An Enigmatic Population of Luminous Globular Clusters in a Galaxy Lacking Dark Matter

We recently identified a galaxy with little or no dark matter (van Dokkum et al. 2018, hereafter vD18). NGC1052–DF2 has a stellar mass of M_stars ≈ 2 × 10⁸ M_⊙ and a 90% confidence upper limit on its dark matter halo mass of M_halo < 1.5× 10⁸ M_⊙, placing it a factor of ≳400 off of the canonical stellar mass—halo mass relation (Behroozi et al. 2013; Moster et al. 2013). NGC1052–DF2 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(V₆₀₆,0) = 24.4 mag arcsec⁻². It has a radial velocity of 1803 km s⁻¹. Its SBF-determined distance is 19.0 ± 1.7 Mpc (vD18), consistent with that of the NGC 1052 group at D ≈ 20 Mpc (Blakeslee et al. 2010).

The kinematics of NGC1052–DF2 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 et al. 2018). In fact, Coma UDGs have on average ∼7 times 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 10 clusters that were analyzed in vD18 are all significantly brighter than this, raising the question of whether the GC luminosity function is systematically offset from that in other galaxies.

Here we focus on the properties of the compact objects in NGC1052–DF2, using imaging from the Hubble Space Telescope (HST) and spectroscopy obtained with the W. M. Keck Observatory. We show that the GC system of NGC1052–DF2 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.

2.1. Spectroscopically Identified Clusters

We obtained spectra of compact objects in the NGC1052–DF2 region with the Keck telescopes, using the Deep Imaging Multi-object Spectrograph (DEIMOS) 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 vD18. The blue-side LRIS data were obtained with the 300/5000 grism and 10 slits, providing a spectral resolution ranging from σ_instr ∼ 350 km s⁻¹ at λ = 3800 Å to σ_instr ∼ 150 km s⁻¹ at λ = 6600 Å. The reduction followed the same procedures as the red side data, and is described in vD18. The spectral resolution is too low for accurate radial velocity measurements, but the wide wavelength coverage provides constraints on the stellar populations (Section 5). Small sections of the spectra of the 11 confirmed GCs are shown in Figure 1. Note that we analyze one more object in this paper than in vD18; this is because the signal-to-noise ratio (S/N) of the red spectrum of GC-93 is too low for an accurate velocity measurement.⁸

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2.2. Photometrically Identified Clusters

In order 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 V₆₀₆ and I₈₁₄ HST images (described in vD18). 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 V₆₀₆ − I₈₁₄ colors were corrected for the wavelength dependence of the point-spread function (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 Figure 2 shows all of the objects with I₈₁₄ < 26.5 in the plane of V₆₀₆ − I₈₁₄ color versus I₈₁₄ mag. The 11 spectroscopically identified clusters have a remarkably small range in color: we find $\langle {V}_{606}-{I}_{814}\rangle =0.36$ with an observed rms scatter of σ_V−I = 0.039. This is not a result of selection; we obtained spectra of nearly all of the compact objects in the vicinity of NGC1052–DF2, irrespective of their color. The bottom panel of Figure 2 shows the relation between the SExtractor FWHM and I₈₁₄ mag for all of the objects that have colors in the range $\langle {V}_{606}-{I}_{814}\rangle \pm 2{\sigma }_{V-I}$. 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 $\mathrm{FWHM}\lt \langle \mathrm{FWHM}\rangle \,+2.5{\sigma }_{\mathrm{FWHM}}=4.7$ pixels.

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We find that the spectroscopic completeness is 100% for I₈₁₄ < 23 objects that satisfy the color and size criteria. We find 16 candidate GCs with 23 < I₈₁₄ < 25.5, but as we show below most are probably compact background galaxies. The grayscale panel of Figure 2 shows the I₈₁₄ data after masking all of the objects that do not satisfy these criteria. The masked image was smoothed with a Gaussian of FWHM = 09.

