MNRAS 000, 000–000 (0000) Preprint 18 May 2019 Compiled using MNRAS LATEX style file v3.0

The globular cluster systems of 54 Coma ultra-diffusegalaxies: statistical constraints from HST data

N. C. Amorisco1,2?, A. Monachesi1, S. D. M. White11Max Planck Institute for Astrophysics, Karl-Schwarzschild-Strasse 1, 85748 Garching, Germany,2Institute for Theory and Computation, Harvard-Smithsonian Center for Astrophysics, 60 Garden St., MS-51, Cambridge, MA 02138, USA

18 May 2019

ABSTRACTWe use data from the HST Coma Cluster Treasury program to assess the richnessof the Globular Cluster Systems (GCSs) of 54 Coma ultra-diffuse galaxies (UDGs),and hence to constrain the virial masses of their haloes. For 18 of these the half-lightradius exceeds 1.5 kpc. We use a maximum-likelihood method to take account of thehigh contamination levels. UDG GCSs are poor: for 14 of the largest 18, NGC < 29with 90% confidence, NGC 6 46 for the remaining 4. From a stacked analysis of the18 largest UDGs we estimate 〈NGC〉 = 4.9+4.3

−3.3 (median, 10 and 90% quantiles); the

corresponding number for the complementary 36 systems is 〈NGC〉 = 0.8+0.9−0.6. These

results strongly suggest that most Coma UDGs have low-mass haloes. Their GCSs donot display significantly larger richnesses than nearby dwarf galaxies of similar stellarmass.

Key words: galaxies: dwarf — galaxies: structure — galaxies: formation — galaxies:haloes — galaxies: clusters

1 INTRODUCTION

Ultra-diffuse galaxies (UDGs) are a population of low-surface brightness systems (effective surface brightness〈µ〉r & 24 mag/arcsec2) with stellar masses typical of dwarfgalaxies (7 . logM∗/M� . 9). Ubiquitous in nearby galaxyclusters (van Dokkum et al. 2015; Koda et al. 2015; Munozet al. 2015; van der Burg et al. 2016; Mihos et al. 2015),UDGs have also been found outside cluster environments(Martinez-Delgado et al. 2016; Roman & Trujillo 2016).They appear as roundish featureless spheroids (e.g. Yagi etal. 2016), which extend the red sequence of cluster galaxiesin the colour-magnitude diagram into the regime of dwarfgalaxies (Koda et al. 2015; van der Burg et al. 2016), withhints of a trend to bluer colours in less dense environments(Roman & Trujillo 2016).

Interest in this population has been sparked by the pro-posal that their halo mass could be much larger than sug-gested by their stellar mass (van Dokkum et al. 2015; Kodaet al. 2015; van Dokkum et al. 2016). According to this pro-posal, the largest UDGs (e.g. half-light radii &1.5 kpc) wouldbe hosted by Milky Way (MW) mass haloes rather than byhaloes with masses below or similar to that of the LargeMagellanic Cloud (LMC). In either case, UDGs are highlydark matter dominated systems (van Dokkum et al. 2015;Beasley et al. 2016; Amorisco & Loeb 2016; van Dokkum et

? E-mail: nicola.amorisco@cfa.harvard.edu

al. 2016). However, if hosted by MW mass haloes, they arestrong outliers from the M∗ −Mvir relation: this would re-quire their formation pathway to differ fundamentally fromthat of ‘normal’ haloes of the same total mass, which arethought to be the most efficient at converting gas into stars(e.g. Guo et al. 2010; Behroozi et al. 2013; Moster et al. 2013,and references therein). As suggested by a simplistic ΛCDMframework, this is not necessary. A scenario in which UDGsare the low surface brightness tail of the abundant popula-tion of dwarf galaxies can capture the abundances and sizedistribution of cluster UDGs in detail (Amorisco & Loeb2016). In addition, if hosted by low mass haloes, internalstellar feedback might provide a promising way to ‘expand’them to large sizes (Di Cintio et al. 2016), both inside andoutside clusters, without the need for ad hoc mechanismsto make them depart so significantly from the M∗ −Mvir

relation.

Unfortunately, only three UDG halo mass measure-ments are available so far to inform this discussion. Theseare indirect measurements, based either on the richness ofthe globular cluster system (GCS), used as a proxy for halomass, or on an extrapolation to the virial radius of a dy-namical mass measurement (Beasley et al. 2016; Beasley &Trujillo 2016; Peng & Lim 2016; van Dokkum et al. 2016).Both techniques have their limitations. The approximate lin-earity of the relation between the GCS richness and halovirial mass is supported by a solid pool of evidence (e.g.,Harris et al. 2013; Hudson et al. 2014; Forbes et al. 2016,

c© 0000 The Authors

arX

iv:1

610.

0159

5v1

[as

tro-

ph.G

A]

5 O

ct 2

016

2 N. C. Amorisco, A. Monachesiâ

â

âââ

â

â

â

â

ââ

â

â

ââ â

â

â

â

â â

ââ

ââ

â

â

â

ââ

â

â

â

â

â

â

â

â

â

â

â

â

â

â

â

â

â

â

â

â

â

â

ââ

ââ

â

â

â

â

ââ

â

â

â

â

â

â

â

â

++

+

236

238

534

194.1 194.2 194.3 194.4 194.5 194.6

27.2

27.3

27.4

27.5

â

â

â

â

â

ââ

â

â

â

â

â

â âââ

â

â

ââ â

â

â â

â

â

â

â

â

ââ

ââ

âââ

ââ

â

â

âââ

â

ââ

ââ

â

â

â

â

â

â

â

â

â

â

â

â

â

â

â

â

â

â

ââ

â

â

â

â

â

â

â

â

ââ

â

â

â

â â

â

â

ââ

â

â

â

â

â

â

âââ

â

â

â

â

â

â

ââ

â

â

ââ

â

â

â

â

ââ

â

â

â

â

âââ

â

â

â

â

â

â

â

â

â

â

â

ââ

â

â

+

+

+

+

++

+

+

+

+

++

+

+

++

+ +

+

++

+

++

+

+

+ +

++

+++

+++

+

+

+

+

+

+++

++

+

+

+

+

+85

89

91

99

102104

105

107

108

112

113

114

115

118

121

122

325

331

358

366

367

370

372373

374

380

386

387

391 395

402406

407

408

409410

412

415

419

421

423

424

425

427

432433

434

435

436

437

438

194.7 194.8 194.9 195.0 195.1 195.2

27.8

27.9

28.0

28.1

RA (J2000)

Dec

(J20

00)

RA (J2000)

Figure 1. A composite of the HST/ACS fields observed as part of the Coma Cluster Treasury program, together with the Coma UDGsfrom Yagi et al. (2016), shown as black and red cross symbols. Green points are candidate GCs selected from the Hammer et al. (2010)

catalog, as described in Sect. 2.1. The 54 UDGs whose centers fall within the observed HST fields are marked in red, their size is shownby a blue circle (with a radius of 6×RS), and their ID number in the Yagi et al. (2016) catalog is displayed.

and references therein), but the mean conversion factor re-mains uncertain (Harris et al. 2015; Zaritsky et al. 2016;Georgiev et al. 2010, hereafter G10) and might not apply tothese unusual systems. Dynamical measurements, however,do not guarantee higher precision, as the extrapolation fromthe galaxy’s half-light radius (e.g. Walker et al. 2009; Wolfet al. 2010; Amorisco & Evans 2011; Campbell et al. 2016)to the virial radius is very substantial.

In this Letter, we set out to solidify the sample of virialmass estimates for UDGs by enlarging it by over an orderof magnitude. We use imaging data from the HST ComaCluster Treasury program to constrain the richness of theGCS of 54 Coma UDGs. With respect to ground-based data,HST/ACS data are ideal to disentangle candidate GCs frommost background galaxies (e.g., Peng et al. 2011; Beasley& Trujillo 2016; Peng & Lim 2016). However, the poorUDG GCSs and the high contamination imply that a fullystatistical framework has to be adopted to gather reliableconstraints. Sect. 2.1 describes the data; Sect. 2.2 sets outthe maximum-likelihood approach we employ, and Sect. 3presents our results. Sect. 4 lays out the Conclusions.

2 OBSERVATIONS AND METHODS

We use the compilation of 854 Coma UDGs presented byYagi et al. (2016, hereafter Y16), based on Subaru SuprimeCam archival data analysed in Koda et al. (2015). These areselected to have 〈µ〉R < 24 mag/arcsec2 and a stellar halflight radius > 0.7 kpc. Among these, we select those UDGswhose centers lie within the footprint of the Coma ClusterTreasury program, which we use to explore the propertiesof their GCSs. There are 54 such UDGs. Their locations aredisplayed in Fig. 1, together with their ID numbers in theY16 catalog. We adopt half-light radii RS from the singleSersic fits presented by Y16. Where these were not deemedreliable, for example, because of light from nearby systems,we adopt the listed values returned by SExtractor.

