Astronomy & Astrophysics manuscript no. firefly-dr14-sdss-boss_arxiv c©ESO 2017November 20, 2017

Stellar population properties for 2 million galaxies from SDSSDR14 and DEEP2 DR4 from full spectral fitting

Johan Comparat1, Claudia Maraston2, Daniel Goddard2, Violeta Gonzalez-Perez2, Jianhui Lian2, SofiaMeneses-Goytia2, Daniel Thomas2, Joel R. Brownstein3, Rita Tojeiro4, Alexis Finoguenov1, Andrea Merloni1,

Francisco Prada5, Mara Salvato1, Guangtun B. Zhu6, Hu Zou7, and Jonathan Brinkmann8

1 Max-Planck-Institut für extraterrestrische Physik (MPE), Giessenbachstrasse 1, D-85748 Garching bei München, Germanye-mail: comparat@mpe.mpg.de

2 Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth, PO1 3FX, UK

3 Department of Physics and Astronomy, University of Utah, 115 S. 1400 E., Salt Lake City, UT 84112, USA

4 School of Physics and Astronomy, North Haugh, St. Andrews KY16 9SS, UK

5 Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la Astronomía, E-18080 Granada, Spain

6 Center for Astrophysical Sciences, Department of Physics and Astronomy, Johns Hopkins University, 3400 North Charles Street,Baltimore, MD 21218, USA

7 Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China

8 Apache Point Observatory, P.O. Box 59, Sunspot, NM 88349

Received Nov 16, 2017

ABSTRACT

Aims. We determine the stellar population properties - age, metallicity, dust reddening, stellar mass and the star formation history -for all spectra classified as galaxies that were published by the Sloan Digital Sky Survey (SDSS data release 14) and by the DEEP2(data release 4) galaxy surveys.Methods. We perform full spectral fitting on individual spectra, making use of high spectral resolution stellar population models.Calculations are carried out for several choices of the model input, including three stellar initial mass functions and three input stellarlibraries to the models. We study the accuracy of parameter derivation, in particular the stellar mass, as a function of the signal-to-noise of the galaxy spectra. We find that signal to noise ratio per pixel around 20 (5) allow a statistical accuracy on log10(M∗/M�) of0.2 (0.4) dex, for the Chabrier IMF.Results. We obtain the galaxy stellar mass function probed by SDSS, eBOSS and DEEP2 for galaxies with 0.2 < z < 0.8. Westudy DEEP2 galaxies selected by their [Oii] luminosity in the redshift range 0.83 < z < 1.03, finding that they have stellar masseswith a flat number density in the range 109 < M/M� < 1011.5. We publish all catalogs of properties as well as model spectra of thecontinuum for these galaxies as a value added catalog of the fourteenth data release of the SDSS. This catalog is about twice as largeas its predecessors (DR12) and will hopefully aid a variety of studies on galaxy evolution and cosmology.

Key words. galaxy evolution - stellar population model - galaxy surveys

1. Introduction

In the current paradigm of galaxy evolution, structures andgalaxies form hierarchically: larger halos are formed by the coa-lescence of smaller progenitors. From a macroscopic or thermo-dynamical point of view, galaxies are typically described as sys-tems composed of the following tightly interacting sub-systems:the dark matter halo, the central black hole, the stars, the coldgas, the hot gas and the dust. In addition, the galaxy interactswith its surroundings, the intergalactic medium, where it ejectsgas or from where it aggregates matter. A galaxy in this modelis characterized by the mass of each of its components and theshare of mass constituted by elements heavier than hydrogen.The visible component of galaxies is approximated as a tri-

phased system made of stars, inter-stellar medium and circum-galactic medium. This system is driven by the stellar activity;e.g. star formation rate, supernovae rate, the activity of the cen-tral active part of the galaxy; that induce gas movements: winds,accretion and expulsion (Mo et al. 2010). What stars populategalaxies is thus a central question in galaxy evolution.

The method to infer a galaxy stellar properties (e.g. stellarages, chemical composition, dust effects, the star formation his-tory and the stellar mass) consists in fitting models to the ob-served spectral energy distribution. There exist many variants ofthis method. Variations occurs in all dimensions of the problem:the models of the stellar population, the wavelength covered byobservations or by models, the fitting method to compare mod-els and data (e.g. statistics, priors, etc.). In this study we use

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the Maraston & Strömbäck (2011) (M11 hereafter) stellar pop-ulation models together with the firefly fitting routine (Wilkin-son et al. 2015; Goddard et al. 2017a,b; Wilkinson et al. 2017).These code and models are shown to be able to reconstruct accu-rately the complete star formation history for spectra with signalto noise ratios (SNR) of about 5 per pixel, as confirmed by exten-sive testing using mock galaxies, real galaxies and star clusters(see, Wilkinson et al. 2017, and Sec. 3.2).

We perform model fitting to the optical spectra measuredby the Sloan Digital Sky Survey (SDSS DR14) and the DEEP2survey (DR4) (Abolfathi et al. 2017; Newman et al. 2013). Wechose these two medium resolution optical spectroscopic sur-veys because they sample the stellar mass vs. redshift planein a complementary manner, as one can see on Fig. 1. Simi-lar stellar population model catalogs are available for the SDSSDR12. Stellar properties from broad-band SED fitting were pub-lished by Maraston et al. (2013) and emission-line properties byThomas et al. (2013). Here we present a work that follows theirapproach and extends calculations to full spectral fitting.

We present the set of observed spectra in Section 2. The fire-fly fitting routine and models are described in Section 3. In Sec-tion 4, we detail the results obtained, in particular the level atwhich properties such as the stellar masses are constrained. Fi-nally, we show a couple of scientific applications based on thisdata set: the galaxy stellar mass function in SDSS and the stellarmass function of [Oii] emitters in DEEP2.

Throughout the work we assume a standard flat ΛCDM(Planck Collaboration et al. 2014) cosmology. All results areavailable through the SDSS website 1 and are linked fromthe official Firefly page 2. Main catalogs are also available atMPE/MPG34. The software is available at the official Fireflypage and via the SDSS svn 5.

