Main

NGC1052–DF2 was identified with the Dragonfly Telephoto Array6 in deep, wide-field imaging observations of the NGC 1052 group. The galaxy is not a new discovery; it was catalogued previously in a visual search of digitized photographic plates7. It stood out to us because of the remarkable contrast between its appearance in Dragonfly images and Sloan Digital Sky Survey (SDSS) data: with Dragonfly it is a low-surface-brightness object with some substructure and a spatial extent of about 2′, whereas in SDSS it appears as a collection of point-like sources. Intrigued by the likelihood that these compact sources are associated with the low-surface-brightness object, we obtained follow-up spectroscopic observations of NGC1052–DF2 using the 10-m W. M. Keck Observatory. We also observed the galaxy with the Hubble Space Telescope (HST).

A colour image generated from the HST V606 and I814 data is shown in Fig. 1. The galaxy has a striking appearance. In terms of its apparent size and surface brightness, it resembles dwarf spheroidal galaxies such as those recently identified8 in the M101 group at 7 Mpc, but the fact that it is only marginally resolved implies that it is at a much greater distance. Using the I814 band image, we derived a surface-brightness-fluctuation distance of DSBF = 19.0 ± 1.7 Mpc (see Methods). It is located only 14′ from the luminous elliptical galaxy NGC 1052, which has distance measurements ranging from 19.4 Mpc to 21.4 Mpc (refs 9, 10). We infer that NGC1052–DF2 is associated with NGC 1052, and we adopt D ≈ 20 Mpc for the galaxy.

Figure 1: HST/Advanced Camera for Surveys (ACS) image of NGC1052–DF2.
figure 1

NGC1052–DF2 was identified as a large (approximately 2′) low-surface-brightness object, at right ascension α = 2 h 41 min 46.8 s, declination δ = −8° 24′ 12″ (J2000). HST imaging of NGC1052–DF2 was obtained on 2016 November 10, using the ACS. The exposure time was 2,180 s in the V606 filter and 2,320 s in the I814 filter. The image spans 3.2′ × 3.2′, or 18.6 kpc × 18.6 kpc at the distance of NGC1052–DF2; north is up and east is to the left. Faint striping is caused by imperfect charge-transfer-efficiency removal. Ten spectroscopically confirmed luminous compact objects are marked.

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We parameterized the galaxy’s structure with a two-dimensional Sérsic profile11. The Sérsic index is n = 0.6, the axis ratio is b/a = 0.85, the central surface brightness is μ(V606,0) = 24.4 mag arcsec−2, and the effective radius along the major axis is Re = 22.6″, or 2.2 kpc. We conclude that NGC1052–DF2 falls in the ‘ultra-diffuse galaxy’ (UDG) class5, which have Re > 1.5 kpc and μ(g, 0) > 24 mag arcsec−2. In terms of its structural parameters, it is very similar to the galaxy Dragonfly 17 in the Coma cluster5. The total magnitude of NGC1052–DF2 is M606 = −15.4, and the total luminosity is LV = 1.1 × 108 solar luminosities, L☉. Its colour V606 − I814 = 0.37 ± 0.05 in the AB magnitude system, similar to that of other UDGs and metal-poor globular clusters12. The stellar mass was determined in two ways: by placing a stellar population at D = 20 Mpc that matches the global properties of NGC1052–DF2 (see Methods), and by assuming M/LV = 2.0 as found for globular clusters13. Both methods give Mstars ≈ 2 × 108 solar masses, M☉.

We obtained spectroscopy of objects in the NGC1052–DF2 field with the W. M. Keck Observatory. Details of the observations and data reduction are given in the Methods section. We found ten objects with a radial velocity close to 1,800 km s−1 (all other objects are Milky Way stars or background galaxies). We conclude that there is indeed a population of compact, luminous objects associated with NGC1052–DF2. Their spectra near the strongest calcium triplet lines are shown in Fig. 2. The mean velocity of the ten objects is  =  km s−1. The NGC 1052 group has a radial velocity of 1,425 km s−1, with a 1σ spread of only ±111 km s−1 (based on 21 galaxies). NGC1052–DF2 has a peculiar velocity of +378 km s−1 (3.4σ) with respect to the group and +293 km s−1 with respect to NGC 1052 itself (Fig. 3).

