Galactic Dark Matter Halos and Globular Cluster Populations. III: Extension to Extreme Environments

0.49 MB·

by  William E. Harris

to be submitted to ApJ
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
GALACTIC DARK MATTER HALOS AND GLOBULAR CLUSTER POPULATIONS. III: EXTENSION TO
EXTREME ENVIRONMENTS
William E. Harris1, John P. Blakeslee2, and Gretchen L. H. Harris3
(Dated: January 19, 2017)
to be submitted to ApJ
ABSTRACT
7
Thetotalmass M intheglobularcluster(GC)systemofagalaxyisempiricallyanear-constant
1 GCS
fraction of the total mass M ≡ M +M of the galaxy, across a range of 105 in galaxy mass.
0 h bary dark
This trend is radically unlike the strongly nonlinear behavior of total stellar mass M versus M . We
2 (cid:63) h
discuss extensions of this trend to two more extreme situations: (a) entire clusters of galaxies, and

n (b)theUltra-DiffuseGalaxies(UDGs)recentlydiscoveredinComaandelsewhere. Ourcalibrationof
a the ratio η = M /M from normal galaxies, accounting for new revisions in the adopted mass-
J M GCS h
to-light ratio for GCs, now gives ηM =2.9×10−5 as the mean absolute mass fraction. We find that
7 the same ratio appears valid for galaxy clusters and UDGs. Estimates of η in the four clusters we
M
1
examine tend to be slightly higher than for individual galaxies, but more data and better constraints

onthemeanGCmassinsuchsystemsareneededtodetermineifthisdifferenceissignificant. Weuse
]
A the constancy of ηM to estimate total masses for several individual cases; for example, the total mass
of the Milky Way is calculated to be M =1.1×1012M . Physical explanations for the uniformity of
G h (cid:12)
η arestilldescriptive, butpointtoapictureinwhichmassive, densestarclustersintheirformation
M
. stages were relatively immune to the feedback that more strongly influenced lower-density regions
h
where most stars form.
p
Subject headings: galaxies: formation — galaxies: star clusters — globular clusters: general
-
o
r
st 1. INTRODUCTION withinafixedphysicalradius. FollowingSpitler&Forbes
a Twodecadesago, Blakesleeetal.(1997)usedobserva- (2009),Georgievetal.(2010),andourPapersIandIIin
[ this series, here we discuss the link between GC popula-
tions of ∼ 20 brightest cluster galaxies (BCGs) to pro-
1 posethatthe numberofglobularclusters (GCs)ingiant tionsandgalaxytotalmassintermsofthedimensionless
mass ratio η ≡ M /M , where M is the total
v galaxies is directly proportional to the total mass Mh massofallthMeGCscoGmCSbinehdandM isGthCeStotalgalaxy
5 of the host galaxy, which in turn is dominated by the h
mass including its dark halo plus baryonic components.
4 dark matter (DM) halo. This suggestion was followed
In some sense, η represents an absolute efficiency of
8 up with increasing amounts of observational evidence in M
GC formation, after accounting for subsequent dynami-
4 several papers, including McLaughlin (1999b); Blakeslee
0 (1999); Spitler & Forbes (2009); Georgiev et al. (2010); cal evolution up to the present day (cf. Katz & Ricotti
. Kruijssen (2015), Hudson et al. (2014) (hereafter Paper 2014; Kruijssen 2015; Forbes et al. 2016). Direct esti-
1
mates of η for several hundred galaxies indicate that
0 I), Harris et al. (2015) (hereafter Paper II), and Forbes M
this ratio is indeed nearly uniform (Papers I and II),
7 etal.(2016),amongothers(seePaperIIforamorecom-
far more so than the more well known ratio M /M . A
1 plete review of the literature). This remarkable trend (cid:63) h
second-order dependence on galaxy type has been found
: may be a strong signal that the formation of GCs, most
v of which happened in the redshift range 8 (cid:38) z (cid:38) 2, was in the sense that S/Irr galaxies have a ∼ 30% lower ηM
i than do E/S0 galaxies (Paper II).
X relatively resistant to the feedback processes that ham-
So far, the case that η (cid:39)const has been built on the
peredfield-starformation(e.g.Kravtsov&Gnedin2005; M
r observed GC populations in ‘normal’ galaxies covering
a Mooreetal.2006;Lietal.2016). Ifthatisthecase,then
the range from dwarfs to giants. However, opportunities
thetotalmassinsideGCsattheirtimeofformationmay
have recently arisen to extend tests of its uniformity in
have been closely proportional to the original gas mass
two new directions. The first is by using the GC popu-
present in the dark-matter halo of their parent galaxy
lations in entire clusters of galaxies, including their GCs
(Papers I, II, and Kruijssen 2015), very unlike the total
in the Intracluster Medium (ICM). The second is from
stellar mass M .
(cid:63) the newly discovered ultra-diffuse galaxies (UDGs) and
Blakeslee et al. (1997) introduced the number ratio
the GCs within them. It is also worth noting that in
η ≡N /M (where N is the total number of GCs
N GC h GC both these cases, the masses of the systems concerned
in a galaxy) and showed that it was approximately con-
have been measured with different methods than by the
stant for their sample of BCGs, at least when measured
gravitational-lensing approach used to build the calibra-
tion of η in our Papers I and II, which makes the test
1DepartmentofPhysics&Astronomy,McMasterUniversity, M
Hamilton,ON,Canada;[email protected] of the hypothesis even more interesting.
2Herzberg Astronomy & Astrophysics, National Research The plan of this paper is as follows. In Section 2, we
Council of Canada, Victoria, BC V9E 2E7, Canada; describe improved methodology for determining M ,
[email protected] GCS
followed by a recalibration of the mass ratio η . In Sec-
3Dept. of Physics and Astronomy, University of Waterloo, M
Waterloo,ONN2L3G1,Canada;[email protected] tion 3 the discussion is extended to include four clusters
2 Harris et al.
of galaxies in which measurements now exist for both
M and M , while in Section 4 the relation is ex-
GCS h
tended in quite a different direction to selected UDGs.
InSection5, thekeyratioη isappliedtoseveralinter-
M
esting sample cases with accompanying predictions for
their GCS sizes. We finish with brief comments about
the implications of the constancy of η for understand-
M
ing the conditions of formation for GCs.
