The large-scale structure of globular clusters in the NGC 1052 group

For the source detection, we used SExtractor (version 2.19.5, Bertin, 2002) in single-mode in each band. GCs at the distance of the NGC 1052 group (20 Mpc) are point sources in the CFHT images. Thus, we defined a threshold of 2$\sigma$ above the background to detect sources, assuming, given our seeing, that point sources should have most of their light within apertures of $\sim$3 pixels diameter (pixel scale of CFHT is 0.206 arcsec per pixel). For the aperture photometry, we used a smaller aperture with a diameter of 2 pixels to avoid contamination from the sky or nearby sources in the GC candidate photometry. Then we performed local sky subtraction and added in an aperture correction calculated using the growth curves of isolated bright point sources. The corrections are 0.94, 0.55, and 0.54 mag in the $u$, $g$ and $i$ bands, respectively. Errors in the photometry are the nominal errors from SExtractor. As the last step, we corrected the data for Galactic extinction using the correction derived by Calzetti et al. (2000) and the dust maps of Schlafly & Finkbeiner (2011).

As mentioned before, GCs at a distance of 20 Mpc are point sources in our imaging and, thus, they cannot be distinguished from foreground stars or high-redshift galaxies. To account for that, we have applied both morphological (ellipticity and concentration) and photometric (colours and magnitudes) GC selection criteria. The morphological selection criteria are summarised as:

• •

  Concentration ($C_{3-6}$):
  Given our seeing, we assume that point sources should have most of their light within 3 pixels. Thus, the magnitude difference measured in 3 and 6 pixels diameter apertures should be consistent with zero, allowing a scatter of 0.1 mag (typical photometric error).

• •

  Ellipticity ($\epsilon$):
  Point sources should be nearly circular with $\epsilon<0.2$.

In addition to these criteria, we adopted two different approaches for photometric selection. The first selection was based on photometric properties of GCs in general and the second on photometric properties of spectroscopically confirmed GCs around DF2 and DF4.
For the first approach, we used the universal GCLF and simple stellar population (SSP) models consistent with universal GC populations to select GCs. The SSP models were constructed using the Flexible Stellar Population Synthesis package (FSPS; Conroy et al., 2009, 2010; Conroy & Gunn, 2010, version 0.4.2). We used the Padova isochrones (Marigo & Girardi, 2007; Marigo et al., 2008) and allowed for metallicities in the range [$Z$/H] = $-$2.2 to 0.0 dex and ages (t${}_{\rm age})$ = 8–14 Gyr. The predicted CFHT colours of these SSP models are shown in Figure 1, where each coloured line corresponds to one metallicity, while the extent of the lines is defined by the age range of the SSPs.

• •

  Magnitude:
  All sources 3$\sigma$ brighter and 1$\sigma$ ($1\sigma=1.0$ mag) fainter than the peak of the universal GCLF (i.e., $M_{g}=-7.2$ or $g=24.3$ mag, Jordán et al., 2007) were selected. The unbalanced cuts (i.e., 3$\sigma$ up and 1$\sigma$ down) were applied based on photometric errors, i.e., only objects with $g$-band photometric uncertainties smaller than 0.2 were selected.

• •

  Colour ($u-i$ and $g-i$):
  The colour cuts were determined by fitting a line to the SSP distribution in the colour–colour space, allowing a scatter of 3$\sigma$ (0.15 mag). The fit is best parametrized by:

  $$(g-i)=0.44\times(u-i)-0.01$$

  (1)

  The selected GCs are those within the red-shaded area in Fig. 1.

The second selection consisted of selecting sources with colours and magnitudes similar to those of spectroscopically confirmed GCs around DF2 and DF4.

• •

  Magnitude:
  All sources within $\pm$1 mag of the mean of the GCLF of DF2 and DF4 recovered by van Dokkum et al. (2018), i.e., $M_{g}=-8.8$ ($g=22.7$) mag were selected. We note the caveat that DF2 and DF4 were found to have both a population of overluminous GCs and a population of “normal” GCs, i.e., consistent with the universal GCLF (van Dokkum et al., 2022b), and by applying this criterion we are including only the overluminous ones.