Figure 2: Spectra of the compact objects.
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The square panels show the HST/ACS images of the ten confirmed compact objects. Each panel spans 1.7″ × 1.7″, or 165 pc × 165 pc at the distance of NGC1052–DF2. The Keck spectra are shown next to the corresponding HST images. The regions around the reddest λ8,544.4, λ8,664.5 Ca ii triplet lines are shown, as illustrated in the model spectrum at the top; the λ8,500.4 Ca triplet line was included in the fit but falls on a sky line for the radial velocity of these objects. The spectra were obtained with the Low Resolution Imaging Spectrometer (LRIS), the Deep Imaging Multi-Object Spectrograph (DEIMOS) or both. The spectral resolution is σinstr ≈ 30 km s−1. Uncertainties in the spectra are in grey. The signal-to-noise ratio ranges from 3.4 per pixel to 12.8 per pixel, with 0.4 Å pixels. The red lines show the best-fitting models. Radial velocities cz are indicated, as well as the velocity offset with respect to the central  = 1,803 km s−1. This velocity is indicated with dashed vertical lines.

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Figure 3: Velocity dispersion.
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The filled grey histograms show the velocity distribution of the ten compact objects. a, Wide velocity range including the velocities of all 21 galaxies in the NASA/IPAC Extragalactic Database with cz < 2,500 km s−1 that are within a projected distance of two degrees from NGC 1052. The red dotted curve shows a Gaussian with a width of σ = 32 km s−1, the average velocity dispersion of Local Group galaxies with 8.0 ≤ log(Mstars/M☉) ≤ 8.6. b, Narrow velocity range centred on cz = 1,803 km s−1. The red solid curve is a Gaussian with a width that is equal to the biweight dispersion of the velocity distribution of the compact objects, σobs = 8.4 km s−1. Taking observational errors into account, we derive an intrinsic dispersion of σintr =  km s−1, with the uncertainties 1 s.d. The 90% confidence upper limit on the intrinsic dispersion is σintr < 10.5 km s−1.

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Images of the compact objects are shown in Fig. 2, and their locations are marked on Fig. 1. Their spatial distribution is somewhat more extended than that of the smooth galaxy light: their half-number radius is Rgc ≈ 3.1 kpc (compared with effective radius Re = 2.2 kpc for the light) and the outermost object is at Rout = 7.6 kpc. In this respect, and in their compact morphologies (they are just-resolved in our HST images, as expected for their distance) and colours, they are similar to globular clusters and we will refer to them as such. Their luminosities are, however, much higher than those of typical globular clusters. The brightest (GC-73) has an absolute magnitude of M606 = −10.1, similar to that of the brightest globular cluster in the Milky Way (ω Centauri). Furthermore, the galaxy has no statistically significant population of globular clusters near the canonical peak of the luminosity function at MV ≈ −7.5. The properties of these enigmatic objects are the subject of another paper (P.v.D. et al., manuscript in preparation).

The central observational result of the present study is the remarkably small spread among the velocities of the ten clusters (Fig. 3). The observed velocity dispersion is σobs = 8.4 km s−1, as measured with the biweight estimator (see Methods). This value is much smaller than that in previously studied (cluster) UDGs12,14 and not much higher than the expectation from observational errors alone. Taking the errors into account, we find an intrinsic dispersion of σintr =  km s−1. The 90% confidence upper limit is σintr < 10.5 km s−1. Within the Local Group, typical galaxies with velocity dispersions in this range are small (Re ≈ 200 pc) and have a low stellar mass (Mstars ≈ (2–3) × 106M☉)15. The average velocity dispersion of Local Group galaxies with 8.0 ≤ log(M/M☉) ≤ 8.6 is 32 km s−1 (dotted curve in Fig. 3a).

We calculate the corresponding 90% confidence upper limit on the mass of NGC1052–DF2 using the tracer mass estimator (TME) method16, which provides an estimate of the dynamical mass, Mdyn, within the radius of the outermost discrete tracer, Rout. We find Mdyn < 3.4 × 108M☉ within Rout = 7.6 kpc. We also determine the dynamical mass within the projected half-number radius of the globular cluster system17 and find Mdyn < 3.2 × 108M☉ within Rgc = 3.1 kpc.

In Fig. 4a, the enclosed mass is compared to the expected mass from the stars alone (orange line) and to models with different halo masses. The dynamical mass is consistent with the stellar mass, leaving little room for dark matter. The best fit to the kinematics is obtained for Mhalo = 0, and the 90% confidence upper limit on the dark matter halo mass is Mhalo < 1.5 × 108M☉. We note that the combination of the large spatial extent and low dynamical mass of NGC1052–DF2 yields an unusually robust constraint on the total halo mass. Typically, kinematic tracers are only available out to a small fraction of the virial radius, and a large extrapolation is required to convert the measured enclosed mass to a total halo mass4. However, for a halo of mass M200 ≈ 108M☉, the virial radius is only about 10 kpc, similar to the radius at which the outermost globular clusters reside. As shown in Fig. 4b, a galaxy with a stellar mass of Mstars = 2 × 108M☉ is expected to have a halo mass of Mhalo ≈ 6 × 1010M☉, a factor of about 400 higher than the upper limit that we derive. We conclude that NGC1052–DF2 is extremely deficient in dark matter, and a good candidate for a ‘baryonic galaxy’ with no dark matter at all.

