Draft version February 14, 2020Typeset using LATEX preprint2 style in AASTeX63

One hundred SMUDGes in S-PLUS: ultra-diffuse galaxies flourish in the field

C. E. Barbosa ,1, 2 D. Zaritsky ,1 R. Donnerstein ,1 H. Zhang ,1 A. Dey ,3

C. Mendes de Oliveira ,2 L. Sampedro,2 A. Molino,2 M. V. Costa-Duarte,2 P. Coelho ,2

A. Cortesi ,2 F. R. Herpich ,2 J. A. Hernandez-Jimenez,2, 4 T. Santos-Silva,2

E. Pereira ,2 A. Werle ,2, 5 R. A. Overzier ,2, 6 R. Cid Fernandes ,5

A. V. Smith Castelli,7, 8 T. Ribeiro,3, 9 W. Schoenell ,10, 11 and A. Kanaan5

1Steward Observatory, University of Arizona, 933 N Cherry Ave, Tucson, AZ 85719, USA2Universidade de Sao Paulo, Instituto de Astronomia, Geofısica e Ciencias Atmosfericas, Departamento de

Astronomia, Rua do Matao 1225, Sao Paulo, SP, 05508-090, Brazil3NSF’s National Optical-Infrared Astronomy Research Laboratory, P.O. Box 26732, Tucson, AZ 85726, USA

4Universidad Andres Bello, Departamento de Ciencias Fısicas, Fernandez Concha 700, Las Condes, Santiago, Chile5Universidade Federal de Santa Catarina, Departamento de Fısica, SC 88040-900, Brazil, Florianopolis, SC

88040-900, Brazil6Observatorio Nacional, Ministerio da Ciencia, Tecnologia, Inovacao e Comunicacoes, Rua General Jose Cristino,

77, Sao Cristovao, 20921-400 Rio de Janeiro, RJ, Brazil7Instituto de Astrofısica de La Plata, UNLP, CONICET, Paseo del Bosque s/n, B1900FWA La Plata, Argentina8Facultad de Ciencias Astronomicas y Geofısicas, UNLP, Paseo del Bosque s/n, B1900FWA, La Plata, Argentina

9Universidade Federal de Sergipe, Departamento de Fısica, Av. Marechal Rondon, S/N, 49000-000 Sao Cristovao, SE,Brazil

10GMTO Corporation, 465 N. Halstead Street, Suite 250, Pasadena, CA 91107, USA11Universidade Federal do Rio Grande do Sul (UFRGS), Instituto de Fısica, Departamento de Astronomia, Av. Bento

Goncalves 9500, Porto Alegre, RS, Brazil

(Received January 7, 2020; Revised February 7, 2020; Accepted February 12, 2020)

Submitted to ApJS

ABSTRACT

We present the first systematic study of the stellar populations of ultra-diffuse galaxies(UDGs) in the field, integrating the large area search and characterization of UDGs bythe SMUDGes survey with the twelve-band optical photometry of the S-PLUS survey.Based on Bayesian modeling of the optical colors of UDGs, we determine the ages,metallicities and stellar masses of 100 UDGs distributed in an area of ∼ 330 deg2 inthe Stripe 82 region. We find that the stellar masses and metallicities of field UDGsare similar to those observed in clusters and follow the trends previously defined instudies of dwarf and giant galaxies. However, field UDGs have younger luminosity-weighted ages than do UDGs in clusters. We interpret this result to mean that fieldUDGs have more extended star formation histories, including some that continue toform stars at low levels to the present time. Finally, we examine stellar population

Corresponding author: C. E. Barbosakadu.barbosa@gmail.com

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scaling relations that show that UDGs are, as a population, similar to other low-surfacebrightness galaxies.

Keywords: Low surface brightness galaxies (940), Stellar populations (1622), Stellarages (1581), Metallicity (1031), Stellar masses (1614)

1. INTRODUCTION

Ultra-diffuse galaxies (UDGs) are a recentlydefined class of low surface brightness (LSB)galaxy initially found in large numbers in theComa Cluster (van Dokkum et al. 2015). Theirunusually large half-light radii, Re ≥ 1.5 kpc,for galaxies with such low central surface bright-ness, µ0,g ≥ 24 mag arcsec−2, are striking. Al-though large LSB galaxies have been knownfor quite some time (Disney 1976; Sandage &Binggeli 1984; Impey et al. 1988; Schombert& Bothun 1988; Schwartzenberg et al. 1995;Dalcanton et al. 1997; Sprayberry et al. 1997),the current excitement originates from indica-tions, either from kinematic measures of theunresolved light or globular clusters in thesegalaxies (Beasley et al. 2016; Toloba et al. 2018;van Dokkum et al. 2019), or from the numbersof globular clusters alone (Peng & Lim 2016;Beasley & Trujillo 2016; van Dokkum et al.2017, 2018a), that at least some UDGs lie inmassive (> 1011 M�) halos.

The detection of populations of UDGs ingalaxy clusters (e.g. van Dokkum et al. 2015;Mihos et al. 2015; van der Burg et al. 2016;Venhola et al. 2017; Shi et al. 2017) led to theexploration of a possible evolutionary link be-tween these galaxies and their harsh environ-ment (Safarzadeh & Scannapieco 2017; Con-selice 2018; Ogiya 2018; Bennet et al. 2018;Carleton et al. 2019). However, UDGs werealso found in less dense environments, such asfilaments (e.g.. Martınez-Delgado et al. 2016),groups (e.g. Makarov et al. 2015; Smith Castelliet al. 2016; Roman & Trujillo 2017; van derBurg et al. 2017; van Dokkum et al. 2018b), thefield (e.g. Leisman et al. 2017; Greco et al. 2018)

and even voids (Roman et al. 2019). More-over, observational studies (e.g. Yozin & Bekki2015; Zaritsky 2017; Sifon et al. 2018; Amor-isco et al. 2018) and theoretical ones (e.g. Amor-isco & Loeb 2016; Di Cintio et al. 2017; Ronget al. 2017; Chan et al. 2018; Liao et al. 2019;Jiang et al. 2019) found that UDGs span a widerange of physical properties, and perhaps a cor-respondingly large range of origin stories.

A key challenge in developing a unified under-standing of UDGs and their relation to othergalaxies is that the data so far come from dis-parate studies, with different selection criteria,and mostly focus on high density environments.These deficits are exacerbated by the difficul-ties posed in observing such low surface bright-ness galaxies. Photometric information, suchas broadband colors (e.g. Prole et al. 2019),are available for many UDGs but are of lim-ited value in determining the properties of thestellar populations, while spectroscopy, whichcan provide the necessary information, is onlyavailable for a small number of galaxies (e.g.Martınez-Delgado et al. 2016; Kadowaki et al.2017; Ruiz-Lara et al. 2018; Ferre-Mateu et al.2018; Gu et al. 2018).

Recently, Zaritsky et al. (2019) presented theinitial results from the Systematically Measur-ing Ultra-diffuse Galaxies (SMUDGes) survey,a systematic study to detect and characterizethe photometric properties of UDGs over a largearea of the sky (∼14000 deg2) using data fromthe Legacy survey (Dey et al. 2019). In its ini-tial release, SMUDGes provided a catalog con-taining 275 UDG candidates, including most ofthe galaxies previously reported within 10◦ ofthe Coma cluster by van Dokkum et al. (2015)and Yagi et al. (2016), using a relatively small

100 SMUDGes in S-PLUS 3

area of the total survey (334 deg2). SMUDGeshas now analyzed the SDSS Stripe 82 region andidentified 172 candidate UDGs in this region,which is a much more typical region of the skythan that around the Coma cluster (Zaritsky etal. in prep.).

