Dwarf galaxies in the MATLAS survey: Hubble Space Telescope observations of the globular cluster system in the ultra-diffuse galaxy MATLAS-2019
Oliver Müller, Patrick R. Durrell, Francine R. Marleau, Pierre-Alain Duc, Sungsoon Lim, Lorenzo Posti, Adriano Agnello, Rúben Sánchez-Janssen, Mélina Poulain, Rebecca Habas, Eric Emsellem, Sanjaya Paudel, Remco F. J. van der Burg, Jérémy Fensch
DDraft version January 27, 2021
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Dwarf galaxies in the MATLAS survey: Hubble Space Telescope observations of the globular clustersystem in the ultra-diffuse galaxy MATLAS-2019
Oliver M¨uller , Patrick R. Durrell, Francine R. Marleau , Pierre-Alain Duc, Sungsoon Lim, Lorenzo Posti , Adriano Agnello, Rub´en S´anchez-Janssen, M´elina Poulain, Rebecca Habas, Eric Emsellem,
8, 9
Sanjaya Paudel , Remco F. J. van der Burg, and J´er´emy Fensch Observatoire Astronomique de Strasbourg (ObAS), Universite de Strasbourg - CNRS, UMR 7550 Strasbourg, France Department of Physics & Astronomy, Youngstown State University, Youngstown, OH 44555 USA Institut f¨ur Astro- und Teilchenphysik, Universit¨at Innsbruck, Technikerstraße 25/8, Innsbruck, A-6020, Austria University of Tampa, 401 West Kennedy Boulevard, Tampa, FL 33606, USA DARK, Niels-Bohr Institute, Lyngbyvej 2, Copenhagen, Denmark UK Astronomy Technology Centre, Royal Observatory, Blackford Hill, Edinburgh, EH9 3HJ, UK Institut f¨ur Astro- und Teilchenphysik, Universit¨at Innsbruck, Technikerstraße 25/8, Innsbruck, A-6020, Austria European Southern Observatory, Karl-Schwarzschild-Str. 2, D-85748 Garching, Germany Univ. Lyon, ENS de Lyon, Univ. Lyon 1, CNRS, Centre de Recherche Astrophysique de Lyon, UMR5574, F-69007 Lyon, France Department of Astronomy, Yonsei University, Seoul 03722, Republic of Korea (Received January 27, 2021; Revised —; Accepted —)
Submitted to APJABSTRACTUltra-diffuse galaxies (UDGs) are very low-surface brightness galaxies with large effective radii.Spectroscopic measurements of a few UDGs have revealed a low dark matter content, based on theinternal motion of stars or globular clusters (GCs). This is in contrast to the large number of GCsfound for these systems, from which it would be expected to correspond to a large dark matter halomass. Here we present
Hubble Space Telescope
Advanced Camera Survey observations for the UDGMATLAS-2019 in the NGC 5846 group of galaxies. Using images in the F W and F W filters, wetrace the GC population two magnitudes below the peak of the GC luminosity function. EmployingBayesian considerations, we find a total of 37 ± S N = 84 ±
12. Due to the superior image quality of the HST, we are able toresolve the GCs and measure their sizes, which are consistent with the sizes of GCs from Local Groupgalaxies. Using the linear relation between the total mass of a galaxy and the total mass of GCs wederive a halo mass of 1 . ± . × M (cid:12) , corresponding to a mass-to-light ratio of over 1000. Thissuggests that either this UDG has an overly massive dark matter halo for its stellar mass, comparedto other dwarfs – though not as massive as the Milky Way – or that the linear relation between thenumber of GCs and the dark matter halo mass breaks down for UDGs like MATLAS-2019. The highabundance of GCs, together with the small uncertainties, make MATLAS-2019 one of the most extremeUDGs, which likely sets an upper limit of the number of GCs for such objects. Keywords: editorials, notices — miscellaneous — catalogs — surveys INTRODUCTION
Corresponding author: Oliver M¨[email protected]
Dwarf galaxies are by far the most numerous galaxiesin the Universe (Ferguson & Binggeli 1994) and exist inall kind of environments, from dense clusters to isolatedvoids (e.g. Binggeli et al. 1990; Rekola et al. 2005; Kim& Jerjen 2015; M¨uller et al. 2017; Makarov et al. 2017).They are thought to be the most dark matter dominatedobjects, with the most extreme cases consisting of more a r X i v : . [ a s t r o - ph . GA ] J a n M¨uller et al. than 99% of this elusive material (Walker et al. 2007;McGaugh & Wolf 2010; Collins et al. 2020). A subsam-ple of the dwarf galaxy population is called ultra-diffusegalaxies (UDGs), a term coined by van Dokkum et al.