2.1 Candidate GC selection

We cross-correlate the position of the Y16 UDGs with thecatalog of the HST/ACS Coma Cluster Treasury program(CCTp) presented by Hammer et al. (2010, hereafter H10).This lists all SExtractor sources detected in the deep F814Wimages, as well as the measurements for the F475W images,and we use it to select GC candidates (GCCs) within thefootprint of the survey. AB magnitude system photometryis available at different apertures: we use the 4 pixel radiusaperture (0.′′2) and apply the aperture corrections from Siri-anni et al. (2005). We correct magnitudes for Galactic ex-tinction following Schlafly & Finkbeiner (2011), using theE(B-V) reddening values from Schlegel et al. (1998). TheF814W−band photometry is 80% and 50% complete at 26.8and 27.3, respectively (H10 and Peng et al. 2011). This de-fines our completeness function S814, for which we adopt thefunctional form suggested by Salinas et al. (2015, eqn. 3, re-sulting in α = 1.5).

HST/ACS imaging (0.′′05/pixel) is ideal to disentan-gle GCCs (point sources at the distance of Coma) frommost background galaxies, which appear resolved. We firstselect objects flagged as ‘point source’ in the H10 catalog(FLAGS_OBJ=1). Following Peng et al. (2011), we then de-fine the concentration index C4−10 as the difference in mag-nitudes between a 4- and a 10-pixel radius aperture. Thelocus of point sources is at C4−10 = 0.13. Using the con-centration index and F814W magnitudes we generate oursample of GCCs, including all objects within ±0.2 mag ofthe C4−10 locus and with F814W < 27.3. In addition, weapply a colour cut 0.5 < F475W − F814W < 1.5 to isolateGCs from compact red galaxies (Peng et al. 2011; Beasley& Trujillo 2016), and we impose a bright magnitude limit ofF814W < 22 to avoid foreground MW stars and saturatedpixels (H10). The final catalog contains ∼ 12000 GCCs1.

1 We estimate that 42 sources in our catalog might be duplicate

detections from coadding the catalogs of the 25 HST/ACS fieldsobserved in the CCTp, which is negligible.

MNRAS 000, 000–000 (0000)

The GC systems of 54 Coma UDGs 3

2.2 Statistical analysis

As shown by Peng et al. (2011) using the same data, theComa cluster possesses an abundant population of intra-cluster GCs (ICGs), and several tens of background galax-ies per ACS field survive the selection just described. Al-though the CCTp data is 50% complete at the turnoverof the GC luminosity function (GCLF) of dwarf ellipticals(F814W = 27.33 Miller & Lotz 2007; Peng et al. 2011;Beasley & Trujillo 2016), visual inspection rarely reveals anyapparent over-density of GCCs near the UDG centers. Theseover-densities are readily seen by eye at the locations of highsurface brightness Coma galaxies. On average, UDGs havepoor GCSs relative to the background, implying that weare forced to adopt a statistical approach to constrain theirrichness (NGC). Given (i) the lack of evident overdensities,(ii) the properties of the background and (iii) the magnitudecompleteness function, we can extract constraints on NGC.

We isolate the GCCs in the vicinity of each UDG, andmodel them as the superposition of a population of contami-nants and of a population of GCs physically associated withthe UDG. In absence of close luminous galaxies, we modelall GCCs within 35 × RS from the UDG’s center. This isa compromise between getting better statistics for the con-taminants, and modelling their spatial distribution as locallyuniform, with surface density Σc. The spatial distributionof the UDG GCS is modelled with either a Plummer or anexponential profile Σ(r), whose half-count radius Rh is afree parameter. Following Walker & Penarrubia (2011) andAmorisco et al. (2014), the probability of observing a sampleof N GCCs at distances ri from the UDG is

L =

N∏i

[fSsp(ri)Σ(ri, Rh)∫

SspΣ(r,Rh)+ (1− f)

Ssp(ri)∫Ssp

], (1)

which is the likelihood function for the free parameters fand Rh/RS (Σc cancels out). Here, (i) Ssp(r) is the spatialselection function, which takes into account that the areaavailable to study might be limited by the edges of the foot-print; (ii) f is the fraction of the N GCCs to be associatedwith the UDG; (iii) integrals extend over the studied areas.

To ensure that our results are not strongly model de-pendent, we explore the following set of models:

• model 1: Plummer distribution, 0.5 < Rh/RS < 3.5;• model 2: as model 1, enforcing a Gaussian prior on the

ratio Rh/RS , Rh/RS = 1.8±0.7 (Kartha et al. 2014; Beasleyet al. 2016; Peng & Lim 2016);• model 3: as model 1, enforcing a Gaussian prior on the

GCLF of the UDG GCS, F814W = 27.33± 1.1 mag;• model 4: exponential distribution, 0.5 < Rh/RS < 3.5.

In all cases, a uniform prior is imposed on 0 6 f 6 1 andinference on NGC is obtained from the inference on f by cor-recting the latter for both spatial and magnitude selections:

NGC,j = Nfj ×∫

Σ(r,Rh,j)∫Ssp(r)Σ(r,Rh,j)

∫G(F814W )∫

S814G(F814W ), (2)

where j runs over the Monte Carlo chains, G is the GCLFand S814 is the completeness function defined in Sect. 2.1.The turnover and spread of the GCLF vary with galaxymass, becoming respectively fainter and tighter in dwarfgalaxies (e.g. Jordan et al. 2007). We conservatively adopt a

2.3.

4.

5.6.

1. Plummer

4. exponential

2. prior Rh

3. prior GCLF

Figure 2. A summary of the statistical constraints on the GCSs

of the first 3 Coma UDGs in the footprint of the CCTp. A com-plete version of this Figure is available here. For each UDG, the

upper-left panel shows a zoom of Fig. 1, with size l × l, with l

indicated in the lower left of the panel. Black concentric circlesdisplay {5, 10, 15}×RS , the stellar half-light radius of the UDG.

The blue circle indicates the median half-counts radius Rh of the

GCS we infer from model 1. Where visible, red lines show the edgeof the footprint, or areas excluded due to bright galaxies. Dots are

candidate GCs, color-coded by the probability of membership in

the UDG, as shown in the legend. The upper-right panels displayinferences (as posterior probability distributions) obtained for the

ratio Rh/RS using our models, as indicated in the legend. The

lower panels show the associated inferences for the GCS richness,NGC; vertical lines indicate 90% quantiles from model 1 and 3.

dwarf-like GCLF (e.g., Miller & Lotz 2007; Peng et al. 2009,G10, mean and spread as in model 3), as this implies a largercorrection through eqn. 2.

3 RESULTS

We apply the analysis described above to each UDG in oursample individually, and then to (i) the stack of the 18 sys-tems with RS > 1.5 kpc (and the stack of the comple-mentary set of 36); (ii) the stack of the 18 systems withlogM∗/M� > 7.5 (and the stack of the complementary setof 36).

3.1 Analyses on individual systems

Results for all our 54 UDGs are presented in Fig. 2 andTable 1. For each UDG, Fig. 2 displays posterior probabil-ity distributions for Rh/RS (upper-right panels) and NGC

(lower panels). Quantiles for the NGC distributions (10, 50and 90%) are collected in Table 1. Zooms of Fig. 1 centeredon the UDG locations (upper-left panels) show all GCCs,colour-coded according to their probability of membershipto the UDG GCS (from model 1). As mentioned earlier, mostcases show no obvious over-density of sources close to thecenter of the UDG, hence the paucity of high-probability

MNRAS 000, 000–000 (0000)

4 N. C. Amorisco, A. Monachesi

Table 1. Summary of the statistical constraints from our models, in terms of {10%, 50%, 90%} quantiles for all listed quantities. We

list our 4 stacks and the first 3 Coma UDGs in the footprint of the CCTp. A complete version of this Table is available here.

stack Rs logM∗ Rh/RS NGC Mvir NGC NGC NGC

or ID kpc M� 1010M�model 1 model 1 model 1 model 2 model 3 model 4

RS > 1.5 kpc 1.99 7.64 {2.1, 2.9, 3.4} {1.7, 4.9, 9.0} {0.5, 1.4, 2.5} {1.3, 4.1, 7.9} {1.0, 3.3, 6.4} {1.6, 4.9, 9.2}RS 6 1.5 kpc 1.03 7.08 {1.5, 2.5, 3.3} {0.2, 0.8, 1.7} {0.1, 0.2, 0.5} {0.2, 0.7, 1.6} {0.1, 0.6, 1.4} {0.2, 0.7, 1.6}logM∗ > 7.5 1.80 7.79 {1.8, 2.7, 3.3} {0.9, 3.3, 6.5} {0.3, 0.9, 1.8} {0.8, 2.8, 5.7} {0.4, 1.9, 4.2} {0.9, 3.2, 6.3}logM∗ 6 7.5 1.13 7.01 {1.7, 2.7, 3.3} {0.3, 1.3, 2.7} {0.1, 0.4, 0.8} {0.3, 1.1, 2.4} {0.4, 1.2, 2.4} {0.3, 1.3, 2.7}

85 0.94 7.2 {1.0, 2.3, 3.2} {0.8, 4.2, 10.8} {0.2, 1.2, 3.0} {0.8, 4.4, 10.7} {0.8, 4.1, 10.7} {0.8, 4.2, 10.6}89 1.10 7.5 {1.4, 2.6, 3.3} {1.8, 8.1, 18.8} {0.5, 2.3, 5.3} {1.7, 8.1, 18.4} {1.2, 6.3, 15.7} {1.7, 7.6, 17.8}91 1.58 6.8 {1.0, 2.2, 3.2} {0.7, 3.8, 10.2} {0.2, 1.1, 2.9} {0.7, 3.8, 9.7} {0.8, 4.0, 11.0} {0.7, 3.8, 10.3}