The limited passbands of the Legacy surveypreclude stellar population modeling and spec-troscopic observations of the SMUDGes candi-dates will always be highly limited (Kadowakiet al. 2017, Kadowaki et al., in prep). Inter-estingly, the requirement of large field-of-view(FoV), multi-passband imaging in the studyof UDGs intersects with the interest of sev-eral ongoing cosmological surveys, such as theJavalambre-Physics of the Accelerated UniverseAstrophysical Survey (J-PAS, Benitez et al.2014), the Javalambre Photometric Local Uni-verse Survey (J-PLUS, Cenarro et al. 2019) andthe Southern Photometric Local Universe Sur-vey (S-PLUS, Mendes de Oliveira et al. 2019).Here we explore the synergy between SMUDGesands S-PLUS to perform the first statisticalstudy of the stellar populations of UDG can-didates over an area of sky that is not domi-nated by high density environments. Despitelimited overlap within Stripe 82 between thetwo surveys, we were able to study a sampleof 100 UDG candidates and perform the largestdetailed population study of these galaxies todate.

This paper is structured as follows. In §2, wedescribe the two datasets used in this work. In§3, we describe the photometry of the UDG can-didates in the context of S-PLUS, and in §4,we present the method developed to determinetheir stellar populations using a Bayesian frame-work. In §5, we present our results and discussthe main implications of our work for our under-standing of the nature of UDGs. We concludeand summarize this work in §6. Throughout, weassume a standard ΛCDM cosmology whenevernecessary, assuming H0 = 70 km s−1 Mpc−1.

All magnitudes use the AB system (Oke 1964;Oke & Gunn 1983).

2. DATA

2.1. SMUDGes sample

Our ability to locate LSB galaxies have beenlimited both by the lack of sensibility and in-strumental constraints, and various attemptshave been made to optimize observations at lowsurface brightness (e.g. Gonzalez et al. 2001;Mihos et al. 2015; Abraham & van Dokkum2014). However, there have been no systematicattempt to use current, large volume archivaldata to search for LSB galaxies, which havenot been identified before because standardpipelines are not optimized to find such systems.The SMUDGes project (Zaritsky et al. 2019)was conceived to develop an automatized wayto search for LSB galaxies over a large area ofthe sky using data from the Legacy imaging sur-vey (Dey et al. 2019), a deep three-band obser-vational campaign that supports the Dark En-ergy Spectroscopic Instrument (DESI) project(Schlegel et al. 2011; DESI Collaboration et al.2016a,b).

Most of what is known about UDGs as a pop-ulation is based on observations of the Comacluster (van Dokkum et al. 2015; Yagi et al.2016). In this initial stage of the project, theSMUDGes detection algorithm has been con-strained to search UDGs similar to those foundin Coma, and thus is focused on systems withangular sizes Re & 5 arcsec, which are easierto classify than smaller objects in the absenceof redshift information. The methodology usedto identify UDGs is described in detail in Zarit-sky et al. (2019) and Zaritsky et al. (in prep.),and here we summarize the main steps of theprocess. First, bright, saturated sources aredetected, modeled and replaced in the DESIimages by background noise, whereas fainterbackground and foreground sources are care-fully modeled and subtracted. Then, wavelet

4 Barbosa et al.

filtering is used to detect sources according tosize and surface brightness criteria, defined tohave µ0,g ≥ 24 mag arcsec−2 and Re > 5.3′′. Fi-nally, all UDG candidates are modeled with asingle Sersic component using GALFIT (Penget al. 2002, 2010).

In this work, we use a sample of 172 UDG can-didates in the Stripe 82 area. From SMUDGeswe adopt the values of mg,mr,mz, Sersic in-dex n, and Re in arcsec, position angle andaxis ratio. Without distance estimates, we can-not determine whether these systems pass thecommon defining criteria for UDGs, Re ≥ 1.5kpc, and some of these galaxies may actuallybe dwarf galaxies at small distances. The red-shift by association (defining high density re-gions in terms of normal galaxies and assigningSMUDGes to the redshift of that overdensity)worked for 25 candidates in Stripe 82 and all25 satisfy the Re > 1.5 kpc criterion at the as-signed distance. Only 1 has Re > 6 kpc, whichseems to be about the upper limit on size - ithas Re = 8.6 kpc - which suggests that this onemay have the wrong redshift. In this particularcase, the UDG candidate is close in projectionto a nearby bright galaxy and so it may insteadbe a satellite of that galaxy (Zaritsky et al., inprep). Therefore, we work under the hypothesisthat we have a sample of UDGs with low con-tamination by dwarf galaxies, but we examinethis issue again further below.

2.2. S-PLUS DR1 data

We use data from the S-PLUS first data re-lease (DR1), which covers an area of 336 deg2

in the Stripe 82 equatorial field, observed withthe T80S, a 0.8m robotic telescope with a wideFoV of ∼ 1.8 deg2, located in Cerro Tololo,Chile. The DR1 data are already reduced andare publicly available in the NSFs NationalOptical-Infrared Astronomy Research Labora-

tory archive1. Details about the survey strat-egy and data reduction process are describedby Mendes de Oliveira et al. (2019) while thephotometric calibration is described in Sampe-dro et al. (in prep.).

The main survey strategy is aimed at obtain-ing large coverage of the Southern sky (∼ 9000deg2) for astronomical and cosmological stud-ies in the local universe. The S-PLUS uses thesame photometric system of the J-PLUS survey(Marın-Franch et al. 2012), which consists oftwelve optical bands, including 5 broad-bandssimilar to those used by the Sloan digital skysurvey (SDSS) ugriz system, and a set of sevennarrow-band (∆λ = 100 − 200A) filters placedat various rest-frame optical features, including[OII] (λeff = 3771 A), Ca H+K (λeff = 3941 A),Hδ (λeff = 4094 A), G-band (λeff = 4292 A),Mg b triplet (λeff = 5133 A), Hα (λeff = 6614A) and the Ca triplet (λeff = 8611 A). Consid-ering a signal-to-noise ratio (SNR) threshold of3, the survey is complete in the broad bands tomagnitudes of u = 21.07, g = 21.79, r = 21.6,i = 21.22 and z = 20.64, whereas it is completeto magnitudes of ∼ 20.4 in all narrow bands(Mendes de Oliveira et al. 2019).

The S-PLUS DR1 data cover Stripe 82 using apair of exposures at each right ascension, limit-ing the declination to the range −1.4◦ ≤ dec ≤+1.4◦. Moreover, the SPLUS DR1 data did notuse dithering, causing occasional gaps betweenexposures, resulting in a few UDGs that arenot observed despite being within the footprintof the survey. In total, we have observationsfor only 100 SMUDGes from the initial sampleof 172. Figure 1 shows the spatial distributionof the SMUDGes Stripe 82 sample overlappedwith the S-PLUS DR1 footprint.

3. PHOTOMETRY OF UDGS FROM THES-PLUS DATA

1 https://datalab.noao.edu/splus/index.php

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Figure 1. Distribution of the SMUDGes Stripe 82 UDG candidates on the sky and their overlap withS-PLUS. The grid lines represent the S-PLUS footprint for the Stripe 82 area, red crosses indicate allSMUDGes galaxies that are outside the footprint or fell within gaps between exposures, and filled circlesindicate the location of all UDG candidates with S-PLUS data.

UDGs are not easily detected given the sur-face brightness limits of the S-PLUS survey, andonly one UDG was previously detected in theDR1 catalog of photometric redshifts (Molinoet al. 2019). Therefore, we had to obtainour own photometry of the UDGs from the S-PLUS images leveraging the information fromthe deeper SMUDGes photometry.