• •

  Colour ($u-i$ and $g-i$):
  Colour cuts were defined using the locus of spectroscopically confirmed GCs in DF2 and DF4 in the colour–colour plane (see Fig. 1). We assume that these follow the same distribution as the SSP models, but with narrower ranges both in $u-i$ and $g-i$ colours, i.e., $1.54<u-i<1.90$ and a scatter of 0.1 mag in $g-i$ .

We note that the spectroscopically confirmed GCs #926 and #4366 were excluded from our sample for having different colours to the remaining GCs around DF2 and DF4. Visual inspection has confirmed that these GCs are contaminated by foreground stars in our imaging. GCs #3602 and #1755 were also excluded for not meeting the ellipticity criterion (see middle panel of Fig. 2). Thus, in the end of the selection process, we have 20 out of the 24 spectroscopically confirmed GCs around DF2/DF4.

In summary, we selected two samples of GC candidates, i.e., one based on SSP criteria to resemble typical GCs and one based on the spectroscopically confirmed GCs around DF2/DF4. All of the selection criteria are summarised in Table 1 and shown in Fig. 2.

To quantify our completeness, we have carried out tests using artificial stars. We first modelled our PSF using the routine DAOPHOT II (Stetson, 1987) in the $g$ band, using a sample of 15 isolated, bright and unsaturated stars. We then injected 30000 artificial stars in the range of $19<g<26$ magnitudes onto blank areas of our $g$-band image. The completeness was calculated by comparing the total number of artificial stars injected in different magnitude bins and the number of detected artificial stars using the same methodology as the one we used to detect the GCs (i.e., SExtractor).

We find that we are 94% complete down to the universal GCLF turnover magnitude, i.e., $M_{g}=-7.2$ ($g$ = 24.3) mag, and a 50% completeness limit of $M_{g}=-6.8$ ($g=25.0$) mag. We inspected different areas of the images and have found little-to-no difference in completeness throughout our FoV, with the exception of the centre of NGC 1052.

The spectroscopically confirmed GCs around DF2 and DF4 were used to select a range of new GC candidates throughout the NGC 1052 group. It is important, none the less, to understand how our recovered photometric properties align with other studies in the literature of the GCs around DF2 and DF4. Upon cross-matching our GC catalogues with Shen et al. (2021), we detect all 24 spectroscopically confirmed GCs around these galaxies. Out of the 24, only 20 met all of our selection criteria (GCs #926, #3602, #1755 and #4366 were excluded) and are the ones discussed in what follows.

The GCLF reconstructed from these 20 GCs around DF2 and DF4 reveals a mean value at $M_{g}=-8.8$ ($g=22.7$), consistent with the findings of a top-heavy GCLF for DF2 and DF4 by van Dokkum et al. (2018, 2019) and Shen et al. (2021). We investigated the extent that the age of a GC can influence its brightness to understand if this top-heavy GCLF could be explained by an age difference other than mass. The magnitude difference of a GC of age 8 Gyr and a GC of 14 Gyr at fixed stellar mass and metallicity is 0.5 mag in the $g$ band. This difference is less than a third of the magnitude difference observed between the peak of the universal GCLF and the one found for DF2 and DF4. We thus conclude that the overluminous nature of the GCs is unlikely due to age and most likely due to mass. The locus of the overluminous GCs around DF2/DF4 in the colour–colour plane is consistent with the SSPs with metallicities $-1.4<$[$Z$/H]$<-1.0$ dex, which is in agreement with the findings of Fensch et al. (2019a) and Buzzo et al. (2022). They have an average colour of $\langle g-i\rangle=0.76\pm 0.10$ and $\langle u-i\rangle=1.66\pm 0.12$. These values correspond to an average age of $9.1\pm 0.8$ Gyr and [$Z$/H]=$-1.2\pm 0.2$ dex.