2. RECALIBRATIONOFTHEMASSRATIO:METHOD
ThetotalGCSmasswithinagalaxyorclusterofgalax-
ies is calculated as
(cid:90) M
M = ( )Ln(L)dL (1)
GCS L
where n(L) represents the number of GCs per unit lu-
minosity L, and M/L is their mass-to-light ratio. Here,
we use V−band luminosities L following most previ-
V
ous studies. The GC luminosity function (GCLF) is as-
sumed to have a Gaussian distribution in number per
unit magnitude. The parameters defining n(L), namely
theGaussianturnovermagnitudeµ andintrinsicdisper-
0
sion σ, are in turn weak functions of galaxy luminosity,
as described in Villegas et al. (2010); Harris et al. (2013,
2014). From the observations covering a large range of
host galaxies, µ and σ bothexhibit shallow increasesas
0 Figure 1. Upper panel: Mean GC mass (in Solar units) versus
galaxy luminosity increases.
hostgalaxyluminosityMT. Lowerpanel: Meanmass-to-lightratio
In the present paper, unlike all previous discussions of V
fortheGCswithinagalaxyofluminosityMT,definedasthetotal
this topic, we now assume that the mass-to-light ratio V
M/L for individual GCs is also a function of GC mass, massMGC(tot)inallGCsdividedbythetotalluminosityLV(tot)
followVing empirical evidence from recent literature (e.g. ogfaltahxeieGssCims.ilaTrhteovtehretiMcaillkdyasWheady.line at MVT = −21.5 marks L(cid:63)
Rejkuba et al. 2007; Kruijssen 2008; Kruijssen & Mieske
2009; Strader et al. 2011). Of necessity, however, we as- The intrinsic galaxy-to-galaxy scatter in (cid:104)M (cid:105) is ±0.2
GC
sumethatM/LfollowsthesamefunctionofGCmass(or dex, based on the observations from the Virgo and For-
luminosity,whichisthemoreeasilyobservablequantity) nax clusters (Villegas et al. 2010).
within all galaxies. We have used these calibrations to recalculate the val-
In the Appendix below, we assemble recent observa- ues of M and η in the complete sample of galaxies
GCS M
tional data and define a convenient interpolation func- discussedinPapersIandII.Inparticular, forthispaper
tion for M/L versus GC luminosity. Using Eq. 1, we use these recalibrated values for the 175 ‘best’ galax-
V
we can then readily derive a mean mass-to-light ratio ies of all types used in Paper II.5 In addition, to help
averaged over all GCs in any given galaxy, defined as tie down the high-mass end of the range of galaxies, we
(cid:104)M/L (cid:105)(tot) = M /L (tot). We can also define a have updated the N values for five Brightest Cluster
V GCS GC GC
mean GC mass as (cid:104)M (cid:105) = M /N .4 For exam- Galaxies(BCGs)includingNGC4874, 4889, 6166, UGC
GC GCS GC
ple, for a typical L galaxy at MT (cid:39) −21.4 (the type 9799, and UGC 10143 from the recent data of Harris et
of galaxy within w(cid:63)hich most GCsV in the universe are al. (2016, ApJ in press).
found; see Harris 2016), we obtain (cid:104)M/L (cid:105)(cid:39)1.73. The The results are shown in Figure 2. First, the up-
V
mean ranges from (cid:104)M/LV(cid:105) (cid:39) 1.3 for very small dwarfs per panel shows the number per unit mass ηN versus
(MT ∼ −15) up to (cid:104)M/L (cid:105) (cid:39) 2.1 for very luminous Mh (following the notation convention of Georgiev et al.
V V 2010). Anunweightedleast-squaresfittotheE/S0galax-
supergiants (MT ∼−23).
V ies gives the simple linear relation
In Figure 1 the trends of GC mean mass and global
(cid:104)M/LV(cid:105)areplottedversusgalaxyluminosityMVT. Accu- logηN = (−8.56±0.34)−(0.11±0.03)log(Mh/M(cid:12)). (4)
rate numerical approximations to these results are given
by the interpolation curves Thus the total number of GCs in galaxies, observed at
redshift 0, scales approximately as N ∼ M0.9. The
GC h
log(cid:104)M (cid:105) = 5.698+0.1294MT +0.0054(MT)2 (2) rms scatter around this relation is ±0.26 dex.
GC V V
Second, the lower panel shows the trend for the mass
and ratio η . Because the mean mass of the GCs increases
M
log(cid:104)M/L (cid:105) = 1.041+0.117MT +0.0037(MT)2. (3)
V V V 5 This ‘best’ sample consists of all the galaxies for which the
raw GC photometry was of high enough quality to separate the
4Byconvention,tomaintainaconsistentcalculationprocedure, conventional red and blue GC subpopulations. In most cases this
theGCLFisassumedtobeGaussianandNGC isdefinedforour criterion also means that the limiting magnitude of the photome-
purposes as twice the number of GCs brighter than the GCLF try was faint enough to be near the GCLF turnover, making the
turnoverpoint;seeHarrisetal.(2013). calculationofthetotalpopulationNGC relativelysecure.
3
progressively with galaxy mass, the shallow decrease of
η with M nearly cancels, leaving the mass ratio η
N h M
approximately constant over the entire run of galaxies.
Theweightedmeanis(cid:104)logη (cid:105)=−4.54,or(cid:104)η (cid:105)=2.9×
M M
10−5, with a residual rms scatter ±0.28 dex.
In Fig. 2, the lower panel (η ) and the upper panel
M
(η ) are obviously closely linked, but they are not en-
N
tirelyequivalent. AsdescribedinPaperI,M isdeduced
h
from the K−band luminosity M as calibrated through
K
gravitational lensing. On the other hand, M is de-
GCS
rived from N and the visual luminosity MT through
GC V
Eq. (1).
Five points near M ∼ 1013M sit anomalously high
h (cid:12)
above the mean relations. These five are NGC 4636 and
theBCGsNGC3258,3268,3311,5193. Theclusterpop-
ulations for these systems are well determined and very
unlikely to be overestimated by the factor of ∼ 5 that
would be needed to bring them back to the mean lines.
The alternate possibility is that their halo masses may
havebeenunderestimated,whichinturnmeansthatthe
K−band luminosities of these very large galaxies (from
2MASS;seeHarrisetal.2013)wouldhavetobeunderes-
timated(see Schombert &Smith2012; Scottet al.2013,
for more extensive comments in this direction).