Regarding the data quality of S-PLUS, all im-ages in the S-PLUS Main Survey, which includesStripe 82, are obtained during photometricnights with seeing ≤ 2′′. Among the 61 differ-ent tiles used in this work, the mean full widthat manuscripthalf maximum (FWHM) over allbands is 1.4′′. Moreover, because each field isimaged in all bands consecutively in a given ob-servational block, there are only small seeingvariations among all bands for each tile (meanstandard deviation among bands of 0.14′′). Weconclude that there is no need to homogenizethe seeing across the images for our photome-try.

For each UDG, we perform aperture photom-etry in each of the 12 bands from S-PLUS usingthe photutils package (Bradley et al. 2019).To ensure consistent photometry, for each UDGwe define an elliptical aperture with a semi-major axis length of Re, and location, positionangle and ellipticity determined from the GAL-

FIT Sersic profile fitting from the SMUDGesanalysis. We subtract local sky using an el-liptical annulus with inner and outer radii of2.5Re and 4Re, respectively. Presuming thatthe Sersic profile is a good approximation to thesurface brightness profile of the UDGs, this an-nulus is large enough to avoid contamination ofthe sky region by the galaxy itself (see Graham& Driver 2005). We use sigma-clipping to re-move the contribution of other sources when weestimate the median background. All observedmagnitudes are corrected for the foregroundGalactic extinction using the dust maps fromSchlegel et al. (1998) recalibrated by Schlafly &Finkbeiner (2011) assuming that RV = 3.1 forthe Milky Way (Savage & Mathis 1979).

The aperture photometry method describedabove has the advantage of allowing the detec-tion of most UDGs in individual bands despitetheir low SNR. However, in most cases (87galaxies), at least one band was not detected,as the measured flux inside the galaxy is smallerthan the flux in the sky annulus. In these cases,we are only able to set an upper limit on thesource flux. There are missing detections inmost of the bands, but the blue bands are themost affected, in particular the narrow bandsF378 and F395, for which there are flux detec-tions in only ∼ 60% of the galaxies. Never-

6 Barbosa et al.

theless, in the majority of the cases (97 galax-ies), we have flux detections in at least 6 bands,which already provides better spectral coveragein the optical than do the SDSS bands, and 80%of the galaxies have detected flux in at least 9bands.

In Figure 2, we show a sample of detection im-ages of SMUDGes UDGs, produced by stackingall 12 S-PLUS bands, ordered in decreasing cen-tral surface brightness in the g band, µ0,g, andhighlight the photometric apertures.

4. STELLAR POPULATIONS FROMMULTI-BAND OBSERVATIONS

We quantify the properties of the stellar popu-lations of our sample by performing spectral en-ergy distributions (SED) fitting of the galaxiesin all detected bands of the S-PLUS data. Con-sidering that the star formation history (SFH)of galaxies is difficult to determine from photo-metric data alone, and that simulations indicatethat UDGs may have bursty SFHs (Di Cintioet al. 2017; Chan et al. 2018), we assume thatSEDs may be described by a single stellar pop-ulation (SSP), such that

fλ(λ) = f0 · SSP([Fe/H],Age, z)10−0.4Aλ (1)

where f0 is a scale factor for the spectral fluxdensity of the galaxy, SSP represents a sin-gle stellar population model that depends ofthe metallicity ([Fe/H]) and age, and the red-shift z of the galaxy, and Aλ represents a dust-screen attenuation model. One important cau-tionary point about the use of SSPs to repre-sent a potentially more complicated SFH is thatthe derived properties are luminosity weighted.As appreciated previously (cf. Serra & Trager2007), luminosity-weighted ages are expected tobe biased toward the youngest populations, incontrast to the luminosity-weighted metallicity,which reflects more closely the mass-weightedaverage.

Considering both the low SNR of the obser-vations and the low spectral resolution of thephotometric system, we expect that derived pa-rameters may be correlated, as is the case in thewell-known age-metallicity degeneracy problem(Worthey 1994), and that some parameters willnot be properly estimated. Therefore, we usea Bayesian statistical model to fit the SED ofthe galaxies and to estimate the stellar pop-ulation parameters. Using this approach, wecan identify possible parameter correlations andprovide uncertainties that are marginalized overthe distribution of all the other parameters inthe model.

Bayes’ theorem allows for the inference of theprobability distribution of a set of parametersθ in a statistical model based on a dataset Dusing the relation

p(θ|D) ∝ p(θ)p(D|θ), (2)

where p(θ|D) represents the posterior probabil-ity distribution of the parameters θ given thedata D, p(θ) represents the prior distribution ofthe parameters, and p(D|θ) is the likelihood dis-tribution (see, e.g. Gelman et al. 2004). Belowwe describe the priors for all of the parametersin our model.

4.1. Prior and likelihood distributions

The flux scale factor f0 can vary by ordersof magnitude depending on the brightness ofthe source. Therefore, it is more convenient tomodel its logarithm, which can be described bythe prior

log f0 ∼ Normal(µ0, σ20), (3)

where µ0 and σ20 indicate the mean and the vari-

ance of the distribution respectively. In prac-tice, we estimate µ0 using the data, and we as-sume σ0 = 3 to allow a large range of magni-tudes.

Our modeling is parameterized in terms oftwo stellar population parameters, the age and

100 SMUDGes in S-PLUS 7

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Figure 2. Six example detection images of SMUDGes galaxies in S-PLUS. The panels are ordered accordingto decreasing g-band central surface brightness, starting in the upper left. The solid red ellipses outline the1Re photometric aperture while the dashed red lines indicate the annulus used for background estimation.

metallicity, whose priors are set by the limits ofthe model ranges. In this work, we use the E-MILES models (Vazdekis et al. 2016), assumingprior distributions given by

[Fe/H](dex) ∼ Uniform(−1.79, 0.4) (4)

Age(Gyr) ∼ Uniform(0.4, 14). (5)

The main reason to set the limits above is toensure that the SSP models have good qualityin the ultra-violet according to the classifica-tion of Vazdekis et al. (2010), resulting in theexclusion of SSP models with [Fe/H]= −2.27,which may not be appropriate for metallicityestimation. Additionally, we also require a reg-

ular grid in the parameter space to perform lin-ear interpolation of the SSP models, allowinga continuous coverage of ages and metallicities.As a consequence, we had to restrict the mod-els to ages greater than 0.4 Gyr because partof the young SSP models are not extended tothe near-infrared, which is necessary to coverthe S-PLUS z band properly. In particular,we adopt SSP models with bimodal initial massfunction (IMF), a piecewise function defined byVazdekis et al. (1996) that matches the SalpeterIMF for masses > 0.8M� but is flattened atlower masses similarly to the Milky Way IMF(e.g. Chabrier 2003). Given that the currentversion of the E-MILES stellar population mod-

8 Barbosa et al.

els do not include the abundance of individualor alpha elements yet, we are restricted to thebase models, which assume that [M/H]=[Fe/H]at solar metallicity. However, this assumptiondoes not hold at low metallicities because theMilky Way stars used in the computation ofthe models are themselves alpha-enhanced (seeVazdekis et al. 2010). The consequences of pos-sible offsets resulting from non-solar abundanceratios are discussed further below.

The redshifts of our galaxies are of great in-terest because they set the distances to thegalaxies and their physical parameters, and al-low a proper classification of the candidatesas UDGs. Without additional spectroscopic orredshift-by-association for our sample, we con-sider a prior that takes into consideration a fewassumptions. LSB galaxies with angular sizesRe & 5′′ have only been associated to envi-ronments with distances smaller than 100 Mpc(see Gonzalez et al. 2018), thus we can assumeall UDG candidates are nearby. Moreover, allUDG candidates were selected with a minimumeffective radius of Re = 5.3′′, which implies aphysical radius of Re = 2.5 kpc at the distanceof Coma, 100 Mpc, or a redshift of z ≈ 0.023.At a distance as low as 200 Mpc, or z ≈ 0.046,these UDGs would all already have an effectiveradius of Re ≥ 5 kpc, which is larger than mostUDGs found so far (e.g. Venhola et al. 2017).We conclude that it is very unlikely that manyof our candidates lie at z > 0.04. Based on theseconsiderations, we use the prior

z ∼ HalfNormal(0.032), (6)

where we adopt the half-normal distribution torestrict the redshifts to positive values, and weassume a variance of 0.032. In practice, thisprior implies a median redshift z ≈ 0.02, similarto Coma, with peak probability at z = 0.