2. Spectroscopic data

In this analysis, we consider galaxies from the SDSS and DEEP2spectroscopic surveys. The redshift range spanned by the data is0 < z < 1.4 and most derived stellar masses are in the range106M� to 1012.5M�. The two surveys cover this parameter spacein a complementary fashion. SDSS covers the most luminousgalaxies over a wide area (order of 10,000 deg2) and DEEP2samples fainter galaxies (by about 2 magnitudes) over a smallarea (order of 2 deg2). Fig. 1 shows the redshift distribution ofthe two data sets. In both samples, the median signal to noiseratio per pixel in galaxy spectra with a robust redshift spans awide range of values between 0.1 to 100, see Fig. 2. We commenton the correlation between signal to noise ratio and uncertaintyon the stellar mass later in the paper.

2.1. SDSS

We consider spectra obtained with the SDSS or BOSS spectro-graph (Gunn et al. 2006; Smee et al. 2013) as in the fourteenthdata release (Dawson et al. 2016; Blanton et al. 2017; Abol-fathi et al. 2017). The SDSS (BOSS) spectrographs cover 3800-9200Å (3650−10, 400Å) at a resolution 1500 at 3800Å and 2500at 9000Å with 3 (2) arc seconds diameter fibers. Due to the va-riety of target selection algorithms successively applied to tar-

1 http://www.sdss.org/dr14/data_access/vac/2 http://www.icg.port.ac.uk/firefly/3 http://www.mpe.mpg.de/~comparat/DEEP2/4 http://www.mpe.mpg.de/~comparat/firefly_catalogs/5 http://www.sdss.org/dr14/software/products/

get galaxies within SDSS, the magnitude limit assumes differentvalues. In the i-band, the different magnitude limits are mostlycontained in the range 17 and 22.5.

For the stellar population fitting, we consider objects clas-sified as galaxies following criteria used in previous SDSSgalaxy products6. We consider objects for which a defi-nite positive redshift was derived using galaxy templates(CLASS=="GALAXY", Z > ZERR > 0, ZWARNING == 0)in the current redshift pipeline (Bolton et al. 2012, versionv5_10_0). For the data observed with the BOSS spectrograph,we consider the "NOQSO" version of these quantities. Theobtain about 2.4 million optical galaxy spectra; 851, 755 mil-lion were observed with the SDSS spectrograph setup and with1, 618, 192 with the BOSS spectrograph setup, see Table A.1.

Compared to previous stellar population model catalogs, weroughly double the number of stellar masses measured (DR12Maraston et al. 2013; Thomas et al. 2013). In particular the num-ber of well-constrained stellar masses (parameter constrained tobetter than 0.2 dex at given IMF) has also doubled. Such a gainin precision is enabled by fitting every pixel of the spectra ratherthan fitting the broad-band magnitudes (photometry) at the spec-troscopic redshift. However, this is at the cost of having a lesshomogeneous sample. Indeed, the uncertainty on the stellar pop-ulation parameters depends on the signal to noise ratio obtainedin individual spectra, which varies according to observing con-ditions, position in the spectrograph and survey strategy. Hence,the tighter constrain on stellar parameters is gained at the priceof completeness. The first row of panels of Fig. 2 shows how themedian signal to noise per good pixels are distributed with red-shift. Low redshift galaxies (z < 0.4) were observed on averageat higher signal to noise ratio than higher redshift galaxies. Thesecond row of panels of Fig. 2 shows how the median signal tonoise per good pixels in the i-band correlate with the uncertaintyon the stellar mass (for 4 redshift bins).

The complete set of observed spectra we processed occupiesabout 0.8T of disk space. The data considered for fitting in thisanalysis is available via the SDSS server,

– BOSS spectrograph data https://dr14.sdss.org/sas/dr14/eboss/spectro/redux/v5_10_0/spectra/PLATE/spec-PLATE-MJD-FIBERID.fits.

– SDSS spectrograph data https://dr14.sdss.org/sas/dr14/sdss/spectro/redux/26/spectra/PLATE/spec-PLATE-MJD-FIBERID.fits.

The data model for the spectra is described herehttps://data.sdss.org/datamodel/files/BOSS_SPECTRO_REDUX/RUN2D/spectra/PLATE4/spec.html.

2.2. DEEP2

DEEP2 is a deep pencil beam survey that acquired spectra forgalaxies brighter than R < 24.1 to study the evolution of galax-ies. The survey is split in four fields that cover 2.7 deg2 (New-man et al. 2013). The DEIMOS spectrograph at Keck was used,which covers approximately the wavelength range 6500−9300Åat a resolution ∼6000 (Faber et al. 2003). It accommodates orderof 120 slits per mask. Although DEEP2 is a major galaxy evolu-tion survey and stellar masses for galaxies observed by DEEP2are mentioned in many publications, there does not seems tobe a public stellar mass catalog available online for comparison(Kassin et al. 2007; Covington et al. 2010; Mostek et al. 2013;Coil et al. 2017).6 http://www.sdss.org/dr12/spectro/galaxy/

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Johan Comparat et al.: Stellar populations in SDSS and DEEP2

Fig. 1. Redshift distribution for the galaxies considered in this analysis. Galaxies with stellar mass constrained within ±0.2dex (solid lines) and±0.4dex (dashed lines) are depicted. The second row of panels shows the stellar mass (for a Chabrier IMF and and models adopting the ELODIElibrary) v.s. redshift.

Fig. 2. Median signal-to-noise over all good pixels v.s. redshift (first row of panels). The second row of panels shows the correlation between themedian signal-to-noise over all good pixels in the SDSS i-band and the uncertainty on the stellar mass for four redshift bins 0-0.1, 0.2-0.3, 0.4-0.5,0.6-0.7. The SDSS u,g,r,i,z filters transition from one another at 4000, 5500, 7000, 8500Å i.e. at redshift 0, 0.375, 0.75 and 1.125 for the 4000Åbreak. We see in the last two redshift bins that information is shifted towards redder bands. Sadly, the median SN in the z band is not reliable dueto difficult sky subtraction.

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In this analysis we consider the galaxy spectra that have aredshift in the range 0.001 < z < 1.7 and that are classifiedwith a flag Z_FLG ≥ 2. We use flux-calibrated spectra pro-duced by Comparat et al. (2016). Out of the 50, 319 entries in theDEEP2 DR4 catalog, 34, 851 are considered for a stellar popu-lation model fit, see Table A.1 for the detailed numbers. To com-pare to the numbers obtained in Comparat et al. (2016), we fur-ther divided the data after the eventual detection of emission linein the spectrum.