4 N. C. Amorisco, A. Monachesi

Table 1. Summary of the statistical constraints from our models, in terms of {10%, 50%, 90%} quantiles for all listed quantities. We

list our 4 stacks and the first 3 Coma UDGs in the footprint of the CCTp. A complete version of this Table is available here.

stack Rs log M⇤ Rh/RS NGC Mvir NGC NGC NGC

or Id. kpc M� 1010M�model 1 model 1 model 1 model 2 model 3 model 4

RS > 1.5 kpc 1.99 7.64 {3., 3.3, 3.5} {8.5, 13.7, 19.6} {2.4, 3.8, 5.5} {7.2, 12.5, 18.9} {5.1, 9.2, 14.2} {9.5, 14.2, 19.4}RS 6 1.5 kpc 1.03 7.08 {1.6, 2.7, 3.4} {0.4, 1.4, 2.8} {0.1, 0.4, 0.8} {0.4, 1.3, 2.5} {0.3, 1., 2.1} {0.4, 1.3, 2.6}log M⇤ > 7.5 1.8 7.79 {2.8, 3.2, 3.5} {5.4, 9.6, 14.6} {1.5, 2.7, 4.1} {4.6, 8.7, 13.7} {2.2, 5.4, 9.3} {5.4, 9.6, 14.6}log M⇤ 6 7.5 1.13 7.01 {2.4, 3.1, 3.4} {1.7, 3.6, 6.1} {0.5, 1., 1.7} {1.4, 3.1, 5.3} {1.3, 2.8, 4.7} {2., 3.9, 6.2}

85 0.94 7.18 {1.1, 2.3, 3.2} {0.9, 4.4, 11.1} {0.3, 1.2, 3.1} {0.8, 4.2, 11.1} {0.8, 4., 10.} {0.9, 4.1, 10.6}89 1.1 7.5 {1.5, 2.6, 3.3} {1.7, 7.8, 18.} {0.5, 2.2, 5.} {1.8, 7.9, 18.4} {1.3, 6.2, 15.1} {1.8, 7.8, 18.}91 1.58 6.78 {1.1, 2.4, 3.2} {0.8, 4.4, 11.6} {0.2, 1.2, 3.3} {0.8, 4., 10.6} {0.8, 4.3, 11.2} {0.8, 3.9, 10.7}

Full Table

Figure 3. A summary of the statistical constraints on the GCSs

from the stacks based on the UDG sizes, hRh/RSi RS > 1.5 kpc(top row) and RS 6 1.5 kpc (bottom row). Line styles are as in

Fig. 2.

36); (ii) the stack of the 18 systems with log M⇤/M� > 7.5(and the stack of the complementary set of 36).

3.1 Analyses on individual systems

Results for all our 54 UDGs are presented in Fig. 2 andTable 1. For each UDG, Fig. 2 displays posterior probabil-ity distributions for Rh/RS (upper-right panels) and NGC

(lower panels). Quantiles for the NGC distributions (10, 50and 90%) are collected in Table 1. Zooms of Fig. 1 centeredon the UDGs’ locations (upper-left panels) show GCCs fromour deep catalog, sized and colour-coded according to theirprobability of membership to the UDG GCS (from model1). As mentioned earlier, most cases show no obvious over-density of sources close to the center of the UDG, hence thepaucity of high-probability members. In several instances,the surface density of contaminants is such that even GCCslocated within a few RS from the UDG’s center cannot beconsidered physically associated beyond doubt.

We find no appreciable di↵erence between constraints

obtained through di↵erent model assumptions or using pri-ors. We have also explored using a more restrictive catalogof GCCs (applying cuts as from Peng et al. 2011), whichreduces the sample to ⇠ 5400. Results remain consistent,although, as the deeper catalogue best probes the statisticsof the contaminant population, we deem the inferences ex-tracted from it more reliable.

As seen in Fig. 2, most posteriors on NGC increase al-most all the way to NGC = 0: only 18 of our UDGs haveNGC,5 > 1, i.e. are associated with more than 1 GC at 95%confidence. Therefore, we stress that the medians obtainedfor individual systems should not be interpreted as mea-surements. Rather, we are only able to extract individualupper bounds. This does not a↵ect results: even in the casewe use the loosest 90% quantile among those returned bythe 4 explored models – like done in the abstract – our 54-strong sample remains a sample of dwarf galaxies. We followHarris et al. (2015), and interpret our results on NGC as in-ferences on the virial mass of the studied UDGs. We adoptthe conversion factor suggested by G10, who used HST dataand dynamical mass estimates of nearby dwarf galaxies tocalibrate the following mean relation

Mvir ⌘ 1

⌘MGCS ⌘ NGC

hMGCi⌘

⇠ NGC1.69 ⇥ 105M�

6 ⇥ 10�5, (3)

where MGCS is the mass of the GCS and hMGCi is the masscorresponding to the turno↵ of the GCLF. It is reassuringthat independent studies with di↵erent systematics agree onthis calibration2 to about a factor ⇠2 (e.g., Harris et al. 2015;Zaritsky et al. 2016; Forbes et al. 2016). If sticking to theresults of model 1, 51 out of 54 of our UDGs have Mvir,90 <1011M� (90% quantile). Of the 18 UDGs with RS > 1.5 kpc,16 have Mvir,90 < 1011M�. A single system, ID 425 in theY16 catalog, qualifies for having NGC,90 = 58, correspondingto Mvir,90 ⇠ 1.7⇥1011M�. This is the most extended amongthe UDGs we can study, with RS ⇠ 3.1 kpc, although itslocation implies an especially high density of contaminants,likely ICGs and/or GCs from the nearby N4889, which mighta↵ect our result (see the complete version of Fig. 2). Table 1provides the conversion of the results of model 1 in virialmasses for all 54 UDGs.

2 Massive galaxies lie on the relation Mvir ⇠NGC

�2.4 ⇥ 105M�/4 ⇥ 10�5

�; the halo-to-halo scatter in

dwarfs appears wider than this di↵erence (G10).

MNRAS 000, 000–000 (0000)

The GC systems of 54 Coma UDGs 5

3.2 Analyses on stacks

The combination of the paucity of physically associated GCsand the ⇠

pN/N Poisson uncertainty deriving from the

background counts implies we are not able to extract mea-surements for individual systems, but only reliable upperbounds. We circumvent this by applying the same statisti-cal technique described in Sect. 2 on stacked data: we con-struct a stack based on the UDG sizes, which separates the18 systems with RS > 1.5 kpc and one stack which includesthe 18 systems with log M⇤ > 7.5. This allows us to extractinformation on the average richness of UDG GCSs, hNGCi.

Fig. 3 illustrates results obtained for the stack based onsize, and Table 1 lists quantiles for both stacks. Like shownby the posterior probability distributions on hNGCi in Fig. 3,these stacks allow us to perform actual measurements. Forboth largest and most luminous UDGs, the average richnesshNGCi remains that typical of dwarf galaxies. Independentlyof model assumptions, our 18 UDGs with RS > 1.5 kpc havehNGC,50 . 14i, which nominally corresponds to an averagehalo mass of hMvir,50i . 3.9 ⇥ 1010M�.

4 DISCUSSION AND CONCLUSIONS

UDGs are a startling class of systems because of the ap-parent mismatch between their stellar mass and size, whichresult in very high dark matter fractions within their stellarbodies (Beasley et al. 2016; Beasley & Trujillo 2016; Peng& Lim 2016; van Dokkum et al. 2016), independently onwhether they are hosted by dwarf or MW-sized haloes. Oneaspect that has not been su�ciently highlighted so far is thealmost perfect linearity of the relation between the abun-dance of UDGs in clusters (NUDG) and the cluster massitself (van der Burg et al. 2016). This indicates that UDGsare an approximately constant fraction of cluster popula-tions, bearing little additional dependence on the clusterrichness, and by extension on the local environment. In turn,this would advocate that the physical mechanism that givesUDGs their unusual properties may in fact have an inter-nal origin, rather than being caused by interactions withthe environment, as corroborated by the detection of UDGsoutside cluster cores (Martinez-Delgado et al. 2016; Roman& Trujillo 2016).

There is no shortage of mechanisms proposed so far toform galaxies with the properties of UDGs, including (i) highangular momentum content of primordial origin (Amorisco& Loeb 2016); (ii) especially strong and prolonged stellarfeedback (Di Cintio et al. 2016); (iii) premature quenchingdue to early infall onto the cluster (Yozin & Bekki 2015; vanDokkum et al. 2015); (iv) 2-body galaxy-encounters withinthe cluster itself (Baushev 2016; Burkert 2016). Amongthese, the first two are of internal origin, while the lattertwo require the external influence of a dense environment,in combination with early infall.