(2015). UDGs are characterized by their large effectiveradii and very low-surface brightnesses. While their ex-istence has been known since the 1980’s (e.g., Sandage& Binggeli 1984; McGaugh & Bothun 1994; Dalcantonet al. 1997), recently they have become the focus of en-hanced attention by the astronomical community, dueto the discovery of hundreds of these objects rangingfrom cluster to group environments (e.g., Koda et al.2015; Mihos et al. 2015; Mart´ınez-Delgado et al. 2016;van der Burg et al. 2017; Venhola et al. 2017; M¨ulleret al. 2018; Zaritsky et al. 2019; Lim et al. 2020; Habaset al. 2020; Iodice et al. 2020; M¨uller et al. 2021), andas a result unlocked the potential to study these objectsin unprecedented detail.Due to their diffuse nature, they are an excellentprobe of the underlying gravitational potential (e.g.,Danieli et al. 2019; B´ılek et al. 2019; Mancera Pi˜naet al. 2019; Gannon et al. 2020). Such studies have beenconducted on some specific UDGs, like the two UDGs[KKs2000] 04/NGC 1052-DF2 (Karachentsev et al. 2000;van Dokkum et al. 2018a) and NGC 1052-DF4 (vanDokkum et al. 2019a) in the NGC 1052 group of galaxies,NGC 5846 UDG1/MATLAS-2019 (Forbes et al. 2019;Habas et al. 2020) in the NGC 5831 group of galaxies,VCC 1287 (Binggeli et al. 1985; Beasley et al. 2016) inthe Virgo cluster, and DF17 (Peng & Lim 2016) andDF44 (van Dokkum et al. 2016) in the Coma cluster.The extraction of the stellar velocity dispersion of thebody of the galaxy or the velocity dispersion of the glob-ular cluster (GC) population associated to the UDGshas enabled the study of the dark matter content ofthe galaxies (van Dokkum et al. 2018a, 2019a; Emsellemet al. 2019; M¨uller et al. 2020). While the measurementsat face values can be interpreted as an absence of darkmatter in these galaxies, both the observational (Martinet al. 2018) and systematic uncertainties (Laporte et al.2019) are too large to yet be conclusive.Two main mechanisms have been proposed for theformation of UDGs: either they are failed Milky Waylike galaxies which couldn’t build up their baryonic con-tent (e.g., van Dokkum et al. 2016; Peng & Lim 2016;Toloba et al. 2018), or they are the extended populationof dwarf galaxies, which were puffed up through tidaleffects (e.g. tidal interactions or tidal heatings, Ogiya2018; Toloba et al. 2018; Carleton et al. 2021). Thesetwo scenarios result in quite different dark matter halomasses for the galaxies. X-Ray observations of multipleUDGs (Kov´acs et al. 2019), as well as their location in the scaling relations (Habas et al. 2020), have revealedthat the majority of UDGs are consistent with beingnormal dwarf galaxies, adding evidence that UDGs aresimply the extension of the dwarf galaxy population to-wards larger radii. Still, this does not exclude the possi-bility that some UDGs could belong to the former groupof failed Milky Way galaxies. One archetypal UDG –namely DF44 in the Coma cluster – has been studiedin detail with spectroscopy (van Dokkum et al. 2016,2019b), deep imaging (van Dokkum et al. 2017), andX-ray observations (Bogdan 2020). While initial claims(van Dokkum et al. 2016) pointed it towards the group offailed galaxies – based on a high count of GCs, as wellas an atypical mass for a dwarf galaxy – these claimshave been weakened by more recent studies (Amoriscoet al. 2018; van Dokkum et al. 2019b; Saifollahi et al.2020; Bogdan 2020).One way to estimate the mass of a galaxy withoutmeasuring the internal stellar dynamics is through thenumber of GCs (Beasley et al. 2016; Burkert & Forbes2020). In a ΛCDM framework, the dark matter halos ofgalaxies are directly correlated with the abundance ofGCs, i.e. a high number of GCs indicates a vast haloof dark matter. Several studies based on deep imaginghave estimated the number of GCs associated to UDGs(Lim et al. 2018; Amorisco et al. 2018; Prole et al. 2019).They again indicate that UDGs are consistent with be-ing from the dwarf galaxy population, but due to thestatistical nature of these studies, the scatter and un-certainties are large. Furthermore, these studies weremainly conducted in dense cluster environments.The low-mass environments of groups of galaxies isstill uncharted territory. This has started to change inrecent years (e.g., Chiboucas et al. 2009; M¨uller et al.2015, 2017; Javanmardi et al. 2016; Park et al. 2017;Danieli et al. 2018; Carlsten et al. 2020; M¨uller & Jerjen2020). Among these campaigns is the Mass Assembly ofearly Type gaLAxies with their fine Structures (MAT-LAS, Duc et al. 2015; Duc 2020; B´ılek et al. 2020) sur-vey, a MegaCam based survey of over 200 nearby earlytype galaxies within 45 Mpc. The multi-color imagingin the ugri -filters and good image quality made it pos-sible to simultaneously detect dwarf galaxies and GCs.Over 2000 dwarfs have been discovered (Habas et al.2020), with ∼
5% of them being UDGs (Marleau et al.,in prep.). The UDG with the highest number of GCsin this systematic survey is MATLAS-2019 (Marleau etal., in prep.). This UDG has an effective surface bright-ness of ≈ . − in the g band, an effec-tive radius of 17.2 (cid:48)(cid:48) (= 2 . d = 26 Mpc, corresponding to thecenter of the NGC 5846 group), and a systemic veloc- he GC system of the UDG MATLAS-2019 ± − (M¨uller et al. 2020), which isconsistent with the NGC 5846 group of galaxies (Eigen-thaler & Zeilinger 2010, see also Fig. 1 in M¨uller et al.2020). Spectroscopic follow-up observations with MUSEhave confirmed that at least 11 GCs are associated withMATLAS-2019 (M¨uller et al. 2020). They are all con-sistent with being metal-poor and old. Intriguingly, atthe putative distance to the host group, the brightestGC would be almost as bright as ω Cen, which is unex-pectedly bright for such a low-surface brightness object.However, the data was too shallow to trace the GC pop-ulation to the faint end. A similar case is NGC 1052-DF2, with the claim that it has a population of too-luminous GCs (van Dokkum et al. 2018b). Either theseGCs are indeed too bright, or they are just the tip of theiceberg, i.e. the bright tail of a largely populated GCluminosity function (GCLF). In this work, we present
