The study focuses on the ultra-diffuse galaxies (UDGs) DF2 and DF4 within the NGC 1052 galaxy group. These UDGs present a unique challenge to our understanding of galaxy formation and the role of dark matter. They are characterized by their exceptionally large sizes relative to their stellar mass, their abundance of luminous and large globular clusters, and most strikingly, their remarkably low velocity dispersions. This low velocity dispersion points to a significant deficiency or complete absence of dark matter, a component typically considered crucial for galaxy structure and stability. The unusual properties of DF2 and DF4 have fueled considerable debate within the astrophysics community. Previous research has suggested various formation scenarios, but a compelling and comprehensive explanation remains elusive. The researchers aim to address this gap by proposing a novel explanation for the formation of DF2 and DF4 and the peculiar characteristics they share. Understanding the formation mechanisms of these dark matter-deficient galaxies is crucial for our understanding of galaxy evolution, the distribution of dark matter within galaxies and groups, and the underlying physical processes governing the interactions of galaxies in dense environments. The implications extend beyond the specific objects studied; shedding light on their origin could refine our models of cosmological simulations and constrain the properties of dark matter itself.

Prior research on DF2 and DF4 has individually explored their unusual properties. Studies have documented their large sizes, the overluminous and numerous globular clusters within them, and the surprising lack of dark matter inferred from their low velocity dispersions. Several theoretical models have attempted to explain these properties, focusing on the formation of a single dark matter-deficient galaxy through high-velocity collisions of gas-rich galaxies, drawing parallels to the well-studied Bullet Cluster collision. These models suggest that during a high-speed collision, the gas component of the colliding galaxies gets separated from their dark matter and pre-existing stars. The subsequent star formation within the compressed gas leads to a new galaxy formation lacking dark matter. However, these previous studies primarily focused on the formation of individual galaxies and did not fully consider the possibility of multiple galaxies forming simultaneously from a single event. The current study expands upon this research by exploring the relationship between DF2 and DF4 and their joint formation in a single collisional event, proposing a new scenario that explains the spatial distribution and kinematic properties of multiple galaxies.

The researchers started by assuming that the similar properties of DF2 and DF4 are not coincidental, implying a shared formation history. Using their present-day radial velocities and three-dimensional locations, they demonstrated that a high-velocity collision is consistent with their formation. The large relative radial velocity (358 km/s) between DF2 and DF4 is significantly higher than the velocity dispersion of the NGC 1052 group itself, indicating a dynamic interaction. Furthermore, a precise measurement of their line-of-sight separation showed a significantly large value, suggesting that they are moving away from each other. By tracing their positions back in time, they infer a high-velocity encounter around 6 Gyr ago. This timing and scenario align closely with the initial conditions of mini-bullet-cluster scenarios proposed in previous research. A detailed collisional scenario was constructed, considering the position of the central elliptical galaxy, NGC 1052, which likely played a crucial role in accelerating the collision. It was assumed that at least one progenitor galaxy was a satellite of NGC 1052, significantly increasing the likelihood of a collision. The velocities of DF2 and DF4 relative to NGC 1052 were used to infer the initial velocities and orbits of the progenitor galaxies. The team utilized a Hough Transform, a mathematical technique used to detect lines in images, to objectively search for linear structures in the spatial distribution of galaxies along the DF2-DF4 axis. The transform revealed a statistically significant linear feature containing both DF2 and DF4 and additional galaxies, strengthening the hypothesis of their joint formation from a single collisional event. Further analysis examined the size-magnitude relationship of galaxies along this linear structure, demonstrating that trail galaxies are significantly larger than other galaxies of the same magnitude in the NGC 1052 group. The team also used the ages of globular clusters in DF2 (9 ± 2 Gyr) as a constraint on the timing of the collision. The authors then explored the implications of this finding, including the potential identification of the remnants of the progenitor galaxies. By combining kinematic, spatial, and morphological data, the research provided a more comprehensive understanding of this unusual system and its implications for galaxy formation and dark matter.

The study's central finding is the identification of a trail of seven to eleven large, low-luminosity galaxies, including DF2 and DF4, which are aligned along a linear structure. The researchers propose that this trail is the result of a 'bullet-dwarf' collision, a high-velocity collision between two gas-rich dwarf galaxies that occurred approximately eight billion years ago. This collision resulted in the separation of gas and dark matter, leading to the formation of multiple dark-matter-deficient galaxies. The estimated age of the collision aligns with the observed ages of globular clusters within DF2, providing further support for the proposed scenario. The statistical significance of the linear structure's identification was established using a Hough Transform, demonstrating the low probability (0.6%) of this alignment occurring randomly. The analysis reveals that galaxies within the trail are significantly larger than other galaxies of similar luminosity in the group, highlighting their distinct nature. The researchers suggest that two of the identified galaxies, RCP 32 and DF7, might be the remnants of the two progenitor galaxies, located at the leading edges of the trail. The proposed model also predicts kinematic properties for the trail galaxies, consistent with baryon-only models except for the potential remnants. The linear arrangement and the sizes of the galaxies involved suggest a common origin related to the bullet-dwarf collision. The team also note that some galaxies seemingly off the main trail might be part of the structure due to foreshortening effects. The existence of this trail provides strong evidence for the proposed bullet-dwarf collision scenario, offering a new perspective on galaxy formation in dark-matter-deficient environments.

The findings of this research directly address the long-standing question of how dark-matter-deficient galaxies like DF2 and DF4 form. The proposed 'bullet-dwarf' collision scenario offers a compelling explanation for their unusual properties and their alignment within a linear structure. The consistency between the collision's estimated age and the observed ages of globular clusters strengthens this model. The discovery of a trail of dark-matter-free galaxies has significant implications for our understanding of galaxy evolution and dark matter properties. This model predicts that such events, while less common than the larger-scale bullet cluster collision, are still frequent enough to be detectable, offering possibilities for future investigations. The study enhances our understanding of galaxy formation processes, especially those involving high-velocity collisions and the interplay between gas, stars, and dark matter. This work serves as a strong foundation for further research into the nature of dark matter and its interactions on different scales. Future studies could focus on obtaining kinematic and spectral data for other galaxies along the trail, which would help to further refine and test the proposed model.

This paper presents compelling evidence for a novel mechanism of galaxy formation, specifically the formation of a trail of dark-matter-free galaxies from a high-velocity collision of two gas-rich dwarf galaxies. The analysis of the spatial distribution, kinematics, and properties of the galaxies in the NGC 1052 group strongly supports the 'bullet-dwarf' collision scenario. This discovery offers a new perspective on the formation of dark-matter-deficient galaxies and provides crucial insights into galaxy evolution and the properties of dark matter. Future observational studies focusing on the kinematics and spectral properties of other galaxies along the trail, as well as detailed numerical simulations, will be needed to fully test and refine the proposed model.

The study relies heavily on the interpretation of the spatial distribution of galaxies. The identification of the trail is based on a statistical analysis using the Hough Transform, and there is a possibility of some galaxies being chance projections. While the authors account for this possibility, it remains a limitation in definitively establishing the physical connection between all galaxies within the identified structure. Additionally, the models rely on assumptions about the initial conditions and orbital parameters of the progenitor galaxies. More precise measurements of distances and velocities, particularly for galaxies other than DF2 and DF4, could further refine the models and strengthen or challenge the conclusions. Finally, the identification of potential progenitor remnants remains tentative, relying on morphological and positional considerations alone.