At bright magnitudes it is straightforward to measure the luminosity function of the GCs because the spectroscopic completeness is 100%, but at I₈₁₄ > 23 a correction needs to be made for interlopers. This is evident from the distribution of objects in the bottom panel of Figure 2: at I₈₁₄ < 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 V₆₀₆ and I₈₁₄ images of the All-wavelength Extended Groth Strip International Survey (AEGIS) field from the 3D-HST data release (Skelton et al. 2014), and analyzed these in the exact same way as the NGC1052–DF2 data.

The results are shown in the top panels of Figure 3. The expected contamination increases steadily with magnitude at I₈₁₄ > 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 I₈₁₄ = 22.0 with a 1σ width of 0.4 mag, consisting of the 11 confirmed clusters.

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The bottom panel of Figure 3 shows the luminosity function. For consistency with other work we focus on M_V,606, determined from the total I₈₁₄ mag through M_V,606 = I₈₁₄ + (V₆₀₆ − I₈₁₄) − 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) catalog⁹ 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 NGC1052–DF2 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 NGC1052–DF2 is not far removed from the bright end of the luminosity function of the Milky Way: NGC1052–DF2 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 NGC1052–DF2: after correcting for interlopers, the total number of GCs with −8.5 < M_V,606 < −6.5 is ${N}_{\mathrm{peak}}\,={4.2}_{-2.1}^{+3.4}$ (compared to N_peak = 84 in the Milky Way).

Taking the total number of GCs as ≈15, we derive a specific frequency ${S}_{N}\equiv {N}_{\mathrm{GC}}\times {10}^{0.4({M}_{V}^{{\rm{g}}}+15)}\approx 11$, where ${M}_{V}^{{\rm{g}}}=-15.4$ is the total magnitude of the galaxy (see vD18). The 11 spectroscopically confirmed clusters constitute 4% of the total luminosity of NGC1052–DF2 (with 1% contributed by GC-73 and 3% by the other clusters).

We use the HST imaging to compare the morphologies of the NGC1052–DF2 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 V₆₀₆ and four in I₈₁₄). 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 $\sqrt{b/a}$). The listed values are the biweight averages (see Beers et al. 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 Sérsic (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.

Table 1.  Properties of Globular Clusters

Id	R.A.	Decl.	MV,606	rha
39	2h41m4507	−8°25'249	−9.3	7.5 ± 0.7	0.16 ± 0.03
59	2h41m4808	−8°24'575	−8.9	6.5 ± 1.0	0.31 ± 0.03
71	2h41m4513	−8°24'230	−9.0	6.7 ± 0.8	0.08 ± 0.05
73	2h41m4822	−8°24'181	−10.1	6.4 ± 0.7	0.19 ± 0.06
77	2h41m4654	−8°24'140	−9.6	9.4 ± 0.6	0.31 ± 0.02
85	2h41m4775	−8°24'059	−9.2	5.2 ± 0.8	0.19 ± 0.09
91	2h41m4217	−8°23'540	−9.2	8.4 ± 0.7	0.13 ± 0.04
93	2h41m4672	−8°23'513	−8.6	4.1 ± 1.0	0.22 ± 0.06
92	2h41m4690	−8°23'511	−9.4	4.3 ± 1.0	0.21 ± 0.06
98	2h41m4734	−8°23'352	−8.7	5.4 ± 1.7	0.20 ± 0.04
101	2h41m4521	−8°23'283	−8.6	4.8 ± 1.1	0.16 ± 0.04

Note.

^aCircularized half-light radius of King profile, in parsecs.

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The sizes and ellipticities are compared to those of Milky Way GCs in Figure 4, again making use of the 2010 version of the Harris (1996) compilation. The (biweight) mean size of the 11 objects is $\langle {r}_{h}\rangle =6.2\pm 0.5$ pc, a factor of 2.2 larger than the mean size of Milky Way GCs in the same luminosity range. The mean ellipticity is $\langle \epsilon \rangle =0.18\pm 0.02$, a factor of 2.6 larger than Milky Way GCs.