Hubble Space Telescope (HST) imaging of MATLAS-2019 to study its GC population by to tracing the fullGCLF. OBSERVATIONS AND DATA REDUCTIONOur HST images were obtained through a single orbitin the Mid-Cycle 27 program GO-16082, (PI: M¨uller)to observe the UDG MATLAS-2019, previously iden-tified in the MATLAS survey (Habas et al. 2020), aswell as independently reported in the VST Early-typeGAlaxy Survey (VEGAS, Forbes et al. 2019). We ob-served MATLAS-2019 with the HST Advanced Camerafor Surveys (ACS) in the F606W and F814W filters.The galaxy itself was placed at the center of one of theCCDs to maximize a suitable background/control sam-ple. Two dithered images (separated by 0.5 (cid:48)(cid:48) ) of 515 seach were taken in each filter. We used the final, reducedCTE-corrected (Charge Transfer Efficiency corrected) .drc.fits images produced by the standard pipeline andused the VEGAmag zeropoints provided by the ACSonline documentation .We performed aperture photometry on each filter withthe python package photutils (Bradley et al. 2020). Toremove the smooth light profile of the galaxy, we havemodelled and subtracted it with galfit (Peng et al.2002). To create a catalog of objects, we first ran sep(Barbary 2016), the Source Extractor (Bertin & Arnouts1996) implementation in python, with a 3 σ thresholdand a minimum of 5 adjacent pixels. On this catalog wemade a first cut, namely we rejected all sources with adetected radius smaller than 3 px or an ellipticity largerthan 0.2. This removed noise peaks as well as elon- gated objects such as background galaxies. On this cat-alog we performed photometry with a circular aperturewith a radius of 3 px. The median background valuewas estimated in an annulus with inner and outer radiiof 8 px and 23 px, respectively, employing a 3 σ clipping,and was subtracted from the photometry of the object.Aperture corrections were applied according to the ACSdocumentation . The F W and F W magnitudeswere corrected for extinction ( A F W = 0 .
131 mag and A F W = 0 .
081 mag) according to the extinction calcu-lator tool on NED (using Schlafly & Finkbeiner 2011).We then matched the catalogs in the two filters witha 0.5 arcsec tolerance. Finally, we applied a magni-tude cut in the F W band of 22 . < F W < . F W − F W ) color cutof 0 . < F W − F W < . N tot = 51 GC candidates located within 1.75 r eff of the galaxy center (this optimal aperture size is de-rived in Section 3.3). They are presented in Fig. 1 andFig. 2. As a reference background field, we use an areaof 100 < x < < y < r eff (see Fig. 1).To assess our completeness and photometric errors wehave injected artificial point sources in the HST dataand re-run our detection and photometry pipeline. Forthat we have created a PSF model using 14 hand-picked,isolated stars. These artificial stars were added on aevenly-spaced grid. We have repeated this for a mag-nitude range between 21 and 28.3 in both filters. Toget the completeness, we have compared the number ofinjected vs. number of detected objects. To not countreal objects as successfully detected artificial objects,we have provided Source Extractor with the originalsegmentation map of the image as a mask. For thephotometric error we have compared the injected andextracted magnitudes. The completeness drops below95% at F W = 26 .
74 mag and F W = 25 .
82 mag.The results of our artificial star experiments are shownin Fig. 3.To convert the HST F W and F W magnitudesinto the standard BV I system, we employed the trans-formations provided by Harris (2018) and assumed a( V − I ) = 0 . http://ned.ipac.caltech.edu/extinction calculator. M¨uller et al. h m s s s D e c li n a t i o n ( J ) Figure 1.
The full ACS field of view of our HST observations. In red we indicate the detected GCs, in blue the confirmed GCsfrom MUSE observations, and in yellow we show the selected field GCs. The black cirles are multiples of the effective radius,starting with 1 r eff . The white box indicates the reference field. V = F W + 0 . V − I ) (1) I = F W − .
13 + 0 . V − I ) (2)Due to the superior image quality of the HST the GCsin our data are partially resolved. To measure their halflight sizes ( r h ), we have employed galfit using a S´ersicprofile, which was convolved with the PSF model. PROPERTIES OF THE GLOBULAR CLUSTERPOPULATION3.1.