We find an observed scatter of 0.2 mag in $g-i$ and 0.3 in $u-i$. This scatter is consistent with the findings of Román et al. (2021) (using DECam data) and Shen et al. (2021) (using 1-orbit HST data), which also found a spread of 0.3–0.4 mag in the GC colours of DF2/DF4, but using different filter bands. The scatter is, however, broader than the recent findings of van Dokkum et al. (2022b), who found that GCs in DF2/DF4 have an intrinsic spread in colours of less than 0.02 mag. This is not unexpected since we are using much shallower ground-based data. In contrast, van Dokkum et al. (2022b) applied a careful flat-fielding analysis on very deep HST data (19 orbits for DF2 and 7 orbits for DF4) to get to their results, revealing that colour scatters can be found to be larger with lower quality data.

For consistency, using FSPS we converted our average $g-i$ colour of the GCs around DF2 and DF4 into $V_{606}-I_{814}$ to compare it with van Dokkum et al. (2022b). We find that our colours translate to $V_{606}-I_{814}=0.39\pm 0.10$, which is consistent with their findings of $V_{606}-I_{814}=0.375\pm 0.005$. van Dokkum et al. (2022b) found the DF2 and DF4 GCs to be significantly bluer on average than GCs around low-luminosity Virgo cluster dEs (Peng et al., 2006). This conclusion, however, required a chain of three different conversions between $g-z$ and $V_{606}-I_{814}$ colours, which likely resulted in accumulated systematic errors. Here we apply a single conversion between $g_{475}-z_{850}$ and $g-i$ from Usher et al. (2012) (equation A1). We find that our average is $\langle g-z\rangle=1.03\pm 0.10$ and, thus, we find that the colours of the GCs around DF2/DF4 and around Virgo dwarfs ($g-z\sim 0.9$ mag, Peng et al., 2006) are consistent within the uncertainties.

To study in detail the intragroup GC distribution and the GCs around the LSB galaxies, we have modelled and subtracted from our distribution the overpowering GC system of NGC 1052. For this analysis, we have used the broader GC selection based on the properties of GCs in general.

We first characterised the GC system of NGC 1052 by performing a radial number count analysis around the galaxy. In addition, the overall GC distribution around NGC 1052 was divided into blue ($0.4<g-i\leq 0.85$) and red ($0.85<g-i\leq 1.2$) GCs, following typical red/blue GC separations in the literature (e.g., Lee et al., 2010). We measured the average GC surface density around the galaxy in log spaced radial bins. Uncertainties were calculated by assuming Poisson statistics for the innermost bins. For the outer ones, in addition to the Poisson errors, we performed number count measurements with the same bin size in random places in our images to estimate the level of uncertainty in the background. These uncertainties were added quadratically.

We then fitted a Sérsic function to the GC density profile of the overall GC distribution of NGC 1052, as well as the red and blue GC distributions. The Sérsic index ($n$), GC half-number radius ($R_{\rm GC}$) and background+intragroup density ($\rho_{N}$ (bg+ig)) were free parameters. The profiles were fitted from the fourth radial bin on in order to avoid the incompleteness in the innermost bins due to the bright galaxy light. The three resulting density profiles are shown in Fig. 3. The overall background and intragroup GC densities were calculated in isolated areas throughout the group, corresponding to $\rho_{\rm N(bg)}+\rho_{\rm N(intragroup)}=0.27\pm 0.03$ GCs/arcmin² and are shown in Fig. 3 as well. GCs are considered as not being bound to NGC 1052 once the GC number density reaches the background+intragroup level. In Table 2, we summarise the results of the model of these GC systems. We note that for all calculations of $R_{\rm GC}$/$R_{\rm e}$, we assumed the effective radius of the stellar body of NGC 1052 recovered by Forbes et al. (2017), i.e., $R_{\rm e}=21.9$ arcsec. We find that the overall GC distribution of NGC 1052 has a Sérsic index of $3.04\pm 0.02$ and $R_{\rm GC}$/$R_{\rm e}$ = $10.79\pm 0.32$. The red GCs have a Sérsic index of $2.92\pm 0.12$ and $R_{\rm GC}$/$R_{\rm e}$ = $8.82\pm 0.56$. The blue GCs have a Sérsic index of $2.50\pm 0.07$ and a more extended system with $R_{\rm GC}$/$R_{\rm e}$ = $13.20\pm 0.43$. Additionally, as seen in Table 2, the fit of the background density in the total GC profile is reassuringly consistent with the overall background density ($\rho_{\rm N(bg)}+\rho_{\rm N(intragroup)}$) measured in isolated areas, as previously mentioned. The finding of blue GCs extending out to larger radii than red GCs is in agreement with the expectation that the metal-rich red GCs are mostly formed in-situ and have a shallower radial profile, while metal-poor blue GCs are mostly formed ex-situ and are later accreted onto the galaxy (Brodie & Strader, 2006).