3. CLUSTERSOFGALAXIES
Useful estimates of the total GC populations within
entire clusters of galaxies have now been made for four
rich clusters: Virgo, Coma, Abell 1689, and Abell 2744
(sources listed below). This material has in each case
taken advantage of wide-field surveys or unusually deep
sets of images taken with HST. The quoted N val-
GC
ues include both the GCs associated directly with the Figure 2. Upperpanel: LogoftheratioηN =NGC/Mh,plotted
individual member galaxies, and the intracluster globu- versus total galaxy mass Mh. Solid dots: E/S0 galaxies. Open
circles: BCGs. Bluetriangles: S/Irrgalaxies. Magentadiamonds:
lar clusters (IGCs) that are now known to be present in
Thefourclustersofgalaxiesdiscussedinthetext. Greendiamonds:
rich clusters. It is likely that the IGCs represent GCs Theultra-diffusegalaxies. TheopendiamondforDragonfly44in
stripped from many different systems during the exten- theComaclusterisveryuncertain(seetext). Greenhexagon: the
sive history of galaxy/galaxy merging and harassment Fornax dSph satellite of the Milky Way. The dashed line is the
least-squaresfitdefinedinthetext. Lowerpanel: Logofthemass
that takes place within such environments (Peng et al.
ratioηM = MGCS/Mh versusMh;symbolsarethesameasinthe
2011). Simulations (e.g. Purcell et al. 2007) show that upperpanel. Thedashedlineisthemeanvalue(cid:104)logηM(cid:105)=−4.54.
L −typegalaxiescontributethemosttotheIntracluster
(cid:63)
light. For such galaxies the mean globular cluster mass η =(3.4±0.7)×10−5. Thisη estimateis17%higher
M M
is (cid:104)MGC(cid:105)(cid:39) 2.6×105M(cid:12) (Fig. 1), and the GCLF mean than the value quoted by Durrell et al. (2014), but the
and dispersion are µ0(MV) = −7.4, σ = 1.2 mag (Har- increase results entirely from the difference in assumed
ris et al. 2013). However, the total GC population in (cid:104)M (cid:105). Just asfor the Comasurveydata (discussed be-
GC
the entire cluster of galaxies consists of the IGCs plus low), in this case the limiting magnitude of the survey is
the individual galaxies in roughly similar amounts. For close to the GCLF turnover (peak) magnitude, so that
the giant ellipticals and BCGs that dominate the indi- approximately half the total GC population is directly
vidualgalaxies,theGCLFsarebroaderwithσ (cid:39)1.4and observed, and the estimated N count is virtually in-
GC
(cid:104)MGC(cid:105) is higher. For the present purpose, we therefore dependent of the assumed GCLF dispersion σ.
adopt averages σ (cid:39)1.3 mag and (cid:104)M (cid:105)(cid:39)2.8×105M
GC (cid:12) Coma: Peng et al. (2011) find that within a projected
for an entire galaxy cluster. Knowing N , the total
GC radius of r (cid:39)520 kpc, the cluster contains 71000±5000
mass M in all the GCs within the cluster can then
GCS GCs (here we combine their estimates of internal and
be directly estimated, albeit with more uncertainty than
systematic uncertainties, and renormalize the total to
for a single galaxy.
σ = 1.3 mag instead of their value of 1.37 mag), and
Virgo: Durrelletal.(2014),fromtheNextGeneration thus M = (1.99 ± 0.14) × 1010M . This survey
GCS (cid:12)
Virgo Cluster Survey, calculate that the entire cluster radius is well within the Coma virial radius, which is
contains (37700±7500) GCs brighter than g0 = 24.0, 2.5−3.0 Mpc (e.g. Hughes 1989; Colless & Dunn 1996;
which is 0.2 mag fainter than the GCLF turnover point. Rines et al. 2003; L(cid:32) okas & Mamon 2003; Kubo et al.
Adopting the fiducial value σ = 1.3 mag as explained 2007; Gavazzi et al. 2009; Okabe et al. 2014; Falco et al.
above, we then obtain NGC = (67000±13000), which 2014). From these sources, which use methods including
then gives MGCS = (1.88±0.37)×1010M(cid:12). Durrell et X-ray light, galaxy dynamics, weak lensing, and galaxy
al.alsoquoteatotalVirgomass5.5×1014M ,leadingto sheets to derive the Coma mass profile, the mass within
(cid:12)
4 Harris et al.
theGCsurveyradiusof520kpcisM (cid:39)(4±1)×1014M . and Coma where the raw observations reach to limit-
(cid:12)
The resulting mass ratio within this radius is then η = ing magnitudes approaching the turnover magnitude µ ,
M 0
(4.98±1.25)×10−5. but they become critically important where only the
bright tip of the GCLF is observed. The turnover µ
A1689: Alamo-Mart´ınez et al. (2013) used unusually 0
exhibits an intrinsic galaxy-to-galaxy scatter at the level
deep HST imaging of the core region of this massive
of ±0.2 mag, while the dispersion σ has an intrinsic
cluster, which is at redshift z = 0.183, to find a large
scatter of ±0.05 − 0.1 mag (Jord´an et al. 2006; Ville-
and extended population of GCs. In contrast to Virgo
gas et al. 2010; Rejkuba 2012). For the baseline values
and Coma, the limiting magnitude of their photometry
of σ(GCLF) = 1.3 mag and a limiting magnitude 2.93σ
was 2.3 mag brighter than the expected GCLF turnover
brighter than the turnover, the fraction N(obs)/N(tot)
and thus only the brightest 4.0% of the GC popula-
equals 0.0017 (+0.0010,−0.00066) due to a ±0.2−mag
tion was measurable. From an analysis of the known
uncertaintyintheturnoverluminosity,andanadditional
statistical and systematic uncertainties, they deduced
(+0.00166,−0.00094)duetoa±0.1−maguncertaintyin
N = 162,850(+75,450,−51,300) GCs within a pro-
GC σ. Treating the uncertainties as independent, we obtain
jected400-kpcradiusofthecentralcD-typegalaxyafter
N = 3.9(+7.2,−2.1)×105. If we further assume the
using a GCLF-extrapolated fit to the observed number GC
GC counts extend out to 600 kpc (the limit that can be
of GCs brighter than the photometric limit. However,
probedwithintheACSfieldofviewatthisredshift)and
that number assumed σ = 1.4 mag; converting to our
followasimilarprofiletothatofA1689, thenthecorrec-
fiducial σ = 1.3 mag, the total becomes N = 209,600
GC tion to a radius of 1 Mpc is a factor of 1.21, yielding
(+97,100, −66,000) within r < 400 kpc. From gravi-
N =4.7(+8.6,−2.5)×105.