Globular Cluster Luminosity Function
In the following we will model the GCLF usingBayesian considerations. For the GCLF we assume anormal distribution G V : G V,j ( m V , δ V,err ) = 1 √ π σ obs exp − ( m V,j − µ V ) σ obs , (3)with σ obs = σ V,j + δ V,err . (4)The magnitude of the GC candidate j is given by m V,j .The total width σ obs is the combination of the intrin-sic width of the GCLF σ V and the mean error δ V,err of all the GCs. To model the background contamina-tion B V we use all GC-like objects outside 1.75 r eff tocreate a histogram with a bin size of 0.5 mag. We theninterpolate the midpoints of the bins to create B V . Sim-ilarly, we model the color of the GC distribution with anormal distribution G ( V − I ) and derive the background he GC system of the UDG MATLAS-2019 h m s s s D e c li n a t i o n ( J ) Figure 2.
The zoom in view of our HST observations. The radius of our GC selection (2 r eff ) is shown with the black line.The dashed black line corresponds to the radius where the GC count drops to a background level (i.e. at 1.75 r eff ) In red weindicate the detected GCs, in blue the confirmed GCs from MUSE observations, and in yellow we show the selected field GCs.One side is ≈ (cid:48)(cid:48) . contamination B ( V − I ) from all the GC-like objects out-side 1.75 r eff .We use a Plummer profile P to model the spatial dis-tribution of the GCs: P ( r ) j = 1 π r GC (1 + r j /r GC ) , (5)where r j is the galactocentric distance of the GC can-didate j and r GC is the half number radius of the GCsystem, which is a free parameter. To be consistent inthe dimensions, we multiply this density with the num-ber of GCs N GC associated with the galaxy:Σ( r ) j = N GC · P ( r ) j (6) The contamination c out to the outermost GC candi-date (having the radius R out ) is given by: c = ( N − N GC ) /R out . (7)Finally, the likelihood for a source j in our catalog isgiven by: L j = Σ j · G V,j G ( V − I ) ,j + c · B V,j B ( V − I ) ,j Σ j + c . (8)The parameters we are marginalizing over are µ V and σ V , i.e. the peak and the width of the GCLF; the num-ber of true GCs N GC associated with MATLAS-2019;the half number radius r GC of the GC system; and µ ( V − I ) and σ ( V − I ) , i.e. the peak and the width of the M¨uller et al.
22 24 26 28Artificial star magnitude0.00.20.40.60.81.0 D e t e c t i o n r a t e F606WF814W22 24 26 28Artificial star magnitude0.00.10.20.30.40.50.6 E rr o r ( m a g ) F606WF814W
Figure 3.
Results of the artificial star experiments. The toppanel shows the detection rate, the bottom panel the meanuncertainty of the recovered artificial stars. color distribution. As priors we use flat priors, namelyfor σ we allow values between 0 and 2 mag, which arewell motivated by observations (Rejkuba 2012); for µ weimpose that it must be within our magnitude range (i.ebeing in between 22 and 26.8 mag); for N GC we imposethat the number must be between 0 and the number ofdetected sources within our aperture ( N = 51); for r GC we set them to be between 0 and R out (i.e. 30 (cid:48)(cid:48) ); andfor the colors we demand that they must be between0 . < ( V − I ) < . σ ( V − I ) must belarger than 0.To estimate the posterior distributions for these sixparameters ( µ V , σ V , N GC , r GC , µ ( V − I ) , and σ ( V − I ) )we employ a Markov Chain Monte Carlo (MCMC) algo-rithm (Goodman & Weare 2010) implemented throughthe python package emcee (Foreman-Mackey et al.2013). As a first guess for the parameters, we use amaximum likelihood method implemented in scipy (i.e.minimize from the scipy.optimize module), which yields µ V = 23 .
92 mag, σ V = 0 .
80 mag, N GC = 35 .
0, and r GC = 10 . (cid:48)(cid:48) , µ ( V − I ) = 0 .
87 mag, and µ ( V − I ) =0 .
03 mag. For the MCMC we use 100 walkers with10 000 steps along the chains, with a burn-in of 1000steps. For the peak of the GCLF we derive µ V =23 . ± .
24 mag, for the width of the GCLF σ V =0 . ± .
16 mag, for the number of GCs N GC = 36 . ± .
1, for the half number radius r GC = 12 . +7 . − . (cid:48)(cid:48) , and for thecolor a mean of ( V − I ) = 0 . ± .
01 mag with a spreadof σ ( V − I ) = 0 . ± .
01 mag. The posteriors are well-behaved and presented in Fig 4.As a check, we estimate the numbers of GCs expectedin our aperture of the size 1.75 r eff , when consider-ing the contamination estimated on our reference back-ground field. With an area of 5.3 arcmin and 77 GC-like sources in this reference background area, we expect ≈
13 GC candidates in our aperture to be interlopers. Inother words, there is an over-density 38 detection withinour aperture. This number is in excellent agreementwith the number of GCs ( N GC = 36 . ± .