Figure 4: Constraints on the halo mass.
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a, Enclosed mass profiles for Navarro–Frenk–White haloes29 of masses M200 = 108M☉, 109M☉, 1010M☉ and 1011M☉ (grey lines). The 108M☉ halo profile is shown by a dotted line beyond R = R200 ≈ 10 kpc. The orange curve is the enclosed mass profile for the stellar component, and the black curves are the total mass profiles Mtotal = Mstars + Mhalo. The ten globular clusters are at distances ranging from R = 0.4 kpc to R = 7.6 kpc; short vertical bars on the horizontal axis indicate the locations of individual clusters. The 90% upper limits on the total enclosed mass of NGC1052–DF2 are shown by arrows. The limit at R = 7.6 kpc was determined with the TME method16. The arrow at R = 3.1 kpc is the mass limit within the half-number radius of the globular cluster system17. The dynamical mass of NGC1052–DF2 is consistent with the stellar mass and leaves little room for a dark matter halo. b, The upper limit on the halo mass and comparison to the expected dark matter mass from studies that model the halo mass function and the evolution of galaxies2,30. Grey solid symbols are nearby dwarf galaxies with rotation curves extending to at least two disk scale lengths4. Open squares are three cluster UDGs with measured kinematics: VCC 128714, Dragonfly 4412 and DFX112. NGC1052–DF2 falls a factor of at least 400 below the canonical relations.

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It is unknown how the galaxy was formed. One possibility is that it is an old tidal dwarf, formed from gas that was flung out of merging galaxies. Its location near an elliptical galaxy and its high peculiar velocity are consistent with this idea. Its relatively blue colour suggests a lower metallicity than might be expected for such objects18, but that depends on the detailed circumstances of its formation19. An alternative explanation is that the galaxy formed from low-metallicity gas that was swept up in quasar winds20. The lack of dark matter, the location near a massive elliptical, the peculiar velocity and the colour are all qualitatively consistent with this scenario, although it is not clear whether the large size and low surface brightness of NGC1052–DF2 could have been produced by this process. A third option is that the galaxy formed from inflowing gas that fragmented before reaching NGC 1052, either relatively close to the assembling galaxy21 or out in the halo22. This fragmentation may have been aided or precipitated by jet-induced shocks23. In any scenario, the luminous globular-cluster-like objects require an explanation; generically, it seems likely that the three peculiar aspects of the galaxy (its large size, its low dark matter content and its population of luminous compact objects) are related. An important missing piece of information is the number density of galaxies such as NGC1052–DF2. There are several other objects in our Cycle 24 HST programme that look broadly similar, but these do not have dynamical measurements yet—and the fact that other UDGs have anomalously high, rather than low, dark matter fractions12,14 demonstrates that such data are needed to interpret these galaxies.

Regardless of the formation history of NGC1052–DF2, its existence has implications for the dark matter paradigm. Our results demonstrate that dark matter is separable from galaxies, which is (under certain circumstances) expected if it is bound to baryons through nothing but gravity. The ‘bullet cluster’ demonstrates that dark matter does not always trace the bulk of the baryonic mass24, which in clusters is in the form of gas. NGC1052–DF2 enables us to make the complementary point that dark matter does not always coincide with galaxies either: it is a distinct ‘substance’ that may or may not be present in a galaxy. Furthermore, and paradoxically, the existence of NGC1052–DF2 may falsify alternatives to dark matter. In theories such as modified Newtonian dynamics (MOND)25 and the recently proposed emergent gravity paradigm26, a ‘dark matter’ signature should always be detected, as it is an unavoidable consequence of the presence of ordinary matter. In fact, it had been argued previously27 that the apparent absence of galaxies such as NGC1052–DF2 constituted a falsification of the standard cosmological model and offered evidence for modified gravity. For a MOND acceleration scale of a0 = 3.7 × 103 km2 s−2 kpc−1, the expected28 velocity dispersion of NGC1052–DF2 is σM ≈ (0.05GMstarsa0)1/4 ≈ 20 km s−1, where G is the gravitational constant—a factor of two higher than the 90% upper limit on the observed dispersion.

Methods

Imaging

In this paper, we use imaging from the Dragonfly Telephoto Array, the Sloan Digital Sky Survey, the MMT, the Gemini North telescope and the Hubble Space Telescope.

Dragonfly

The Dragonfly Telephoto Array6 data were obtained in the context of the Dragonfly Nearby Galaxy Survey31. Dragonfly was operating with eight telephoto lenses at the time of the observations, forming the optical equivalent of an f/1.0 refractor with a 40-cm aperture. The data reach a 1σ surface brightness limit of μ(g) ≈ 29 mag arcsec−2 in 12″ × 12″ boxes31. The full Dragonfly field is shown in Extended Data Fig. 1, as well as the area around NGC 1052 and NGC1052–DF2.