tational lensing, the total mass within the same radius GC
is M = 6.4 × 1014M . The resulting mass ratio is Thebest-estimatemassofA2744isalsodifficulttopin
thenhη (r < 400kpc) =(cid:12)9.17(+4.25,−2.90)×10−5. We down, since the cluster has complex internal dynamics
M with two major subclusterings at quite different mean
can attempt to define something closer to a global value
velocities, indicative of merging in progress (Boschin
out to larger radius by extrapolating the best-fit r1/4-
et al. 2006; Owers et al. 2011; Jauzac et al. 2016).
law derived to the full GC distribution in A1689 (their
For the dominant central ”a” subcluster Boschin et al.
fit for the case without masking the regions around the
(2006) determine M (< 2.4Mpc) = 2.2(+0.7,−0.6)×
galaxies), which suggests that the estimated number of vir
1015M . With this value for the mass, we conclude
GCs out to 1 Mpc is larger by a factor of 1.48. From (cid:12)
η =6.0(+11,−3.2)×10−5 for A2744.
the multi-probe mass profile of Umetsu et al. (2015, us- M
TheunderlyingassumptionabouttheGaussianGCLF
ing h = 0.7), the total mass within the same radius is
shapeis harder toquantify. Thestrongestempirical test
M =1.3×1015M . Wethereforeestimate,forthewhole
h (cid:12) available is the measurement of GCLFs in seven BCG
cluster, η =6.7(+3.1,−2.1)×10−5 within r <1 Mpc.
M galaxies from Harris et al. (2014), which extend from
The total mass of A1689 out to the virial radius exceeds
the turnover point to an upper limit almost 5 magni-
2×1015M ,andthustheglobalvalueofη mightbestill
(cid:12) M tudes brighter (equivalent to almost 4σ), thanks to the
lower. In any case, given the uncertainties, the value of
extremely large numbers of GCs per galaxy. The results
η inA1689appearsconsistentwiththestandardrange
M indicate that the Gaussian assumption fits the data re-
calculated above.
markably well to that level. However, these tests all ap-
A2744: Lee & Jang (2016) have used HST imaging ply to single galaxies, whereas the IGCs are a composite
from the HST Frontier Field to find the brightest GCs population of GCs stripped from galaxies of all types.
and UCDs in this very rich cluster, which is at redshift This composite GCLF will in general not have a simple
z = 0.308. Intracluster Light (ICL) is also detectably Gaussianshapeevenifalltheprogenitorgalaxieshadin-
present at least in the inner part of the cluster (Montes dividually normal GCLFs (see Gebhardt & Beers 1991).
& Trujillo 2014). From M. G. Lee (private communi- Unfortunately, no direct measurements of the GCLF for
cation), the raw number of observed GCs brighter than apureIGCpopulationareyetavailable. Forthepresent
F814W = 29.0, after photometric completeness correc- time,wesimplyadopttheparametersforgalaxyclusters
tion,fieldsubtractionandremovalofUCDs,is(664±41) as described above and recognize that further observa-
(Poisson uncertainty). This limiting magnitude is (cid:39) 3.8 tions and analysis could change the results for A2744
mag brighter than the GCLF turnover point, or 2.93σ quite significantly. While uncertainties are also sizable
shortoftheturnover. Here, wehaveadopteda0.2−mag for A1689, the fraction of the GC population directly
brighteningoftheGCLFturnoverluminositytoaccount observed there is 20 to 40 times greater than in A2744;
for passive evolution for its redshift of z =0.3; note that thus, the results for A1689 are robust by comparison.
Alamo-Mart´ınezetal.(2013)determinedanetbrighten- It is evident from the preceding discussion that esti-
ing in F814W of 0.12 mag in A1689 (z =0.18), and for mates of η on the scale of entire clusters of galaxies
M
small z the correction scales nearly linearly. Extrapolat- put us in a much more challenging regime of uncertain-
ing from the observed total, then NGC (cid:39)390,000. ties than is the case for single galaxies. In particular,
Given that only ∼0.2% of the inferred total was ac- better results will be possible if η as a function of r
M
tually detected, the dominant sources of error in this can be more accurately established. Ideally the global
case are not the internal count statistics, but instead valueshouldbeestimatedouttothevirialradius,butso
the uncertainties in the adopted GCLF turnover and far this is the case only for Virgo, the cluster for which
dispersion, as well as the basic assumption that the the estimated η is closest to the mean for individual
M
GCLF follows a strictly Gaussian shape all the way to galaxies. Nevertheless, for all four galaxy clusters, the
luminosities far above the turnover magnitude. These weightedaverageresultisη =(3.9±0.6)×10−5,slightly
M
uncertainties are unimportant for situations like Virgo
5
larger than the mean value of 2.9×10−5 characterizing An additional residual outcome is that the slight nonlin-
the individual galaxies. It is difficult to say at this point earity in the trend of η (see Papers I and II) is now
M
whether or not the mean difference is significant. One reduced.