1) estimatedby our MCMC scheme.The histogram of the GCs within 1.75 r eff and thebest-fitting model are presented in Fig. 5. The peakof the GCLF puts the galaxy at 20 . +2 . − . Mpc (as-suming the peak of the GCLF is at − ± ≈ ± Luminosities and colors
In Fig. 6 we present the color magnitude diagrams(CMD) of our observations. We considered three cases:all detected point sources within i) one effective radius( r eff ), ii) within 1 and 2 r eff , and iii) outside of 2 r eff .Remarkably, within 1 r eff the GCs follow an extremelytight sequence. All confirmed GCs from our MUSEobservations (M¨uller et al. 2020) within 1 r eff are lo-cated within this sequence. For the other two CMDs,the color scatter of the GCs increases, which is due toan increase of the background contamination. This in-dicates that the GC population contribution drops af-ter one effective radius and the contamination by back-ground/foreground sources increases. This is a similartrend as seen the GC population of DF44, where the GCpopulation drops significantly after one effective radius(Saifollahi et al. 2020). We will quantify this further inthe next subsection.In Fig. 7 (left panel) we plot the sizes of the GCs asfunctions of luminosity and color. Most of the GC candi-dates are smaller than 10 pc, which is well expected fromstudies of the sizes of Milky Way GCs (Harris 2010). he GC system of the UDG MATLAS-2019 (mag) = 23.95 +0.240.24 . . . . V ( m a g ) V (mag) = 0.86 +0.180.14 N _ G C N_ GC = 36.56 +4.765.57 r G C ( " ) r GC (") = 12.02 +7.385.16 . . . . . ( V I ) ( m a g ) ( V I ) (mag) = 0.87 +0.010.01 . . . . . (mag) . . . . . ( V I ) ( m a g ) . . . . V (mag)
20 30 40 50 N_ GC r GC (") .
82 0 .
84 0 .
86 0 .
88 0 . ( V I ) (mag) .
015 0 .
030 0 .
045 0 .
060 0 . ( V I ) (mag) ( V I ) (mag) = 0.03 +0.010.01 Figure 4.
The posterior distributions from our MCMC modelling with its six free parameters ( µ V , σ V , N GC , r GC , µ ( V − I ) ,and σ ( V − I ) ). All of our spectroscopically confirmed GCs are in thisrange. Some of the faint GC candidates, however, tendto have larger sizes than the brighter GCs. This couldhave a few explanations. The fainter GC candidateshave a lower S/N, which could systematically increasetheir sizes due to modelling uncertainties (which are notwell captured by galfit). Alternatively, and more likely,they are the background objects contaminating our se-lection. We expect N tot − N GC = 14 objects in ourcatalog to be background interlopers. It is also possiblea few of these objects could be faint, diffuse GCs, muchlike those seen in M31 Huxor et al. 2014 with r h valuesup to 30-35 pc. Up to 4 GC candidates (including theiruncertainties) could have half light radii larger than the one of Crater-I (i.e. r eff = 20 pc, Torrealba et al. 2016)– which is one of the most extreme GCs in terms ofsize associated with the Milky Way (Voggel et al. 2016)– and could therefore be such extreme GCs. However,until spectroscopically confirmed, it is the safest bet tosuppose those are the expected interlopers.In Fig. 7 (right panel) we also plot the GC candidatesof MATLAS-2019 compared to other known GCs fromthe Local Group (Peacock et al. 2010; Harris 2010), aswell as ultra-compact dwarfs (UCDs, Hilker et al. 1999)in the Virgo cluster (Liu et al. 2015, 2020). The par-ticular cases of Crater-I and Pal 14, the largest MilkyWay GC, are highlighted in the figure. While most ofthe GC candidates associated with MATLAS-2019 fol- M¨uller et al. M V [mag]0.00.10.20.30.40.5 + Figure 5.
The histogram of the V band magnitudes ofthe GC candidates of MATLAS-2019. The dashed line corre-sponds to the GCLF, the dash-dotted line to the backgroundmodel, and the thick line to the combination of the two. low the distribution of the Local Group GCs, one GCin particular – the brightest GC in our sample dubbedGC6 in M¨uller et al. (2020) – is getting close to theUCD regime, with a size of r eff = 6 . ± . − . V band. In Ta-ble 1 GC6 is number 31. We note that the GCLF peakdistance prefers a value of 20 Mpc, while the velocity ofthe galaxy rather puts it at 25 to 30 Mpc. If the dwarfis at a larger distance, the sizes and luminosities of theGCs would increase, and with that GC6 would gettingcloser to the UCD regime. For the UCD FCC 47-UCD1(Fahrion et al. 2019) in the Fornax cluster, Fahrion et al.(2019) (among others) suggested that it could originatefrom the brightest star cluster in the progenitor galaxyand was accreted through a minor merger. However,GC6 of MATLAS-2019 would fall out of the selection ofUCDs in the Virgo cluster, with it being too small to beconsidered a UCD.3.3. Radial profile
In the following we quantify the radial extent of theGC distribution. For this, we counted the numberof GCs per area in increasing annuli of multiples of0.25 r eff . The results are presented in Fig. 8. At 1 r eff ,the GC density is at roughly 10% compared to the inner-most circle, and after 1.75 r eff , the GC count drops tothe background level (being calculated from the densityof GC candidates on the reference field on the secondchip). While most of the GCs reside within one effec-tive radius, the GC population extends to roughly twoeffective radii, or ≈ σ of the GCLF at the bright end). The density pro-file of the bright GCs is centrally peaked and quicklydrops to zero within 0.75 r eff , while the density profileof the faint GCs is more extended (up to 1.75 r eff ) andless peaked. However, the contamination of backgroundgalaxies will increase at the faint end, so this could biasthe signal. Ultimately, spectroscopic follow-up observa-tions are needed to confirm this mass segregation. SPECIFIC FREQUENCYIs the abundance of GCs associated to MATLAS-2019consistent with other UDGs and dwarf galaxies? Oneway to assess the number of GCs as a function of thebrightness of the host galaxy is with the specific fre-quency S N (Harris & van den Bergh 1981). It is calcu-lated as: S N = N GC · . M V +15) (9)The peak of the GCLF yields a distance modulus of m − M = 31 .
