The Formation of Faint Fuzzies (FFs), Ultra-Compact Dwarf Galaxies (UCDs and compact Ellipticals (cEs)

The Milky Way (MW) has a globular cluster system containing about 150 globular clusters (GCs, Harris 1996). Most of the GCs are compact with effective radii of a few pc. But, 13 GCs (9%) have effective radii larger than 10 pc. Most of these extended clusters (EC) are faint (MV > -7) which makes them hard to detect in far away galaxies. Further ECs have been found in the LMC and the Fornax dwarf galaxy (e.g. Mackey & Gilmore 2004, McLaughlin & van der Marel 2005). Comparable objects have been around M31 (Huxor et al. 2005), which have effective radii above 30 pc, even though these size estimates where later reduced to lower values (Huxor et al. 2011). In S0 galaxies EC where found inside the disc and dubbed faint fuzzy (FF) star clusters (Larsen & Brodie 2000). Finally ECs are now found in all types of galaxies from dwarfs to ellipticals (e.g. da Costa et al. 2009 and many more).

Hilker et al. (1999) discovered compact objects with luminosities above the brightest globular cluster. They have masses between a few 106 and and effective radii between 10 and 100 pc. These objects were later dubbed ultra-compact dwarf galaxies (UCD). Again many UCDs have been found until now in galaxy cluster environments (e.g. Hasegan et al. 2005 and many more) as well as around more isolated galaxies (Hau et al. 2009). Mieske et al. (2008) analysed larger samples of UCDs and find that they form a coherent data set together with ECs where size andmass-to-light (M/L) ratio increases continuously with their mass. While the majority of the found UCDs are old, W3 in NGC 7252 is a massive object of 108 Msun which has an age of about 500 Myr (Maraston et al. 2004). At the top end of small, compact objects we have compact dwarf ellipticals like M32 in Andromeda. Their dark matter content (i.e. their M/L ratio) seems to be inconclusive (Howley et al. 2012). High resolution HST imaging of gas-rich interacting galaxies show very intense star bursts. These star formation events are found in the discs and in the tidal tails. They show complexes spanning a few hundred pc to a kpc containing hundreds of young star clusters in a confined area (e.g. the Antennae, Whitmore et al. 1999). These objects are called cluster complexes (CC).

Kroupa (1998) pointed out that the CCs will undergo a rapid dynamical transformation. The SCs inside a complex will merge and build up a compact object. Fellhauer & Kroupa (2002a,b) later used this fact to explain the formation of UCDs and FFs. Also other theories explaining the formation of UCDs were proposed. While Hilker et al. (1999) speculated that they might just be the massive end of the globular cluster distribution, Bekki et al. (2001) proposed that they are the remnant nuclei of stripped dwarf ellipticals. But as this stripping process needs several Gyr to complete, this theory could not explain W3 (Fellhauer & Kroupa 2005). The elevated M/L ratios of UCDs may not stem from a DM halo but could be obtained by tidal heating (Fellhauer & Kroupa 2006) or through a top-heavy initial mass function (Dabringhausen et al. 2010). The theory of merging star clusters was also used in a more complete parameter study to explain the formations of FFs and UCDs (Bruens et al. 2009, 2011). On a more theoretical base, the time-scales on which SCs in CCs merge and form a compound object were studied by Fellhauer et al. (2002, 2009). They find that sub-structure is erased fast within a few crossing times of the complex. But, in those studies they find that even though the sub-structure is erased very fast in positional space, some structure in velocity space still survives and may explain, for example, the enhanced velocity dispersions and velocity gradients in dwarf spheroidal galaxies (Assmann et al. 2012a,b; although those models use a dark matter halo).

Even though there has been a parameter study about the formation of FFs and UCDs out of merging star clusters, the parameter space was rather narrow and focused on cluster complexes as they form in the present. Furthermore, it was focused on explaining the shapes andappearance of the objects and not on the dynamics (M/L ratios). We want to extend this parameter study much further, encompassing the strong star bursts we expect in the early universe. The previous study hinted at a possible relation between initial mass of the cluster complex and the maximum effective radius (depending on the scale-length of the CC). We want to extend this research and establish this relation, which is also a function of the tidal field strength. As mentioned previously we found that dynamical structures in velocity space are able to survive much longer than in positional space. In positional space we see violent relaxation acting on the time-scale of a few crossing times. The structures in velocity space can survive on a time-scale of a relaxation time of the object. In our previous study of dwarf spheroidal galaxies, this time scale is much longer than a Hubble time and we are still able to detect these structures in our models. In the case of compact objects without dark matter we are exactly at the transition region. While extended star clusters of a few 105 solar masses have relaxation times shorter than a Hubble time, the border-line lies at about 2 x 106 solar masses, exactly in the mass region of UCDs. This could be a very straightforward explanation for why some of the UCDs show enhanced M/L ratios which are not explainable by single stellar population models. Furthermore, compact ellipticals have masses, and therefore relaxation times, of dwarf galaxies. We would expect that in their mass regime the velocity sub-structures will survive until present, even though they formed in the early universe. We will try to find a general description of spherical objects which explains the luminosity – M/L – relation and the luminosity-dispersion relations (Mieske et al. 2008) by investigating the formation scenario of hierarchical merging of spherical components into larger objects that mimic larger M/L ratios when the objects get massive enough to reach relaxation times longer than the age of the universe. Our group has a very strong expertise in carrying out such simulations. We study, in particular, the formation of star clusters during and shortly after their embedded phase. We investigate how fast the clumpy structure seen in very young star forming regions are able to merge and build a spherical star cluster. We thereby search the parameter space of different initial conditions like the initial distribution (clumpy or fractal), the initial virial state of the stars (equilibrium or cold, i.e. without velocity) and the shape of the background gas potential and investigate their influence on the formation-timescale and their ability to survive of young star clusters (Smith et al. 2011a,b, Farias Osses et al. 2015). On the other end of the spectrum, we have expertise in the field of the formation of UCDs and Faint Fuzzy star clusters, as well as the investigation of a new formation scenario for dSph satellites. In this project we want to include all our previous work and fill the gaps in parameter space to see if our models really can reproduce the observed relations. Our working hypothesis is that as soon as the object reaches a certain mass and size, we will not see a fully relaxed entity. Instead we will have out of equilibrium streaming motions (as we already found in our dSph models), thereby mimicking a higher M/L ratio. As seen in observations this border-line should appear at roughly 2 x 106 solar masses. We therefore require a postdoc with sufficient knowledge and experience in carrying out numerical simulations for two years to perform all the numerical models on the different mass- scales, investigating a large parameter-space to connect our star cluster models with the previous UCD models, and beyond to dwarf compact elliptical galaxies.

This work is/was supported by the following grants:

• FONDECYT regular No.1095092 and No. 1130521; PI: Michael Fellhauer
• BASAL: CATA