possible evolutionary difference between the GCs within
galaxies and the IGCs is that the IGCs are subjected to 5.1. Galaxy Mass Estimation
muchlowerratesofdynamicaldestructionthantheGCs Inadirectpracticalsense,η isusableasahandyway
M
deepwithinthepotentialwellsofindividualgalaxies,and to estimate the total mass of a galaxy (dark plus bary-
so may have kept a higher fraction of their initial mass. onic) to better than a factor of 2. This direction is the
emphasis taken notably by Spitler & Forbes (2009); van
4. ULTRA-DIFFUSEGALAXIES
Dokkum et al. (2016); Peng & Lim (2016) and Beasley
UDGshaverecentlybeenfoundwithintheVirgo, For- etal.(2016)andwasalsousedinPaperItoapplytoM31
nax, and Coma clusters in large numbers (e.g. Mihos and the Milky Way. As these authors emphasize, it re-
et al. 2015; van Dokkum et al. 2015; Koda et al. 2015; mains surprising that a method apparently unconnected
Mun˜oz et al. 2015). Deep imaging has revealed GC pop- with internal satellite dynamics, lensing, or other fairly
ulations around two of the Coma UDGs, Dragonfly 44 directmeasuresofagalaxy’sgravitationalfieldcanyield
(van Dokkum et al. 2016) and Dragonfly 17 (Peng & suchanaccurateresult. Theprescriptionfordetermining
Lim 2016), as well as VCC1287 in Virgo (Beasley et al. M is:
h
2016). All three of these systems have anomalously high
specific frequencies SN ∼ NGC/LV, but the interest for 1. Count the total GC population, NGC. Given the
this discussion is their mass ratio. Beasley et al. (2016) uncertainties discussed in Section 3 above and in
and van Dokkum et al. (2016) have already commented Harris et al. (2013), it is important to have raw
thatη forthetwoUDGstheystudiedfallsclosetothe photometricdatathatreachorapproachtheGCLF
M
standard level applicable for more normal galaxies. turnover point, which helps avoid uncomfortably
For the Virgo dwarf VCC1287, Beasley et al. (2016) largeextrapolationsfromobservationsthatresolve
find a GC population N =22±8, which would trans- only the bright tip of the GCLF.
GC
late to M = (2.2 ± 0.8) × 106M if we adopt a
GCS (cid:12) 2. Use the galaxy luminosity MT to define the ap-
mean GC mass of 1.0×105M appropriate for a mod- V
(cid:12) propriate mean GC mass (cid:104)M (cid:105) (from Fig. 1 and
erate dwarf galaxy. Fortunately, (cid:104)M (cid:105) does not vary GC
GC Eq. 2). The total mass in the galaxy’s GC system
strongly across the dwarf luminosity range (see Fig. 1).
follows as M =N (cid:104)M (cid:105).
From a combination of the velocity dispersion of the GCS GC GC
GCs themselves, and comparison with EAGLE simu- 3. Divide M by η to obtain M .
GCS M h
lations, they estimate a virial mass for the galaxy of
M = (8±4)×1010M , giving an approximate mass Moregenerally,thismethodforestimatinggalaxymass
200 (cid:12)
ratio η =(2.75±1.70)×10−5. is workable only for systems near enough that the GC
M
population can be resolved and counted. The practical
For Dragonfly 44, van Dokkum et al. (2016) find a
‘reach’ of the procedure is d (cid:46) 200−300 Mpc through
relativelyrichGCpopulationN (cid:39)94±25and,again,
GC
deep HST imaging (e.g. Harris et al. 2014), though with
a specific frequency S higher by an order of magnitude
N
the use of SBF techniques, the effective limit may be
than normal galaxies with similar L . With (cid:104)M (cid:105) =
V GC
extended somewhat further; cf. Blakeslee et al. (1997);
1.1 × 105M for the galaxy luminosity MT = −16.1,
(cid:12) V Blakeslee (1999); Mar´ın-Franch & Aparicio (2002).
then M =(1.0±0.3)×107M . Their measurement
GCS (cid:12)
of the velocity dispersion of the stellar light gives M(<
5.2. Sample Cases
r ) = 7.1 × 109M . The total (virial) mass M is
1/2 (cid:12) h We provide some sample specific examples of the pro-
likely to be at least an order of magnitude higher, but
cedure:
scaling from the comparable results for VCC1287 above
(seeBeasleyetal.2016),weobtainavery roughestimate Milky Way: Harris(1996)(2010edition)lists157GCs
M ∼ 2×1011M . In turn, the final result is η ∼ in the Milky Way, but many of these are extremely
h (cid:12) M
5.5×10−5, again very uncertain. faint or sparse objects that would be undetectable in
almost all other galaxies. To treat this system in the
5. DISCUSSIONANDCONCLUSIONS same way as other galaxies, we note that the GCLF
turnover is at M (cid:39) −7.3 and that there are 72 clus-
From Fig. 2, we find that the near-constancy of the V
ters brighter than that point. Doubling this, we then
massratioη over5ordersofmagnitudeinM remains
M h adopt N = 144 in the sense that it is defined here.
valid. The addition of two quite different environments GC
At MT(MW) (cid:39) −21.0 (Licquia et al. 2015; Bland-
to the mix, UDGs and entire galaxy clusters, has not V
Hawthorn & Gerhard 2016), close to an L galaxy, the
changed the essential result. It is worth noting that the (cid:63)
Mh estimates for the galaxy clusters and UDGs relied meanGCmassisthen(cid:104)MGC(cid:105)=2.3×105M(cid:12),fromwhich
on internal dynamics rather than the weak-lensing cali- MGCS =3.3×107M(cid:12). Finallythen,Mh (cid:39)1.1×1012M(cid:12),
bration used for the normal galaxies (except A1689, for which is well within the mix of estimates obtained from
which the mass is based on a combination of weak and a wide variety of methods involving satellite dynamics
strong lensing). The new calibration of the mean mass andLocalGrouptimingarguments(see,e.g.Wangetal.
ratio η =(2.9±0.2)×10−5 is significantly lower than 2015;Eadie&Harris2016,forcompilationsandcompar-
M
in previous papers (see Paper II for comparisons); the isons).
difference is due mainly to our lower adopted GC mass- Dragonfly 17: For this UDG in Coma, Peng & Lim
to-light ratio and its nonlinear dependence on GC mass. (2016) estimate a total population N =28±14 based