Our results show that most UDGs are hosted by dwarf-sized haloes: we find no candidate for a massive MW-likehalo. Beasley & Trujillo (2016) and Peng & Lim (2016) havesuggested that, though hosted by LMC-sized haloes, UDGsmight still show signs of ‘failure’, having rich GCSs for theirstellar mass. We explore this further in Fig. 4, by compar-ing our UDGs with nearby galaxies from the compilations

++

+

+

+

+

+

++

+

++

+

+

+

+

++

+

+

+

+

+

+

+ +

+

++

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+ +

+

+

++

+

+

+ +

++

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+ +

+

+

+

+

+

+

+

+

+

++

+

+

+

+ +++++

+

+

+ +

+

+

++

+++

+

+

+

+

+

+

+

++

+

+

+

+

+

+

++++

+

+

+

+

+

+

+

+

+

+

+

+ +

+

++

+

++

+

+ +

+

+

+

+

+

+

Ÿ

ŸŸ

Ÿ

Ÿ

ŸŸ

Ÿ

Ÿ

Ÿ

Ÿ

Ÿ

Ÿ

Ÿ

Ÿ Ÿ

Ÿ

Ÿ

Ÿ

Ÿ

Ÿ

Ÿ

Ÿ

Ÿ

ŸŸŸ

Ÿ

Ÿ

Ÿ

Ÿ

Ÿ

Ÿ

Ÿ

Ÿ

DF44

DF17VirgoUDG

RSêkpc1.1 1.8 2.5 3.2 4.6

6.5 7.0 7.5 8.0 8.5 9.0 9.5

0.0

0.5

1.0

1.5

2.0

log10M*êMü

log 10N

GC

Figure 4. The abundance of the GCS of ‘normal’ galaxies from

the H13 catalog (grey rectangles) and dwarf galaxies from G10(pink stars) compared to upper bounds for our sample of 54 Coma

UDGs (error bars reach the 90% quantile). Blue rectangles with

coloured points are results from the literature for three additionalUDGs. Arrows and points for all UDGs are colour-coded and sized

according to their stellar half-light radius, like indicated in the

legend.

of Harris et al. (2013, H13, grey rectangles) and G10 (pinkstars, from their Table 1). Points with blue error-bars iden-tify the measurements by Beasley et al. (2016) for VCC 1287in Virgo, Peng & Lim (2016) and Beasley & Trujillo (2016)for DF17, van Dokkum et al. (2016) for DF44. Stellar massesare obtained assuming that B �R ⇠ 1 for the UDGs (Kodaet al. 2015), and using morphological type as a proxy forcolour within the H13 catalog. Horizontal error-bars (onlyone displayed in the top-left for our UDGs) display the in-terval between the masses inferred using the M/L relationsof Zibetti et al. (2009) and Bell et al. (2003). For our 54UDGs, downward arrows display individual upper bounds(NGC,90 from model 1); large asterisks with error-bars showresults obtained by the analyses of our stacks. UDG sym-bols are colour-coded according the stellar half-light radius.Large asterisks show a clear correlation for richer GCSs withincreasing stellar mass (and size), which is also hinted by theindividual upper bounds. Our UDGs do not deviate from thesample of dwarf galaxies of G10, and we can rule out largesystematic discrepancies between the two samples, althoughwe note that the G10 dwarfs do not reside in clusters butmostly in groups and loose associations. Interestingly, withthe only ground-based measurement, DF44 remains a strongoutlier (see also the analysis of Zaritsky 2016), though alsofeaturing the highest stellar mass and largest half-light ra-dius.

ACKNOWLEDGEMENTS

It is pleasure to thank Mike Beasley and Abraham Loebfor comments on an early version of this draft, and ChervinLaporte for stimulating discussions.

MNRAS 000, 000–000 (0000)

The GC systems of 54 Coma UDGs 5

Table 1. Summary of the statistical constraints from our models, in terms of {10%, 50%, 90%} quantiles for all listed quantities. We

list our 4 stacks and the first 3 Coma UDGs in the footprint of the CCTp. A complete version of this Table is available here.

stack Rs log M⇤ Rh/Rs NGC Mvir NGC NGC NGC

or Id. kpc M� 1010M�model 1 model 1 model 1 model 2 model 3 model 5

RS > 1.5 kpc 1.99 7.64 {3., 3.3, 3.5} {8.5, 13.7, 19.6} {2.4, 3.8, 5.5} {7.2, 12.5, 18.9} {5.1, 9.2, 14.2} {9.5, 14.2, 19.4}RS 6 1.5 kpc 0.82 6.93 {1.6, 2.7, 3.4} {0.4, 1.4, 2.8} {0.1, 0.4, 0.8} {0.4, 1.3, 2.5} {0.3, 1., 2.1} {0.4, 1.3, 2.6}log M⇤ > 7.5 1.8 7.79 {2.8, 3.2, 3.5} {5.4, 9.6, 14.6} {1.5, 2.7, 4.1} {4.6, 8.7, 13.7} {2.2, 5.4, 9.3} {5.4, 9.6, 14.6}log M⇤ 6 7.5 1.03 6.75 {2.4, 3.1, 3.4} {1.7, 3.6, 6.1} {0.5, 1., 1.7} {1.4, 3.1, 5.3} {1.3, 2.8, 4.7} {2., 3.9, 6.2}