53 mag. The apparent and absolute mag-nitudes of MATLAS-2019 are m V = 17 .
69 mag and M V = − . ± . S N = 84 ±
12, where the error is acombination from the uncertainty in the absolute mag-nitude ( ± .
23 mag) and the number of GCs ( ± S N value), thedirect comparison between the literature UDG sampleand MATLAS-2019 is tricky, mainly due to the high un-certainty of the number of GCs in the literature, as wellas different approaches in counting the number of GCs. he GC system of the UDG MATLAS-2019 F W r < 1.75 r eff r < 1 r eff eff < r < 2 r eff eff < r Figure 6.
The CMD of detected sources within 1.75 r eff (left), corresponding to the full extent of the GC system; within 1 r eff (middle left); within 1 and 2 r eff (middle right); and outside of 2 (right). The dotted line corresponds to our selection ofGCs. In the left panel, we indicate in red the spectroscopically confirmed GCs from M¨uller et al. (2020). [mag]0510152025303540 r h [ p c ] V [ m a g ] g [mag]10 r h [ p c ] Virgo UCDs (Liu et al. 2020)M87 UCDs (Liu et al. 2015)M31 GCs (Peacock et al. 2010)MW GCs (Harris et al. 2010)MW GC Crater-I (Torrealba et al. 2016)MW GC Pal 14 (Harris et al. 2010)MATLAS-2019 GCs (M ¨u ller et al. 2021)MATLAS-2019 GCs MUSE (M ¨u ller et al. 2020) Figure 7.
Left: The size of the GCs as a function of their ( V − I ) color. The points are further shaded based on their luminosity.The spectroscopically confirmed GCs (M¨uller et al. 2020) are represented with the squares. The dashed line indicates the sizeof Crater-I (Torrealba et al. 2016), an extreme example of an extended GC in the Milky Way. Right: The size of the GCs as afunction of their luminosity and compared to Local Group GCs (Peacock et al. 2010; Harris 2010) and Virgo cluster UCDs (Liuet al. 2015, 2020). The red filled circles indicate the GCs associated with MATLAS-2019 and the gold filled squares are thosespectroscopically confirmed with MUSE. We discuss the caveats of comparing the number of GCsin the following.For UDGs with a high specific frequency in the Limet al. (2018) UDG sample (i.e. UDGs with S N > ≈
15% level.There are also different selection functions used in theliterature. Lim et al. (2018) had to correct for their in-0
M¨uller et al. G C p e r a r e a [ / a r c s e c ] GCs, allGCs, brightGCs, faint
Figure 8.
The GC density (red line) in increasing annuliof radii of 0.25 r eff . The densities of bright GCs and fainterGCs are marked with the violet dashed line and cyan dash-dotted line, respectively. The dark and light blue shadedregions indicate one and two effective radii, respectively. Thehorizontal straight and dashed black lines represents to thebackground GC density on chip two of the ACS field. completeness of the GC population – the Coma dwarfsare four times farther away than MATLAS-2019, mean-ing that not the full GCLF could be traced. They se-lected the GCs within 1.5 r eff , multiplied by a factor2 to correct for the full extent of the GC population(i.e. assuming that the half of the GC population willbe within 1.5 r eff ), and an additional factor 2 for theincompleteness of the GCLF (i.e. assuming that halfthe GCLF is sampled). If we estimate our the numberof GCs for MATLAS-2019 in the same way as Lim et al.(2018) we get 12 GCs within 1.5 r eff and brighter thanthe peak of the GCLF, i.e. a total number of 48 GCsand a specific frequency of 111 for MATLAS-2019.In Fig. 10 we directly compare the Lim et al. (2018)sample with our estimation of MATLAS-2019 adoptedfor their method. MATLAS-2019 stands out as the mostextreme UDG. However, the assumption that half theGCs of MATLAS-2019 are outside of 1.5 r eff is not valid,as we demonstrated in Fig. 8. While e.g. Amorisco et al.(2018) found that the majority of the Coma dwarfs have R GC /R eff ≈ R GC /R eff = 0 .