Regarding the dust attenuation, our data in-clude only wavelengths λ > 3000 A for lowredshift galaxies, avoiding the 2175 A bump

(Stecher 1965). For these wavelengths, mostof the extinction laws, such as those obtainedfor the Milky Way (Allen 1976; Fitzpatrick &Massa 1986), the Large Magellanic Cloud (Fitz-patrick & Massa 1986), the Small MagellanicCloud (Prevot et al. 1984; Bouchet et al. 1985),and starburst galaxies (Calzetti et al. 2000),agree (see Werle et al. 2019). We adopt aparametrized extinction law from Cardelli et al.(1989), which depends on two parameters, thetotal extinction in the V -band, AV , and thetotal-to-selective extinction, RV . The total ex-tinction is modeled according to the prior

AV ∼ Exponential(0.2), (7)

where 0.2 represents the mean value of the ex-ponential distribution. This prior restricts thevalue of the extinction to positive values andalso favors smaller extinction values rather thanlarge. We also allow RV to vary in our modelsusing the prior

RV ∼ Normal+(3.1, 1.), (8)

which assumes that the total-to-selective extinc-tion is similar to that measured generally withinthe Milky Way (Savage & Mathis 1979). Theplus signal indicates that we restrict RV to pos-itive values.

Finally, it is necessary to define a log-likelihood for the use of the Bayes’ theorem.The widely common assumption is that theobserved SED consists of independent, normalrandom variables, and thus the log-likelihoodcan be simply described as a χ2-distribution.However, the accuracy of the model determinedusing the normal assumption may be compro-mised if the observations contain outliers (seeVanhatalo et al. 2009). In observational set-tings, the causes of outliers may be either ex-ternal to the source, such as contamination bycosmic rays or the incomplete removal of sky, orinternal to the source, as is the case when the

100 SMUDGes in S-PLUS 9

model is incomplete, for example when it doesnot account for emission lines.

Emission lines have been directly observed inoptical observations of at least one cluster UDG(Kadowaki et al. 2017), and may be commonin field UDGs (Leisman et al. 2017). Obser-vationally, emission lines systematically inflatethe observed fluxes in passbands in which theyappear, an effect that is likely to be most no-ticeable in the bluer, narrow bands. However,the modeling of emission lines requires the inclu-sion of secondary stellar population with youngages (< 0.01 Gyr) and/or post-asymptotic giantbranch stars (Byler et al. 2017) plus a prescrip-tion for nebular emission (e.g. Fioc & Rocca-Volmerange 1999; Leitherer et al. 1999). Tosimplify the modeling, we instead adopt a ro-bust fitting approach that may deal with out-liers, including possibly emission lines, adoptinga Student’s t-distribution log-likelihood.

Similar to the normal distribution, the Stu-dent’s t-distribution is a symmetric and bell-shaped distribution, but with long tails thatallow for a non-negligible probability far fromthe center of the distribution (see Gelman et al.2004). Assuming that we are modeling N dis-crete bands in a given SED, the log-likelihoodthat we map is given by

ln p(D|θ)=N log

[Γ(ν+1

2

)√π(ν − 2)Γ

(ν2

)]

− 1

2

N∑i=1

log σ2i

− ν + 1

2

N∑i=1

log

[1 +

µ2i

σ2i (ν − 2)

],(9)

where Γ(x) represents the gamma function ofvariable x, ν represents the degrees of freedomof the Student’s t-distribution, σi represents theuncertainties of a given SED for the i-th band,and the mean µi represents the difference be-tween the observed and the model SED. The

Student’s t-distribution log-likelihood does notdepend solely on the data and its uncertainties,but also on the value of another variable, ν,which controls the amount of weight on the tailsof the Student’s t-distribution. For instance, ifν → 2, the tails of the distribution have moreweight in the distribution, whereas if ν → +∞,the distribution tends to a normal distribution.We also model the value of ν during the log-likelihood mapping assuming a non-informativeprior for the degrees-of-freedom given by

ν ∼ Uniform(2, 50), (10)

which is required to be open-ended only in thelower bounds to avoid the undefined likelihoodthat occurs if ν = 2.

4.2. Sampling and results

To deploy the above SED fitting modeling inthe context of the S-PLUS project, we devel-oped a Bayesian SED fitter (BSF, Barbosa,in prep.) as a general tool to model eitherSEDs or spectra of galaxies. BSF is writtenin the Python programming language based onthe pymc3 statistical package (Salvatier et al.2016), which allows for the construction of gen-eral Bayesian models while abstracting the com-plex issues related to the actual modeling andsampling. An attractive feature of the pymc3

package, not found in other commonly adoptedpackages such as the emcee (Foreman-Mackeyet al. 2013), is the implementation of the NoU-Turn Sampler (NUTS, Hoffman & Gelman2011), a Hamiltonian Monte Carlo sampler thathas been shown to perform well in complex,multidimensional problems without the needof manual tuning. This sampler works bet-ter than other traditional samplers, such as theMetropolis-Hastings algorithm (Hastings 1970)and the Gibbs sampler (Gelfand & Smith 1990),in problems with highly-correlated variables ina space parameter with hundreds of dimensions(see Hoffman & Gelman 2011).

10 Barbosa et al.

As discussed in §3, there are a number of non-detections in our photometry. To simplify ourmodeling, we only included detected bands inthe SED fitting for each UDG, and we leavethe modeling including non-detections for forth-coming work. The samples from the posteriordistributions were generated with BSF in fourchains with 500 burn-in interactions and 500draws. Figure 3 shows the comparison betweenthe observations and the models for the sampleof galaxies previously shown in Fig. 2.

To illustrate the process of obtaining rep-resentative values and uncertainties for themodel parameters, Fig. 4 shows the posteriorsamples determined with BSF for two of theUDGs presented in Fig. 2: SMDG0123079-002109, representing a relatively faint galaxyand SMDG0238220-011927 representing a rel-atively bright galaxy. Throughout our analysis,we use the median to determine the represen-tative value of all parameters, and we use thepercentile values of 16% and 84% to estimatethe 1σ confidence intervals of the parameters,always using the marginalized posterior distri-bution, shown in the histograms. In Table 1,we present the results of this analysis for thefirst ten entries of the SMUDGes sample. Thefull table is available online in machine-readableformat.

4.3. Stellar masses

We determine the stellar mass of each UDGcombining our SED fitting results of the S-PLUS data with the photometric propertiesmeasured in the deeper SMUDGes images. Weadopt two different approaches. First, we usethe SED fitting photometric redshift to esti-mate the distance and the total apparent r-bandmagnitude from SMUDGes to determine thetotal magnitude, assuming a Hubble-Lemaıtrelaw with H0 = 70 ± 2 km s−1 Mpc−1. Next,we use the r-band mass-to-light ratio from theE-MILES models (Vazdekis et al. 2010; Ric-ciardelli et al. 2012) to obtain the total stel-

lar mass, assuming that M�,r = 4.65 (Willmer2018). These calculations are performed usingthe Monte Carlo chains, and thus the uncer-tainties are marginalized over all parameters inthe SED fitting model. Second, we estimate thestellar mass using the color-mass relation fromTaylor et al. (2011), which is based on data fromthe Galaxy And Mass Assembly (GAMA) sur-vey (Driver et al. 2009, 2011). Reassuringly, thestellar masses resulting from the two approachesalways agree to within 0.1 dex, which is a differ-ence that is much smaller than the typical massuncertainties (∼0.8 dex). We conclude that ourstellar mass estimates are likely to be dominatedby internal random uncertainties rather than bya systematic error in the conversion between lu-minosity and stellar mass. For the remainder ofthis work, we use the stellar masses determinedusing the first method. The stellar masses de-rived by the first method are also presented inTable 1.