85 0.94 7.18 {1.1, 2.3, 3.2} {0.9, 4.4, 11.1} {0.3, 1.2, 3.1} {0.8, 4.2, 11.1} {0.8, 4., 10.} {0.9, 4.1, 10.6}89 1.1 7.5 {1.5, 2.6, 3.3} {1.7, 7.8, 18.} {0.5, 2.2, 5.} {1.8, 7.9, 18.4} {1.3, 6.2, 15.1} {1.8, 7.8, 18.}91 1.58 6.78 {1.1, 2.4, 3.2} {0.8, 4.4, 11.6} {0.2, 1.2, 3.3} {0.8, 4., 10.6} {0.8, 4.3, 11.2} {0.8, 3.9, 10.7}99 2.09 7.22 {1.4, 2.4, 3.2} {6.6, 19.9, 38.4} {1.9, 5.6, 10.8} {6.4, 18.8, 36.5} {4.3, 14.7, 30.3} {6., 18.4, 35.6}102 0.89 7.02 {1.4, 2.5, 3.3} {1.2, 6., 14.8} {0.3, 1.7, 4.1} {1.1, 5.5, 13.5} {0.8, 4.6, 13.3} {1.3, 6.1, 15.1}104 1.05 7.3 {1., 2.2, 3.2} {0.6, 3.1, 8.5} {0.2, 0.9, 2.4} {0.6, 3.1, 8.1} {0.6, 2.9, 7.6} {0.6, 3., 7.6}105 1.22 6.58 {1.2, 2.4, 3.3} {0.9, 4.9, 13.2} {0.3, 1.4, 3.7} {0.9, 4.9, 12.7} {1., 5.3, 14.5} {1., 4.9, 12.9}107 1.99 6.78 {1.2, 2.4, 3.2} {0.9, 4.6, 12.6} {0.3, 1.3, 3.5} {0.8, 4.5, 11.8} {0.9, 4.5, 12.5} {0.9, 4.5, 11.9}108 0.81 6.58 {1., 2.2, 3.2} {0.6, 3., 8.3} {0.2, 0.8, 2.3} {0.6, 3., 7.4} {0.7, 4., 10.1} {0.6, 3., 8.}112 1.53 7.74 {1.4, 2.6, 3.3} {1.7, 7.8, 19.3} {0.5, 2.2, 5.4} {1.5, 7.3, 17.9} {2.3, 10., 23.3} {1.7, 7.9, 19.2}113 0.84 6.38 {1.2, 2.5, 3.3} {0.9, 4.5, 12.2} {0.2, 1.3, 3.4} {0.8, 4.1, 11.2} {0.7, 3.4, 8.8} {1., 5.2, 13.3}114 1.52 7.74 {1.1, 2.2, 3.2} {1.3, 5.8, 14.1} {0.4, 1.6, 3.9} {1.1, 5.4, 13.3} {0.9, 4.6, 11.8} {1., 5., 12.}115 1.16 6.58 {0.8, 1.9, 3.1} {1., 4.5, 10.9} {0.3, 1.3, 3.} {1., 4.7, 10.8} {0.9, 4.1, 10.} {1., 4.5, 10.7}118 0.88 6.82 {1.1, 2.3, 3.2} {0.9, 4.2, 10.9} {0.2, 1.2, 3.1} {0.8, 4., 10.4} {1.1, 5.1, 12.5} {0.8, 4.1, 10.7}121 1.67 7.82 {1.2, 2.4, 3.2} {1.1, 5.6, 14.4} {0.3, 1.6, 4.} {1., 5.6, 14.1} {1.4, 6.7, 16.6} {1., 5.2, 13.7}122 1.47 7.58 {1.3, 2.4, 3.3} {1.1, 5.7, 14.9} {0.3, 1.6, 4.2} {1.1, 5.9, 14.8} {1.4, 6.5, 15.9} {1.1, 5.8, 15.2}236 1.25 6.86 {1.1, 2.2, 3.2} {1., 4.4, 10.8} {0.3, 1.2, 3.} {1., 4.6, 10.7} {2., 6.9, 15.1} {1., 4.4, 10.7}238 1.06 7.34 {1.6, 2.7, 3.3} {1.9, 7.5, 16.3} {0.5, 2.1, 4.6} {1.6, 6.7, 14.9} {2.5, 8.9, 18.} {1.9, 7.2, 15.4}325 1.01 7.02 {1.3, 2.4, 3.2} {1.5, 6., 13.6} {0.4, 1.7, 3.8} {1.5, 5.9, 13.4} {1.1, 5.1, 12.2} {1.4, 6.1, 13.6}331 1.47 7.58 {1.1, 2.3, 3.2} {1.1, 5.4, 14.7} {0.3, 1.5, 4.1} {1.1, 5.5, 13.9} {0.9, 4.6, 12.7} {1.1, 5.6, 14.6}358 1.75 8.1 {1.7, 2.7, 3.3} {5.1, 15.5, 30.2} {1.4, 4.3, 8.4} {4.4, 14.6, 28.9} {4.6, 14.7, 29.3} {4.5, 14.8, 28.7}366 1.57 7.74 {1.2, 2.4, 3.2} {0.8, 4.1, 11.8} {0.2, 1.1, 3.3} {0.8, 4.2, 11.3} {0.8, 3.9, 10.5} {0.8, 4.3, 11.7}367 1.48 7.58 {1.5, 2.4, 3.2} {4.1, 13.2, 25.4} {1.1, 3.7, 7.1} {3.6, 12.3, 25.} {4.6, 14., 27.3} {3.6, 12.3, 24.5}370 3.03 7.66 {1.3, 2.4, 3.2} {2.4, 11.9, 28.4} {0.7, 3.3, 8.} {2.4, 11.6, 26.9} {1.1, 5.5, 13.9} {2.5, 11.6, 27.9}372 1.25 7.62 {1.1, 2.1, 3.2} {1.5, 6.6, 15.3} {0.4, 1.8, 4.3} {1.5, 6.4, 14.6} {1.3, 6.1, 14.7} {1.5, 6., 14.}373 1.52 7.74 {1., 2., 3.1} {2.1, 7.9, 17.5} {0.6, 2.2, 4.9} {2.1, 8.1, 18.} {1.9, 7.6, 17.1} {1.8, 7., 15.8}374 1.01 7.34 {1., 2.1, 3.2} {1.1, 4.8, 11.9} {0.3, 1.3, 3.3} {1.1, 4.8, 11.4} {0.8, 4., 10.} {1., 4.6, 10.8}380 0.74 6.9 {1., 2.1, 3.2} {0.6, 2.9, 8.1} {0.2, 0.8, 2.3} {0.5, 2.7, 7.3} {0.6, 3.1, 8.3} {0.5, 2.6, 7.4}386 1.93 8.1 {1.3, 2.5, 3.3} {1.7, 8.4, 21.9} {0.5, 2.4, 6.1} {1.5, 7.6, 19.3} {1.3, 6.4, 16.7} {1.6, 8.3, 21.8}387 1.2 7.66 {1.1, 2.3, 3.2} {0.8, 4.1, 10.6} {0.2, 1.2, 3.} {0.8, 4.1, 10.6} {0.7, 3.4, 8.7} {0.8, 4.1, 10.5}391 0.78 6.82 {1.1, 2.3, 3.3} {0.7, 3.6, 9.7} {0.2, 1., 2.7} {0.7, 3.4, 9.7} {0.6, 3.3, 9.2} {0.7, 3.5, 9.8}395 0.69 6.74 {1.2, 2.4, 3.3} {0.9, 4.3, 11.8} {0.2, 1.2, 3.3} {0.8, 4.4, 11.1} {0.7, 3.7, 10.} {0.9, 4.6, 12.2}402 0.77 7.22 {1., 2.2, 3.2} {0.6, 3.1, 8.4} {0.2, 0.9, 2.3} {0.6, 3.2, 8.4} {0.6, 2.8, 7.2} {0.6, 3.2, 8.6}406 1.15 7.18 {1.2, 2.5, 3.3} {0.9, 4.5, 12.5} {0.2, 1.3, 3.5} {0.9, 4.3, 11.7} {0.9, 4.9, 13.9} {0.8, 4.3, 11.5}407 2.85 8.1 {1., 2.1, 3.2} {1.8, 8.8, 22.3} {0.5, 2.5, 6.2} {1.8, 8.9, 22.4} {2.4, 11.5, 27.9} {1.6, 8.1, 20.7}408 0.82 6.74 {1.2, 2.3, 3.2} {1.3, 5.5, 12.3} {0.4, 1.6, 3.5} {1.6, 5.9, 12.4} {1.8, 5.8, 12.7} {1.4, 5.6, 12.1}409 2.27 7.86 {1.3, 2.5, 3.3} {2.1, 10.4, 27.4} {0.6, 2.9, 7.7} {1.9, 9.7, 25.3} {2.1, 11.3, 30.3} {2., 10.7, 28.1}410 0.69 7.38 {0.9, 1.9, 3.1} {1.3, 4.6, 10.2} {0.4, 1.3, 2.9} {1.2, 4.6, 10.1} {1.1, 4.2, 9.4} {1.2, 4.3, 9.2}412 0.88 7.14 {1., 2.2, 3.2} {0.6, 2.9, 7.9} {0.2, 0.8, 2.2} {0.5, 2.8, 7.1} {0.6, 3., 8.2} {0.6, 2.9, 7.6}415 1.1 6.86 {1., 2.2, 3.2} {0.6, 3.2, 8.2} {0.2, 0.9, 2.3} {0.6, 3.1, 8.1} {0.6, 3., 8.1} {0.6, 3., 8.}419 1.66 8.1 {1.8, 2.8, 3.4} {3.9, 13.8, 27.6} {1.1, 3.9, 7.7} {3.2, 12., 25.7} {2.4, 10., 22.2} {3.7, 12.7, 25.7}421 0.74 6.86 {1.1, 2.2, 3.2} {0.7, 3.4, 8.9} {0.2, 0.9, 2.5} {0.7, 3.5, 9.2} {0.8, 3.9, 9.7} {0.7, 3.3, 8.9}423 0.77 7.22 {1., 2.2, 3.2} {0.5, 2.6, 7.} {0.1, 0.7, 2.} {0.5, 2.7, 7.1} {0.5, 2.6, 7.} {0.5, 2.6, 6.7}424 1.36 6.7 {1.3, 2.1, 3.} {8.1, 19.7, 35.} {2.3, 5.5, 9.8} {8., 19.5, 34.3} {6.1, 15.6, 28.8} {7.3, 18.1, 31.9}425 3.11 7.42 {1.7, 2.7, 3.3} {7.7, 28.7, 58.1} {2.2, 8., 16.3} {6.9, 25.4, 52.5} {10.4, 29.3, 54.5} {8.5, 29.5, 59.5}427 0.83 6.82 {1., 2.2, 3.2} {0.6, 3.4, 8.8} {0.2, 0.9, 2.5} {0.6, 3.3, 8.6} {0.6, 3.1, 8.2} {0.6, 3.1, 8.3}432 1.1 7.34 {1.2, 2.3, 3.2} {1.6, 7., 15.7} {0.4, 1.9, 4.4} {1.6, 6.4, 14.2} {1.2, 5.5, 13.8} {1.5, 6.2, 14.7}433 1.54 7.14 {1.4, 2.6, 3.3} {1.3, 7.2, 19.3} {0.4, 2., 5.4} {1.2, 6.4, 16.3} {1.1, 5.7, 15.} {1.3, 6.7, 17.8}434 1.38 7.42 {1.1, 2.3, 3.2} {0.7, 3.4, 9.1} {0.2, 1., 2.5} {0.6, 3.3, 8.8} {0.7, 3.5, 9.3} {0.6, 3.3, 8.9}435 0.95 6.74 {0.8, 1.8, 3.} {3.9, 10., 18.7} {1.1, 2.8, 5.2} {3.8, 9.5, 18.5} {2.9, 8.3, 15.8} {3.8, 9.8, 18.4}436 2.5 7.74 {1.1, 2.2, 3.1} {3.2, 12.9, 28.} {0.9, 3.6, 7.8} {3.2, 12.5, 27.3} {2.4, 10.6, 23.8} {2.8, 12.1, 27.3}437 0.77 7.22 {1.1, 2.3, 3.2} {0.7, 3.4, 8.7} {0.2, 1., 2.4} {0.7, 3.3, 8.5} {0.8, 3.8, 9.3} {0.7, 3.2, 8.5}438 1.45 7.1 {1.4, 2.4, 3.2} {2.6, 9.9, 21.2} {0.7, 2.8, 5.9} {2.5, 9.8, 20.9} {1.8, 7.7, 17.5} {2.3, 9.3, 19.9}534 1.66 7.78 {1.3, 2.4, 3.2} {2.8, 9.5, 19.3} {0.8, 2.7, 5.4} {2.8, 9.2, 18.7} {4.1, 11.3, 21.2} {2.6, 8.8, 18.4}

MNRAS 000, 000–000 (0000)

The GC systems of 54 Coma UDGs 5

Table 1. Summary of the statistical constraints from our models, in terms of {10%, 50%, 90%} quantiles for all listed quantities. We

list our 4 stacks and the first 3 Coma UDGs in the footprint of the CCTp. A complete version of this Table is available here.