SDSS

SDSS images in the g, r and i bands were obtained from the DR14 Sky Server32. To generate the image in Extended Data Fig. 4, the data in the three bands were summed without weighting or scaling. The object is located near the corner of a frame. We note that the SDSS photometry for the compact objects is not reliable, as it is ‘contaminated’ by the low surface brightness emission of the galaxy (which is just detected in SDSS).

MMT

MMT/Megacam imaging of the NGC 1052 field was available from a project to image the globular cluster systems of nearby early-type galaxies33. The data were taken in the r and i bands, in 0.9″ seeing. They were used for target selection in our first Keck spectroscopic run.

Gemini

We obtained imaging with the Gemini-North Multi Object Spectrograph34 (GMOS) in programme GN-2016B-DD-3. The observations were made on 2016 October 10, with total exposure times of 3,000 s in the g band and 3,000 s in the i band. The seeing was 0.65″ in i and 0.70″ in g. The data were reduced using the Gemini IRAF package. Low-order polynomials were fitted to individual (dithered) 300-s frames after carefully masking objects, to reduce large-scale background gradients at low surface brightness levels. The images were used to aid in the target selection and mask design for the LRIS spectroscopy. The Gemini data also provide the best available information on the regularity of the galaxy at low surface brightness levels (see below). The combined frames still show some background artefacts, but they are less prominent than those in the HST data. Finally, a visual inspection of the Gemini images prompted us to request a change in the scheduling of HST program GO-14644, moving the already-planned ACS observation of NGC1052–DF2 to an earlier date.

HST

The HST data were obtained as part of programme GO-14644. The aim of this programme is to obtain ACS images of a sample of 23 low-surface-brightness objects that were identified in fields of the Dragonfly Nearby Galaxy Survey31. NGC1052–DF2 was observed on 2016 November 16, for a total of two orbits. Exposure times were 2,180 s in V606 and 2,320 s in I814. In this paper we use images processed by the drizzle (variable-pixel linear reconstruction) method, which have been corrected for charge-transfer efficiency (CTE) effects. Despite this correction, some CTE artefacts are still visible in the data (see Fig. 1).

Structural parameters

The size, surface brightness and other structural parameters of NGC1052–DF2 were determined from the HST data. First, the I814 image was rebinned to a lower resolution to increase the signal-to-noise (S/N) ratio per pixel. A preliminary object mask was then created from a segmentation map produced by SExtractor35, using a relatively high detection threshold. A first-pass Sérsic model36 for the galaxy was obtained using the GALFIT software11. This model was subtracted from the data, and an improved object mask was created using a lower SExtractor detection threshold. Finally, GALFIT was run again to obtain the final structural parameters and total magnitude. The total magnitude in the V606 band, and the V606 − I814 colour, were determined by running GALFIT on the (binned and masked) V606 image with all parameters except the total magnitude fixed to the I814 values. The structural parameters, total magnitude and colour are listed in the main text. We note that we measured nearly identical structural parameters from the Gemini images.

Spectroscopy

We obtained spectroscopy of compact objects in the NGC1052–DF2 field in two observing runs. The first set of observations was obtained on 2016 September 28 with DEIMOS37 on Keck II, and the second was obtained on 2016 October 26 and 27 with LRIS38 on Keck I.

DEIMOS observations

Conditions were variable, with cirrus clouds increasing throughout the night. We obtained 4 h of total on-source exposure time on a single multi-object mask; a second mask was exposed but yielded no useful data owing to clouds. The target selection algorithm gave priority to compact objects with i < 22.5 near NGC1052–DF2, selected from the MMT data. We used the 1,200 lines mm−1 grating with a slit width of 0.75″, providing an instrumental resolution of σinstr ≈ 25 km s−1. The data were reduced with the same pipeline that we used previously12,39 for the Coma UDGs Dragonfly 44 and DFX1. The globular clusters GC-39, GC-71, GC-73, GC-77, GC- 85, GC-92 and GC-98 (see Figs 1 and 2) were included in this mask.

LRIS observations

Two multi-slit masks were observed, one for 3.5 h (on source) on October 26 and a second for 4 h on October 27. Targets were selected from the Gemini data, giving priority to compact objects that had not been observed with DEIMOS. Conditions were fair during both nights, with intermittent cirrus and seeing of about 1″. We used the gold-coated grating with 1,200 lines mm−1 blazed at 9,000 Å. The instrumental resolution σinstr is about 30 km s−1. A custom pipeline was used for the data reduction, modelled on the one that we developed for DEIMOS. LRIS suffers from considerable flexure, and the main difference from the DEIMOS pipeline is that each individual 1,800-s exposure was reduced and calibrated independently to avoid smoothing of the combined spectra in the wavelength direction. The clusters GC-39, GC-59, GC-73, GC-91 and GC-101 were included in the first mask; GC-39, GC-71, GC-77, GC-85 and GC-92 were included in the second.