4.4. Evaluating the posterior distributions

To understand how well we constrain the pa-rameters in our model, we compare the poste-rior distributions with the prior distributions.We perform this exercise in Fig. 5, where weshow the posterior medians and uncertaintiesfor five free parameters in our model (AV , RV ,Age, [Fe/H], z) as a function of mr, the appar-ent magnitude of the galaxies according to theSMUDGes measurements. Overall, the fittingis better constrained, i.e., is restricted to a nar-rower range of values in the posterior distribu-tion, for the brighter sources (mr . 19), whilethe posterior distributions tend to be more sim-ilar to the prior distribution for the faintersources (mr & 19). We discuss the results forthe individual parameters below.

The extinction law parameters have limitedimpact on the optical SED shape of the UDGs,and no strong dust attenuation was required tofit the models. The median total extinction ofAV ≈ 0.1−0.2 is recovered in all cases, whereas

100 SMUDGes in S-PLUS 11

0

2

4

6fλ

[10−

17

erg

/(s

cm

2A

)] SMDG0249232-004458AV =0.2+0.2

−0.1

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dex

Age=7.9+3.8−3.7

Gyr

z=0.02+0.02−0.01

logM∗=8.3+0.6−1.0

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[10−

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−0.1

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dex

Age=6.0+5.2−3.5

Gyr

z=0.01+0.02−0.01

logM∗=8.1+0.8−1.1

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[10−

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)] SMDG0229481+011243AV =0.1+0.1

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dex

Age=6.1+5.2−3.9

Gyr

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dex

Age=3.7+6.5−2.5

Gyr

z=0.01+0.02−0.01

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[10−

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/(s

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)] SMDG0128559-011210AV =0.1+0.2

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dex

Age=7.3+4.4−4.1

Gyr

z=0.02+0.02−0.01

logM∗=7.7+0.7−1.1

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fλ

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/(s

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)] SMDG0123079-002109AV =0.1+0.2

−0.1

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dex

Age=3.6+6.7−2.7

Gyr

z=0.02+0.02−0.01

logM∗=7.5+0.7−1.1

M�

4000 5000 6000 7000 8000 9000

λ (A)

0

5

∆fλ

Figure 3. Resulting SED fits for the six examples presented in Fig. 2. The blue filled circles represent theS-PLUS flux densities in detected bands. The shaded regions indicate the confidence percentile levels of theSED fitting, from 5 to 95% in intervals of 10%. Each panel comes in two portions, where the upper areashows the data and SED fit and the lower shows the residuals. A summary of the most relevant parametersis included in upper right of each panel.

12 Barbosa et al.

−2

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H]

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(Gyr)

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SMDG0123079-002109

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Age=3.6+6.7−2.7 Gyr

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SMDG0238220-011927

AV =0.1+0.1−0.1

[Fe/H]=−1.4+0.4−0.3 dex

Age=6.0+5.2−3.5 Gyr

z=0.01+0.02−0.01

Figure 4. Sampled posterior distributions for two UDGs, SMDG0123079-002109 (left) and SMDG0238220-011927 (right) representing cases of the faint and bright end of the apparent magnitude distribution in oursample, respectively. The histograms along the diagonal contain the marginalized posterior distribution ofparameters from where the resulting values and uncertainties are evaluated. The panels under the diagonalcontain projections between pairs of variables, indicating how they are correlated. Solid lines mark themedians of the distributions, whereas dashed lines mark the 16% and 84% percentiles used to define the 1σuncertainties. A summary of the results is included in the upper right corner of each panel.

100 SMUDGes in S-PLUS 13

Table 1. Stellar population parameters for SMUDGes UDGs obtained from SEDfitting of the S-PLUS optical data.

Name AV [Fe/H] (dex) Age (Gyr) z logM?

(1) (2) (3) (4) (5) (6)

SMDG0006543-000029 0.07+0.12−0.05 −1.3+0.7

−0.34 2.8+7.0−2.1 0.018+0.020

−0.013 7.5+0.7−1.1

SMDG0016502-002756 0.11+0.17−0.08 −1.0+0.8

−0.5 7.1+4.5−4.0 0.021+0.020

−0.015 8.0+0.6−1.0

SMDG0021031+004447 0.18+0.28−0.13 −0.4+0.6

−0.8 8.0+4.3−4.5 0.022+0.021

−0.015 7.9+0.7−0.9

SMDG0025396+011515 0.10+0.19−0.07 −1.1+0.8

−0.5 5.8+5.5−4.5 0.019+0.020

−0.013 7.5+0.7−1.0

SMDG0035569+010149 0.08+0.14−0.06 −1.2+0.6

−0.4 3.1+6.9−2.3 0.017+0.021

−0.011 7.4+0.7−1.0

SMDG0045200-011839 0.07+0.12−0.05 −1.3+1.0

−0.4 1.5+6.0−0.9 0.018+0.018

−0.013 7.4+0.7−1.2

SMDG0055526-011739 0.14+0.24−0.10 −0.8+0.8

−0.7 7.4+4.4−4.6 0.020+0.022

−0.014 7.5+0.7−1.1

SMDG0058071-010201 0.09+0.14−0.07 −1.2+0.8

−0.4 4.6+6.1−3.5 0.021+0.021

−0.015 8.0+0.6−1.0

SMDG0108359-002834 0.18+0.28−0.14 −0.5+0.6

−0.8 8.0+4.1−4.4 0.022+0.024

−0.015 7.9+0.7−1.1

SMDG0113101-001223 0.10+0.15−0.07 −1.1+0.8

−0.5 4.3+6.6−3.4 0.020+0.020

−0.014 7.4+0.7−1.1

Note—Table sample containing only the first ten entries. The full table is availablein machine-readable form.

the total-to-selective extinction RV is mostlyunchanged from the prior distribution. In prac-tice, both parameters have the role of nuisanceparameters in our analysis, as they are not ofdirect interest for this work, but are still takeninto consideration in the analysis of the stellarpopulations parameters and the redshift.

The metallicity clearly departs from the priordistribution in most cases, with median metal-licities systematically small ([Fe/H]≈ −1 dex).Even though the 1σ uncertainties remain sim-ilar to the prior for the faint UDGs, the pos-terior distributions for the metallicity are usu-ally skewed towards low metallicities in mostcases, and are not flat-shaped like the priors.The main concern in the derived metallicitiesoccur for the more metal-poor galaxies, giventhat they are sometimes compatible with thelowest metallicity available in our SSP grid([Fe/H]=−1.79). Without a larger grid of mod-els, we can not rule out that some of thesesystems have even lower metallicities. Overall,

however, we conclude that our metallicities es-timates are well constrained by our SED fitting.

Similarly, despite the large uncertainties forthe faint UDGs, we do find that the luminosity-weighted ages tend to be smaller than the priormedian (Age ≈ 7 Gyr). One important pointin the evaluation of the ages is that we can seemore variation in the SED’s of younger galaxies,in the sense that it is easier to differentiate be-tween a 1 Gyr and a 2 Gyr old population thanto differentiate between a 10 Gyr and a 12 Gyrold population. We see that effect in practice inour modeling in Fig. 5, as the posterior distri-bution for galaxies with young ages are usuallynarrower than the prior distribution, while forthose with old ages we tend to obtain relativelyflat posteriors. Overall, we conclude that we areable to differentiate between young and old stel-lar populations in our UDG candidates, whichis enough to allow a broad discussion of the for-mation of these systems.