The spectra used in this analysis were obtained viathe DEEP2 server, here: http://deep.ps.uci.edu/DR4/spectra.html. The subset of processed flux-calibrated spec-tra are available here http://www.mpe.mpg.de/~comparat/DEEP2/spectra.

3. Stellar population modeling

We adopt the code Firefly (Wilkinson et al. 2017) and the stellarpopulation models of Maraston & Strömbäck (2011) with differ-ent options for the Initial Mass Function (IMF) and input stellarlibrary (see 3.4).

3.1. Firefly fitting routine

Firefly 7 is a chi-squared minimization fitting code that fora given input observed Spectral Energy Distribution (SED),compares combinations of single-burst stellar population mod-els (SSP), following an iterative best-fitting process controlledby the Bayesian Information Criterion until convergence isachieved. No priors - other than the assumed models - are ap-plied, rather all solutions within a statistical cut are retained withtheir weight. The weight of each component can be arbitraryand no regularization or additional prior than the adopted modelgrid is applied. Dust attenuation is added in a novel way, using aHigh-Pass Filter (HPF) in order to rectify the continuum beforefitting. The returned attenuation array is then matched to knownanalytical approximations to return an E(B-V) value. This proce-dure allows for removal of large scale modes of the spectrum as-sociated with dust and/or poor flux calibration. Firefly provideslight- and mass-weighted stellar population properties (age andmetallicity), E(B-V) values and stellar mass for the most likelybest fitting model and all of its SSP components. Errors on theseproperties are obtained by the likelihood of solutions within thestatistical cut.

The fitting routine follows these steps.

1. Match the resolution of the models to that of the data (usu-ally, downgrading the models)

2. Mask emission lines.3. Determine dust attenuation in the continuum through high

pass filtering.4. Get the best fitting stellar population model as a linear com-

bination of single-burst models without any prior else thanconvergence.

5. Compute the light- and mass-weighted synthetic stellar pop-ulation contributions.

6. Convert χ2 into probabilities and calculates average proper-ties and errors (both mass weighted and light weighted).

For full details about the Firefly code please turn to Wilkinsonet al. (2017). The code and the models used to create this datasetare public via the SDSS server:

7 http://www.icg.port.ac.uk/firefly

– Fitting code: https://svn.sdss.org/repo/sdss/firefly/tags/v1_0_4/

– Stellar population models: https://svn.sdss.org/public/data/sdss/stellarpopmodels/tags/v1_0_2/

– A development version of the code where you may findscripts for running fits on large computer infrastructureis available here https://github.com/JohanComparat/firefly_code (this is only informative)

– The official website of the Firefly team is http://www.icg.port.ac.uk/firefly links to the official maintainedversion of the firefly software.

Note that the official version is ahead (v1_1) of the version usedfor the DR14 run (v1_0). As ‘stellar mass’ in the SDSS datarelease (v1_0), we consider the total mass that went into stars,in order to avoid mismatching with the literature for which thefraction of mass lost via stellar evolution or locked in stellar rem-nants (white dwarfs, neutron stars and black holes) is not alwaysavailable. In the official version (v1_1), are available tables withthe stellar mass calculated including stellar mass loss, and pro-viding its split in stellar remnants. We publish v1_1 level cata-logs as alternate catalogs on the mpe mirror, see Sec. 3.7.

3.2. Performances

The code is able to recover stellar population properties suchas age, metallicity, and stellar mass, and the star formation his-tory, down to an SNR∼ 5, for moderately dusty systems (E(B-V)<0.75). At SNR∼ 20, the recovery of the star formation his-tory is remarkably good independently of reddening, unless thestar formation is very extended (∼10 Gyr). At lower SNR downto SNR∼ 0.5, we find that the stellar masses are in agreement(within errors) with previous estimates based on SED fitting onbroad band magnitudes. At such low SNR, the full star formationhistory cannot be reconstructed accurately. The age-metallicitydegeneracy also becomes important and the individual stellarages and stellar metallicities are uncertain.

The median SNR in all good pixels in the i-band of the spec-trum is anticorrelated to the uncertainty on the stellar mass. Thehigher the SNR, the smaller the uncertainty on the stellar mass,see Fig. 2.8 This correlation holds up to to redshift 0.4-0.5. Thenthe band of importance between 3500-5500Å break starts to en-ter the z-band where the estimation of the SNR are much noisier.So, at lower redshift, selecting the best fits can be done by ei-ther a selection on the SNR or on the uncertainty on the stellarmass. At higher redshift, the median SNR measure provided inthe SDSS specObj summary files is not a reliable estimate of theactual SNR.

We follow the Lee et al. (2013) procedure to mask pixelsaffected by the sky and estimate SNR in a cleaner fashion, wecall it the effective signal to noise ratio SNRe f f . Due to timeconstraints, we only perform this study on a subset of the com-plete sample. We find that in the high SNR regime (S NR > 10),estimations are converging. In the range 1-10, we find large dis-agreement between the two SNR estimators. For a part of thegalaxy population observed, the SN_MEDIAN_ALL estimatorunderestimates the SNR by a factor 3 to 5 compared to SNRe f f .The galaxies with an underestimated SNR (1 instead of 5) havetightly constrained firefly parameters. So that using this SNRe f f ,

8 Chen et al. 2012 achieved a similar conclusion by comparing thestellar mass obtained via their PCA-based full spectral fitting and theone from broad-band SED fitting. The two estimates converge at aS NR around 25. See also discussion in Maraston et al. 2013, Appendix.

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the correlation with uncertainty on the stellar mass holds downto low SNRe f f and to high redshift. We introduce two thresholdsof 0.2 and 0.4 dex uncertainty on the stellar mass that relate toSNRe f f around 20 and 5 where performances were previouslyquantified.

We therefore rely on the estimated uncertainty on the stellarmass to select the best sample at each redshift. At low redshift,this is equivalent to using the available SNR estimate. For thenext release, we will add the estimates of SNRe f f for all spectrato track optimally the code’s performances.