GC
6 Harris et al.
on a well sampled GCLF and radial distribution. For this handful of GCs presents something of an interpre-
MT =−15.1, we have (cid:104)M (cid:105)=0.94×105M and then tive puzzle for understanding their survival over a Hub-
V GC (cid:12)
predict a total mass M =(9.1±4.5)×1010M for this ble time, with several discussions of dynamical mod-
h (cid:12)
galaxy. Peng&Lim(2016)predictedM =(9.3±4.7)× elling in the recent literature (e.g. Cole et al. 2012;
h
1010M , although the agreement with our estimate is Strigari et al. 2006; Pen˜arrubia et al. 2008; Martinez
(cid:12)
something of a coincidence: they used a higher value of 2015). The 5 Fornax clusters add up to a total mass
η from an older calibration, but also a higher mean GC MGCS =3.8×105M(cid:12) assuming (M/LV)=1.3 (Mackey
mass, and these two differences cancelled out. &Gilmore2003). Thepredictedhalomassofthegalaxy
should then be M (cid:39) 1.3 × 1010M if we adopt our
M87: This centrally dominant Virgo giant is the clas- h (cid:12)
normal η , which would give Fornax a global mass-to-
sic “high specific frequency” elliptical. From the GCS M
lightratioM /L (tot)(cid:38)600(assumingthatithaskept
catalog (Harris et al. 2013), N = 13000 ± 800 and h V
GC
its entire halo to the present day against tidal strip-
the luminosity is MT = −22.61, giving a mean clus-
V ping from the Milky Way). By contrast, dynamical
ter mass (cid:104)M (cid:105) = 3.4 × 105M . Thus M =
GC (cid:12) GCS modelling of Fornax with various assumed dark-matter
(4.4 ± 0.3) × 109M(cid:12), leading to the prediction Mh = profiles tends to infer virial masses near M ∼ 109M
1.5×1014M(cid:12). For comparison, Oldham & Auger (2016) (Pen˜arrubiaetal.2008;Coleetal.2012;Anghus&Diafe(cid:12)-
give Mvir = 7.4(+12.1,−4.1)×1013M(cid:12) from the kine- rio2009). Inthatcase,thederivedmassratiowouldthen
matics of the GC system and satellites. A plausible be η (cid:39) 3.8×10−4, an order of magnitude larger than
M
upper limit from McLaughlin (1999a) is MDM(r200) = our standard value. Fornax is plotted in Fig. 2 with this
(4.2±0.5)×1014M(cid:12), obtained from the GC dynamics higher value; although it is not located outrageously far
andtheX-raygasintheVirgopotentialwell,whileDur- fromthescatterofpointsdefinedbythelargergalaxies,it
relletal.(2014)quote5.5×1014M(cid:12) fortheentireVirgo doesleaveacontinuingproblemforinterpretation. With
cluster. For BCGs it is difficult to isolate the galaxy’s M =109M andourbaselinevalueη ∼3×10−5, the
h (cid:12) M
dark-matter halo from that of the entire galaxy cluster, normal prediction would be that Fornax should contain
but given that M87 holds (cid:39)20% of the Virgo GC popu- only one GC.
lation, these estimates of Mh seem mutually consistent. The Fornax dSph case hints that the argument for a
Fornax Cluster: Fornax is the next nearest rich clus- constant η across the range of galaxies may begin to
ter of galaxies after Virgo, with the cD giant NGC 1399 break down at the very lowest luminosities. For a stan-
near its center. GC populations in the individual galax- dard ηM (cid:39) 3×10−5, the boundary below which dwarf
ies have been studied as part of the HST/ACS For- galaxies should be too small to have any remaining GCs
nax Cluster Survey (Villegas et al. 2010; Jord´an et al. is near Mh (cid:46)3×109M(cid:12). In this very low-mass regime,
2015), and the NGC 1399 system particularly has been other physical factors should also come into play deter-
well studied photometrically and spectroscopically (e.g. mining the number of surviving GCs within the galaxy,
Dirsch et al. 2003; Schuberth et al. 2010). The Fornax particularly massive gas loss during the earliest star-
cluster as a whole is not as rich as Virgo or the oth- forming period in such tiny potential wells.
ers discussed here, but an ICM is present at least in the
form of substructured X-ray gas (Paolillo et al. 2002). 5.3. Cluster Formation Conditions
Globalmassmeasurementsfromgalaxydynamicsinand
Inthelongerterm,wesuggestthatthemoreimportant
around Fornax (Drinkwater et al. 2001; Nasonova et al.
implications for the near-constancy of η are for help-
2011) find M(<1.4 Mpc)= (7±2)×1013M , rising to M
(cid:12) ing understand the formation conditions of the dense,
perhaps as high as 3×1014M within 3 Mpc. For NGC
(cid:12) massive star clusters that evolved into the present-day
1399itself,Schuberthetal.(2010)findM approaching
vir GCs (see Papers I and II). These clusters should have
1013M(cid:12). If we use the mean value ηM =3.9×10−5 de- formedwithinverymassivehostGiantMolecularClouds
terminedabovefortheothergalaxyclusters,andwealso (GMCs)underconditionsofunusuallyhighpressureand
use Mh = 7×1013M(cid:12) within a radius of 1.4 Mpc, then turbulence, analogous to the Young Massive Clusters
we predict that the entire Fornax cluster should contain (YMCs) seen today in starburst dwarfs, galactic nuclei,
at least NGC ∼ 10,000 clusters. NGC 1399 alone has andmergingsystems(Harris&Pudritz1994;Elmegreen
NGC = (6450±700) (Dirsch et al. 2003) and the other et al. 2012; Kruijssen 2015).
smaller galaxies together are likely to contribute at least Under such conditions, star formation within these
6000more(Jord´anetal.2015). Thusthepredictionand dense protoclusters will be shielded from external feed-
the actual known total agree to within the internal scat- back such as active galactic nuclei, UV and stellar winds
ter of ηM, which would indicate that the GC population from more dilute field star formation, and cosmic reion-
withinFornaxisalreadyaccountedforandthatfewIGCs ization(e.g.Kravtsov&Gnedin2005;Li&Gnedin2014;
remain to be found. It will be intriguing to see if wide- Howard et al. 2016). In strong contrast, these forms
field surveys (see, e.g. D’Abrusco et al. 2016) will reveal of feedback were much more damaging to the major-
a significant IGC population. ity of star formation happening in lower-density, lower-
Fornax dSph: The dwarf spheroidal satellite of the pressure local environments. Though such a picture
Milky Way, Fornax, is an especially interesting case. needs more quantitative modelling, it is consistent with
It has 5 GCs of its own and a total luminosity of just the idea (Paper II) that M at high redshift may be
GCS
MT = −13.4, placing it among the very faintest galax- nearlyproportionaltothetotalinitialgasmass–atleast,
V
ies known to contain GCs. Since it lacks a measured much more so than the total stellar mass M .