Finally, the quality of the modeled photomet-ric redshifts also depends on the apparent mag-

14 Barbosa et al.

0.0

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H]

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17 18 19 20 21

mr

0.02

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z

Figure 5. SED fitting parameters as a functionof the r-band apparent magnitude. The blue cir-cles indicate the posterior distribution median andthe grey vertical lines represents the 1σ uncertain-ties of the five free parameters, while the orangesolid (dashed) lines indicate the median (±1σ un-certainties) of the prior distributions of the sameparameters.

nitude of the UDGs. The posterior redshift dis-tribution for the faint UDGs is very similar tothe prior distribution. In these cases, the quoteduncertainties in the redshift are around 0.8 dex,which is simply the propagation of allowed prior

range. On the other hand, the bright UDGshave a narrower range of redshifts in the poste-rior distribution, and their median redshifts areusually smaller than the prior median of ≈ 0.02.However, even in these cases, the redshift esti-mate is very uncertain, and we are only ableto constrain the photometric redshift with er-rors σz ≈ 0.01 in the best cases. This has im-portant implications in the classification of theUDG candidates, as we discuss below.

4.5. Implications of the estimated redshifts tothe classification of UDG candidates

The most important implication of the red-shift uncertainty is on the question of whetherthe UDG candidates are real UDGs, i.e., arethey physical large, Re ≥ 1.5 kpc. We showedin §4.4 that we are only able to minimally con-strain photometric redshift for the bright UDGcandidates (mr . 19), and we rely on theprior distribution to estimate the redshift of thefainter UDG candidates.

If, for the sake of argument, we consider thephotometric redshift estimates to be correct, wecan test whether the candidates can be classifiedas UDGs and whether this leads to any obviousirregularities. First, in Fig. 6 we show the es-timated effective radii of our UDG candidatesas a function of the apparent magnitude, usingthe posterior distribution samples for the photo-metric redshift, and adopting the angular sizes,Re, determined by SMUDGes. We use the ap-parent magnitude as the independent variableto emphatize that our ability to constrain thesizes are directly affected by the observed lumi-nosity of the UDGs, but this does not reflect theactual size-luminosity relation that is expectedto exist for UDGs if they are similar to othergalaxies (e.g. Kormendy 1977). All but two can-didates are larger than the UDG criterion withgreater than 50% confidence. Of course, for thefainter systems this is principally a reflectionof the adopted prior distribution, but for thebrighter systems, where the determined redshift

100 SMUDGes in S-PLUS 15

differs from the prior median, we have greaterconfidence that the physical sizes bear some re-semblance to the truth. Second, the adoptedredshifts do not lead to an unexpected set ofvery large (Re > 6 kpc) UDGs. As such, ourdeterminations are not manifestly incorrect.

17 18 19 20 21

mr

0

1

2

3

4

5

6

7

8

Re

(kp

c)

Figure 6. Effective radii of UDG candidates as afunction of their apparent magnitude. The circlesand their uncertainties indicate the median and the1σ uncertainties of the effective radius calculatedusing the posterior distributions of the SED fitting.The orange dashed line indicate the minimum phys-ical radius of UDGs.

Given the limited redshift information con-tained in our observations, we are unable to con-clude that our candidates are all real UDGs, butthe bright ones are likely to be real UDGs, aswell as the ones we discussed previously as con-firmed through distance-by-association. For thesample as a whole, we argue based on volumeconsiderations that they are likely to be fartheraway than our adopted median prior distance.The argument goes as follows. First, we specifythat the maximum size of any UDG is Re = 6kpc, which sets a maximum distance for each ofour candidates. The candidate can lie at anydistance up to this maximum distance. Second,we assume that the parent population of ourcandidates is uniformly distributed throughoutthe local volume. Third, we claim that ourselection is effectively independent of distance,

within this volume, because it depends on sur-face brightness more than on luminosity. Thelatter statement is not strictly correct, but validat the coarse level of this argument (Zaritskyet al. 2019). In such a scenario the mean dis-tance to our candidates is 159 ± 40 Mpc, orz = 0.036 ± 0.01, which is greater than ouradopted median prior and supports the argu-ment that the majority of candidates are in-deed UDGs. In the next sections, we use theterm UDG for all candidates, acknowledgingthat some of them might not meet the physi-cal size criterion for UDGs.

5. DISCUSSION

In this section we examine a variety of es-tablished galactic relations and properties, andplace our UDG sample in context. We restrictour discussion to the stellar population prop-erties and to only one variable that dependson the distance, the stellar mass, to avoid ob-served relations that may be contaminated bylarge correlations among parameters owing toour photometric redshift estimations.

5.1. The stellar mass-metallicity relation ofUDGs

We begin this exploration by determiningwhether UDGs are similar to other LSB galaxies(see McConnachie 2012; Kirby et al. 2013), andthus follow the same stellar mass-metallicity asbright galaxies (Gallazzi et al. 2005). Previ-ous studies found that UDGs usually conformto the stellar mass-metallicity relation definedby dwarf galaxies, but most of those UDGs arein or near clusters, such as Coma (Gu et al.2018; Ferre-Mateu et al. 2018; Ruiz-Lara et al.2018), with a few examples of UDGs not associ-ated to clusters (Martınez-Delgado et al. 2016;Greco et al. 2018; Fensch et al. 2019).

In Figure 7 we show the stellar mass-metallicity relation and include our sample ofUDGs. There is a large variety of data types,models and methods involved in the deter-

16 Barbosa et al.

mination of stellar populations of UDGs inthe literature, and part of the scatter in themass-metallicity and other relations may be at-tributed to that. For instance Greco et al.(2018) have shown a difference of 0.3− 0.5 dexin the metallicity of UDGs by simply changingfrom a single stellar population to an extendedstar formation history. However, despite thisimportant caveat, our measurements are con-sistent with previous work, with UDGs fillingpart of the gap between dwarf and giant galax-ies. In the bottom left of the figure, we includedan ellipse whose shape shows the covariance be-tween the two parameters, which indicates thatthe stellar mass and the metallicity are basicallyindependent in our measurements.

Our large sample of galaxies allows the obser-vation of a range of metallicities that matchesthe variety of metallicities previously indenti-fied in the literature. However, the large un-certainties and the censored limits in the rangeof metallicites do not allows a reliable measureof the metallicity scatter for the UDGs in thesample. Overall, the location of the popula-tion of UDGs in the stellar mass-metallicity di-agram indicates a similarity with other dwarfLSB galaxies, such as those observed by Kirbyet al. (2013). On average, the metallicities ofthe UDGs, as presented, are slightly larger thanthose predicted from the extrapolation of therelation derived from measurements of dwarfgalaxies, but there are a few important consid-erations that favor the idea that the metallicityof UDGs follows the same relation of the dwarfgalaxies.