3.3. Maraston & Strömbäck (2011) models

We use the Maraston & Strömbäck (2011) stellar populationmodels. They assume different input stellar libraries, of whichwe use three, namely :

– STELIB, covering 3200–9300Å with a 3.4Å sampling at5500Å i.e. at a resolution R = 1617 (Le Borgne et al. 2003),

– MILES, covering 3500–7430Å with a 2.54Å sampling at5500Å i.e. at a resolution R = 2165 (Sánchez-Blázquez et al.2006; Falcón-Barroso et al. 2011),

– ELODIE, covering 3900–6800Å with a 0.55Å sampling at5500Å i.e. at a resolution R = 10000 (Prugniel et al. 2007).

Recall that SDSS, BOSS and DEIMOS cover 3800-9200, 3650-10,400, 6500-9300 at R∼2000, 2000, 6000. The mismatch be-tween the wavelength coverage of DEEP2 and those models ex-plain the lack of fits at low redshift. It is part of an ongoing effortto complete the low-redshift extension of DEEP2 with IR ex-tended models, which we shall release in the future.

3.4. Parameters of the run

For this run, we repeat the computation for the following threechoices of the stellar initial mass function (IMF):

– Salpeter, Salpeter (1955),– Chabrier, Chabrier (2003),– Kroupa, Kroupa (2001).

and for each of the input M11 models described above (namely,M11-ELODIE, M11-MILES and M11-STELIB). In total, weprovide up to nine models (depending on the convergence of thefit) of the continuum for each galaxy considered.

The grid of models spans ages in the range 6 <log10(Age[yr]) < 10 and metallicities in the range −3 <log10(Z/Z�) < 3, with each M11 model spanning a differentage/metallicity grid (cfr. Wilkinson et al. 2017, Table1).

Differences corresponding to the various initial parameterchoices are discussed later in the paper.

3.5. Processing

The processing was done on SCIAMA9, a high performancecomputing facility belonging to the University of Portsmouth(United Kingdom). A fit for a single model takes about a minutecpu so that the whole run required about 350,000 cpu hours. Thetotal data volume is about 3.2T, as in Table 1.

9 http://www.sciama.icg.port.ac.uk/

Table 1. Data volume generated in this study.

Survey catalog spectra models totalSDSS 23G 278G 860G 1.1T

eBOSS 49G 0.5T 1.5T 2.1TDEEP2 1.4G 6.2G 17G 24.6G

3.6. Data model

We created three levels (or layers) of data products. ForSDSS, all products are available on the SDSS SAS,here https://data.sdss.org/sas/dr14/eboss/spectro/firefly/v1_0_4. For DEEP2, they are available here http://www.mpe.mpg.de/~comparat/DEEP2.

For a more visual explanation of the data model,please visit http://www.sdss.org/dr14/spectro/eboss-firefly-value-added-catalog/.

3.6.1. Model spectrum

The lowest level data product is the model file. There is onesuch file per galaxy spectrum considered. It is available for bothDEEP2 and SDSS data sets. It is a fits file with a header and9 data units. The primary header contains all input parametersused during the fit. The following nine data units each contain

– Header. The best fit parameters for each SSP entering thebest model.

– Data extension. The best-fitting model spectrum: wavelength(Unit Angstrom) and model flux ( fλ convention, unit 10−17

erg cm−2 s−1 A−1).

The nine data units contain the results obtained for the differ-ent combinations of stellar libraries and initial mass functions.

– HDU1 M11-MILES x Chabrier IMF– HDU2 M11-MILES x Salpeter IMF– HDU3 M11-MILES x Kroupa IMF– HDU4 M11-ELODIE x Chabrier IMF– HDU5 M11-ELODIE x Salpeter IMF– HDU6 M11-ELODIE x Kroupa IMF– HDU7 M11-STELIB x Chabrier IMF– HDU8 M11-STELIB x Salpeter IMF– HDU9 M11-STELIB x Kroupa IMF

The data model for this product, named ’spFly’, is availablehere https://data.sdss.org/datamodel/files/EBOSS_FIREFLY/FIREFLY_VER/RUN2D/SPMODELS_VER/PLATE/spFly.html, where the link to the individual SDSS files aregiven. The DEEP2 result model spectra are provided here http://www.mpe.mpg.de/~comparat/DEEP2/stellarpop/and follow the naming convention ’spFly-deep2-MASK-OBJNUM.fits’.

An automated summary plot is provided for each model file.It illustrates the spectrum, the models, and the fitted parameters,see Fig. A.1. It shows an example of these Figures for a galaxyat redshift z = 0.127 identified by PLATE=0266, MJD=51602,FIBERID=0004. The top panel shows the observed spectrum(grey line) and the models (colored lines). The middle panelshows the normed distribution of the quantity (data-model)/errorfor each pixel considered in the fit and for each of the nine mod-els. It is compared to a normal distribution that it should follow,if the fits are reliable (dashed black line named ’N(0,1)’ in thelegend). The bottom panel shows the output parameters stellarmass vs. stellar age for each of the nine models. Ages and massesare in good agreement. Such a Figure is created for each fittedspectrum and provided together with the models.

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3.6.2. Plate-level summary catalogs (SDSS only)

Due to the size of the SDSS data set and its structure, we createsummary catalogs for each plate, named ’spFlyPlate’. Theycontain all output parameters from the fitting procedure. Thedata model for these catalogs is given here https://data.sdss.org/datamodel/files/EBOSS_FIREFLY/FIREFLY_VER/RUN2D/SPMODELS_VER/PLATE/spFlyPlate.html. Thispage gives the link to the plate catalogs.

For each spFlyPlate file, a representation of the data obtainedis proposed, an example is displayed in Fig. A.2. It shows thedistribution of stellar age and stellar masses measured in plate(0266). It also shows a comparison of the stellar masses de-rived using the M11 models with the ELODIE stellar library andvarying the IMFs. You may note the systematic offset in stellarmasses when assuming a Salpeter or a Chabrier IMF (bottom leftpanel).

As the DEEP2 data is much smaller than the SDSS, we didnot create this second layer of summary files for DEEP2.