It is interesting to note that the GC distribution around NGC 1052 is quite extended for its stellar mass ($\log_{10}(M_{*}/M_{\odot})=11.02$, Forbes et al. 2017). Forbes et al. (2017) and Hudson & Robison (2018) have shown that the sizes of the GC systems of galaxies scale with their stellar and halo masses. According to Forbes (2017), early-type galaxies (ETG) have an average $R_{\rm GC}/R_{\rm e}$ of $3.7\pm 0.4$. Hudson & Robison (2018), similarly, found that the mean ratio is $R_{\rm GC}/R_{\rm e}$ = 3.5. However, both studies show that some galaxies can have much more extended GC systems, reaching in extreme cases even to a ratio of $R_{\rm GC}$/$R_{\rm e}$ = 46. We caution, none the less, that our recovered GC system sizes may be overestimated since the fits do not account for incompleteness in the central regions. This is not a problem for the works in the literature (Forbes, 2017; Hudson & Robison, 2018) which applied methods of galaxy subtraction to better estimate the number of GCs in the innermost regions of the galaxies. A more detailed modelling of the central galaxy is beyond the scope of the paper.

After recovering the morphological parameters of the GC system, we reconstruct the GCLF of NGC 1052. We assume a GCLF that is symmetric about the peak and that our distribution is complete down to the universal turnover magnitude (as discussed in Section 3.3). We then double the number of GCs counted down to the turnover to estimate the total number of GCs around NGC 1052. Additionally, to correct for the missing innermost bins not included in the fit, we extrapolate the galaxy surface density profile to the centre, assuming the completeness calculated using our artificial star tests. Taking all of this into consideration, we find a final count of $402\pm 9$ GCs around NGC 1052, similar to the findings of Forbes et al. 2001 (e.g., 390 GCs).

The average colour of the GCs found around NGC 1052 is $\langle g-i\rangle=0.84\pm 0.16$ and $\langle u-i\rangle=1.93\pm 0.25$. These correspond to an average age of $11.2\pm 1.6$ Gyr and [$Z$/H]=$-0.8\pm 0.3$ dex, i.e., a significantly redder GC population than the one found around DF2/DF4 (see Section 4.1).

The 2D distribution of GCs around NGC 1052 was subtracted from the total GC distribution of the group using the recovered best fitting density profile, i.e., $R_{\rm GC}=10.79\,R_{\rm e}$, assuming an axis ratio of 0.31 and position angle of 120 degrees measured by Forbes et al. (2001). We assumed the same best fitting density profile to subtract the GCs around NGC 1052 from the map based on all GCs and the one based on the colours of DF2/DF4 GCs. After subtracting the GC system of NGC 1052 itself, we can analyse the GC distribution around the fainter galaxies, as well as any intragroup GC structures. The recovered GC large scale structure based on SSP models is shown in Fig. 4. For comparison, we show the LSS based on the colours of the GCs around DF2 and DF4 in Fig. 5.

