Illustration of the collision scenario
The proposed scenario for the formation of DF2, DF4 and the other trail galaxies is shown in Extended Data Fig. 1. As discussed in the main text, the scenario is a combination of the original idea that a bullet-dwarf collision might have formed DF2 and/or DF411; the results from subsequent hydrodynamical simulations, showing that multiple dark-matter-free clumps can form in such a collision12 and that the formation of massive star clusters is indeed promoted13; and the independent finding that feedback from massive cluster formation in these conditions leads to a rapid expansion of the galaxies18.
Faint galaxy sample
We make use of a recently compiled catalogue of low-surface-brightness objects in the NGC 1052 field23, augmented by a catalogue of all brighter galaxies with redshifts in the range of 1,000 km s−1 < cz < 2,000 km s−1 that is provided in the same study. Reference 23 makes use of the publicly available Dark Energy Camera Legacy Survey (DECaLS) dataset31. The galaxies were initially identified with a combination of automated techniques and visual inspection, with the majority coming from visual inspection. Their structural parameters were measured with IMFIT32. We caution that the DECaLS dataset suffers from sky subtraction errors around low-surface-brightness galaxies, and that this may bias the size measurements. The main point of Fig. 4 is a relative comparison of the sizes of galaxies on and off the trail and this should be more robust than the absolute size measurements.
Velocity dispersion of the NGC 1052 group
We use the latest compilation of radial velocities in the NGC 1052 field23 for an updated value of the velocity dispersion of the group. Table 2 of ref. 23 contains 30 galaxies with redshifts cz < 2,000 km s−1. Two were removed: DF2, as it is almost certainly not bound to the group, and LEDA 4014647. LEDA 4014647 was assigned a radial velocity of 1,680 ± 60 km s−1 in earlier Sloan Digital Sky Survey (SDSS) releases (Data Release 3), but its redshift was later revised to z = 0.7 (Data Release 16). A visual inspection of the SDSS spectrum shows no clear features. Using the biweight estimator33, we find a central velocity for the remaining 28 galaxies of ⟨cz⟩ = 1,435 ± 20 km s−1 and a line-of-sight velocity dispersion of σ = 115 ± 15 km s−1.
The Hough transform
We use the Hough transform to look for linear features in the galaxy distribution, a standard method for detecting lines in images24. The transform provides the number of galaxies along all possible directions, characterized by an angle and a distance from the centre. A width and maximum linear extent have to be chosen; we use ±30 kpc (±5.2′) for the width and <400 kpc (69′) for the linear extent. Although the exact number of galaxies that the Hough transform associates with the linear feature depends on the precise limits that are chosen, the qualitative results are not sensitive to them. In Fig. 2b, the orientation of the line is on the vertical axis and offset with respect to NGC 1052 on the horizontal axis.
Statistical significance of the trail
We use simulations to assess the probability that the alignment of the 11 galaxies arose by chance. We generate N = 1,000 realizations of the (x, y) pairs by maintaining the angular distance from NGC 1052 for each pair and randomizing the angle. This procedure ensures that the density profile of the sample is maintained for all realizations. We then create Hough transforms for all realizations and determine how often the strongest linear feature contains ≥11 galaxies. We find that the probability of a chance alignment of ≥11 galaxies is 3%.
This calculation assumes that galaxies are oriented randomly with respect to NGC 1052, and does not take into account anisotropy associated with the filamentary structure of the cosmic web34,35. Galaxy groups are generally not spherical but have an average projected axis ratio of 0.77 (ref. 36). We examined the large-scale structure in the NGC 1052 field using a recently compiled catalogue of galaxies23 in this general area. Selecting all low-surface-brightness galaxies that were identified in that study plus all bright galaxies with cz < 2,000 km s−1 gives a sample of 72 probable group members. Their distribution is shown in Extended Data Fig. 2. The smooth density field was calculated with the non-parametric kernel density estimator37. There is no evidence for large-scale structure associated with the trail. In fact, there are no galaxies in the trail direction in the outskirts of the group, and the overall orientation of the group is perpendicular to the trail. The assumption of isotropy is therefore slightly conservative, in the sense that more galaxies will be scattered towards the line than away from it.