(cid:63)
K−band luminosity it does not appear in the GCS cat- An alternate route (Kruijssen 2015) is that the empir-
alog with a lensing-calibrated M . The existence of ical result η ∼const can be viewed in some sense as a
h M
7
coincidence if it is written as (M /M ), now including the systematic trend
GCS h
of GC mass-to-light ratio with GC mass, yields
M M M
η = GCS = GCS · (cid:63) . (5) (cid:104)η (cid:105) = 2.9×10−5 with a ±0.28−dex scatter be-
M M M M M
h (cid:63) h tween individual galaxies.
The two ratios on the right-hand side show well known
opposite trends with Mh that happen to cancel out 2. Evaluation of ηM for four clusters of galaxies
when multiplied together. The stellar-to-halo mass ra- (Virgo, Coma, A1689, A2744) including all GCs in
tio (SHMR) (M /M ) reaches a peak efficiency near both the cluster galaxies and the IGM, shows that
(cid:63) h
M (cid:39) 1012M and falls off to both higher and lower very much the same mass ratio applies for entire
h (cid:12)
mass by more than an order of magnitude (Leauthaud clusters as for individual galaxies. For these four
et al. 2012; Moster et al. 2013; Behroozi et al. 2010, clusters (cid:104)ηM(cid:105)=(3.9±0.6)×10−5.
2013; Hudson et al. 2015). By contrast, the GCS num-
ber per unit M (that is, the specific frequency S or 3. TwooftherecentlydiscoveredUltra-DiffuseGalax-
(cid:63) N
its mass-weighted version T ) reaches a minimum near ies in Virgo and Coma can also now be included in
N
M ∼ 1012M and rises by an order of magnitude on the relation. Within the (large) measurement un-
h (cid:12) certainties, both such galaxies fall within the nor-
both sides. Both these trends are extremely nonlinear,
mal value of η at the low-mass end of the galaxy
and we suggest that it is difficult to see how their mu- M
range. By contrast, the Fornax dSph in the Local
tual cancellation can be so exact over such a wide range
Group may be a genuine extreme outlier, contain-
of galaxy mass if it is only a coincidence.
ing perhaps 5 times more clusters than expected.
The common factor between the two mass ratios (T ,
N
SHMR)isthegalaxystellarmassM . AsinPaperII,we
(cid:63) 4. Thenear-constantmassratiobetweenGCsystems
suggest that the result can be seen as the outcome of a
and their host galaxy masses is strikingly different
single physical process (the role of galaxy-scale feedback
from the highly nonlinear behavior of total stellar
on M ). If instead we essentially ignore M , then M
(cid:63) (cid:63) GCS mass M versus M . We favor the interpretation
is closer to representing the total initial gass mass, and (cid:63) h
thatGCformation–inessence,starformationun-
thusM . Werecognize,however,thatthisargumentisas
h derconditionsofextremelydensegasinproto-GCs
yet unsatisfactorily descriptive and will require full-scale
embedded in turn within giant molecular clouds –
numerical simulations that track GC formation within
wasnearlyimmunetotheviolentexternalfeedback
hierarchical galaxy assembly over the full range of red-
shifts8(cid:38)z (cid:38)1(Kravtsov&Gnedin2005;Lietal.2016; that hampered most field star formation.
Griffen et al. 2010; Tonini 2013).
ACKNOWLEDGEMENTS
5.4. Conclusions WEH acknowledges financial support from NSERC
(Natural Sciences and Engineering Research Council of
In this paper we have revisited the empirical relation
Canada). WearegratefultoMyungGyoonLeeforhelp-
between the total mass M of the globular clusters in
GCS fully transmitting their observed numbers of globular
a galaxy, and that galaxy’s total mass M . Our findings
h clusters in Abell 2744. JPB thanks K. Alamo-Mart´ınez
are the following:
for helpful discussions about Abell 1689.
1. A recalibration of the mass ratio η ≡
M
APPENDIX
MASS-TO-LIGHT RATIOS FOR GLOBULAR CLUSTERS
A key ingredient in the calculation of M , the total mass in the globular cluster system of a given galaxy, is the
GCS
assumed mass-to-light ratio M/L for GCs. Along with many other GC studies in recent years, we simply used a
V
constant M/L = 2 in Papers I and II. However, much recent data and modelling for internal dynamical studies of
V
GCssupports(a)alowermeanvalue,(b)asignificantcluster-to-clusterscatterprobablybecauseofdifferingdynamical
histories,and(c)asystematictrendforM/L toincreasewithGCmass(orluminosity)particularlyformassesabove
V
106M .
(cid:12)
Figure 3 shows estimates of M/L for Milky Way GCs, determined from measurements of GC internal velocity
V
dispersion combined with dynamical modelling. Data from two widely used previous compilations (Mandushev et al.
1991; McLaughlin & van der Marel 2005) are shown in the upper two panels of the Figure. Since then, dynamical
studies have been carried out on numerous individual GCs based on both radial-velocity and proper-motion data,
that are built on larger and more precise samples than in the earlier eras. Results from these post-2005 studies
are listed in Table 1 and plotted in the bottom panel of Fig. 3. (Note that many clusters appear more than once
because each individual study is plotted. However, the values listed in Table 1 present the weighted mean M/L ,
V
in Solar units, for each cluster.) The cluster luminosities MT are from the catalog of Harris (1996) (2010 edition).
V
For the clusters listed in Table 1, the weighted mean value for 36 GCs excluding NGC 5139 and NGC 6535 is
(cid:104)M/L (cid:105) = (1.3±0.08)M /L with a cluster-to-cluster rms scatter of ±0.45. For comparison, the values in the
V (cid:12) V(cid:12)
upperpanelofFig.3haveamean(cid:104)M/L (cid:105)=(1.49±0.11)M /L withanrmsscatterof±0.58, whileinthemiddle
V (cid:12) V(cid:12)
panel the mean is (cid:104)M/L (cid:105)=(1.53±0.11)M /L with an rms scatter of ±0.64.
