An enigmatic population of luminous globular clusters in a galaxy lacking dark matter
Pieter van Dokkum Yotam Cohen Shany Danieli J. M. Diederik Kruijssen Aaron J. Romanowsky Allison Merritt Roberto Abraham Jean Brodie Charlie Conroy Deborah Lokhorst Lamiya Mowla Ewan O'Sullivan Jielai Zhang








1
Astronomy Department, Yale University, 52 Hillhouse Ave,
New Haven, CT 06511, USA
2
Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität
Heidelberg, Mönchhofstraße 12-14, D-69120 Heidelberg, Germany

3
University of California Observatories, 1156 High Street, Santa
Cruz, CA 95064, USA
4
Department of Physics and Astronomy, San José State University,
San Jose, CA 95192, USA
5
Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117
Heidelberg, Germany
6
Department of Astronomy & Astrophysics, University of Toronto,
   50 St. George Street, Toronto, ON M5S 3H4, Canada
7
Harvard-Smithsonian Center for Astrophysics, 60 Garden Street,
Cambridge, MA, USA
 




We recently found an ultra diffuse
galaxy (UDG) with a half-light radius of R_e=2.2 kpc
and little or no dark matter. The total mass
of   was measured from the
radial velocities of bright compact objects that are associated
with the galaxy.
Here we analyze these objects using
a combination of HST imaging and Keck
spectroscopy.






Their average size is ⟨r_h⟩=6.2±
0.5 pc and their average ellipticity is
⟨ϵ⟩=0.18± 0.02.






From a stacked Keck spectrum we derive an
age of ≳ 9 Gyr and a metallicity of
[Fe/H]=-1.35±0.12.



Their properties are similar to ω Centauri,
the brightest and largest globular cluster in the Milky Way, and



our results demonstrate that the luminosity function
of metal-poor
globular clusters is not universal.



The fraction of the total stellar mass
that is in the globular cluster system is similar
to that in other UDGs, and consistent with
“failed galaxy” scenarios where star formation terminated shortly
after the clusters were formed. However, the galaxy
is a factor of ∼1000 removed from the 
relation between globular cluster
mass and total galaxy mass that has been found for other galaxies,
including other UDGs.
We infer that a dark matter halo is not
a prerequisite for the formation of metal-poor globular cluster-like
objects in high redshift galaxies.

















§ INTRODUCTION


kruijssen






We recently identified a galaxy
with little or no dark matter (van Dokkum et al. 2018, hereafter ).
 has a stellar mass of M_ stars≈ 2
× 10^8  and a 90 % confidence upper limit on its dark
matter halo mass of M_ halo<1.5× 10^8 , placing it
a factor of ≳ 400 off of the canonical stellar mass – halo
mass relation (Moster et al. 2013; Behroozi et al. 2013).
 is a featureless, spheroidal
“ultra diffuse” galaxy (UDG; van Dokkum et al. 2015),
with an effective radius of R_e = 2.2 kpc and a central
surface brightness μ(V_606,0) = 24.4 mag arcsec^-2.
It has a radial velocity of 1803 . Its
SBF-determined distance is 19.0± 1.7 Mpc (), consistent with
that of the NGC 1052 group at D≈ 20 Mpc (Blakeslee et al. 2010).

The kinematics of  were measured from the radial velocities of 10
compact objects
that are associated with the galaxy.
These  objects drew our attention to the galaxy in
the first place: it is a large, low surface brightness blob in our
Dragonfly Telephoto Array imaging (Abraham & van Dokkum 2014; Merritt et al. 2016) but a
collection of point-like sources in the Sloan Digital Sky Survey.


Finding globular clusters (GCs) in a UDG is
in itself not unusual
(Beasley et al. 2016; Peng & Lim 2016; van Dokkum et al. 2016, 2017; Amorisco, Monachesi, &  White 2018). 
In fact, Coma UDGs have on average ∼ 7times more GCs than other galaxies of the same
luminosity (van Dokkum et al. 2017), with large galaxy-to-galaxy scatter
(Amorisco et al. 2018).
However, what is unusual, or at least unexpected, is the
remarkable luminosity of the clusters. 
The luminosity function of the GC
populations of Coma UDGs is consistent with that seen in other galaxies,
peaking at an absolute magnitude
M_V ∼ -7.5 (Peng & Lim 2016; van Dokkum et al. 2017; Amorisco et al. 2018). The
ten clusters that
were analyzed in  are all significantly brighter than this,
raising the question whether the GC luminosity function is
systematically offset from that in other galaxies.

