Testing the tidal stripping scenario of ultra-compact dwarf galaxy formation by using internal properties

Fig. 2 plots mass against metallicity for our sample of simulated stripped nuclei and observed UCDs. There is significant overlap between the two populations. The metallicities of all the UCDs are consistent with those measured for stripped nuclei within the uncertainties. Both observed UCDs and simulated stripped nuclei appear to follow a mass-metallicity relationship, with metallicity increasing with mass, that is especially strong for objects with mass M $>$ 1 $\times$ 10⁷ $\textup{M}_{\odot}$.

This plot also shows that we predict a number of low metallicity stripped nuclei that are not currently observed. This may be a result of the limited number of metallicity measurements that have been made for the population of low mass UCDs, and the uncertainties in EAGLE metallicities for low-mass galaxies. An alternative explanation is that since the divide between globular clusters and UCDs is fairly arbitrary and our stripped nuclei mass estimates are approximations based on the progenitor galaxy stellar mass, these low mass stripped nuclei would be observed as metal poor (blue) globular clusters.

The majority of simulated stripped nuclei are extremely metal poor, although there are a small population of more metal rich objects.

Considering the metallicities of only high mass simulated stripped nuclei with M > 1 $\times$ 10⁷ $\textup{M}_{\odot}$ a Kolmogorov-Smirnov (KS) test does not find that the two distributions are inconsistent (p = 0.22) The mean [Fe/H] for the simulated objects with M > 1 $\times$ 10⁷ $\textup{M}_{\odot}$ is -0.86 $\pm$ 0.07, while the mean [Fe/H] of observed UCDs with M > 1 $\times$ 10⁷ $\textup{M}_{\odot}$ is -0.63 $\pm$ 0.08. Note that the slight underestimation of masses of the 13 UCDs from the Francis et al. (2012) sample may mean some UCDs may have been excluded from this sample, and including them would bring the mean metallicities of simulated nuclei and observed UCDs closer together.

Fitting a one-dimensional Gaussian mixture model to the stripped nuclei metallicity data found no evidence for a bimodal metallicity distribution, like that possibly exhibited by globular clusters (e.g. Forbes et al., 1997; Cote et al., 1998; Brodie & Strader, 2006; Peng et al., 2006; Forbes et al., 2011).

Fig. 3 plots 6 different colours comparing simulated stripped nuclei to observed UCDs. The observed and simulated objects overlap fairly closely. The simulated stripped nuclei can explain all but the reddest and bluest observed UCDs. The simulated samples overall tend to trend towards redder colours. A KS test found that all colours were inconsistent. Fig. 4 plots only high mass M > 1 $\times$ 10⁷ $\textup{M}_{\odot}$ objects and finds more consistency with a KS test finding that 4 out of 6 of the colour distributions are consistent to p > 0.05 and 5 out of 6 to p > 0.01. These plots show that the higher mass simulated stripped nuclei sample trends towards bluer colours than the observed UCDs. It should be noted that accurately calculating colours for the simulated nuclei is difficult, especially at low metallicities because of sensitivities to abundance changes. The u-band is particularly difficult to accurately calculate as it is sensitive to the horizontal branch, alpha abundances and CNO variations (e.g. Fig 1 in Choi et al., 2019). The two M > 1 $\times$ 10⁷ $\textup{M}_{\odot}$ plots with p < 0.05, both involved the u band with u - g having p = 3 $\times$ 10^-4, and u-i having p = 0.035.

Fig. 5 plots g-i colour against mass and confirms that UCDs and stripped nuclei have a similar colour-mass relationship, with more massive objects being redder, and also that the higher mass objects are more consistent, with the low mass sample being slightly offset from each other.

We find that there is some evidence for a bimodal colour distribution of our sample of simulated stripped nuclei. In Fig. 6 the g-i colour of our sample of simulated stripped nuclei is fitted with a one-dimensional Gaussian mixture model. The model selection criteria Bayesian information criterion (BIC) is minimized for a two component model. This shows that the colour distribution can appear bimodal, even when the sample is composed of only a single type of objects that do not have a metallicity bimodality.

Fig. 7 plots colour against metallicity for the simulated stripped nuclei, with points coloured by stellar formation time age. The plot has a wedge-shaped colour distribution, with inflection points at g-i$\approx$0.8, and g-i$\approx$0.95. One explanation for the colour bimodality in Fig. 6 is that it stems from the relationship between colour and mass, plotted in Fig. 5 where more massive objects are redder. As the mass increases, the number of objects decreases, but they also trend to redder colours, creating a secondary peak at the redder end of the distribution. Combined with the inflection points in Fig. 7 this can create the observed bimodality.

In Section 3.1 we compared the ages of observed UCDs against the stellar formation times and merger times of simulated stripped nuclei. We found that both UCDs and stripped nuclei are predominantly old objects, with mean ages in all cases being greater than 9 Gyr. The nuclei of progenitor galaxies form approximately 2.5 Gyrs before their host galaxies merge and produce stripped nuclei, with the mean star formation age being 11.47 $\pm$ 0.09 Gyr, while the mean merger time is 9.0 $\pm$ 0.2 Gyr.