By looking just at the GC large scale structure based on SSP models, we see a nearly uniform distribution, with the exception of GC overdensities around some of the giant galaxies in the group (e.g., NGC 1035 and NGC 1047), as well as many around NGC 1052 itself. NGC 1052 was shown by Müller et al. (2019b) to have several LSB features around it, including stellar streams, arcs and tidal features. Specifically, Müller et al. (2019b) found a loop-shaped LSB feature to the south of NGC 1052 in the direction of NGC 1042 and another one forming an arc connecting NGC 1052 and NGC 1047. We highlight the approximate positioning of these features in our maps in Figs. 4 and 5, but see figure 1 of Müller et al. 2019b for further details. These features coincide with the positions of the GC overdensities found in our maps, and may be indicative of tidal interactions between the main galaxies in the group, with their outermost GCs being now part of these tidal features. In addition to Müller et al. (2019b), van Gorkom et al. (1986) have also previously shown that the HI distribution of NGC 1052 has tidal features extending in the same direction as these identified GC overdensities, once again indicating that the galaxies may be interacting (see figure 2 of Müller et al., 2019b).

The GC map based on DF2 and DF4 selection has very few overdensities since it is based on very narrow selection criteria. Reassuringly, we recover the overdensities around DF2 and DF4 and very weak overdensities around RCP32 and DF9. We highlight in both maps the positions of LSB galaxies found by Román et al. (2021). We investigate if there are any GCs around them or intragroup GC overdensities connecting them. No clear overdensities were found throughout the group, only around NGC 1052 itself. Again, these share the same positions as previously identified tidal tails and stellar streams around NGC 1052 (Müller et al., 2019b).

In the top row of Fig. 4, we show the four dwarf galaxies identified to have GC systems: RCP 32 ($N_{\rm GC}=2$), DF2 ($N_{\rm GC}=11$), DF9 ($N_{\rm GC}=3$) and DF4 ($N_{\rm GC}=10$), respectively. We note that each stamp has 1 arcmin², and the background+intragroup contamination was found to be $\rho_{\rm N(bg+ig)}=0.27$ GCs/arcmin². These findings are discussed in detail in the following section.

The bullet-dwarf scenario makes distinct predictions for the stellar populations (and thus colours) of all of the supposedly DM-free galaxies along the trail, as well as for their GC systems. In this Section, we explore how well the GC distribution around the dwarf galaxies in the group agree with this formation scenario. Additionally, we investigate the presence of intragroup GCs that would have been formed by the same process. If they do exist, they would be expected to have similar stellar populations to the GCs around DF2 and DF4, and also, due to conservation of momentum and inertia, these GCs would be expected to follow the same near-linear spatial distribution as the trail galaxies. The schematic picture, shown in figure 1 (appendix) of van Dokkum et al. (2022a), suggests that some GCs may be formed away from DF2/DF4, i.e., in other trail galaxies and/or as intragroup GCs along the trail.

To be consistent with the scenario, all of the GCs are expected to have an age consistent with $\sim$8 Gyr, as found for the stellar body of DF2 and DF4 by Buzzo et al. (2022). This finding is supported by Fensch et al. (2019a), which using IFU (MUSE/VLT) data, have shown that the stellar body and GC population of DF2 have equivalent ages (8.9 Gyr). Additionally, van Dokkum et al. (2022b) have shown that the GC systems of DF2 and DF4 have the same optical colour, thus, same stellar populations. All of these seem to support the idea that DF2, DF4 and their GCs had a coeval formation.

In what follows, we investigate the other dwarfs in the group found to host GC systems. Combining these findings with what we know about DF2 and DF4, we discuss the level of agreement of the formation scenario with the recovered LSS.

In a group with so many LSB features (Müller et al., 2019b), the existence of the NGC 1052 dwarfs could be the result of galaxy-galaxy interactions, leading to tidal dwarf galaxies (TDGs, Haslbauer et al., 2019; Müller et al., 2019b). This particular mode of formation typically leads to young, metal-rich, gas-dominated (unlike DF2 and DF4) and dark-matter free galaxies. Simulations have shown, none the less, that it is possible for TDGs to be formed at high-redshifts ($0.5<z<2.0$), resulting in old and quiescent dwarfs observed at $z=0$ (Ploeckinger et al., 2018). This scenario for the formation of the NGC 1052 dwarfs would be similar to the idea proposed for the Milky Way plane of satellites (Lynden-Bell, 1976) or to that of the Dentist’s Chair (Weilbacher et al., 2002). Additionally, if the galaxies in the NGC 1052 group were formed by this scenario, they would have formed from gas and stars originating from the outskirts of a massive host after a galaxy-galaxy interaction. In this case, we may expect intragroup GCs with similar stellar populations as the ones from the progenitor massive galaxy, as they would have been stripped together with the gas that formed the TDGs.