3.6.3. Summary catalogs

Top-level summary catalogs contain a subset (for SDSS) or all(for DEEP2) of the fitted parameters. In the SDSS case, thecatalogs become too large when all parameters are written, sowe created catalogs with only subsets of parameters. In thecase of DEEP2, the catalog is small enough that adding allparameters is still manageable. The data model for the summaryfile for the eBOSS data is available at: https://data.sdss.org/datamodel/files/EBOSS_FIREFLY/FIREFLY_VER/RUN2D/eboss_firefly.html while the one for the SDSSdata https://data.sdss.org/datamodel/files/EBOSS_FIREFLY/FIREFLY_VER/RUN2D/sdss_firefly.html. Theydiffer by the redshift column: ’Z’ for SDSS and ’Z_NOQSO’for eBOSS. These summary catalogs are also available in theSCI-SERVER CAS database10.

The DEEP2 summary file is available here http://www.mpe.mpg.de/~comparat/DEEP2/catalogs/zcat.deep2.dr4.v4.LFcatalogTC.Planck15.spm.fits andfollows the same data model.

Assumptions in the IMF or templates induce systematic dif-ferences in the constrained parameters. Therefore, we do not pro-vide a mean stellar mass based on these nine runs.

3.7. Additional catalogs

Beyond the run described above, we did a number of other runswith different setups. From these emerged valuable catalogs.They are hosted here www.mpe.mpg.de/~comparat/DEEP2/or www.mpe.mpg.de/~comparat/firefly_catalogs/ in thedirectory ’additional_catalogs’. Each catalog comes with ashort ’readme’ file that documents its purpose. For example, weprovide nine catalogs (one per IMF x library) with all the mea-sured parameters of the star formation history. We also providepreliminary catalogs of the v1_1 (accounting for remnants) thathave slightly different metallicity and age boundary parameters.

4. Results

We fit the M11 stellar population models using the Firefly soft-ware fitter to 1,618,192 (eBOSS) + 851,755 (SDSS) + 34,851(DEEP2) = 2,504,798 spectra that were identified as galaxies by

10 http://www.sciserver.org/

these surveys. For each spectrum we provide models of the con-tinuum in up to 9 combinations of IMF and input model. This isthe first full spectral fitting release of the BOSS+eBOSS high-redshift extension of SDSS which provide stellar population pa-rameters. Previous work performing spectral fitting was basedon a PCA approach (Chen et al. 2012) aimed at maximising thestellar mass determination, and the other stellar parameters werenot provided.

In the next sections we discuss about the convergence of thefits (Sec. 4.1). Then, we provide two illustrations of scientificapplications of the stellar masses measured by Firefly. In thefollowing we consider the total mass that went into stars, in or-der to avoid mismatching with the literature for which the frac-tion of mass lost by stellar evolution or locked in stellar rem-nants (white dwarfs, neutron stars and black holes) is not alwaysclearly given. Note that we provide calculations of the properM∗ and the various contributions by mass lost in the additionalcatalogs, see Sec. 3.7.

4.1. About convergence

For about 70% (60) of the SDSS (eBOSS) data, the stellarmasses derived are constrained to the 0.2 dex level. By ‘con-strained’, we mean that the statistical errors are small. Comparedto previous studies on the SDSS data, based on spectrophotom-etry (e.g. Maraston et al. 2013), the sample size of galaxies withstellar masses constrained to this level is increased by a factorof 2. Therefore we think that we are gaining significant insighton the stellar population parameters. Parameters based on broad-band SEDs on the other hand could be calculated for all data asthey are less dependent on the SNR of the spectroscopic data.For the DEEP2 data, due to the intrinsic faintness of the spec-tra and the much lower SNR of the continuum, we could tightlyconstrain the stellar mass for about 10% of the sample. Exactnumbers are available in Table A.1. The convergence of the fitsand constraint on the fitted parameters is directly related to thesignal to noise ratio measured in the spectrum, as mentioned inSec. 3.2 and further discussed in Sec. 4.1.1.

Depending on initial setup, 71 to 86% of the fits convergedon the SDSS data and between 50 and 60% on the DEEP2 data.In SDSS and eBOSS, the share of non-converging fits is dom-inated by spectra with low signal to noise ratio and by QSOsthat were mis-classified as galaxies by the automated pipelinewhen the ’_NOQSO’ option is used. In the DEEP2 data, thenon-converging fits are split into two components: low redshiftgalaxies for which the wavelength coverage of the spectra wasnot sufficient; very low signal to noise ratio in the continuum(emission line redshifts). In any case, the obtained sample is nota clean subset of the parent catalogs, rather it is a biased sub-sample of the parent catalogs. In the future, we shall inspect andcharacterize in detail the exact reasons of the non-convergingfits.

4.1.1. Statistical error on the stellar mass

The statistical uncertainty on the stellar mass is estimated usingthe full probability distribution function of the parameters de-rived during the fit. Variations between spectra are mainly drivenby the average signal-to-noise per pixel in the spectra in the bandwhere information is localized (roughly 3800-5500Å).

The last row of panels of Fig. 2 shows how the median signalto noise ratio in the i-band correlates with the statistical error de-rived on the estimated stellar mass. At low redshift, we find that

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the SNR provided in the SDSS catalog is reliable and correlationcomes in as expected. Conversely at redshift higher than 0.5, theband of interest shifts into the z-band so that the correlation withthe i-band seems to disappear. Looking at this correlation withthe SNR in the z-band, we find that the estimator is dominatedby pixels contaminated by sky lines. The expected correlation isnot present in the z-band, the plot is nearly the same as the oneshowed for the i-band. A mentioned before, in future releases,we will provide a more robust estimators of the ’effective’ SNRin the redder part of the spectrum, which will give the user abetter handle on the convergence and sample selection. This red-shift effect set aside, the SNR when used conservatively (> 10),still contains a useful information. For spectra with large erroron the stellar mass, one should be cautious, and combine thismeasurement with stellar masses (and other parameters in gen-eral) based on broad band magnitudes SED fitting (e.g. Marastonet al. 2013, for the same galaxies). In some sense, our new cata-logs provide stellar masses with a better constrains for a subsetof the complete sample SDSS+eBOSS.

4.1.2. Systematical biases and errors

We find that the average uncertainties on the stellar mass is sys-tematically larger when comparing the M11-ELODIE results tothe M11-STELIB ones. It should be noted as showed and fullydiscussed in Maraston & Strömbäck (2011) that the ELODIEstellar library while allowing for a higher spectral resolution anda wider coverage in metallicity, covers a narrower wavelengthrange with respect to the STELIB library (up to ∼ 6800Å vs∼ 8000Å, respectively). The narrower wavelength is probablythe reason why more solutions due to age/metallicity/dust degen-eracy could be accommodated in the fit, hence degrading some-what the constrain. A wider wavelength range usually allows fora more robust determination of the properties of galaxies, notsurprisingly (e.g. Pforr et al. 2012).