Our sample of observed UCDs in Table 2 appears slightly younger than the population of simulated stripped nuclei, with a mean age of 10.6 $\pm$ 0.4 Gyr. An extended star formation history of some UCDs has been cited as a reason why these UCDs may be stripped nuclei as this distinguishes them from globular clusters (Norris et al., 2015; Neumayer et al., 2020). However the youngest stripped nuclei that the stellar formation time can explain is 5 Gyr, inconsistent with these objects. These young objects could be explained if some stripped nuclei experience a significant starburst at merger that is not accurately measured in EAGLE due to the low particle resolution. Studies that have compared dwarf galaxy nuclei to UCDs have found that UCDs are typically older than nuclei (e.g. Evstigneeva et al., 2007). However we find that comparing UCDs to present day dwarf galaxy nuclei is not a fair comparison as the majority of mergers occur >8 Gyr ago (z > 1). Ideally, comparisons between nuclei and UCDs should be made with the z > 1 dwarf galaxy population.

We conclude that our simulated stripped nuclei are old objects with the mean ages being greater than 9 Gyr, which is consistent with the observations that UCDs are also predominantly old objects. Some young UCDs may have experienced a starburst at the time of merger (e.g. Mihos & Hernquist, 1994; Barton et al., 2000).

In Section 3.2.1 we compared the metallicities, [Fe/H], of observed UCDs with the [Fe/H] of simulated stripped nuclei. We found that the metallicity of our simulated objects could explain the metallicities of observed UCDs within 0.1-0.2 dex, a difference within the uncertainties of the correction applied to the EAGLE metallicities. We predict from our sample of simulated stripped nuclei that there should exist a large population of low metallicity stripped nuclei that have not been observed as UCDs. This could be due to the limited measurements made of UCD metallicities at lower masses, or these stripped nuclei may have been observed as blue globular clusters.

The metallicities of simulated stripped nuclei were found to be consistent with UCDs above a mass of 1 $\times$ 10⁷ $\textup{M}_{\odot}$, with a KS test returning p = 0.22. Both observed UCDs and simulated stripped nuclei appear to have a mass-metallicity relationship, with more massive objects being more metal rich. A UCD mass-metallicity relationship that flattens and connects with compact ellipticals at M > 1 $\times$ 10⁸ $\textup{M}_{\odot}$ has been previously reported in the literature (e.g. Zhang et al., 2018), and explained as a result of UCDs possibly being stripped nuclei. Virgo dwarf elliptical nuclei largely follow the UCD mass-metallicity relation, while globular clusters are offset towards higher metallicities at a given mass.

The metallicities of our stripped nuclei sample do not factor in the possibility that some of our stripped nuclei may experience a starburst that the simulation does not account for. In Section 4.1.1 we suggested that the lower ages of some observed UCDs could be explained by some stripped nuclei experiencing a starburst at the time of merger. If this is the case these stripped nuclei would also become more metal rich. However only 4 per cent of observed UCDs are too young to be explained by the ages of the stripped nuclei, so only a few stripped nuclei would need to experience starbursts to explain the observed UCDs. Assuming an extreme scenario where 20 per cent of stripped nuclei with ages 12-13 Gyr experience starbursts to give them the same ages and metallicities as those with ages 6-7 Gyr, the metallicity of the sample would increase by $\approx$0.24 dex. This would bring the metallicities of the simulated sample slightly closer to the observed sample.

The near-solar metallicity of some UCDs has been cited as a reason why they may be stripped nuclei e.g. M59-UCD3 (Liu et al., 2015b), VUCD3 and M59cO (Ahn et al., 2017). UCDs sit above the metallicity–luminosity relation of early-type galaxies and have a similar metallicity to dwarf galaxies (Chilingarian et al., 2011; Francis et al., 2012). At a mass of 4 $\times$ 10⁷ $\textup{M}_{\odot}$ Janz et al. (2015) observe a transition to extremely high metallicities, only paralleled by nuclei. This is roughly the mass that is believed to be the upper mass limit for the true old star cluster population (e.g. Norris et al., 2019) which is consistent with our finding that at M > 1 $\times$ 10⁷ $\textup{M}_{\odot}$ simulated stripped nuclei have near-solar metallicities, consistent with observed UCDs.

It should be noted that UCDs often have lower metallicities and older ages than nuclei (Evstigneeva et al., 2007), however, the older nuclei that represent UCD progenitors would have been less metal rich than nuclei existing at the present day (Chilingarian & Mamon, 2008). In high-density environments which are conductive to forming stripped nuclei, UCDs and dwarf elliptical nuclei are found to have consistent ages and metallicities (Paudel et al., 2010). Our results are consistent with this, with our high mass stripped nuclei also being less metal rich than present day galaxy nuclei.

