0.30 -0.25 -0.36 0.13 0.01		c b b c c c b b c b c b c b b c
		43 110 170 234 296 356 416 475 537 595 655 715 782 849 913 983		HD006229 HD020041 HD033256 HD049331 HD069611 HD083425 HD101501 HD117635 BD+062986 HD148112 HD164353 HD180163 HD200527 HD216385 HD030676 NGC7789-875(873)	5181 11509 6477 3830 5773 4150 5535 5175 3965 10052 15600 18663 3503 6323 6104 4861	2.50 2.01 4.15 0.44 4.09 1.99 4.52 4.48 4.59 3.51 2.55 3.69 0.20 4.06 4.37 2.56	-1.14 0.23 -0.27 0.13 -0.58 -0.47 0.03 -0.42 -0.42 0.47 -0.03 0.04 -0.07 -0.15 0.13 -0.13		b b b c b c b b c b b b c b b b
		46 111 171 235 297 357 417 476 538 596 656 716 783 850 914 984		HD006582 HD020512 HD033276 HD049933 HD069830 HD083618 HD101606 HD117876 BD+302611 BD+090352 HD164432 HD181096 HD200580 HD217382 HD031236 NGC7789-897(881)	5323 5267 7223 6647 5412 4244 6362 4688 4400 6131 21371 6347 6003 4105 7262 4918	4.33 3.81 3.80 4.19 4.49 1.88 4.13 2.26 1.04 4.04 3.81 4.03 4.34 1.96 3.93 2.50	-0.79 -0.13 0.22 -0.45 0.04 -0.20 -0.57 -0.51 -1.45 -1.88 -0.02 -0.17 -0.50 0.09 0.13 -0.13		b b b b b c b c c b b b b c b b
		47 112 172 236 298 358 418 479 539 597 657 717 784 851 917 985		HD006805 HD020619 HD293857 HD050778 HD233511 HD083632 HD102224 HD118244 HD134063 HD148513 HD165195 HD180928 HD200905 HD216640 M79 223 NGC7789-971(946)	4505 5710 5628 4009 6005 4167 4455 6391 4880 4114 4391 4024 3977 4612 4170 3746	2.48 4.47 4.38 1.77 4.13 1.41 2.02 4.19 2.31 2.16 0.75 1.79 0.79 3.11 0.68 1.22	0.07 -0.18 0.10 -0.43 -1.52 -0.85 -0.40 -0.46 -0.69 0.19 -2.32 -0.66 0.10 0.17 -1.60 0.01		c b b c b c c b b c c c c c c c
		48 113 173 237 299 359 419 480 540 598 658 718 785 852 918		HD005848 HD020630 HD033608 HD050420 HD069897 HD233666 BD+511696 BD+302431 HD134083 BD+112998 HD164975 HD181470 HD200779 HD216831 NGC2420-140	4451 5733 6461 7319 6328 5161 5656 16904 6573 5527 5863 9802 4225 13207 4421	2.25 4.45 4.03 3.75 4.18 2.42 4.28 4.20 4.17 2.97 1.22 3.91 4.59 3.05 1.90	0.09 0.12 0.21 0.11 -0.23 -1.62 -1.30 0.77 -0.01 -1.01 0.06 -0.13 0.02 0.05 -0.31		c b b b b b b a b b b b c b c
		49 114 174 238 300 360 420 481 541 599 659 719 786 854 919		HD006834 HD020893 HD034538 HD051440 HD070272 HD083506 HD102328 HD119228 HD134169 HD148816 HD165341 HD182293 HD200790 HD217014 M67 F-108		6482 4363 4870 4313 3921 4875 4380 3705 5807 5828 5349 4437 6115 5674 4235	4.22 2.26 2.96 1.72 1.46 2.36 2.56 1.06 3.99 4.05 4.58 2.74 3.98 4.14 2.21	-0.58 0.07 -0.36 -0.66 -0.06 0.12 0.28 -0.10 -0.81 -0.72 0.16 -0.02 0.02 0.18 0.00		b c b c c c c c b b b c b b c
		50 115 175 239 301 361 421 482 542 600 660 721 787 855 920		HD006755 BD+430699 MS0515.4-0710 HD052005 HD071030 HD084441 HD102634 HD119288 HD134440 HD148897 HD165438 HD182572 HD201078 HD217107 HD107276	5097 4736 5206 4071 6541 5398 6281 6595 4955 4278 4868 5473 6151 5523 7969	2.53 4.72 4.41 0.66 4.03 2.02 4.15 4.18 4.70 0.99 3.43 3.91 1.85 4.11 3.99	-1.58 -0.38 0.05 0.08 -0.15 -0.06 0.22 -0.23 -1.34 -1.20 0.02 0.34 0.09 0.33 -0.05		b c c c b b b b c c b b b b b
		51 116 176 240 302 362 422 483 543 601 661 722 788 856 921		HD006833 HD021017 HD034411 HD052973 HD072184 HD084737 HD102870 HD119291 HD134439 HD150275 HD165908 HD183324 HD201091 HD217754 HD107513		4502 4419 5842 5657 4606 5872 6081 4295 5172 4622 6045 10325 4162 7089 7360	1.78 2.67 4.16 1.12 2.87 4.05 4.07 4.57 4.68 2.40 4.19 4.17 4.64 3.80 3.99	-0.84 0.07 0.08 0.09 0.18 0.12 0.14 0.04 -1.27 -0.70 -0.50 -1.24 -0.31 0.27 -0.05		c c b b c b b c b c b b c b b
		52 117 177 241 303 363 423 484 544 602 662 723 789 857 922		HD007106 HD021197 HD035155 HD053927 HD072324 HD084937 HD103095 HD119667 HD134987 HD148786 HD166208 CD-2415398 HD201601 HD218031 HD109307	4678 4376 3637 4911 4881 6211 5165 3740 5623 5144 5107 6269 7657 4713 8162	2.55 4.50 0.09 4.71 2.43 4.00 4.74 0.89 4.09 2.70 2.73 2.93 3.92 2.42 3.91	-0.02 0.13 -0.53 -0.28 0.00 -2.05 -1.21 -0.11 0.26 0.21 0.15 -1.17 0.07 -0.17 -0.05		c c c b b b b c b b b b a c b