First, the UDGs are not statistically far awayfrom the dwarf sequence. Considering onlyour sample of UDGs, the mean difference be-tween the measured metallicity and the ex-pected metallicity from the Kirby et al. (2013)relation is 0.18 dex, which is similar to thescatter of the dwarf galaxies around the mean(0.14 dex), and much smaller than the mean

6 7 8 9 10 11 12

log M∗/M�

−2.5

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This work

Martınez-Delgado et al. (2016)

Gu et al. (2018)

Ferre-Mateu et al. (2018)

Pandya et al. (2018)

Ruiz-Lara et al. (2018)

Greco et al. (2018)

Fensch et al. (2019)

Kirby et al. (2013)

Gallazzi et al. (2005)

Figure 7. The stellar mass-metallicity relationfThe blue dashed ellipse in the bottom right indi-cates the mean 1σ covariance between the parame-ters, where the direction of largest (smallest) vari-ance corresponds to the major (minor) semi-majoraxis.or UDGs in our sample (filled blue circles) andfrom the literature (Martınez-Delgado et al. 2016;Gu et al. 2018; Ferre-Mateu et al. 2018; Pandyaet al. 2018; Ruiz-Lara et al. 2018; Greco et al. 2018;Fensch et al. 2019). The pink solid and dashed linesare the mean and the scatter of the stellar mass-metallicity of dwarf galaxies around the Milky Wayfrom Kirby et al. (2013). The gray lines are themean and the standard deviation of the propertiesof bright galaxies from Gallazzi et al. (2005). Theshape of the blue dashed ellipse in the bottom leftindicates the mean 1σ covariance between the pa-rameters, where the direction of largest (smallest)variance corresponds to the major (minor) semi-major axis.

error in our measurements (0.6 dex). Second,there may be a systematic error in our mea-surements related to the assumed relation be-tween the total metallicity and the iron abun-dance, [M/H]=[Fe/H], because the low metallic-ity stars used in the E-MILES models containalpha elements. Ferre-Mateu et al. (2018) re-ported a few UDGs with significant over abun-dance of magnesium ( 0 . [Mg/Fe] . 0.4 forthree out of four galaxies) and Martın-Navarro

100 SMUDGes in S-PLUS 17

et al. (2019) reported an even larger over abun-dance in DGSAT I, [Mg/Fe]=1.5. An averagemagnesium abundance of [Mg/Fe]≈ 0.2 dex isenough to account for the difference we findbetween the metallicity of our UDGs and thatpublished for the dwarf galaxies2. Finally, ourSSP models are restricted to a lower limit of[Fe/H]= −1.8, and thus the metallicity of someUDGs in our sample may be over estimated.Note that a factor of two smaller distances,which would then render most of our candidatesas non-UDGs, would lead to a factor of 4 lowerstellar mass and would exacerbate the metallic-ity offset.

In conclusion, the metallicity of the UDGs isroughly consistent with that of other galaxies ofsimilar stellar masses, the high-mass end of thedwarf sequence, and so do not show any signs ofa different formation path than those galaxies.

5.2. The luminosity-weighted ages of fieldUDGs

The reported ages of UDGs have usually beenlarge, > 4 Gyrs, but again almost all publishedresults are for Coma galaxies (Gu et al. 2018;Ruiz-Lara et al. 2018; Ferre-Mateu et al. 2018).In the limited available examples of field UDGs,however, the reported luminosity-weighted ageshave consistently been younger, with ages rang-ing from 1 to 3 Gyr (Martınez-Delgado et al.2016; Greco et al. 2018; Martın-Navarro et al.2019). In fact, the UDG population in the fieldis expected to have a larger variety of colorsthan that of the clusters (Di Cintio et al. 2017)and there is observational support for this trend(van der Burg et al. 2016; Prole et al. 2019).

In Figure 8 we compare the luminosity-weighted age distribution of galaxies in our sam-ple to that of UDGs observed in the Coma (Guet al. 2018; Ruiz-Lara et al. 2018; Ferre-Mateuet al. 2018) and Virgo (Pandya et al. 2018) clus-

2 For the E-MILES models, [Fe/H]=[M/H]-0.75[Mg/Fe].

ters, to contrast the distribution of ages in clus-ters and in the field. Both the field and clusterUDGs typically have intermediate ages, with apeak in the age histogram around 7 Gyr, butour sample also indicates a significant fractionof UDGs with ages smaller than 4 Gyr.

0 2 4 6 8 10

Age (Gyr)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Pro

bab

ilit

y

Field UDGs

Cluster UDGs

Figure 8. Comparison of the luminosity-weightedages of our UDGs, which are primarily in the field,and those of UDGs in the literature (Pandya et al.2018; Gu et al. 2018; Ruiz-Lara et al. 2018; Ferre-Mateu et al. 2018), which are primarily in clusters.

Considering that we only have luminosity-weighted ages, the results from the our analysisare expected to be biased toward the youngestpopulations within a galaxy. Therefore, a fewdifferent, non-exclusive scenarios can explainthe additional fraction of UDGs with youngages. One possible explanation is the existenceof different UDG formation channels not presentin the cluster (e.g. Liao et al. 2019). Other pos-sibilities are that UDGs in the field might havemore continuous star formation activity, pre-sumably in the absence of cluster-related pro-cesses, such as harassment and ram-pressurestripping, and that field UDGs have had a re-cent, even on-going, star formation burst thatoutshines the older and more massive stellar

18 Barbosa et al.

component of the galaxy. Regardless of the de-tailed explanation, UDGs are able to flourishin the field by forming stars until much morerecently than UDGs in clusters.

5.3. The age-metallicity relation of UDGs

We compare in Figure 9 the luminosity-weighted age-metallicity relation for UDGs,both in the field and in galaxy clusters, to thatof bright galaxies. Within our own field UDGsample, there appears to be a correlation be-tween age and metallicity, but considering theexistence of a well-known age-degeneracy prob-lem, we first inspect whether this is causing theobserved relation.

The original age-deneracy problem (Worthey1994) indicates that the colors of an old pop-ulation are similar to those of another popula-tion three times older and with half the metallic-ity. This degeneracy is specific for broad bandsand old stellar systems, and thus it is unclearwhether this holds in our analysis. However, itis an important cautionary note to any stellarpopulation analysis, as degeneracies are boundto happen in SED fitting. As we indicate withthe error ellipse in the bottom of the figure,there is a correlation between the age and themetallicity in our posterior distributions thatis similar to the known age-metallicity degen-eracy. However, the observed relation betweenthe ages and metallicities of our UDGs does nothave a slope in the same direction as the age-degeneracy relation. Therefore, we concludethat the observed relation between ages andmetallicities in our UDG sample is not drivenby the age-metallicity degeneracy, and thus weare able to discuss some properties of the ob-served relation.

For the old UDGs (age& 6 Gyr), the age-metallicity relation follows a similar pattern tothat of bright galaxies (Gallazzi et al. 2005), inthe sense that younger systems have low metal-licity and older systems have high metallicity,although with different slope and offset. The

old UDGs have metallicities similar to those re-ported in other works for UDGs in clusters, butthis possible age-metallicity relation was nothinted at in previous work.

The young UDGs have a flat age-metalicity re-lation, but the modeling limitation in the rangeof very low metallicities limits us in reachingfurther conclusions as to whether the flatteningin the relation is real or a result of the modelingrestriction. The location of our young UDGs inthis space is similar to that of the field UDGsfrom Greco et al. (2018), which were suggestedto be currently star forming.

Interestingly, there are also a few young UDGs(t . 1 Gyr) with relatively high metallicities([Fe/H]≈ −0.5 dex), populating the locationof more massive galaxies. These UDGs arelocated in age-metallicity plane in a locationsimilar to that of DGSAT I, a passive, fieldUDG found in the Pisces-Perseus superclusterfilament (Martınez-Delgado et al. 2016). A vi-sual inspection of our young, metal-rich UDGsdoes not suggest current tidal interactions withbright galaxies, and thus it is not likely thatthese particular UDGs have tidal origins, whichcould have explained their higher metallicity. Amore likely scenario is that these cases indicatemore massive UDGs that have a recent burstin star formation, such that their luminosity-weighted metallicities are driven by a poten-tially old, mass-dominant stellar component,while their luminosity-weighted ages are drivenby a less massive, young component.