Pfeffer et al. (2016) predicted a mass-metallicity relationship for the stripped nuclei much shallower than the mass-metallicity of M87 UCDs observed by Zhang et al. (2018). Zhang et al. (2018) noted however that Pfeffer et al. (2016)’s stripped nuclei metallicities relied on assigning their stripped nuclei sample a fixed metallicity which is simply offset by a constant amount from that of their host galaxy. This is an issue because the metallicity offset between nuclei and host galaxies is mass dependent, with nuclei of massive galaxies being more metal rich than the host, and nuclei of dwarf galaxies being less metal rich (Neumayer et al., 2020).

Our method of using the 5 innermost particles of a galaxy is more self-consistent. Fig. 9 shows the mass comparison between the innermost particles of EAGLE galaxies and their hosts and finds a similar relationship to that plotted in figure 9b of Neumayer et al. (2020) for higher masses. At low masses our relationship breaks down as the low resolution of the EAGLE simulation means there is no difference in the metallicities of the innermost particles and the host galaxy, so at low masses our simulated stripped nuclei sample may be slightly more metal rich than observed nuclei.

We find that our sample of stripped nuclei in Fig. 2 have a mass-metallicity relationship that is steeper than that predicted by Pfeffer et al. (2016), but still somewhat shallower than Zhang et al. (2018). Fig. 9 appears to have a somewhat shallower relation than figure 9b in Neumayer et al. (2020), which may have produced this.

We conclude that the metallicities of UCDs with M > 1 $\times$ 10⁷ $\textup{M}_{\odot}$ can be completely explained by them being stripped nuclei. We predict that there should exist a larger population of low mass, low metallicity stripped nuclei that are not currently observed as UCDs, but may be observed as part of the globular cluster population.

A tight colour-magnitude relation exists for nuclei (Hilker et al., 2003). UCDs have shown evidence of a similar colour-magnitude relation (Côté & et al., 2006; Evstigneeva et al., 2008; Brodie et al., 2011) that has been considered evidence for them being stripped nuclei. in Fig. 5 we confirm that there exists a colour-mass relationship for simulated stripped nuclei, that follows from the mass-metallicity relationship where more massive and hence brighter simulated stripped nuclei are redder, and the colours of higher mass simulated stripped nuclei are consistent with observed UCDs.

In Fig. 3 we compare the colours of simulated stripped nuclei against observed UCDs from Liu et al. (2020) for objects with M > 2 $\times$ 10⁶ $\textup{M}_{\odot}$. Visually the colour distributions appear similar, however KS tests found the samples to be inconsistent. This inconsistency could possibly be due to the incompleteness of the low mass UCD sample, or due to uncertainties in the colour calculation of low metallicity stripped nuclei.

Unlike the age and metallicity data, which are compiled from a variety of different papers, the sample from Liu et al. (2020) is a single uniform sample, although biased towards larger brighter objects. As a consequence of the observed UCDs being selected to have radii r_h > 11 pc, the observed UCDs are undersampled at lower masses (below M $\approx$ 10⁷ $\textup{M}_{\odot}$). Because of the colour-magnitude relationship of UCDs this means that the observed UCD sample may skew slightly redder than a complete sample. However for the lower mass objects the observed UCDs are found to be slightly bluer than the simulated stripped nuclei. This may be a consequence of the difficulty of accurately calculating colour at lower metallicities for our simulated stripped nuclei sample, making colour comparisons at low masses less accurate.

In Fig. 4 we compare the colours of simulated stripped nuclei against observed UCDs from Liu et al. (2020) for objects with M > 1 $\times$ 10⁷ $\textup{M}_{\odot}$. Visually for both the low and high mass plots the colour distributions appear similar, and four out of six of the colour plots are found to be consistent. The two that are found to be inconsistent are those with colours that required the u-band, which is most prone to error due to uncertainties in the bandpass definition and/or changes in the computed spectral energy distribution. A starburst at merger that produces metals would also redden the sample of stripped nuclei, however as the predicted metallicity shift is very small this would not affect our results. The more limited data for low mass UCDs, as well as the difficulty in accurately calculating colour at low metallicities means that we cannot draw any solid conclusions about low mass M < 1 $\times$ 10⁷ $\textup{M}_{\odot}$ UCDs. However, we find that the colours of high mass UCDs are consistent with them being stripped nuclei.

Globular cluster systems in massive elliptical galaxies are known to have a prominent colour bimodality (e.g. Gebhardt & Kissler-Patig, 1999; Kundu & Whitmore, 2001; Peng et al., 2006). In some systems the number of red and blue objects is approximately equal, while in others one colour dominates (Peng et al., 2006).

Liu et al. (2020) found that UCDs have a slight bimodality that is more pronounced than galaxy nuclei but less pronounced than globular clusters. In Section 3.2.2 we found similar evidence for a bimodal fit to our simulated stripped nuclei colours, despite them consisting of a homogenous group of objects formed by a single mechanism. We found no evidence of a metallicity bimodality.

Lee et al. (2020) have suggested that the colour bimodality in some old globular cluster populations could stem from the nonlinear relationship between colour and metallicity, rather than a metallicity bimodality. Thus the bimodality Liu et al. (2020) observe in the UCD population could be explained entirely by them being old predominantly metal-poor stripped nuclei.