Combined spectra

Most compact objects were observed multiple times, and we combined these individual spectra to increase the S/N ratio. All spectra were given equal weight, and before combining they were divided by a low-order polynomial fit to the continuum in the calcium triplet (CaT) region. We tested that weighting by the formal S/N ratio instead does not change the best-fit velocities. The individual spectra were also shifted in wavelength to account for the heliocentric correction; this needs to be done at this stage as the DEIMOS and LRIS data were taken one month apart. Six GCs have at least two independent observations and effective exposure times of about 8 h; four were observed only once: GC-59, GC-91, GC-98 and GC-101. The S/N ratio in the final spectra ranges from 3–4 per pixel for GC-59, GC-98 and GC-101 to 13 per pixel for GC-73. A pixel is 0.4 Å or 14 km s−1.

Velocity measurements

Radial velocities were determined for all objects with detected CaT absorption lines. No fits were attempted for background galaxies (based on the detection of redshifted emission lines), Milky Way stars or spectra with no visible features. The measurements were performed by fitting a template spectrum to the observations, using the emcee MCMC algorithm40. The template is a high-resolution model of a stellar population41, smoothed to the instrumental resolution. The model has an age of 11 Gyr and a metallicity of [Fe/H] = −1, which is consistent with the colours of the compact objects (V606 − I814 ≈ 0.35); the results are independent of the precise choice of template. The fits are performed over the observed wavelength range 8,530 Å ≤ λ ≤ 8,750 Å and have three free parameters: the radial velocity, the normalization and an additive term that serves as a template mismatch parameter (as it allows the strength of the absorption lines to vary with respect to the continuum). The fit was performed twice. After the first pass, all pixels that deviate by more than 3σ were masked in the second fit. This step reduces the effect of systematic sky-subtraction residuals on the fit.

The uncertainties given by the emcee method do not take systematic errors into account. Following previous studies42, we determined the uncertainties in the velocities by shuffling the residuals. For each spectrum, the best-fitting model was subtracted from the data. Next, 500 realizations of the data were created by randomizing the wavelengths of the residual spectra and then adding the shuffled residuals to the best-fitting model. These 500 spectra were then fitted by using a simple χ2 minimization, and the 16th and 84th percentiles of the resulting velocity distribution yield the error bars. To preserve the higher noise at the location of sky lines, the randomization was done separately for pixels at the locations of sky lines and for pixels in between the lines. We find that the resulting errors show the expected inverse trend with the S/N ratio of the spectra, whereas the emcee errors show large variation at fixed S/N ratio.

We tested the reliability of the errors by applying the same procedure to the individual LRIS and DEIMOS spectra for the six objects that were observed with both instruments (GC-39, GC-71, GC-73, GC-77, GC-85 and GC-92). For each object, the observed difference between the LRIS and DEIMOS velocities was divided by the expected error in the difference. The root mean square (r.m.s.) of these ratios is 1.2 ± 0.3, that is, the empirically determined uncertainties are consistent with the observed differences between the independently measured LRIS and DEIMOS velocities.

Velocity dispersion

The observed velocity distribution of the ten clusters is not well approximated by a Gaussian. Six of the ten have velocities that are within ±4 km s−1 of the mean and one is 39 km s−1 removed from the mean. As a result, different ways to estimate the Gaussian-equivalent velocity spread σobs yield different answers. The normalized median absolute deviation σobs,nmad = 4.7 km s−1, the biweight43 σobs,bi = 8.4 km s−1 and the r.m.s. σobs,rms = 14.3 km s−1. The r.m.s. is driven by one object with a relatively large velocity uncertainty (GC-98) and is inconsistent with the velocity distribution of the other nine. Specifically, for ten objects drawn from a Gaussian distribution and including the observed errors, the probability of measuring σbi ≤ 8.4 if σrms ≥ 14.3 is 1.5%, and the probability of measuring σnmad ≤ 4.7 is 3 × 10−3. We therefore adopt the biweight dispersion rather than the r.m.s. when determining the intrinsic dispersion below. We then show that the presence of GC-98 is consistent with the intrinsic dispersion that we derive using this statistic.

The observed dispersion must be corrected for observational errors, which are of the same order as σobs itself. We determined the intrinsic dispersion and its uncertainty in the following way. For a given value of σtest, we generated 1,000 samples of ten velocities, distributed according to a Gaussian of width σtest. The ten velocities in each sample were then perturbed with errors, drawn from Gaussians with widths equal to the empirically determined uncertainties in the measured dispersions. Using the biweight estimator, ‘measured’ dispersions σobs,test were calculated for all samples. If the value 8.4 is within the 16th to 84th percentiles of the distribution of σobs,test then σtest is within the ±1σ uncertainty on σintr. This method gives σintr =  km s−1. As the intrinsic dispersion is consistent with zero, a more meaningful number than the best-fit is the 90% confidence upper limit; we find σintr < 10.5 km s−1.