A comprehensive list has been maintained over the years by David Montes, see https://webs.ucm.es/info/Astrof/invest/ actividad/spectra.html

https://www.iau.org/science/scientific_bodies/working_ groups/306/

Semi-empirical models are still based on theoretical prescriptions for stellar evolution.MNRAS 000, 1-37(2018)

As made available by F. Castelli; downloaded on April 29 2016 from http://wwwuser.oats.inaf.it/castelli/odfnew.html

Available at http://marcs.astro.uu.se

As made available by R. Kurucz; downloaded on Dec 2016 from http://kurucz.harvard.edu/molecules.html MNRAS 000, 1-37 (2018)

MNRAS 000, 1-37 (2018)

This star shows unusually strong molecular bands and is classified as a peculiar star in the SIMBAD Database.

All SPS models were computed for theChabrier (2003) IMF.

The C14 spectra were convolved, rebinned and trimmed to match the resolution, dispersion and wavelength range of MILES.MNRAS 000, 1-37(2018)

ACKNOWLEDGEMENTS

PC acknowledges support from Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq 310041/2018-0). PC and GB acknowledge support from Fundação de Amparo à Pesquisa do Estado de São Paulo through projects FAPESP 2017/02375-2 and 2018/05392-8. PC and SC acknowledge support from USP-COFECUB 2018.1.241.1.8-40449YB. GB acknowledges financial support from the National Autonomous University of Mexico (UNAM) through grant DGAPA/PAPIIT IG100319 and from CONACyT through grant CB2015-252364.

PC thanks A. Ederoclite for his patience and support during the development of this work. PC thanks P. Prugniel for innumerous discussions about stellar parameters and spectra, and for providing his derived E(B-V) values for MILES spectra. The authors thank P. Sánchez-Blázquez for providing the error spectra for MILES, and R. Peletier for providing information on caveats on some MILES spectra.

Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administra-