Here we focus on the properties of the compact objects in
, using imaging from the
Hubble Space Telescope (HST)  and spectroscopy
obtained with the W. M. Keck Observatory.





We show that the GC system of  is unprecedented,
both in terms of the average properties of the clusters and in its offset
from the canonical scaling relation between GC system mass and
total galaxy mass.









§ IDENTIFICATION




 §.§ Spectroscopically-Identified Clusters


We obtained spectra of compact objects in the  region with
the Keck telescopes, using
the Deep Imaging Multi-Object Spectrograph 
on Keck II, the red arm of the Low-Resolution Imaging
Spectrometer (LRIS; Oke et al. 1995), and the blue arm of
LRIS. The sample selection, reduction, and analysis of the
high resolution DEIMOS and red LRIS data are described in detail
in . The 
blue-side LRIS data
were obtained with the 300/5000 grism
and 10 slits,
providing a spectral resolution ranging from σ_ instr∼350  at λ=3800 Å to σ_
instr∼150 at λ=6600 Å. The reduction followed the same procedures as
the red side data, and is described in .
The spectral resolution
is too low for accurate radial velocity measurements, but the wide
wavelength coverage provides
constraints on the stellar populations ( <ref>).
Small sections of the
spectra of the 11 confirmed GCs are shown in Fig. <ref>.
Note that we analyze one more object in this paper than in ;
this is because
the S/N ratio of the red spectrum of GC-93 is too low for
an accurate velocity measurement.[Oddly the red side spectrum of
GC-93 appears to be
featureless in the Ca triplet region.



]






 §.§ Photometrically-Identified Clusters




To measure  the luminosity function we also have to consider
GCs that are fainter
than the spectroscopic limits, as well as any that might not
have been included in the masks. We select all candidate GCs using
the V_606 and I_814 HST images
(described in ).
Photometric catalogs were created using SExtractor (Bertin & Arnouts 1996) in
dual image mode. The photometry was corrected for Galactic
extinction (Schlafley & Finkbeiner 2011),
and the V_606-I_814 colors were corrected for
the wavelength dependence of the PSF. Total magnitudes were determined
from the “AUTO” fluxes, with an object-by-object
correction to an infinite aperture
as determined from
the encircled energy curves of Bohlin (2016).

The top panel in Fig. <ref> shows all objects with
I_814<26.5 in the plane of V_606-I_814 color vs. I_814
magnitude. The 11 spectroscopically-identified clusters have a
remarkably small range in color: we find
⟨V_606-I_814⟩=0.36 with an observed rms scatter of
σ_V-I=0.039. This is not a result of selection;
we obtained spectra of nearly all compact objects in the vicinity
of  irrespective of their color. The bottom panel of
Fig. <ref> shows the relation between the SExtractor
FWHM and I_814 magnitude for all objects that have colors
in the range ⟨V_606-I_814⟩±2σ_V-I.
We note that the results are not sensitive to the precise limits that
are used here.
As expected, the spectroscopically-identified
GCs are small. The dashed line corresponds to
FWHM<⟨ FWHM⟩+2.5σ_ FWHM = 4.7 pixels.

We find that the spectroscopic completeness is 100 % for I_814<23
objects that satisfy the color and size criteria. We find 16 candidate
GCs with 23<I_814<25.5, but as we show below most
are probably compact background galaxies.
The grey scale panel of Fig. <ref>
shows the I_814 data after masking
all objects that do not satisfy these
criteria. The masked image was smoothed with a Gaussian of
FWHM=0 9.










§ LUMINOSITY FUNCTION AND SPECIFIC FREQUENCY


At bright magnitudes it is straightforward to measure the luminosity
function of the GCs because the spectroscopic completeness is 100 %,
but at I_814>23 a correction needs to be made for interlopers.
This is evident from the
distribution of objects in the bottom panel of Fig.<ref>: at I_814<23 the GCs are well-separated from
other objects, but at faint magnitudes there is a continuous distribution
of sources with FWHM∼ 2-15 pixels.
This magnitude-dependent correction for unrelated objects was determined from
ACS imaging obtained in the blank field CANDELS survey (Koekemoer et al. 2011).
We obtained CANDELS V_606 and I_814 images of the AEGIS field from
the 3D-HST data release (Skelton et al. 2014), and analyzed these in the exact
same way as the  data.




The results are shown in the top panels of Fig. <ref>.
The expected contamination increases
steadily with magnitude at I_814>23.

The top right panel shows the
observed magnitude distribution after subtracting the expected contamination,
with the uncertainties reflecting the Poisson errors in the observed
counts in each bin. There is a pronounced peak at I_814=22.0
with a 1σ width of 0.4 mag, consisting of the 11 confirmed
clusters.