We now return to the question whether GC-98 is consistent with the other nine objects. This cluster has a velocity offset of ∆v =  km s−1. For the upper limit on the intrinsic dispersion (σintr = 10.5 km s−1) the object is a 2.4σ outlier, and the probability of having a more than 2.4σ outlier in a sample of ten is 15%. Interestingly, the combination of the biweight constraint of σintr < 10.5 and the existence of GC-98 implies a fairly narrow range of intrinsic dispersions that are consistent with the entire set of ten velocities (assuming that they are drawn from a Gaussian distribution and that the errors are correct). The probability of having at least one object with the velocity of GC-98 is <10% if the intrinsic dispersion is σintr < 8.8 km s−1. Taking both 90% confidence limits at face value, the allowed range in the intrinsic dispersion is 8.8 km s−1 < σintr < 10.5 km s−1.

Expected dispersion from Local Group galaxies

In Fig. 3a we illustrate how unusual the kinematics of NGC1052–DF2 are by comparing the observed velocity distribution to that expected from Local Group galaxies with the same stellar mass (broken red curve). The width of this Gaussian was calculated from the SEPT2015 version of the Nearby Dwarf Galaxies catalogue15. The catalogue has entries for both velocity dispersions and rotation velocities, and for both gas and stars. To obtain a homogeneous estimate we use ‘effective’ dispersions, σeff ≡ (σ2 + 0.5vrot2)0.5, where vrot is the inclination-corrected rotation velocity. When both gas and stellar kinematics are available, we use the highest value of σeff, as this typically is a rotation curve measurement from gas at large radii. Stellar masses were calculated directly from the V-band absolute magnitude assuming M/LV = 2.0, for consistency with NGC1052–DF2. Five galaxies have a stellar mass that is within a factor of two of that of NGC 1052–DF2: these are IC 1613, NGC 6822, Sextans B and the M31 satellites NGC 147 and NGC 185. The average dispersion of these five galaxies is  = 32 km s−1, with an r.m.s. variation of 8 km s−1.

In Extended Data Fig. 2, we compare NGC 1052–DF2 to the nearby dwarf sample in the plane of velocity dispersion versus half-light radius, with the size of the symbols indicating the stellar mass. Comparing NGC1052–DF2 to other galaxies with velocity dispersions in this range, we find that its size is larger by a factor of about 10 and its stellar mass is larger by a factor of about 100.

Distance

The heliocentric radial velocity of NGC 1052–DF2 is 1,803 ± 2 km s−1, or 1,748 ± 16 km s−1 after correcting for the effects of the Virgo cluster, the Great Attractor and the Shapley supercluster on the local velocity field44. For H0 = 70 ± 3 km s−1 Mpc−1, a Hubble flow distance of DHF = 25 ± 1 Mpc is obtained. However, the proximity to NGC 1052 (14′, or about 80 kpc in projection) strongly suggests that NGC1052–DF2 is associated with this massive elliptical galaxy. The distance to NGC 1052, as determined from surface brightness fluctuations (SBFs) and the fundamental plane9,10, is D1052 = 20.4 ± 1.0 Mpc. The velocity of NGC1052–DF2 with respect to NGC 1052 is then +293 km s−1.

A third distance estimate can be obtained from the luminosity function of the compact objects. As discussed elsewhere (P.v.D. et al., manuscript in preparation), the luminosity function has a narrow peak at mV ≈ 22.0. The canonical globular cluster luminosity function can be approximated by a Gaussian with a well-defined peak45 at MV ≈ −7.5. If the compact objects are typical globular clusters, the implied distance is DGC ≈ 8 Mpc. The main conclusions of the paper would be weakened considerably if the galaxy were so close to us. For this distance, the stellar mass estimate is an order of magnitude lower: Mstars ≈ 3 × 107M☉. The four Local Group galaxies that have a stellar mass within a factor of two of this value (Fornax, Andromeda II, Andromeda VII and UGC 4879) have a mean dispersion of  = 11.7 ± 0.5 km s−1, only slightly higher than the upper limit to the dispersion of NGC1052–DF2. The peculiar velocity of the galaxy would be about 1,200 km s−1; this is, of course, extreme, but it is difficult to argue that it is less likely than having a highly peculiar globular cluster population and a lack of dark matter.