7. This does not mean that in generalthis correction is wrong, but for our particular case ofMATLAS-2019 it is not appropriate, which is in linewith Amorisco et al. (2018) finding that 4 out of their55 dwarf galaxies have R GC /R eff <
1. For the dwarfgalaxies in the Fornax cluster (Prole et al. 2019), theapproach to estimate the number of GCs is similar toours, employing Bayesian consideration by taking thebackground contamination into account. Therefore, theselection function should be comparable.Other well studied UDGs with a high specific fre-quency are VCC 1287, NGC 1052-DF2, and DF44. Com- pared to those, MATLAS-2019 has the highest numberof GCs and the highest specific frequency. With thelow uncertainty of our measurement we can claim thatMATLAS-2019 is extraordinary when it comes to theabundance of GCs and possibly sets an upper limit of thenumber of GCs in UDGs. MATLAS-2019 was initiallyselected for follow-up studies as having the highest num-ber of GC candidates in the MATLAS survey. This inprinciple suggest that we should not expect many UDGsin that sample having a higher abundance of GCs. Thefact that MATLAS-2019 has such a high abundance isthus not very surprising. It also suggest that UDGs ofthe failed Milky Way type may be rare (at least based onenvironments probed by MATLAS), as we would expectthem to harbour about 100 GCs or more (van Dokkumet al. 2016). THE DARK MATTER MASSThe number of GCs in a system offers a route to esti-mate the virial mass of UDGs (Beasley et al. 2016). Thevirial mass of a galaxy scales linearly with the numberof GCs over 6 orders of magnitude (Harris et al. 2013;Burkert & Forbes 2020), the relation only flattens forhalos smaller than 10 M (cid:12) . According to Harris et al.(2017), the virial mass M halo of a galaxy is connected tothe total mass of the GC system M GC with: M GC /M halo = 2 . × − (10)Assuming a mean mass of a GC to be 1 × M (cid:12) fordwarf galaxies (Harris et al. 2017), this yields a GC sys-tem mass of M GC = 3 . ± . × M (cid:12) and a halomass of M halo = 1 . ± . × M (cid:12) for MATLAS-2019.This is above the expected range of bright dwarf galax-ies by a factor of two ( M halo = [1 . , . × M (cid:12) ,Behroozi et al. 2013; Read et al. 2017; Bullock & Boylan-Kolchin 2017) but also below the mass of the LMCwith 2 . × M (cid:12) (Pe˜narrubia et al. 2016; Erkal & Be-lokurov 2020) by a factor of two, i.e. it’s somewherebetween the brightest dwarfs and LMC-like galaxies.With an absolute magnitude of − . ± . V band , this gives a mass-to-light ratio of M halo /L V =1775 +966 − M (cid:12) /L (cid:12) . The high number of GCs suggests anoverly massive halo of dark matter for the galaxy stellarmass, but not that of a failed Milky Way – in compar-ison, the Milky Way is ten times more massive with a The apparent magnitude provided in M¨uller et al. (2020) was offdue to an error in the photometric calibration of the zero point.This explains the discrepancy in the photometry between M¨ulleret al. (2020) and Forbes et al. (2020). The correct apparent V band magnitude measured on the MATLAS data is 17 .
44 mag,which is consistent with the value of 17 .
48 mag from Forbes et al.(2020). he GC system of the UDG MATLAS-2019 M V [mag]10 S N MATLAS-2019 DF44 (old)DF44 (new)VCC 1287 DF17NGC1052-DF2
Müller et al. (2021)van Dokkum et al. (2016)Saifollahi et al. (2020)Beasley et al. (2016)Peng & Lim (2016)van Dokkum et al. (2018)Lim et al. (2018)Prole et al. (2019)Harris et al. (2013) 232425262728 e , V [ m a g / a r c s e c ] Figure 9.
The specific frequency of nearby galaxies (Harris et al. 2013), Coma cluster dwarfs (Lim et al. 2018), Fornax clusterdwarfs (Prole et al. 2019), and the UDGs MATLAS-2019 (this work), DF44 (Saifollahi et al. 2020), DF17 (Peng & Lim 2016),VCC1287 (Beasley et al. 2016), and NGC 1052-DF2 (van Dokkum et al. 2018b). The color bar indicates the effective surfacebrightness of the galaxies. The dashed lines correspond to specific frequencies with a constant number of GCs, starting withone GC and then multiples of 10 GCs, until 100 GCs is reached. virial mass of 1 . ± . × M (cid:12) estimated through itsGCs, (Posti & Helmi 2019).How does this compare to the dynamical mass mea-surement with MUSE? Based on the kinematics of the11 GCs we derived a velocity dispersion of σ int =9 . +7 . − . km/s and a dynamical mass-to-light ratio of M dyn /L V = 4 . +9 . − . M (cid:12) /L (cid:12) within one de-projected ef-fective radius (M¨uller et al. 2020). We can compare themeasured value of the dynamical mass within the de-projected effective radius with what the galaxy wouldhave if it were embedded in a standard dark matterhalo with the mass expected from the M GC − M halo relation. taking a Navarro et al. (1997) halo on theconcentration-mass relation (as measured in cosmolog-ical simulations, e.g. by Dutton & Macci`o 2014), witha total mass of 1 . ± . × M (cid:12) , we obtain a dy-namical mass within an effective radius of 1 . M dyn = 1 . ± . × M (cid:12) . Thisgives an expected velocity dispersion of σ int ≈
31 km/s (and a lower limit of σ int ≈
26 km/s). posterior distri-bution of σ int . This is an ≈ σ tension between theobservation presented in M¨uller et al. (2020). However,recently, Forbes et al. (2020) have measured the stellarvelocity dispersion with KCWI with a higher accuracyand found it to be σ int = 17 ± σ upper limit of the value derived by M¨uller et al. (2020).This higher value of the stellar velocity dispersion alsoyields a much higher dark matter mass, because the dy-namical mass of a galaxy is proportional to the square ofthe velocity dispersion. However, while the gap betweenthe predicted and observed velocity dispersion decreases,with the small uncertainties of Forbes et al. (2020) thetension remains. DISCUSSION AND CONCLUSIONSThe discovery of the ultra-diffuse galaxy MATLAS-2019 in the MATLAS deep imaging survey was followed-up with MUSE spectroscopy. While the metallicity and2
M¨uller et al. M V [mag]10 S N MATLAS-2019
Müller et al. (2021)Lim et al. (2018) 232425262728 e , V [ m a g / a r c s e c ] Figure 10.