Finally, we note that the probability that there is a chance alignment and that it is a coincidence that both DF2 and DF4 are part of it is very low. This joint probability can be calculated directly for the isotropic case: of the 31 simulations that have ≥11 aligned galaxies only 6 have both DF2 and DF4 in the sample, corresponding to a combined probability of the observed arrangement of 0.6%.
A 12th low-surface-brightness dwarf galaxy on the trail
Visual inspection of the DECaLS imaging31 readily shows that there is a fairly prominent 12th galaxy that is part of the apparent trail. The object is SDSS J024007.01−081344.4 (ref. 31); it was previously pointed out as a likely low-luminosity group member with a central star cluster38. It is not in the objective catalogue that we use for the main analysis23. This may be because of its redshift in the SDSS database (it is erroneously listed as a z = 0.933 active galactic nucleus) or because the light from the central cluster moved the object outside of the size and surface-brightness criteria. We refer to the galaxy as DF9 as that was the catalogue number in our initial Dragonfly catalogue1. We do not use the galaxy in the objective analysis but we show its DECaLS image in Fig. 3. For convenience, we provide the coordinates of all trail galaxies in Extended Data Table 1.
HST imaging of the candidate dark galaxy DF7
DF7 is at one of the leading edges of the trail, ‘ahead’ of DF4. The galaxy was observed with HST/ACS as part of an exploratory survey of Dragonfly-identified low-surface-brightness galaxies in several groups1. The observations constituted two orbits, one orbit in F606W and one orbit in F814W. In Extended Data Fig. 3, we show the HST imaging at two different contrast levels. The galaxy is elongated and appears distorted, with the elongation in the direction of DF4. DF7’s apparent distortion, combined with its location at the leading edge of the trail, lead us to speculate that the galaxy is the highly dark-matter-dominated remnant of one of the two progenitor galaxies. We note that DF7 may be largely disrupted in this interpretation: the observed1 axis ratio is b/a = 0.42, but given the extreme foreshortening of the geometry the intrinsic axis ratio could be a stream-like approximately 1:20.
Other proposed scenarios
The joint formation of DF2 and DF4 in a bullet-dwarf event explains their lack of dark matter, large sizes, luminous and large globular clusters, striking similarity, large distance between them, large radial velocity difference, and the presence of a trail of other galaxies on the DF2–DF4 axis. Here we briefly discuss other scenarios that have been proposed to explain the properties of DF2 and DF4.
Initially, follow-up studies focused on possible errors in the measurements, either in the masses39 or in the distances of the galaxies40,41. However, with four independent velocity dispersion measurements3,8,9,10 (three for DF2 and one for DF4) and TRGB distances from extremely deep HST data15,16, these issues have now largely been settled.
Most astrophysical explanations centre on the absence of dark matter only, and invoke some form of extreme tidal interaction (with NGC 1052 or other galaxies) to strip the dark matter (along with a large fraction of the initial stellar population)42,43,44,45. These models do not explain the low metallicity of the galaxies, why there are two nearly identical objects in the same group, the newly discovered trail, or their overluminous and too-large globular clusters. The globular clusters, which have the same age (within the errors) as the diffuse light22, show that the galaxies were formed in an unusual way and did not merely evolve in an unusual way. Besides the bullet scenario, the only model that explains the globular clusters is a study of star formation in galaxies that are in the tails of the scatter in the halo mass–stellar mass relation18,19. This model has ad hoc initial conditions and does not account for the presence of two near-identical galaxies, but the key aspects of it (the formation of luminous globular clusters in a compact configuration and the subsequent puffing up of the galaxies owing to feedback) probably apply to the collision products in the bullet scenario (see main text).
It has recently been suggested that DF2 and DF4 are entirely unrelated, with DF4 being stripped of its dark matter by NGC 1035, which is near it in projection, and DF2 a face-on disk galaxy with a normal dark-matter content46,47. The association of DF4 with NGC 1035 is not seen in all datasets21, and there is no compelling evidence that DF2 is a disk7. Furthermore, the globular clusters and the trail remain unexplained, and there is the question of the likelihood that DF2 and DF4 have entirely different explanations but coincidentally share several otherwise-unique properties.
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