Fortunately, we have independent information to verify the distance, namely the appearance of NGC1052–DF2 in the HST images. In Extended Data Fig. 3a, we show the central 33″ × 33″ of the galaxy in the HST I814 band. A smooth model of the galaxy, obtained by median filtering the image, was subtracted; background galaxies and globular clusters were masked. The mottled appearance is not due to noise but due to the variation in the number of giants contributing to each pixel. Following previous studies9,46,47, we measure the SBF signal from this image and determine the distance from the SBF magnitude.

The azimuthally averaged power spectrum of the image is shown in Extended Data Fig. 3b. As is customary46, the smallest and largest wavenumbers are omitted, as they are dominated by residual large-scale structure in the image and by noise correlations, respectively. Again following previous studies46,47, the power spectrum is fitted by a combination of a constant (dotted line) and the expectation power spectrum E(k) (dashed line). The expectation power spectrum is the convolution of the power spectrum of the point spread function and that of the window function. The window function is the square root of the median-filtered model of the galaxy, multiplied by the mask containing the globular clusters and background galaxies.

The normalization of E(k) is the SBF magnitude, m814. We find m814 =29.45 ± 0.10. Using equation (2) in ref. 47, V606 − I814 = 0.37 ± 0.05, and g475 − I814 =1.852(V606 − I814) + 0.096, the absolute SBF magnitude is M814 = −1.94 ± 0.17. The uncertainty is a combination of the error in the V606 − I814 colour and the systematic uncertainty in the extrapolation of the relation between g475 − I814 colour and M814 (as determined from the difference between equations (1) and (2) in ref. 47). The SBF distance modulus m − M = 31.39 ± 0.20, and the SBF distance DSBF = 19.0 ± 1.7 Mpc. This result is consistent with D1052 and rules out the ‘globular cluster distance’ of DGC = 8 Mpc.

Stellar mass

We determined the stellar mass from a stellar population synthesis model41. A two-dimensional model galaxy was created using the ArtPop code49 that matches the morphology, luminosity, colour and SBF signal of NGC1052–DF2. The model has a metallicity [Z/H] = −1 and an age of 11 Gyr. These parameters are consistent with the regular morphology of the galaxy and with spectroscopic constraints on the stellar populations of Coma cluster UDGs50. For a Kroupa51 initial mass function, the stellar mass of this model is 1.8 × 108M☉, similar to that obtained from a simple M/LV = 2.0 conversion13 (Mstars = 2.2 × 108M☉). In the main text and below, we assume Mstars ≈ 2 × 108M☉. We note that the uncertainty in the stellar mass is much smaller than that in the dynamical mass, for reasonable choices of the initial mass function.

Dynamical equilibrium

Some large low-surface-brightness objects are almost certainly in the process of disruption; examples are the ‘star pile’ in the galaxy cluster Abell 54552,53, the boomerang-shaped galaxy DF4 in the field of M10154, and Andromeda XIX in the Local Group55 (marked in Extended Data Fig. 2). Andromeda XIX, and also And XXI and And XXV, are particularly informative as they combine large sizes with low velocity dispersions56, and it has been suggested that tidal interactions have contributed to their unusual properties55. (These galaxies are not direct analogues of NGC1052–DF2: the stellar masses of these Andromeda satellites are a factor of about 100 lower than that of NGC1052–DF2, and their dynamical M/L ratios are at least a factor of 10 higher.) In Extended Data Fig. 4c, we show the Gemini i-band image of NGC1052–DF2 (along with the Dragonfly and SDSS images). There is no convincing evidence of strong position angle twists or tidal features at least out to R ≈ 2Re (see also the Dragonfly image in Extended Data Fig. 4a). The regular appearance strongly suggests that the object has survived in its present form for multiple dynamical times, and we infer that the kinematics can probably be interpreted in the context of a system that is in dynamical equilibrium.

We note that the regular morphology of NGC1052–DF2 also provides an interesting constraint on its formation time: the orbital velocity in the outer parts is 5 Gyr, which means it must have formed very early in order to lose any sign of its assembly. Furthermore, it provides a lower limit for the 3D distance between NGC1052–DF2 and the massive elliptical galaxy NGC 1052. The Jacobi radius (that is, the distance from the centre of the galaxy to the first Lagrangian point) is given by57

with R1052 the distance between NGC1052–DF2 and NGC 1052, and V1052 the circular velocity of NGC 1052. Taking RJ > 5 kpc, M ≈ 2 × 108M☉ and V1052 ≈ 300 km s−1 (the velocity difference between the two galaxies, as well as approximately ), we obtain R1052 greater than about 160 kpc, a factor of two larger than the projected distance.