stack Rs log M⇤ Rh/Rs NGC Mvir NGC NGC NGC

or Id. kpc M� 1010M�model 1 model 1 model 1 model 2 model 3 model 5

RS > 1.5 kpc 1.99 7.64 {3., 3.3, 3.5} {8.5, 13.7, 19.6} {2.4, 3.8, 5.5} {7.2, 12.5, 18.9} {5.1, 9.2, 14.2} {9.5, 14.2, 19.4}RS 6 1.5 kpc 0.82 6.93 {1.6, 2.7, 3.4} {0.4, 1.4, 2.8} {0.1, 0.4, 0.8} {0.4, 1.3, 2.5} {0.3, 1., 2.1} {0.4, 1.3, 2.6}log M⇤ > 7.5 1.8 7.79 {2.8, 3.2, 3.5} {5.4, 9.6, 14.6} {1.5, 2.7, 4.1} {4.6, 8.7, 13.7} {2.2, 5.4, 9.3} {5.4, 9.6, 14.6}log M⇤ 6 7.5 1.03 6.75 {2.4, 3.1, 3.4} {1.7, 3.6, 6.1} {0.5, 1., 1.7} {1.4, 3.1, 5.3} {1.3, 2.8, 4.7} {2., 3.9, 6.2}

85 0.94 7.18 {1.1, 2.3, 3.2} {0.9, 4.4, 11.1} {0.3, 1.2, 3.1} {0.8, 4.2, 11.1} {0.8, 4., 10.} {0.9, 4.1, 10.6}89 1.1 7.5 {1.5, 2.6, 3.3} {1.7, 7.8, 18.} {0.5, 2.2, 5.} {1.8, 7.9, 18.4} {1.3, 6.2, 15.1} {1.8, 7.8, 18.}91 1.58 6.78 {1.1, 2.4, 3.2} {0.8, 4.4, 11.6} {0.2, 1.2, 3.3} {0.8, 4., 10.6} {0.8, 4.3, 11.2} {0.8, 3.9, 10.7}99 2.09 7.22 {1.4, 2.4, 3.2} {6.6, 19.9, 38.4} {1.9, 5.6, 10.8} {6.4, 18.8, 36.5} {4.3, 14.7, 30.3} {6., 18.4, 35.6}102 0.89 7.02 {1.4, 2.5, 3.3} {1.2, 6., 14.8} {0.3, 1.7, 4.1} {1.1, 5.5, 13.5} {0.8, 4.6, 13.3} {1.3, 6.1, 15.1}104 1.05 7.3 {1., 2.2, 3.2} {0.6, 3.1, 8.5} {0.2, 0.9, 2.4} {0.6, 3.1, 8.1} {0.6, 2.9, 7.6} {0.6, 3., 7.6}105 1.22 6.58 {1.2, 2.4, 3.3} {0.9, 4.9, 13.2} {0.3, 1.4, 3.7} {0.9, 4.9, 12.7} {1., 5.3, 14.5} {1., 4.9, 12.9}107 1.99 6.78 {1.2, 2.4, 3.2} {0.9, 4.6, 12.6} {0.3, 1.3, 3.5} {0.8, 4.5, 11.8} {0.9, 4.5, 12.5} {0.9, 4.5, 11.9}108 0.81 6.58 {1., 2.2, 3.2} {0.6, 3., 8.3} {0.2, 0.8, 2.3} {0.6, 3., 7.4} {0.7, 4., 10.1} {0.6, 3., 8.}112 1.53 7.74 {1.4, 2.6, 3.3} {1.7, 7.8, 19.3} {0.5, 2.2, 5.4} {1.5, 7.3, 17.9} {2.3, 10., 23.3} {1.7, 7.9, 19.2}113 0.84 6.38 {1.2, 2.5, 3.3} {0.9, 4.5, 12.2} {0.2, 1.3, 3.4} {0.8, 4.1, 11.2} {0.7, 3.4, 8.8} {1., 5.2, 13.3}114 1.52 7.74 {1.1, 2.2, 3.2} {1.3, 5.8, 14.1} {0.4, 1.6, 3.9} {1.1, 5.4, 13.3} {0.9, 4.6, 11.8} {1., 5., 12.}115 1.16 6.58 {0.8, 1.9, 3.1} {1., 4.5, 10.9} {0.3, 1.3, 3.} {1., 4.7, 10.8} {0.9, 4.1, 10.} {1., 4.5, 10.7}118 0.88 6.82 {1.1, 2.3, 3.2} {0.9, 4.2, 10.9} {0.2, 1.2, 3.1} {0.8, 4., 10.4} {1.1, 5.1, 12.5} {0.8, 4.1, 10.7}121 1.67 7.82 {1.2, 2.4, 3.2} {1.1, 5.6, 14.4} {0.3, 1.6, 4.} {1., 5.6, 14.1} {1.4, 6.7, 16.6} {1., 5.2, 13.7}122 1.47 7.58 {1.3, 2.4, 3.3} {1.1, 5.7, 14.9} {0.3, 1.6, 4.2} {1.1, 5.9, 14.8} {1.4, 6.5, 15.9} {1.1, 5.8, 15.2}236 1.25 6.86 {1.1, 2.2, 3.2} {1., 4.4, 10.8} {0.3, 1.2, 3.} {1., 4.6, 10.7} {2., 6.9, 15.1} {1., 4.4, 10.7}238 1.06 7.34 {1.6, 2.7, 3.3} {1.9, 7.5, 16.3} {0.5, 2.1, 4.6} {1.6, 6.7, 14.9} {2.5, 8.9, 18.} {1.9, 7.2, 15.4}325 1.01 7.02 {1.3, 2.4, 3.2} {1.5, 6., 13.6} {0.4, 1.7, 3.8} {1.5, 5.9, 13.4} {1.1, 5.1, 12.2} {1.4, 6.1, 13.6}331 1.47 7.58 {1.1, 2.3, 3.2} {1.1, 5.4, 14.7} {0.3, 1.5, 4.1} {1.1, 5.5, 13.9} {0.9, 4.6, 12.7} {1.1, 5.6, 14.6}358 1.75 8.1 {1.7, 2.7, 3.3} {5.1, 15.5, 30.2} {1.4, 4.3, 8.4} {4.4, 14.6, 28.9} {4.6, 14.7, 29.3} {4.5, 14.8, 28.7}366 1.57 7.74 {1.2, 2.4, 3.2} {0.8, 4.1, 11.8} {0.2, 1.1, 3.3} {0.8, 4.2, 11.3} {0.8, 3.9, 10.5} {0.8, 4.3, 11.7}367 1.48 7.58 {1.5, 2.4, 3.2} {4.1, 13.2, 25.4} {1.1, 3.7, 7.1} {3.6, 12.3, 25.} {4.6, 14., 27.3} {3.6, 12.3, 24.5}370 3.03 7.66 {1.3, 2.4, 3.2} {2.4, 11.9, 28.4} {0.7, 3.3, 8.} {2.4, 11.6, 26.9} {1.1, 5.5, 13.9} {2.5, 11.6, 27.9}372 1.25 7.62 {1.1, 2.1, 3.2} {1.5, 6.6, 15.3} {0.4, 1.8, 4.3} {1.5, 6.4, 14.6} {1.3, 6.1, 14.7} {1.5, 6., 14.}373 1.52 7.74 {1., 2., 3.1} {2.1, 7.9, 17.5} {0.6, 2.2, 4.9} {2.1, 8.1, 18.} {1.9, 7.6, 17.1} {1.8, 7., 15.8}374 1.01 7.34 {1., 2.1, 3.2} {1.1, 4.8, 11.9} {0.3, 1.3, 3.3} {1.1, 4.8, 11.4} {0.8, 4., 10.} {1., 4.6, 10.8}380 0.74 6.9 {1., 2.1, 3.2} {0.6, 2.9, 8.1} {0.2, 0.8, 2.3} {0.5, 2.7, 7.3} {0.6, 3.1, 8.3} {0.5, 2.6, 7.4}386 1.93 8.1 {1.3, 2.5, 3.3} {1.7, 8.4, 21.9} {0.5, 2.4, 6.1} {1.5, 7.6, 19.3} {1.3, 6.4, 16.7} {1.6, 8.3, 21.8}387 1.2 7.66 {1.1, 2.3, 3.2} {0.8, 4.1, 10.6} {0.2, 1.2, 3.} {0.8, 4.1, 10.6} {0.7, 3.4, 8.7} {0.8, 4.1, 10.5}391 0.78 6.82 {1.1, 2.3, 3.3} {0.7, 3.6, 9.7} {0.2, 1., 2.7} {0.7, 3.4, 9.7} {0.6, 3.3, 9.2} {0.7, 3.5, 9.8}395 0.69 6.74 {1.2, 2.4, 3.3} {0.9, 4.3, 11.8} {0.2, 1.2, 3.3} {0.8, 4.4, 11.1} {0.7, 3.7, 10.} {0.9, 4.6, 12.2}402 0.77 7.22 {1., 2.2, 3.2} {0.6, 3.1, 8.4} {0.2, 0.9, 2.3} {0.6, 3.2, 8.4} {0.6, 2.8, 7.2} {0.6, 3.2, 8.6}406 1.15 7.18 {1.2, 2.5, 3.3} {0.9, 4.5, 12.5} {0.2, 1.3, 3.5} {0.9, 4.3, 11.7} {0.9, 4.9, 13.9} {0.8, 4.3, 11.5}407 2.85 8.1 {1., 2.1, 3.2} {1.8, 8.8, 22.3} {0.5, 2.5, 6.2} {1.8, 8.9, 22.4} {2.4, 11.5, 27.9} {1.6, 8.1, 20.7}408 0.82 6.74 {1.2, 2.3, 3.2} {1.3, 5.5, 12.3} {0.4, 1.6, 3.5} {1.6, 5.9, 12.4} {1.8, 5.8, 12.7} {1.4, 5.6, 12.1}409 2.27 7.86 {1.3, 2.5, 3.3} {2.1, 10.4, 27.4} {0.6, 2.9, 7.7} {1.9, 9.7, 25.3} {2.1, 11.3, 30.3} {2., 10.7, 28.1}410 0.69 7.38 {0.9, 1.9, 3.1} {1.3, 4.6, 10.2} {0.4, 1.3, 2.9} {1.2, 4.6, 10.1} {1.1, 4.2, 9.4} {1.2, 4.3, 9.2}412 0.88 7.14 {1., 2.2, 3.2} {0.6, 2.9, 7.9} {0.2, 0.8, 2.2} {0.5, 2.8, 7.1} {0.6, 3., 8.2} {0.6, 2.9, 7.6}415 1.1 6.86 {1., 2.2, 3.2} {0.6, 3.2, 8.2} {0.2, 0.9, 2.3} {0.6, 3.1, 8.1} {0.6, 3., 8.1} {0.6, 3., 8.}419 1.66 8.1 {1.8, 2.8, 3.4} {3.9, 13.8, 27.6} {1.1, 3.9, 7.7} {3.2, 12., 25.7} {2.4, 10., 22.2} {3.7, 12.7, 25.7}421 0.74 6.86 {1.1, 2.2, 3.2} {0.7, 3.4, 8.9} {0.2, 0.9, 2.5} {0.7, 3.5, 9.2} {0.8, 3.9, 9.7} {0.7, 3.3, 8.9}423 0.77 7.22 {1., 2.2, 3.2} {0.5, 2.6, 7.} {0.1, 0.7, 2.} {0.5, 2.7, 7.1} {0.5, 2.6, 7.} {0.5, 2.6, 6.7}424 1.36 6.7 {1.3, 2.1, 3.} {8.1, 19.7, 35.} {2.3, 5.5, 9.8} {8., 19.5, 34.3} {6.1, 15.6, 28.8} {7.3, 18.1, 31.9}425 3.11 7.42 {1.7, 2.7, 3.3} {7.7, 28.7, 58.1} {2.2, 8., 16.3} {6.9, 25.4, 52.5} {10.4, 29.3, 54.5} {8.5, 29.5, 59.5}427 0.83 6.82 {1., 2.2, 3.2} {0.6, 3.4, 8.8} {0.2, 0.9, 2.5} {0.6, 3.3, 8.6} {0.6, 3.1, 8.2} {0.6, 3.1, 8.3}432 1.1 7.34 {1.2, 2.3, 3.2} {1.6, 7., 15.7} {0.4, 1.9, 4.4} {1.6, 6.4, 14.2} {1.2, 5.5, 13.8} {1.5, 6.2, 14.7}433 1.54 7.14 {1.4, 2.6, 3.3} {1.3, 7.2, 19.3} {0.4, 2., 5.4} {1.2, 6.4, 16.3} {1.1, 5.7, 15.} {1.3, 6.7, 17.8}434 1.38 7.42 {1.1, 2.3, 3.2} {0.7, 3.4, 9.1} {0.2, 1., 2.5} {0.6, 3.3, 8.8} {0.7, 3.5, 9.3} {0.6, 3.3, 8.9}435 0.95 6.74 {0.8, 1.8, 3.} {3.9, 10., 18.7} {1.1, 2.8, 5.2} {3.8, 9.5, 18.5} {2.9, 8.3, 15.8} {3.8, 9.8, 18.4}436 2.5 7.74 {1.1, 2.2, 3.1} {3.2, 12.9, 28.} {0.9, 3.6, 7.8} {3.2, 12.5, 27.3} {2.4, 10.6, 23.8} {2.8, 12.1, 27.3}437 0.77 7.22 {1.1, 2.3, 3.2} {0.7, 3.4, 8.7} {0.2, 1., 2.4} {0.7, 3.3, 8.5} {0.8, 3.8, 9.3} {0.7, 3.2, 8.5}438 1.45 7.1 {1.4, 2.4, 3.2} {2.6, 9.9, 21.2} {0.7, 2.8, 5.9} {2.5, 9.8, 20.9} {1.8, 7.7, 17.5} {2.3, 9.3, 19.9}534 1.66 7.78 {1.3, 2.4, 3.2} {2.8, 9.5, 19.3} {0.8, 2.7, 5.4} {2.8, 9.2, 18.7} {4.1, 11.3, 21.2} {2.6, 8.8, 18.4}