The bottom panel of Fig. <ref> shows the luminosity function.
For consistency with other work we focus on M_V,606, determined
from the total I_814 magnitudes through M_V,606=I_814
+(V_606-I_814)-31.50.
The mean absolute magnitude of the confirmed clusters is M_V,606=-9.1,
and the brightest cluster (GC-73) has M_V,606=-10.1.
The red curve shows the (scaled) luminosity function of Milky Way GCs,
obtained from the 2010 edition of the Harris (1996)
catalog[http://physwww.mcmaster.ca/harris/mwgc.dat]
with M_V,606=M_V-0.05.
The peak magnitude of M_V∼-7.5
for the Milky Way is similar to that seen in other galaxies
(e.g., Rejkuba 2012).
The blue curve is the average luminosity function of GCs in
the two UDGs Dragonfly 44 and DFX1, taken from van Dokkum et al. (2017).

The luminosity function of  is shifted to higher
luminosities than those of other galaxies, including other
UDGs. The difference is a factor of ∼ 4. Phrased differently,
the GC luminosity function of  is not far removed from the
bright end of the luminosity function of the Milky Way:
 has
11 clusters brighter than M_V,606=-8.6, whereas the Milky
Way has 20 
(and only 15 with [Fe/H]<-1).
However,
there is only marginal evidence for the presence of “classical”
GCs with M_V,606∼ -7.5 
in : after correcting for
interlopers, the total number of GCs with -8.5<M_V,606<-6.5
is N_ peak=4.2^+3.4_-2.1 (compared to N_ peak=84
in the Milky Way).

Taking the total number of globular clusters as ≈ 15,
we derive a specific frequency 
S_N≡N_ GC× 10^0.4 (M_V^ g+15)≈11,
where M_V^ g=-15.4 is the total magnitude of the
galaxy (see ).
The 11 spectroscopically-confirmed clusters
constitute 4 % of the total luminosity
of  (with 1 % contributed by GC-73 and 3 % by the other
clusters).



§ STRUCTURAL PARAMETERS










We use the HST imaging
to  compare the morphologies of the  GCs to
those of Milky Way GCs. We fit King (1962) models

to the
individual .flc files 
using the GALFIT software (Peng et al. 2002) with
synthetic PSFs.
This provides eight independent measurements (four in V_606 and
four in I_814). Cosmic rays

and
neighboring objects were masked in the fits.

The results are listed in Table 1.
Circularized
half-light radii r_h were determined from the measured core and tidal
radii (multiplied by √(b/a)).
The listed values are the
biweight averages (see Beers, Flynn, & Gebhardt 1990)
of the eight individual measurements, and for each entry
the listed error is the biweight
scatter in the eight individual measurements.


We verified that very similar values are obtained if a Sersic (1968)
profile is fitted to the objects instead of a King profile.
As a test of
our ability to measure the sizes of these small objects
we also included
four stars of similar brightness to the GCs in the fits.
All four stars
have r_h<0018, whereas the GCs have sizes in the
range 0043≤ r_h≤ 0089.





The sizes and ellipticities are compared to those of Milky Way GCs
in Fig. <ref>, again making use of the 2010
version of the Harris (1996) compilation. The (biweight)
mean size of the 11 objects is ⟨r_h⟩=6.2± 0.5 pc, a factor
of 2.2 larger than the mean size of Milky Way GCs
in the same luminosity range. The mean ellipticity is
⟨ϵ⟩=0.18± 0.02, a factor of 2.6 larger than
Milky Way GCs.




cccccc
Properties Of Globular Clusters

Id     RA     DEC
     M_V,606    
r_ha
    ϵ
39     2^ h41^ m45.07^ s     -825249
    -9.3     7.5±0.7     0.16±0.03

59     2^ h41^ m48.08^ s     -824575
    -8.9     6.5±1.0     0.31±0.03

71     2^ h41^ m45.13^ s     -824230
    -9.0     6.7±0.8     0.08±0.05

73     2^ h41^ m48.22^ s     -824181
    -10.1     6.4±0.7     0.19±0.06

77     2^ h41^ m46.54^ s     -824140
    -9.6     9.4±0.6     0.31±0.02

85     2^ h41^ m47.75^ s     -824059
    -9.2     5.2±0.8     0.19±0.09

91     2^ h41^ m42.17^ s     -823540
    -9.2     8.4±0.7     0.13±0.04

93     2^ h41^ m46.72^ s     -823513
    -8.6     4.1±1.0     0.22±0.06

92     2^ h41^ m46.90^ s     -823511
    -9.4     4.3±1.0     0.21±0.06

98     2^ h41^ m47.34^ s     -823352
    -8.7     5.4±1.7     0.20±0.04

101     2^ h41^ m45.21^ s     -823283
    -8.6     4.8±1.1     0.16±0.04
aCircularized half-light radius of King profile,
in parsecs.