This formation scenario successfully explains the DM depletion, and it may also explain the normal GC population of the dwarf galaxies. However, this scenario, as it stands, cannot explain the overluminous population of GCs around DF2 and DF4. This is because low-redshift TDGs do not have star formation rates high enough to form overmassive GCs (Fensch et al., 2019b, and reference therein). In fact, Fensch et al. (2019b) suggest that although TDGs created by major mergers can lead to the formation of massive young clusters, their survival times are expected to be only of some hundreds of Myr. None the less, they hypothesise that if similar TDGs would have been formed at high-redshift ($0.5<z<2.0$), where gas fractions were higher and could lead to stronger star formation episodes, then the formation of ultramassive GCs that would survive for a Hubble time is possible.

Another problem encountered by the tidal dwarf scenario for DF2 and DF4 is that the gas content forming TDGs and their GCs is supposed to be pre-enriched in metals, leading to metallicities of one third to half solar. Thus, they are expected to have significantly higher metallicities than those observed for the GCs in this study, i.e., average [Z/H]$=-1.2\pm 0.2$ dex. However, if we once again resort to high-redshift TDGs (Fensch et al., 2019b), these would have been formed at a time where the interstellar medium would not have been as pre-enriched and, thus, their GCs would possibly display metallicities closer to the observed values. The formation of TDGs and their GCs at high-redshift ($z\sim 1.9$) would also be in agreement with the average age of the GCs in the dwarf galaxies of $9.1\pm 0.9$ Gyr.

High-redshift TDGs, thus, seem to be able to explain many of the properties of the dwarfs in the NGC 1052 group, i.e., DM depletion, overluminous GC population and low metallicities. One problem though is that the two DM-free dwarf galaxies in the NGC 1052 group were shown to be close only in projected distance, but far apart in the line-of-sight TRGB distance (Shen et al., 2021), which is hard to reconcile with any tidal dwarf-like formation at low- or high-redshift, as TDGs by definition never leave the gravitational potential of their progenitors, being always within one or two hundred kpc from them (Ploeckinger et al., 2018).

We conclude that a high-redshift tidal dwarf galaxy model as it is, similarly to the bullet-dwarf scenario, has points of agreement with our findings, e.g., GC metallicities and ages; and aspects that need further investigation, i.e., physical separation of dwarf galaxies. Simulations of high-redshift TDGs that can overcome the physical separation inconsistencies would provide a consistent formation scenario for the galaxies and GCs in the NGC 1052 group.

Since the first claim that the galaxies in the NGC 1052 group could be dark matter-free, the most prominent model to explain their formation relied on tidal stripping by a more massive galaxy (e.g., Ogiya, 2018; Ogiya et al., 2021; Moreno et al., 2022). Such models were shown to successfully explain the lack of DM and the presence of GCs in the galaxies, but even using different simulations, they were not able to create GCs as massive as the ones seen in DF2 and DF4.

Tidal stripping models, additionally, are expected to leave a trail of stripped GCs between the stripped dwarf galaxy and the massive host (Lee et al., 2010), but such structures are not seen in any of our LSS maps.

On the other hand, GC streams and other GC LSS structures are observed all around NGC 1052, indicating recent interactions between NGC 1052, NGC 1047 and NGC 1402, as suggested by Müller et al. (2019b). Thus, tidal stripping could explain the connections found between the massive galaxies in the group, but do not seem to have any connection with the dwarfs.

Models that are alternative to the existence of dark matter may also be suitable explanations for the existence of these DM-free galaxies (e.g., MOND; Kroupa et al., 2012). They have been proposed as possible formation pathways for DF2 by Kroupa et al. (2018) and for DF4 by Müller et al. (2019a). These models, however, do not make predictions about the globular cluster population of the galaxies nor about their stellar populations, thus, they are more difficult to test with this study. They remain a possibility to be further developed and tested.