MNRAS 000, 000–000 (0000)

Figure 3. Analysis on the stacks RS > 1.5 kpc (top row) and

RS 6 1.5 kpc (bottom row). Line styles are as in Fig. 2. Zoomsdisplay all GCCs in the stacks.

members. In several instances, the surface density of con-taminants is such that even GCCs located within a few RS

from the UDG’s center cannot be considered physically as-sociated beyond doubt.

We find no appreciable difference between constraintsobtained through different model assumptions or using pri-ors. We have also explored using a more restrictive catalogof GCCs (applying cuts as from Peng et al. 2011), whichreduces the sample to ∼ 5400. Results remain consistent,although, as the deeper catalogue best probes the statisticsof the contaminant population, we deem the inferences ex-tracted from it more reliable.

As seen in Fig. 2, most posteriors on NGC increase al-most all the way to NGC = 0: only 19 of our UDGs haveNGC,5 > 1, i.e. are associated with more than 1 GC at 95%confidence. This result depends critically on the prior distri-bution adopted for f , and a large fraction of these detectionsare not confirmed when imposing a uniform prior on log f(rather than on f). Therefore, we stress that lower limitsand medians obtained for individual systems should not beinterpreted as measurements. However, we can extract reli-able individual upper bounds. Even if we adopt the loosest

90% upper limits among those returned by our 4 models –as in the abstract – these show our 54-strong sample to bemade of dwarfs. We follow Harris et al. (2015), and interpretour results on NGC as inferences on the virial mass of thestudied UDGs. We adopt the conversion factor suggested byG10, who used HST data and dynamical mass estimates ofnearby dwarf galaxies to calibrate the following mean rela-tion

Mvir ≡ 1

ηMGCS ≡ NGC

〈MGC〉η

∼ NGC1.69× 105M�

6× 10−5, (3)

where MGCS is the mass of the GCS and 〈MGC〉 is the masscorresponding to the turnoff of the GCLF. It is reassuringthat independent studies with different systematics agreeon this calibration2 to about a factor ∼2 (e.g., Harris et al.2015; Zaritsky et al. 2016; Forbes et al. 2016). Sticking to theresults of model 1, 49 of our 54 of our UDGs have Mvir,90 <1011M� (90% quantile). Of the 18 UDGs with RS > 1.5 kpc,14 have Mvir,90 < 1011M�, with the remaining 4 satisfyingMvir,90 < 1.3 × 1011M�. We also note that systems in thelatter group of 4 are characterised by especially high densityof contaminant densities (likely ICGs and/or GCs from thenearby N4889), which substantially inflate the uncertainties(see, for example, the system ID 425 in the complete versionof Fig. 2). Table 1 provides the conversion of the results ofmodel 1 to virial mass for all 54 UDGs.

3.2 Analyses on stacks

The combination of the paucity of physically associated GCsand the ∼

√N Poisson uncertainty deriving from the dom-

inant background counts implies we can only extract up-per bounds for individual systems. We can partially circum-vent this and improve our statistics by stacking: we com-bine UDGs based on their size, stacking the 18 systems withRS > 1.5 kpc, or based on their stellar mass, combining the18 systems with logM∗ > 7.5, as well as the complementarysamples of 36. This allows us to extract information on theaverage richness of UDG GCSs, 〈NGC〉.

Fig. 3 illustrates the results obtained for the stacksbased on size, and Table 1 lists quantiles for both analy-ses. As shown by the posterior probability distributions on

2 Massive galaxies lie on the relation Mvir ∼NGC

(2.4× 105M�/4× 10−5

); the halo-to-halo scatter in

dwarfs appears wider than this difference (G10).

MNRAS 000, 000–000 (0000)

The GC systems of 54 Coma UDGs 5

〈NGC〉 in Fig. 3, this strategy allows us to extract significantmeasurements for the stack of the largest UDGs (as well asfor the stack of the most luminous). The average richness〈NGC〉 remains as typical for dwarf galaxies: independentlyof model assumptions, our 18 UDGs with RS > 1.5 kpc have〈NGC,50〉 ∼ 5, which corresponds to an average halo mass of〈Mvir,50〉 ∼ 1.4× 1010M�.

4 DISCUSSION AND CONCLUSIONS

UDGs are a startling class of systems because of the ap-parent mismatch between their stellar mass and size, whichresults in very high dark matter fractions within their opti-cal radii (Beasley et al. 2016; Beasley & Trujillo 2016; Peng& Lim 2016; van Dokkum et al. 2016), independently ofwhether they are hosted by dwarf or MW mass haloes. Oneaspect that has not been sufficiently highlighted so far is thealmost perfect linearity of the relation between the abun-dance of UDGs in clusters and the cluster mass itself (vander Burg et al. 2016). This indicates that UDGs are an ap-proximately constant fraction of cluster populations, bearinglittle additional dependence on the cluster richness, and byextension on local environment. In turn, this would suggestthat the physical mechanism that gives UDGs their unusualproperties may in fact have an internal origin, rather thanbeing caused by interactions with the environment, as cor-roborated by the detection of UDGs outside cluster cores(Martinez-Delgado et al. 2016; Roman & Trujillo 2016).