The other crucial systematic uncertainty on the stellar massand on stellar mass functions is due to the assumptions of dif-ferent stellar population models. It is discussed in depth byBernardi et al. (2016). They showed that for the same IMF,different assumptions on the adopted stellar population mod-els and dust lead to different stellar masses and stellar massfunctions. Different stellar population models cause up to 0.3dex systematic differences. Different dust models cause up to0.2 dex systematic differences. Hence, stellar mass values avail-able in different catalogues will show systematic differences.The catalogs presented here follow the ’starforming’ flavour ofthe calculations by the Portsmouth group for the data release12 (Maraston et al. 2013) and available at http://www.sdss.org/dr14/spectro/galaxy_portsmouth. We compared thestellar masses obtained in the previous and the current cata-logs. We found the distribution normed by area of the quantity

|M1−M2|/√σ2

M1 + σ2M2 where M1 and M2 are the DR12 and the

DR14 versions of the stellar mass measurement to be very closeto a normal distribution if using 2σ errors. If using 1σ errors,there is a some level of tension between the catalogs. However,when we consider the subset where galaxies have the same red-shift (within 0.001) and the same E(B-V) (within 0.02), then thetension at 1σ disappears. Overall, agreement with its predeces-sor is very good.

4.1.3. Total mass vs. stellar mass

Using a sub sample of the SDSS plates and the ‘Chabrier-M11-MILES’ setup, we estimate the mass correction due tostellar mass losses (the corresponding catalogs are available atwww.icg.port.ac.uk/firefly and as additional catalogs, see Sec.3.7). For 54,117 galaxies older than 6 Gyr, the distribution ofthe correction to the stellar mass has quartiles with values Q1,Q2, Q3 = -0.007, 0.009, 0.03. For 100,621 galaxies with anage 3 <age/Gyr< 6, we get Q1, Q2, Q3 = 0.001, 0.003, 0.026.For 44,560 galaxies with an age 1 <age/Gyr< 3, we obtain Q1,Q2, Q3 = -0.004, 0.0007, 0.005. For 3,711 galaxies with an ageage/Gyr< 1, the quartiles are Q1, Q2, Q3 = -0.012, 0.001, 0.018.As expected, the older the stellar population are more stronglyaffected (e.g Maraston 1998, 2005). All in all, the variation be-tween these catalogues is small: < 0.03 dex with dependenceon age. For future SDSS releases (starting with DR15) we shallinclude all types of mass output in the default run.

4.1.4. Overlap between SDSS, eBOSS and DEEP2

There are galaxies in common which were observed by bothSDSS and DEEP2, precisely 64 (493) galaxies were observedby both DEEP2 and SDSS (eBOSS). Among these, 31 (261)have redshift values that agree within |zDEEP2 − zS DS S (eBOS S )| <0.0005. 3 (31) galaxies have a stellar mass constrained within±0.2 dex. For these 3+31 galaxies, the masses measured agreewithin errors.

4.2. Stellar mass function probed by SDSS, eBOSS andDEEP2

The galaxy stellar mass function and its evolution with redshiftis a crucial property to perform galaxy formation and evolu-tion studies (Bundy et al. 2006; Pozzetti et al. 2010; Marastonet al. 2013; Ilbert et al. 2013; Bernardi et al. 2016; Etheringtonet al. 2017). The study of this function requires large numbersof galaxies hence usually ∼ M∗ from broad-band photometry isadopted. Here we show - without aiming at performing a fullscientific analysis - what we obtain for the galaxy mass func-tion when using our results based on spectral fitting rather thanbroad-band photometry, and for three different datasets in tworedshift bins.

We consider stellar masses constrained to better than 0.2dex based on the Chabrier IMF for the three libraries ELODIE,STELIB and MILES. For eBOSS galaxies, we consider the areacovered to be 10,000 deg2; for SDSS 7,900 deg2 and for DEEP20.5 deg2 (low redshift) or 2.78 deg2 (high redshift). For SDSSand eBOSS each galaxy represents itself only, no weightingother than the area is applied. We do not correct for the even-tual incompletenesses present in the SDSS and eBOSS data.For DEEP2, we use the statistical weights from Comparat et al.(2016). These weights correct from the target selection algorithmused in DEEP2 and allow the recovery of the correct galaxy den-sity as a function of redshift and magnitude. For each catalog(3 surveys x 3 libraries), we estimate the observed stellar massfunction (OSMF) and its Poisson error (cosmic variance is nottaken into account). Then, per survey, we compute the medianof the three measurements (3 libraries) and the minimum andmaximum of the three measurements (with only Poisson errorsconsidered). The OSMF obtained constitutes a robust a lowerlimit to the stellar mass function. Indeed because we use onlystellar masses that are tightly constrained, we are certain that atleast this density of stellar mass exists in galaxies.

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Fig. 3. Stellar mass function measured on SDSS, eBOSS and DEEP2samples containing only tightly constrained stellar masses. Two redshiftbins 0.2 < z < 0.5, 0.5 < z < 0.8 show how each survey spans thestellar mass function. For comparison, we added the Ilbert et al. (2013)model (green, they have the exact same redshift bins) and the BOSSSMF from Maraston et al. (2013), their mean measurement is at redshift0.5 (magenta line).

We compare our results with the stellar mass functions ob-tained in COSMOS Ilbert et al. (2013) and in BOSS (Marastonet al. 2013). This COSMOS stellar mass function is based on aK-band selected sample that is known to be biased at low red-shift as it misses a fraction of the massive star-forming galaxypopulation i.e. at the high mass end our measurements are ex-pected to be above that of COSMOS. We show the results in tworedshift bins: 0.2 < z < 0.5, 0.5 < z < 0.8, see Fig. 3. Wesee how each sample (DEEP2, SDSS, eBOSS), considering onlythe tightly constrained stellar masses, is related to the bulk ofthe galaxy population depicted by the COSMOS and BOSS stel-lar mass functions. The comparison with Maraston et al. (2013)(purple line on the Figure) shows the level of incompleteness wehave due to our selection on the error on the stellar mass.