Source of dynamical support

The morphology of the galaxy strongly indicates that it is supported by random motions rather than rotation: the Sérsic index is 0.6, similar to that of dSph galaxies; the isophotes are elliptical rather than disk-like; and there are no bars, spiral arms, or other features that might be expected in a thin disk. The galaxy has not been detected in moderately deep H i observations58. It is also difficult to imagine a physical model for the formation of a huge, extremely thin disk of massive blue globular clusters, even in spiral galaxies: although the kinematics of the metal-rich globular cluster population in M31 are clearly related to its disk, the metal-poor ones have a large velocity dispersion59. Finally, there is no evidence for a velocity gradient. In Extended Data Fig. 5a, we show the measured velocities of the globular clusters as a function of the projected distance along the major axis. There is no coherent pattern. Based on these arguments, our default mass measurement assumes that the galaxy is supported by random motions.

Dynamical mass measurement

Following a previous study of the kinematics of globular clusters in a UDG14, we use the TME to determine the dynamical mass. This method was developed to determine the enclosed mass from an ensemble of discrete tracers, such as satellite galaxies or globular clusters16,48. The mass within the distance of the outermost object is given by

with v the velocities of individual clusters with respect to the mean, r the projected distances of the clusters from the centre of the galaxy, rout the distance of the furthest cluster, and α the slope of the potential (with density ρ ∝ r−(α + 2)). For the case α = 1, the potential is similar to that of a point mass; α = 0 corresponds to ρ ∝ r−2 and a flat rotation curve; and for α = −1 the density ρ ∝ r−1. Equation (2) does not take observational errors or outliers into account; we therefore introduce the modified expression

Here observational errors are taken into account by setting vintr = f−1(∆vobs), with ∆vobs listed in Fig. 2 and f−1 = σintr/σobs. Sbi(x) denotes the biweight estimator of the width of the distribution. Note that equation (3) reduces to  = (C/G), for α = 0. The constant C is given by

with γ the power-law slope of the density profile of the clusters, β = 1 − σt2/σr2 the Binney anisotropy parameter and Γ(x) the gamma function. We determine the 3D density profile from a power-law fit to the distribution of the spectroscopically confirmed globular clusters, finding γ = 0.9 ± 0.3.

For an isothermal velocity dispersion profile (α = 0) and isotropic orbits (β = 0) we determine MTME < 3.4 × 108M☉ at 90% confidence. The results are not very sensitive to the assumed slope of the potential or moderate anisotropy. Changing α to 1 or −1 reduces the mass by 10% or 20% respectively. Tangential anisotropy with σt2 = 2σr2 increases the mass limit to MTME < 4.2 × 108M☉; radial anisotropy with σt2 = 0.5σr2 yields MTME < 2.4 × 108M☉. We also consider errors in the density profile of the globular clusters; for γ = 0.5 the mass decreases by 20% and for γ = 1.5 the mass increases by 30%.

Robustness tests

As a test of the robustness of our results, we consider three alternative mass estimates. The first is the dynamical mass within the half-number radius of the globular cluster system17. This mass estimate does not extend as far in radius as the TME method but is less sensitive to the assumed level of anisotropy. For Rgc = 3.1 kpc and σintr < 10.5 km s−1 we find Mdyn < 3.2 × 108M☉ (see Fig. 4). As the halo profile is still rising at R = 3.1 kpc, the constraint on the halo mass is weaker than our default value, and we find Mhalo < 8 × 108M☉.

The second test replaces σbi with σrms, even though the r.m.s. is driven by a single cluster (GC-98) and the velocity distribution of the other nine objects is inconsistent with this. The observed r.m.s. is σobs,rms = 14.3 km s−1, or σintr,rms =12.2 km s−1 after taking observational errors into account. The implied TME mass is Mdyn ≈ 5 × 108M☉, and the halo mass Mhalo ≈ 3 × 108M☉.

The third test sets the arguments against a disk aside and assumes that the observed velocities reflect rotation in an inclined, infinitely thin disk. The axis ratio of NGC1052–DF2 is b/a = 0.85 ± 0.02, which means that the inclination-corrected velocities are a factor of (sin(cos−1 (b/a)))−1 ≈ 1.9 higher than the observed ones. Assuming an (unphysical) disk dispersion of 0 km s−1, the inclination-corrected rotation velocity would be vrot ≈ 1.4 × 3.2 × 1.9 =  km s−1, where it is assumed that the rotation velocity is approximately 1.4 times the line-of-sight velocity dispersion60,61. The enclosed mass within R = 7.6 kpc would be Mdisk = × 108M☉.

For all these mass estimates, the implied ratio Mhalo/Mstars is less than 4. This is the lowest ratio measured for any galaxy and two orders of magnitude below the canonical relation between stellar mass and halo mass.

Data availability

The HST data are available in the Mikulski Archive for Space Telescopes (MAST; http://archive.stsci.edu), under programme ID 14644. All other data that support the findings of this study are available from the corresponding author upon reasonable request.

Code availability

We have made use of standard data reduction tools in the IRAF and Python environments, and the publicly available codes SExtractor35, GALFIT11 and emcee40.