The specific frequency of the Coma clusterdwarfs (Lim et al. 2018) and the UDGs MATLAS-2019 (thiswork). The specific frequency of MATLAS-2019 in this plotis estimated with the same corrections as applied in Limet al. (2018) to make a direct comparison possible. The colorbar indicates the effective surface brightness of the galaxies.The dashed lines correspond to specific frequencies with aconstant number of GCs, starting with one GC and thenmultiples of 10 GCs, until 100 GCs is reached. age estimation of the stellar body is consistent with thatof other dwarf galaxies, the number of luminous GCsseemed to be too high and the measured velocity dis-persion suggested a low dark matter content within thisgalaxy. To assess these two issues, we have observedMATLAS-2019 with the HST using two band imaging.These observations revealed a large population of 37 ± V band magnitudes that follow a normal distribution, asexpected from a well-populated GCLF. This would solvethe question about the luminous GCs: they are sim-ply the bright end of the GCLF. We derive a specificfrequency of S N = 84 ±
12, which is at the high endof the measurements of other dwarf galaxies and maytherefore be one of the UDGs with the largest numberof GCs. This is expected, since MATLAS-2019 was se-lected for follow-ups because it had the highest numberof possible GCs based on ground-based observations ofover 2000 dwarf galaxies in the MATLAS survey. This,however, also suggests that failed Milky Way type galax-ies, which were proposed as the origin for UDGs, maybe relatively rare in the environments we have probedwith MATLAS, because we would expect them to haveover 100 GCs. If the UDG with the highest number ofpotential GCs in the MATLAS survey has only half thenumber of GCs to be considered a failed Milky Way typegalaxy, it is unlikely that other UDGs in this survey areof this type.Because the GCs are partially resolved with the su-perior image quality of space-based telescopes like the HST, we were able to measure their sizes. All GCs areconsistent with the sizes expected from the GCs of theLocal Group.What can we learn about the history of MATLAS-2019 from the abundance of GCs? This low-surfacebrightness galaxy must have had a high-density star for-mation and high star formation rate to form such mas-sive GCs as we observe today. And while much of themass was locked up in GCs, the remaining stars musthave spread out to form such a diffuse galaxy. Carletonet al. (2021) suggested based on simulations of clusterUDGs they may have an excess of GCs due a combina-tion of a) a higher star formation rate densities at highredshift, when most of their star formation occurred,and b) earlier cluster infall times, shutting down thestar formation. Because they would fall in earlier, theywill experience more tidal effects enlarging the galaxies.While MATLAS-2019 is not in a cluster, the NGC 5846group of galaxies is a dense galactic environment, so thismodel may provide an avenue to understand the forma-tion history of MATLAS-2019.The number of GCs correlates linearly with the virialmass of a galaxy. This idea has its origins in the forma-tion of galaxies through minor mergers: the more merg-ers a halo experienced, the more mass and the more GCsit accreted. Following such a trend, MATLAS-2019 withits 37 GC candidates would host a vastly dark matterdominated halo with a mass-to-light ratio of over 1000.The virial mass estimated through the count of GCsis more massive than the expectations from abundancematching and suggests an overly massive dark matterhalo. This provides grounds to state that MATLAS-2019 is not lacking dark matter, on the contrary, it pos-sesses a massive dark matter halo compared to otherdwarf galaxies. he GC system of the UDG MATLAS-2019
Facilities:
HST(STIS)
Software: emcee (Foreman-Mackey et al. 2013), gal-fit (Peng et al. 2002),sep (Barbary 2016), photutils(Bradley et al. 2020), astropy (Astropy Collaborationet al. 2013), Source Extractor (Bertin & Arnouts 1996)REFERENCES
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Table 1.
All detected GC-like sources within 1.75 effective radius of MATLAS-2019, of which we estimate that 37 are real GCassociated with MATLAS-2019. For the calculation of r h in parsec we used a distance modulus of 31.53 derived from the peakof the GCLF. The asterics denotes whether the GC was listed in M¨uller et al. (2020). The magnitudes are extinction corrected.The errors for the absolute V band magnitudes are a combination of the photometric error and the uncertainty in the distancemodulus, which dominates the error.Number RA (J2000.0) Dec (J2000.0) F606W (mag) F606W - F814W (mag) M V ( mag ) r h (arcsec) r h (pc)1 226.328690 1.811024 24.557 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ∗ ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ∗ ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ∗ ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ∗ ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ∗ ± ± ± ± ± ∗ ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ∗ ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ∗ ± ± ± ± ± ± ± ± ± ± ∗ ± ± ± ± ± ± ± ± ± ± ∗ ± ± ± ± ± ∗ ± ± ± ± ± ± ± ± ± ± ∗ ± ± ± ± ± ∗ ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±±