§ STELLAR POPULATIONS






We modeled
the LRIS-blue spectra with the most recent version
of the  code (Conroy & van Dokkum 2012; Conroy et al. 2018).









To improve the constraints on the stellar population parameters
we stacked the 11 GC spectra, weighting by
the S/N ratio.




The stacked spectrum is shown in Fig. <ref>.
The S/N ratio ranges from
≈ 12 pix^-1 at λ=3800 Åto ≈ 55 pix^-1 at λ=5400 Å (with
1.5 Å pix^-1). 
The best fitting model, shown in red, has
[Fe/H]=-1.35± 0.12,  [Mg/Fe]=0.16±
0.17, and age=9.3^+1.3_-1.2 Gyr.
The mass-to-light ratio is M/L_V=1.8± 0.2.
The errors were determined using an MCMC fitting technique,
as described in Conroy & van Dokkum (2012).

We conclude that the objects are old and metal poor. This likely
applies to the entire system: the scatter in the V_606-I_814
colors of the GCs is very small, and their average color is
consistent with that of
the diffuse galaxy light: ⟨V_606-I_814⟩_ gc=0.36
±0.02 and
(V_606-I_814)_ gal=0.37± 0.05.






The α-enhancement appears to be low, but typical values for
globular clusters (0.3-0.5) are only 1-2σ removed from the
best fit. Importantly, the
age (and also the M/L ratio)
should be regarded as lower limits, due to the possible effects
of blue horizontal branch (BHB) stars. As discussed in, e.g.,
Schiavon (2007) and Conroy et al. (2018) the presence of BHB stars reduces
the ages that are derived from integrated-light spectra.


The average spectrum of the 11  GCs is
similar to the integrated-light spectra of Galactic GCs with 
[Fe/H]∼ -1.4 and ages of ∼ 12 Gyr
(see Marín-Franch et al. 2009).















§ DISCUSSION


We analyzed the population of globular clusters
associated with the UDG .
Superficially the galaxy resembles many other UDGs.
For example,
the morphology of the diffuse light and the fraction of the light
that is in GCs are similar
to the well-studied UDG Dragonfly 17 in the Coma cluster
(van Dokkum et al. 2015; Peng & Lim 2016; Beasley & Trujillo 2016). The stellar populations
are also similar; the V_606-I_814 colors 
are identical within the errors
to those of Dragonfly 44
(van Dokkum et al. 2017), and Gu et al. (2017)
report ages and metallicities for three Coma UDGs that are consistent
with what we find here.






A generic explanation for such diffuse, globular cluster-rich
systems may be that they are “failed”
galaxies, in which star formation terminated 
shortly after the
metal-poor GCs appeared
and before a metal-rich component began to form. This naturally
explains their specific frequencies and uniform stellar populations,
and is qualitatively consistent with the observation that S_N
in dwarf galaxies is much higher when only metal-poor
stars are considered (e.g., Larsen et al. 2014).


 is also very different from other UDGs (and indeed
all other known galaxies), in two distinct ways
that may be related to one another. First, the luminosity function
of the GCs has a narrow peak at M_V,606≈ -9.1 
(Fig. <ref>). This
is remarkable as the canonical value of M_V≈ -7.5
was thought to be universal, with only ∼ 0.2 mag
variation between galaxies
(see Rejkuba 2012). 
The origin of 
this unusual luminosity function is unknown; it
could be related to enhanced hierarchical
merging of lower mass clusters
(S. Trujillo-Gomez et al., in prep.).
The sizes and ellipticities of the GCs are different too, but this
may not be very fundamental. Since ρ∝Mr_h^-3 the
GCs are a factor of ∼2 less dense than is typical. However,
their virial velocities are a factor of √(2) higher, which
means that their kinetic energy densities 
e_ kin∼ P∝ρv^2 are similar.
Therefore, the same gas pressures were needed to form these
clusters as those that led to the formation of typical Galactic
GCs (see Elmegreen & Efremov 1997). 
The higher ellipticities may simply reflect the initial angular
momentum of the GCs; as t_ r∝√(M)r_h^1.5 the
relaxation times are a factor of ∼ 5 longer than in typical
Milky Way GCs. We note that the effects of the external
gravitational potential on the structure of the GCs
are likely weak, due to the lack of dark
matter in  and the high masses of the clusters
(see, e.g., Goodwin 1997; Miholics et al. 2016).