5.4. The stellar mass-age relation

In Figure 10 we present the relation betweenthe stellar mass and the luminosity-weightedage for our UDG sample and more massivegalaxies. Similarly to the age-metallicity rela-tion, we also observe a correlation between theages and the stellar masses. However, in thiscase, the error ellipse in the bottom of the fig-ure indicates that the observed correlation maybe caused by a degeneracy in the parameters,

100 SMUDGes in S-PLUS 19

0 2 4 6 8 10

Age (Gyr)

−2.5

−2.0

−1.5

−1.0

−0.5

0.0

[Fe/

H]

1σ

This work

Martınez-Delgado et al. (2016)

Gu et al. (2018)

Ferre-Mateu et al. (2018)

Pandya et al. (2018)

Ruiz-Lara et al. (2018)

Greco et al. (2018)

Fensch et al. (2019)

Gallazzi et al. (2005)

Figure 9. Comparison between luminosity-weighted ages and metallicities of UDGs in thefield (this work) and from the literature (Martınez-Delgado et al. 2016; Gu et al. 2018; Ferre-Mateuet al. 2018; Pandya et al. 2018; Ruiz-Lara et al.2018; Greco et al. 2018; Fensch et al. 2019). Solidand dashed lines are the mean and the standard de-viation of the relation for bright galaxies (Gallazziet al. 2005). The blue dashed ellipse in the bottomright indicates the mean 1σ covariance between theparameters.

and thus we do not have any confidence thatthis relation actually exists.

Most old UDGs (Age & 6 Gyr) follow the stel-lar mass - mass weighted age relation observedby Thomas et al. (2005), extrapolated to theUDG regime. We explain this agreement bynoting that the luminosity-weighted and mass-weighted ages converge the longer a galaxy isnot forming stars. However, the young UDGsare displaced from the relation of Thomas et al.(2005), and have ages similar to those in thelow-mass end of the Gallazzi et al. (2005) re-lation. We expect these young field UDGs tomove upward in this diagram when they even-tually stop forming stars.

6. SUMMARY AND CONCLUSION

7 8 9 10 11 12

log M∗/M�

0

2

4

6

8

10

12

14

Age

(Gyr)

1σ

This work

Martınez-Delgado et al. (2016)

Gu et al. (2018)

Ferre-Mateu et al. (2018)

Pandya et al. (2018)

Ruiz-Lara et al. (2018)

Greco et al. (2018)

Fensch et al. (2019)

Gallazzi et al. (2005)

Thomas et al. (2005)

Figure 10. Same as Fig. 9 for the relation betweenstellar mass and luminosity-weighted age for UDGsand bright galaxies.

Ultra-diffuse galaxies (UDGs) are large, lowsurface brightness galaxies. Although such sys-tems are now known in significant numbers, es-tablishing physical characteristics has proven tobe challenging even when using the largest tele-scopes of this generation. Field UDGs, in par-ticular, have barely been studied. In this work,we perform the first systematic study of thestellar populations of field UDGs combining thedeep and large area search of UDGs performedby the SMUDGes survey (Zaritsky et al. 2019)with the multiband capabilities of the S-PLUSsurvey (Mendes de Oliveira et al. 2019). Cover-ing an area of the ∼330 deg2 in the Stripe 82 re-gion, we fit spectral energy distributions (SEDs)to a sample of 100 field UDGs, representing thelargest sample of UDGs (field or cluster) forwhich ages and metallicites have been measuredto date.

We constrain our Bayesian SED fittingmethod with up to 12 broad and narrowbands from S-PLUS, resulting in estimatedluminosity-weighted ages, metallicities and stel-lar masses of the field UDGs. While stellarmasses and metallicities are mostly in agree-

20 Barbosa et al.

ment with previous studies, we observed a num-ber of UDGs with ages younger than thosefound in cluster. This result suggests thatUDGs in the field may have extended star for-mation histories that may, in some cases, extendto the current time, contrasting with the typi-cal old ages of UDGs found in clusters. We alsofound a few cases of relatively high-metallicityUDGs ([Fe/H]≈ −0.5) with young ages (ages. 1 Gyr) without clear indications of tidal inter-actions, which suggest ongoing episodes of starformation among the most massive UDGs.

Previous studies have already indicated thatUDGs may represent the extension of normalgalaxy properties rather than arising from a dis-connected, new path of galaxy formation, butthese conclusions have been based on small sam-ples of galaxies (Beasley & Trujillo 2016; Zarit-sky 2017) or models (Amorisco & Loeb 2016).By placing a large sample of field UDGs in stel-lar population scaling relations, we were able toconfirm that UDGs, as a population, are sim-ilar to dwarf and giant galaxies. There arestill puzzles to solve, such as the large globu-lar cluster abundances in the largest UDGs (van

Dokkum et al. 2017; Toloba et al. 2018) and theoffset from the baryonic Tully-Fisher relation(Mancera Pina et al. 2019), but we concludethat these should arise naturally from consider-ing a broader range of galaxies within the cur-rent picture of galaxy formation (Martin et al.2019) rather than any exotic processes (Bennetet al. 2018). Of course, these statements applyto the general case and individual exceptions,where UDGs form in tidal tails, for example,are not excluded.

Despite the improvement in sample size in thiswork, there is still much to be gained from evenlarger samples. In particular, we want to ap-ply the same analysis methods to UDGs in arange of environments, including massive clus-ters, to more confidently compare results. Evenlarger samples will enable us to test for furtherdependencies on UDG mass, environment, andmorphology. Both SMUDGes and S-PLUS arestill in their early phases. A much larger areaof the sky will be probed by both surveys inthe next years, increasing the sample for whichthis type of analysis can be replicated into thethousands.

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ACKNOWLEDGMENTS

The authors thank the anonymous referee for his/her comments. We are thankful to Stavros Akras,Yoli Jimenez Teja, Marco Grossi, Alvaro Alvarez-Candal, Jose Luis Nilo Castellon, Paulo Lopes,Kanak Saha, Eduardo Telles and Ana Chies Santos for providing comments and suggestions. CEB,CMdO gratefully acknowledges the Sao Paulo Research Foundation (FAPESP), grants 2011/51680-6,2016/12331-0 and 2018/24389-8. DZ, RD, and HZ gratefully acknowledge financial support from NSFAST-1713841. PC acknowledges support from FAPESP project 2018/05392-8, and Conselho Nacionalde Desenvolvimento Cientıfico e Tecnologico (CNPq) project 310041/2018-0. LS thanks the FAPESPscholarship grant 2016/21664-2. FRH thanks FAPESP for the financial support, grants 2019/23141-5 and 2018/21661-9. J. A. H. J. thanks to Brazilian institution CNPq for financial support throughpostdoctoral fellowship (project 150237/2017-0) and Chilean institution CONICYT, Programa deAstronomıa, Fondo ALMA-CONICYT 2017, Codigo de proyecto 31170038. The T80South robotictelescope (Mendes de Oliveira et al. 2019) was founded as a partnership between FAPESP, the Obser-vatorio Nacional (ON), the Federal University of Sergipe (UFS) and the Federal University of SantaCatarina (UFSC), with important financial and practical contributions from other collaborating in-stitutes in Brazil, Chile (Universidad de La Serena) and Spain (CEFCA). This work has made useof the computing facilities of the Laboratory of Astroinformatics (Instituto de Astronomia, Geofısicae Ciencias Atmosfericas, Departamento de Astronomia/USP, NAT/Unicsul), whose purchase wasmade possible by FAPESP (grant 2009/54006-4) and the INCT-A. This research has made use ofthe NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Labora-tory, California Institute of Technology, under contract with the National Aeronautics and SpaceAdministration.

Facilities: T80South

Software: astropy (Astropy Collaboration et al. 2013), matplotlib (Hunter 2007), numpy (van derWalt et al. 2011), pymc3 (Salvatier et al. 2016), scipy (Jones et al. 2001), photutils (Bradley et al. 2019).