There is no shortage of mechanisms proposed so far toform galaxies with the properties of UDGs, including (i) highangular momentum content of primordial origin (Amorisco& Loeb 2016); (ii) especially strong and prolonged stellarfeedback (Di Cintio et al. 2016); (iii) premature quenchingdue to early infall onto the cluster (Yozin & Bekki 2015; vanDokkum et al. 2015); (iv) 2-body galaxy-encounters withinthe cluster itself (Baushev 2016; Burkert 2016). Amongthese, the first two are of internal origin, while the lattertwo require the external influence of a dense environment,in combination with early infall.

Our results show that most UDGs are hosted by dwarfmass haloes: we find no candidate for a massive MW-likehalo. Beasley & Trujillo (2016) and Peng & Lim (2016) havesuggested that, though hosted by LMC mass haloes, UDGsmight still show signs of ‘failure’, having rich GCSs for theirstellar mass. We explore this further in Fig. 4, by compar-ing our UDGs with nearby galaxies from the compilationsof Harris et al. (2013, H13, grey rectangles) and G10 (greenstars, from their Table 1). Galaxies from the G10 compila-tion include nearby dwarfs in groups or loose associations inwhich at least a GC has been observed. Dots with blue error-bars identify the measurements by Beasley et al. (2016) forVCC 1287 in Virgo; Peng & Lim (2016) and Beasley & Tru-jillo (2016) for DF17; van Dokkum et al. (2016) for DF44,which is a strong outlier in this plane (see also the analy-sis of Zaritsky 2016). Stellar masses are obtained assumingthat B − R ∼ 1 for the UDGs (Koda et al. 2015), and us-ing morphological type as a proxy for colour within the H13catalog. The uncertainty displayed in the top-left shows thedifference between the masses inferred using the M/L re-lations of Zibetti et al. (2009) and Bell et al. (2003). Forour 54 UDGs, downward arrows display individual upper

++

+

+

+

+

+

+

+

+

++

+

+

+

+

++

+

+

+

+

+

+

+ +

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+ +

+

+

+

+

+

+

+ +

++

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+ +

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+ ++++

+

+

+

+ +

+

+

++

+

++

+

+

+

+

+

+

+

++

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

++

+

++

+

+

+

+

+ +

+

+

+

+

+

+

÷÷

÷÷

÷

÷

÷÷÷

÷

÷ ÷÷

÷

÷

÷÷ ÷

÷

÷

÷

÷

÷÷

÷

÷÷÷÷

÷

÷

÷

÷

÷

÷

÷

÷

DF44

DF17VirgoUDG

RS�kpc1.1 1.8 2.5 3.2 4.6

6.5 7.0 7.5 8.0 8.5 9.0 9.5

-0.5

0.0

0.5

1.0

1.5

2.0

log10M*�M�

log 1

0N

GC

Figure 4. The richness of the GCS of ‘normal’ galaxies from the

H13 catalog (grey rectangles), dwarf galaxies from G10 (greenstars) and three Coma and Virgo UDGs from the literature (blue

rectangles with full dots), compared to our sample of 54 Coma

UDGs. Individual upper bounds (90% quantiles) are shown bydownward arrows. Large asterisks show the results of our stacking

analyses (medians with 10-90% quantile error-bar for NGC; meanwith 1σ scatter for logM∗). Symbols for all UDGs are colour-

coded according to their stellar half-light radius.

bounds (NGC,90 from model 1); large asterisks with error-bars show results obtained from our stacking analyses. UDGsymbols are colour-coded according to the stellar half-lightradius. The large asterisks show that more luminous (and/orlarger) UDGs have on average richer GCSs, a result that isalso hinted to by the individual upper bounds. While wecannot exclude that some GCs have been lost as a resultof cluster tides, our UDGs do not appear to deviate fromthe galaxies in the H13 catalog, or from the sample of dwarfgalaxies of G10: we can rule out large systematic discrep-ancies in the richness of their GCSs. On a sample of 54systems, all the data agree that GCSs of UDGs have verysimilar richnesses to those of ‘normal’ dwarfs of similar stel-lar mass. This strongly suggests that their halo masses arealso similar.

ACKNOWLEDGEMENTS

NA and AM aknowledge stimulating discussions withChervin Laporte. NA thanks Adriano Agnello, Mike Beasleyand Abraham Loeb for comments on an early version of thisdraft.

REFERENCES

Amorisco, N. C., & Evans, N. W. 2011, MNRAS, 411, 2118

Amorisco, N. C., Evans, N. W., & van de Ven, G. 2014, Nat, 507,335

Amorisco, N. C., & Loeb, A. 2016, MNRAS, 459, L51

Baushev, A. N. 2016, arXiv:1608.04356

Beasley, M. A., Romanowsky, A. J., Pota, V., et al. 2016,arXiv:1602.04002

Beasley, M. A., & Trujillo, I. 2016, arXiv:1604.08024

MNRAS 000, 000–000 (0000)

6 N. C. Amorisco, A. Monachesi

Behroozi, P. S., Wechsler, R. H., & Conroy, C. 2013, ApJ, 770,57

Bell, E. F., McIntosh, D. H., Katz, N., & Weinberg, M. D. 2003,

ApJS, 149, 289Burkert, A. 2016, arXiv:1609.00052

Campbell, D. J. R., Frenk, C. S., Jenkins, A., et al. 2016,

arXiv:1603.04443Di Cintio, A., Brook, C. B., Dutton, A. A., et al. 2016,

arXiv:1608.01327

Forbes, D. A., Alabi, A., Romanowsky, A. J., et al. 2016, MNRAS,458, L44

Georgiev, I. Y., Puzia, T. H., Goudfrooij, P., & Hilker, M. 2010,MNRAS, 406, 1967

Guo, Q., White, S., Li, C., & Boylan-Kolchin, M. 2010, MNRAS,

404, 1111Hammer, D., Verdoes Kleijn, G., Hoyos, C., et al. 2010, ApJS,

191, 143

Harris, W. E., Harris, G. L. H., & Alessi, M. 2013, ApJ, 772, 82Harris, W. E., Harris, G. L., & Hudson, M. J. 2015, ApJ, 806, 36

Hudson, M. J., Harris, G. L., & Harris, W. E. 2014, ApJL, 787,

L5Jordan, A., McLaughlin, D. E., Cote, P., et al. 2007, ApJS, 171,

101

Kartha, S. S., Forbes, D. A., Spitler, L. R., et al. 2014, MNRAS,437, 273

Koda, J., Yagi, M., Yamanoi, H., & Komiyama, Y. 2015, ApJL,807, L2

Mackey, A. D., & Gilmore, G. F. 2003, MNRAS, 338, 85

Martinez-Delgado, D., Laesker, R., Sharina, M., et al. 2016,arXiv:1601.06960

Mihos, J. C., Durrell, P. R., Ferrarese, L., et al. 2015, ApJL, 809,

L21Miller, B. W., & Lotz, J. M. 2007, ApJ, 670, 1074

Moster, B. P., Naab, T., & White, S. D. M. 2013, MNRAS, 428,

3121Munoz, R. P., Eigenthaler, P., Puzia, T. H., et al. 2015, ApJL,

813, L15

Peng, E. W., Jordan, A., Blakeslee, J. P., et al. 2009, ApJ, 703,42

Peng, E. W., Ferguson, H. C., Goudfrooij, P., et al. 2011, ApJ,730, 23

Peng, E. W., & Lim, S. 2016, ApJL, 822, L31

Roman, J., & Trujillo, I. 2016, arXiv:1603.03494Salinas, R., Alabi, A., Richtler, T., & Lane, R. R. 2015, AA, 577,

A59

Schlafly, E. F., & Finkbeiner, D. P. 2011, ApJ, 737, 103Schlegel, D. J., Finkbeiner, D. P., & Davis, M. 1998, ApJ, 500,

525

Sirianni, M., Jee, M. J., Benıtez, N., et al. 2005, PASP, 117, 1049van der Burg, R. F. J., Muzzin, A., & Hoekstra, H. 2016,

arXiv:1602.00002van Dokkum, P. G., Abraham, R., Merritt, A., et al. 2015, ApJL,

798, L45van Dokkum, P., Abraham, R., Brodie, J., et al. 2016, ApJL, 828,

L6Yagi, M., Koda, J., Komiyama, Y., & Yamanoi, H. 2016, ApJS,

225, 11Yozin, C., & Bekki, K. 2015, MNRAS, 452, 937

Walker, M. G., Mateo, M., Olszewski, E. W., et al. 2009, ApJ,704, 1274

Walker, M. G., & Penarrubia, J. 2011, ApJ, 742, 20

Wolf, J., Martinez, G. D., Bullock, J. S., et al. 2010, MNRAS,

406, 1220Zaritsky, D., Crnojevic, D., & Sand, D. J. 2016, ApJL, 826, L9

Zaritsky, D. 2016, arXiv:1609.08169Zibetti, S., Charlot, S., & Rix, H.-W. 2009, MNRAS, 400, 1181

MNRAS 000, 000–000 (0000)