4.3. Stellar mass function sampled by emission line galaxiesin DEEP2

How emission line galaxies populate the cosmic web is a hottopic in cosmology nowadays (Favole et al. 2016, 2017; Rai-choor et al. 2017; Gonzalez-Perez et al. 2017). To character-ize how emission line galaxies are related to the overall galaxypopulation, we project the DEEP2 observed stellar mass func-tion in the redshift range 0.83 < z < 1.03 for three [Oii] lu-minosity threshold, log10(L[[Oii] ]) > 41.8, 42 and 42.2, seeFig. 4.3. It is known that there is scatter in SFR at fixed massand that the [Oii]– SFR relation also has scatter. Therefore wedo not expect to find that only a narrow range of masses ispopulated by the strongest [Oii] emitters. Indeed, the distribu-tions we find are quite broad, covering the stellar mass range109 < M(M�) < 1011.5. More interestingly, these distributionsare quite flat and their shape do not seem to depend on theluminosity threshold. Similar distributions were found in Rai-choor et al. (2017). Given that the DEEP2 sample is completefor the [Oii] luminosity limits applied, we conclude that up toz = 1.5 there is no preferred host galaxy mass (in the range109 < M(M�) < 1011.5) to find a strong [Oii] emission.

Recently, a broad range of properties of ELGs was predictedby the model presented in Gonzalez-Perez et al. (2017). In ourdata, it seems that massive galaxies are selected as [Oii] emitters,something that was not expected from that model. This discrep-ancy might be related to the treatment of the dust in the model,although a further detailed analysis will be needed to understandthis better, a very interesting puzzle.

The broad distribution in stellar mass means that studyingstacked spectra of galaxies selected by emission line luminositythresholds will result in a statement about their mean stellar pop-ulations, that is unlikely to capture the variety of galaxies con-stituting the emission line galaxy population. Said differently,ELG stacks might not capture how diverse the ELG populationactually is. This happens also because the light of emission-lineselected galaxies is dominated by their latest generation of stars,which overshine the underlying structure of older stellar popula-tions (known as the ’iceberg effect’ Maraston et al. 2010).

5. Summary and future releases

We provide the stellar population properties as obtained by fullspectral fitting of models to the observed spectra for SDSS DR14galaxies, including their high-z extensions (eBOSS), and for theDEEP2 survey. Compared to previous releases, this one doublesthe number of galaxies with a tightly constrained stellar massparameter. Thanks to the high performance computing environ-ment "SCIAMA" at the University of Portsmouth, we could cre-ate models of the continuum for nine configurations of IMF andstellar libraries for about 2.5 million galaxies. This catalog isthe continuation of the Portsmouth SDSS galaxy property cata-logs, which were using the spectroscopic redshift combined withthe broad-band photometry. To do so, we adopted the newly re-leased Firefly fitting code coupled with the stellar populationmodels by Maraston & Strömbäck (2011). This combination hasimproved the precision of derived parameters. In particular, thestellar mass for SDSS galaxies is obtained with a precision ofabout 0.2 dex for a given IMF, when SNR> 20. This shows thatbeyond providing an accurate redshift measurement and thus anaccurate distance, there is large amount of valuable informationin the spectra to help further constrain the stellar population his-tory.

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Fig. 4. Stellar mass function as measured in the DEEP2 [Oii] emittersample in the redshift range 0.83 < z < 1.03 (considering all com-binations of IMF and libraries). We show the stellar mass function issampled by the [Oii] emitters for different thresholds in log10(L[Oii] )luminosity 41.8, 42 and 42.2.

We explored the observed stellar mass function probed bySDSS, eBOSS and DEEP2 for galaxies with 0.2<z<0.8, settinga strict lower limit to them.

We explore for the first time the stellar population models ofDEEP2 emission line galaxies and find that these galaxies spana variety of properties, which is in broad agreement with predic-tions of the state-of-the-art semi-analytical models. In particular,DEEP2 galaxies selected by their [OII] luminosity in the redshiftrange 0.83<z<1.03, have stellar masses with a constant numberdensity in the range 109 < M(M�) < 1011.5.

Ongoing firefly developments expected for the next SDSSpublic release (DR15 onwards) are:

– A plugin to the SDSS webapp11 to access interactively thecontinuum models.

– Emission line measurements on the residuals.– An AGN mode to firefly to allow for fitting all the pixels of

AGN spectra (e.g. Calderone et al. 2017).

There are a variety of science cases that will be explored indepth in upcoming companion papers.

6. Acknowledgements

JC thanks the firefly team for the team work and this milestone! We all thank Gary Burton for his superb help and technicalsupport with the SCIAMA machine, and Anne-Marie Weijmansfor her guidance through the VAC emission.

VGP acknowledges support from the University ofPortsmouth through the Dennis Sciama Fellowship award. Nu-merical computations were done on the SCIAMA High Perfor-mance Compute cluster which is supported by the ICG, SEPNetand the University of Portsmouth. This research used resourcesof the National Energy Research Scientific Computing Center, a

11 https://dr14.sdss.org/optical/spectrum/view

DOE Office of Science User Facility supported by the Office ofScience of the U.S. Department of Energy under Contract No.DE-AC02-05CH11231. This work has benefited from the pub-licly available programming language python.

Funding for the Sloan Digital Sky Survey IV has been pro-vided by the Alfred P. Sloan Foundation, the U.S. Departmentof Energy Office of Science, and the Participating Institutions.SDSS acknowledges support and resources from the Center forHigh-Performance Computing at the University of Utah. TheSDSS web site is www.sdss.org.