The second difference is that the galaxy has no (or very little) dark
matter (see ). This stands in stark contrast to cluster UDGs
(see Beasley et al. 2016; van Dokkum et al. 2016; Mowla et al. 2017), and is inconsistent with
the idea that the old, metal-poor globular cluster systems
of galaxies are always closely connected to their
dark matter halos. Specifically,
previous studies
found that the ratio between the total mass in GCs and the
total (dark + baryonic) mass of galaxies is
remarkably constant, with M_ gc^
tot≈3×10^-5 M_ gal^ tot
(Blakeslee et al. 1997; Harris et al. 2015; Forbes et al. 2016).




Taking M/L_V≈ 2 ( 5) we find
≈9×10^6  for the total mass of the
globular clusters in , and in  we derived a
90 % upper limit of
<3.4× 10^8  for its total galaxy mass.
Therefore, the mass in the GC system is ≳ 3 % of the
mass of the galaxy, a factor of ∼ 1000 higher than the
Harris et al. value.

The existence of  suggests that the approximately linear
correlation
between GC system mass and total galaxy mass is not the result of 
a fundamental relation between the 
formation of metal-poor globular clusters and the
properties of dark matter halos
(as had been suggested by, e.g., Spitler & Forbes 2009; Trenti, Padoan, & Jimenez 2015; Boylan-Kolchin 2017).
Instead, the correlation may be
a by-product of other relations, with globular cluster formation
ultimately a baryon-driven process
(see, e.g., Kruijssen 2015; Mandelker et al. 2017).


Taking these ideas one step further, perhaps a key aspect of forming a UDG
– or at least UDGs with many GCs – is, paradoxically, the presence of
very dense gas at high redshift. After a short period of very intense
star formation the gas was blown out, possibly by supernova
(or black hole) feedback from the forming clumps themselves 
(e.g., Calura et al. 2015). If the gas contained most of the mass
in the central regions of the forming galaxy this event may have led
to the extreme puffing up of the inner few kpc
(see also Di Cintio et al. 2017; Chan et al. 2017). The gas never returned,
either because the galaxy ended up in a cluster (Dragonfly 17) or
because it had very low mass (). In this context having a massive
dark matter halo is not a central aspect of UDGs, but one of several
ways to reach sufficiently high gas densities for efficient
globular cluster formation at early times.

Of course, all this is speculation; also, this description of
events does not address the origin of
∼ 10^8-9  of extremely dense gas without a dark matter
halo. In this context,
an important unanswered question is whether
 is a “pathological” galaxy
that is the result of a rare set of circumstances
or representative of a class of similar objects. There are several
galaxies in our Cycle 23 HST program that superficially
resemble it, although none has quite as many luminous star 
clusters. 

-like objects may have been more common in the past,
as large galaxies without dark matter lead a tenuous existence; in
clusters and massive groups they are easily destroyed, donating their
star clusters to the intracluster population of GCs and
ultra compact dwarfs (UCDs).
We note that progenitors  of galaxies like could readily be identified in JWST observations
if its luminous GCs did indeed form within ∼ 10^8 yr
of each other in a dense region.
















































Finally, we briefly discuss whether the compact
objects in  should be considered globular clusters at all.
In terms of
their  average luminosity and size they are
intermediate between GCs and UCDs
(see, e.g., Brodie et al. 2011), and
this question
hinges on whether we focus on the
population or on individual objects: the population characteristics
are unprecedented, but
for each individual object in  a match can be found
among the thousands of GCs with measured sizes and luminosities
in other galaxies
(e.g., Larsen et al. 2001; Barmby et al. 2007).
Intriguingly, in terms
of their sizes, flattening, stellar populations,
and luminosities the 11 compact
star clusters are remarkably similar to ω Centauri –
an object whose nature has been the topic of decades of debate
(see, e.g., Norris & Da Costa 1995).



























Support from HST grant HST-GO-14644
and NSF grants AST-1312376, AST-1515084, 
AST-1518294, and AST-1613582
is gratefully acknowledged.
JMDK gratefully acknowledges funding from the German Research Foundation (DFG) in the form of an Emmy Noether Research Group (grant number KR4801/1-1) and from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme via the ERC Starting Grant MUSTANG (grant agreement number 714907).
AJR is a Research Corporation for Science Advancement Cottrell Scholar.
















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