V (cid:12) V(cid:12)
There is also now much new observational material for GC mass measurements in other nearby galaxies. For other
galaxies, the spatial structures of the GCs are unresolved or only partially resolved, and the measurements most often
consist of a luminosity-weighted average of the internal velocity dispersion of each cluster, converted to mass via some
8 Harris et al.
Table 1
Mass-to-Light Ratios for Milky Way Clusters
Cluster M/LV ± MVT Sources
NGC104 1.32 (0.03,0.03) −9.42 6,15
NGC288 1.53 (0.17,0.17) −6.75 6,10,15
NGC362 1.10 (0.10,0.10) −8.43 6,15
NGC2419 1.55 (0.10,0.10) −9.42 1,15
NGC2808 2.24 (0.19,0.19) −9.39 6,9
NGC3201 1.91 (0.17,0.17) −7.45 15
NGC4147 1.47 (0.54,0.54) −6.17 6
NGC4590 1.40 (0.43,0.43) −7.38 6
NGC5024 1.38 (0.16,0.16) −8.72 6,10
NGC5053 1.30 (0.26,0.26) −6.76 6
NGC5139 2.45 (0.04,0.04) −10.26 12,13,15
NGC5272 1.32 (0.14,0.14) −8.88 4,6
NGC5466 0.72 (0.23,0.23) −6.98 6
NGC5904 1.36 (0.21,0.21) −8.81 6
NGC6121 1.32 (0.14,0.14) −7.19 6,15
NGC6205 2.10 (0.27,0.17) −8.55 4
NGC6218 1.12 (0.10,0.10) −7.31 6,10,15
NGC6254 1.61 (0.19,0.19) −7.48 15
NGC6341 1.69 (0.07,0.07) −8.21 4,6,15
NGC6388 1.45 (0.13,0.13) −9.41 8,14
NGC6397 1.9 (0.10,0.10) −6.64 5
NGC6402 1.82 (0.35,0.35) −9.10 6
NGC6440 1.23 (0.27,0.27) −8.75 14
NGC6441 1.07 (0.19,0.19) −9.63 6,14
NGC6528 1.12 (0.39,0.42) −6.57 14
NGC6535 11.06 (2.68,2.12) −4.75 14
NGC6553 1.02 (0.31,0.36) −7.77 14
NGC6656 1.30 (0.13,0.13) −8.51 6,15
NGC6715 1.52 (0.45,0.45) −9.98 6
NGC6752 2.65 (0.19,0.19) −7.73 6,10
NGC6809 0.81 (0.05,0.05) −7.57 3,6,10,15
NGC6838 1.36 (0.39,0.39) −5.61 6
NGC6934 1.52 (0.49,0.49) −7.45 6
NGC7078 1.14 (0.05,0.05) −9.19 6,11,15
NGC7089 1.66 (0.38,0.38) −9.03 6
NGC7099 1.84 (0.19,0.19) −7.45 6,10
Pal5 1.60 (0.85,0.59) −5.17 7
Pal13 2.4 (5.0,2.4) −3.76 2
Sources: (1)Bellazzinietal.(2012);(2)Bradfordetal.(2011);(3)Diakogiannisetal.(2014);(4)Kamannetal.(2014);(5)Kamannetal.
(2016);(6)Kimmigetal.(2015);(7)Ku¨pperetal.(2015);(8)Lu¨tzgendorfetal.(2011);(9)Lu¨tzgendorfetal.(2012);(10)Sollimaetal.
(2012);(11)vandenBoschetal.(2006);(12)vandeVenetal.(2006);(13)Watkinsetal.(2013);(14)Zaritskyetal.(2014);(15)Zocchi
etal.(2012).
appropriate form of the virial theorem or mass profile model. Data from several galaxies are displayed in Figure 4,
including M31 (Meylan et al. 2001; Strader et al. 2011), M33 (Larsen et al. 2002), NGC 5128 (Martini & Ho 2004;
Rejkuba et al. 2007; Taylor et al. 2010), and M87 (Ha¸segan et al. 2005).
TheM/L resultsfromthesedifferentstudiesoccupysimilarrangesasintheMilkyWay,butperhapsnotsurprisingly
V
the scatter is much larger for these fainter targets. Some puzzling issues remain, for example in NGC 5128 for which
the Taylor et al. (2010) values are roughly 50% larger than those from Rejkuba et al. (2007) and Martini & Ho (2004)
for 14 objects in common, though again with considerable scatter. The source of this discrepancy is unclear. Possible
trends of M/L with GC metallicity as deduced from the M31 sample are discussed by Strader et al. (2011); Shanahan
& Gieles (2015); Zonoozi et al. (2016) and are also not yet clear.
By contrast, there is general agreement that M/L should increase systematically with GC mass (Kruijssen 2008;
Kruijssen & Mieske 2009; Rejkuba et al. 2007; Strader et al. 2011), since the high-mass clusters have relaxation times
large enough that the preferential loss of low-mass stars has not yet taken place to the same degree as for lower-mass
clusters. The mean M/L is expected to increase from ∼1−2 at M <106M progressively up to the level (cid:39)5−6
V (cid:12)
for the mass range 107−108M characterizing UCDs (Ultra-Compact Dwarfs) and dwarf E galaxies (e.g. Baumgardt
(cid:12)
& Mieske 2008; Mieske et al. 2008). For convenience of later calculation, we define a simple interpolation curve for
M/L as a function of cluster luminosity,
M 4.5
= 1.3+ . (A1)
LV 1+e2.0(MVT+10.7)
This function gives a roughly linear increase of M/L from MT (cid:39) −10 up to −12, saturating at the level of ∼ 5−6
V
9
Figure 3. Mass-to-lightratiosforMilkyWayglobularclustersplottedversusGCluminosity,fromthreedifferentobservationaleras. Top
panel: Mandushev et al. (1991). Middle panel: McLaughlin & van der Marel (2005). Bottom panel: Dynamically based measurements
fromavarietyofindividualstudies(seetext). Thelow-luminosityclustersNGC6535andPal13donotappearontheplot;seeTable1.
appropriate for UCDs and dE’s. The ‘baseline’ at M/L = 1.3 is chosen to match the observed data for Milky Way
V
clusters. Atverylowluminosity,themass-to-lightratioshouldincreaseagainbecauselow-massandhighlydynamically
evolved clusters should become relatively more dominated by binary stars and stellar remnants (cf. the datapoint for
Palomar 13 as an example). However, clusters at the low-mass end are also relatively few in number, and contribute
little mass per cluster to the system in any case, so the particular M/L value adopted for them has negligible effects
on the total mass of the system M .
GCS
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Figure 4. Dynamically measured mass-to-light ratios M/LV in Solar units, for globular clusters in several galaxies. Solid dots: Milky
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