SDSS is managed by the Astrophysical Research Consor-tium for the Participating Institutions of the SDSS Collabora-tion including the Brazilian Participation Group, the CarnegieInstitution for Science, Carnegie Mellon University, the ChileanParticipation Group, the French Participation Group, Harvard-Smithsonian Center for Astrophysics, Instituto de Astrofísicade Canarias, The Johns Hopkins University, Kavli Institute forthe Physics and Mathematics of the Universe (IPMU) / Univer-sity of Tokyo, Lawrence Berkeley National Laboratory, Leib-niz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institutfür Astronomie (MPIA Heidelberg), Max-Planck-Institut für As-trophysik (MPA Garching), Max-Planck-Institut für Extrater-restrische Physik (MPE), National Astronomical Observatoriesof China, New Mexico State University, New York University,University of Notre Dame, Observatório Nacional / MCTI, TheOhio State University, Pennsylvania State University, Shang-hai Astronomical Observatory, United Kingdom ParticipationGroup, Universidad Nacional Autónoma de México, Universityof Arizona, University of Colorado Boulder, University of Ox-ford, University of Portsmouth, University of Utah, Universityof Virginia, University of Washington, University of Wisconsin,Vanderbilt University, and Yale University.

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Appendix A: Large figures and tables

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Fig. A.1. Example of a fit taken from the first plate of SDSS considered in this analysis: 0266. The top panel shows the observed spectrum (greyline) and its models (colored lines). The middle panel shows the χ2 distribution per pixel for each fit compared to a normal distribution (labeledN(0,1), dashed line). The bottom panel shows the output parameters stellar mass (y-axis) vs stellar age (x-axis), which nicely agree. Each bluepoint refers to one of the nine models. The blue points are related to their respective caption by black arrows. This Figure is generated for each fitand is available in the data repository.

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Fig. A.2. Summary plot for SDSS plate 0266. It shows the cumulative normed distributions of stellar ages and stellar masses derived for allIMF + library setups (top row). The bottom panels compare the stellar masses derived assuming different IMFs. It shows the known fact that theassumption of a Salpeter IMF implies stellar masses that are on average 30% larger than those for Kroupa and Chabrier IMFs (bottom left panel).Chabrier and Kroupa IMFs give on average the same stellar masses (bottom right panel).

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Table A.1. Summary table of observed spectra and fit results. The Table is divided in four subsets, BOSS, SDSS, DEEP2 and DEEP2 [Oii]galaxies. The last set shows the subset of the DEEP2 set that have a detection with a signal to noise ratio greater than 5 of the [Oii] emission line.The first line in each subset gives the total number of spectra available in the survey and how many of them are considered as galaxies. The assumedfitting setup (model and IMF) is given in the first 2 columns. The third column gives the number of galaxies for which the fit converged. The lasttwo columns gives the number of galaxies for which the stellar mass parameter is constrained within less than 0.4 dex and 0.2 dex, respectively.The number in parenthesis give the percentage relative to the total number of galaxies.

eBOSS DR14: 1, 618, 192 galaxiesIMF Library fit converged σlog10 M < 0.4 dex σlog10 M < 0.2 dexChabrier ELODIE 1379359 (84.6) 1256410 (77.1) 881505 (54.1)Chabrier MILES 1335712 (82.0) 1280841 (78.6) 1012161 (62.1)Chabrier STELIB 1169474 (71.8) 1153782 (70.8) 1011511 (62.1)Kroupa ELODIE 1385286 (85.0) 1277104 (78.4) 931287 (57.2)Kroupa MILES 1337641 (82.1) 1292001 (79.3) 1054591 (64.7)Kroupa STELIB 1178920 (72.3) 1168610 (71.7) 1037048 (63.6)Salpeter ELODIE 1387851 (85.2) 1285903 (78.9) 944953 (58.0)Salpeter MILES 1341917 (82.3) 1303597 (80.0) 1074847 (66.0)Salpeter STELIB 1182866 (72.6) 1173918 (72.0) 1047226 (64.3)

SDSS DR14: 851, 755 galaxiesIMF Library fit converged σlog10 M < 0.4 dex σlog10 M < 0.2 dexChabrier ELODIE 732903 (86.0) 708203 (83.1) 587198 (68.9)Chabrier MILES 728753 (85.6) 715473 (84.0) 617754 (72.5)Chabrier STELIB 656725 (77.1) 653374 (76.7) 547312 (64.3)Kroupa ELODIE 732568 (86.0) 712164 (83.6) 610797 (71.7)Kroupa MILES 730150 (85.7) 719723 (84.5) 639171 (75.0)Kroupa STELIB 658873 (77.4) 657115 (77.1) 565229 (66.4)Salpeter ELODIE 729621 (85.7) 711918 (83.6) 617604 (72.5)Salpeter MILES 735896 (86.4) 727513 (85.4) 655569 (77.0)Salpeter STELIB 657501 (77.2) 656244 (77.0) 571803 (67.1)

DEEP2 DR4: 34, 851 galaxiesIMF Library fit converged σlog10 M < 0.4 dex σlog10 M < 0.2 dexChabrier ELODIE 20529 (58.7) 8325 (23.8) 2516 (7.2)Chabrier MILES 19333 (55.3) 9957 (28.5) 4277 (12.2)Chabrier STELIB 18880 (54.0) 11398 (32.6) 3262 (9.3)Kroupa ELODIE 20893 (59.7) 9332 (26.7) 2892 (8.3)Kroupa MILES 19605 (56.1) 10622 (30.4) 4755 (13.6)Kroupa STELIB 19264 (55.1) 12211 (34.9) 3891 (11.1)Salpeter ELODIE 20987 (60.0) 9893 (28.3) 3065 (8.8)Salpeter MILES 19927 (57.0) 11136 (31.8) 5088 (14.5)Salpeter STELIB 19394 (55.5) 12582 (36.0) 4308 (12.3)

DEEP2 DR4: 19, 656 [Oii] galaxiesIMF Library fit converged σlog10 M < 0.4 dex σlog10 M < 0.2 dexChabrier ELODIE 11181 (56.9) 3824 (19.5) 1054 (5.4)Chabrier MILES 9762 (49.7) 4354 (22.2) 1851 (9.4)Chabrier STELIB 10014 (50.9) 5080 (25.8) 1368 (7.0)Kroupa ELODIE 11458 (58.3) 4340 (22.1) 1221 (6.2)Kroupa MILES 10004 (50.9) 4628 (23.5) 2034 (10.3)Kroupa STELIB 10228 (52.0) 5447 (27.7) 1534 (7.8)Salpeter ELODIE 11551 (58.8) 4672 (23.8) 1267 (6.4)Salpeter MILES 10248 (52.1) 4879 (24.8) 2164 (11.0)Salpeter STELIB 10374 (52.8) 5642 (28.7) 1711 (8.7)

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