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We modeled the LRIS-blue spectra with the most recent version of the alf 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 Figure 5. The S/N ratio ranges from ≈12 pix⁻¹ at λ = 3800 Å to ≈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 $\mathrm{age}={9.3}_{-1.2}^{+1.3}\,\mathrm{Gyr}$. The mass-to-light ratio (M/L) is M/L_V = 1.8 ± 0.2. The errors were determined using an Markov Chain Monte Carlo (MCMC) fitting technique, as described in Conroy & van Dokkum (2012).

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We conclude that the objects are old and metal-poor. This likely applies to the entire system: the scatter in the V₆₀₆ − I₈₁₄ colors of the GCs is very small, and their average color is consistent with that of the diffuse galaxy light: $\langle {V}_{606}-{I}_{814}{\rangle }_{\mathrm{gc}}=0.36\pm 0.02$ and (V₆₀₆ − I₈₁₄)_gal = 0.37 ± 0.05.

The α-enhancement appears to be low, but typical values for GCs (0.3–0.5) are only 1–2σ removed from the best fit. Importantly, the age (and also the M/L) 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 NGC1052–DF2 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).

We analyzed the population of GCs associated with the UDG NGC1052–DF2. 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; Beasley & Trujillo 2016; Peng & Lim 2016). The stellar populations are also similar; the V₆₀₆ − I₈₁₄ colors are identical within the errors to those of Dragonfly 44 (van Dokkum et al. 2017), and Gu et al. (2018) reported ages and metallicities for three Coma UDGs that are consistent with what we find here. A generic explanation for such diffuse, GC-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).

NGC1052–DF2 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 (Figure 3). 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. 2018, in preparation). The sizes and ellipticities of the GCs are different too, but this may not be very fundamental. Because $\rho \propto {{Mr}}_{h}^{-3}$, the GCs are a factor of ∼2 less dense than is typical. However, their virial velocities are a factor of $\sqrt{2}$ higher, which means that their kinetic energy densities e_kin ∼ P ∝ ρv² 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 ${t}_{{\rm{r}}}\propto \sqrt{M}{r}_{h}^{1.5}$, 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 NGC1052–DF2 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 vD18). 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 GC 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 ${M}_{\mathrm{gc}}^{\mathrm{tot}}\approx 3\times {10}^{-5}\,{M}_{\mathrm{gal}}^{\mathrm{tot}}$ (Blakeslee et al. 1997; Harris et al. 2015; Forbes et al. 2016). Taking M/L_V ≈ 2 (Section 5) we find ≈9 × 10⁶ M_⊙ for the total mass of the GCs in NGC1052–DF2, and in vD18 we derived a 90% upper limit of <3.4 × 10⁸ M_⊙ 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 NGC1052–DF2 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 GCs and the properties of dark matter halos (as had been suggested by, e.g., Spitler & Forbes 2009; Trenti et al. 2015; Boylan-Kolchin 2017). Instead, the correlation may be a by-product of other relations, with GC formation ultimately a baryon-driven process (see, e.g., Kruijssen 2015; Mandelker et al. 2018).

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 Chan et al. 2018; Di Cintio 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 (NGC1052–DF2). 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 GC formation at early times.

Of course, all of this is speculation; also, this description of events does not address the origin of ∼10^8–9 M_⊙ of extremely dense gas without a dark matter halo. In this context, an important unanswered question is whether NGC1052–DF2 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. NGC1052–DF2-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 NGC1052–DF2 could readily be identified in James Webb Space Telescope (JWST) observations if its luminous GCs did indeed form within ∼10⁸ year of each other in a dense region.

Finally, we briefly discuss whether the compact objects in NGC1052–DF2 should be considered GCs 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 NGC1052–DF2 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. J.M.D.K. acknowledges support from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program. A.J.R. is a Research Corporation for Science Advancement Cottrell Scholar.