Stars forming in Giant Molecular clouds are observed to form in small sub-clumps distributed throughout the star forming region of the cloud. In Fellhauer et al. (2009), a mechanism to form star clusters from these initial conditions was proposed. The sub-clumps merge hierarchically within the background potential of the gas forming a star cluster. However, this mechanism is subject to a limited time scale - the first supernovae within the newly formed stars can easily expel the gas from within the cluster, and this sudden mass removal may dissolve the cluster entirely.
Together with M.I. Wilkinson (Leicester, UK) and P. Kroupa (Bonn, Germany) we made simulations of sub-clumps in a background potential mimicking the remaining gas. We used a particle-mesh code to perform the simulations. The initial conditions were that the sub-clumps are in virial equilibrium with the gas potential. We investigated the time-scales of the merging and the formation of the final star cluster. We found three different regimes for the merging time-scales. If the mass of the sub-clumps is too low compared with the velocities they have due to the background potential (low star formation efficiency), efficient merging is inhibited. The transition to this slow regime happens with star formation efficiencies of around 0.25. Above this value the fast regime takes over. We could show that the very simple velocity criterion already proposed by Gerhard and Fall (1983) gives the correct answer for most of the parameter range. Then the behaviour of the merging is similar to the 'slow' (in contrary to the very fast exponential decrease) regime described already in Fellhauer et al. (2002). With the presence of a background potential the change towards the very fast regime happens at much larger filling factors as described in Fellhauer et al. (2002). In our standard setup the change happened at ratios between the scale-length of the clumps and the star forming region of about 0.2.
Furthermore, we show that in the area, the star cluster forms, the ratio between mass of stars and total mass is significantly higher than the over-all star formation efficiency, helping the formed star cluster to survive its gas-expulsion phase. We confirm the finding of McMillan et al. 2007 that the merging process conserves mass-segregation.
We then investigate if the general results for the merging time-scales, obtained by using a collision-less code (Fellhauer et al. 2009) are still valid, when re-simulated with a direct N-body code, taking the low number of stars and their interactions into account using the direct N-body code Nbody 6 ('topico' project of R. Slater). Smith et al. (2011b) found that in contrary to the results of Fellhauer et al. (2009) the merging happens fast, almost independent of the star formation efficiency (i.e. strength of the background potential) used. The sub-clumps get dissolved (instead of proper merging) as soon as they meet in the centre of the star forming region and thereby stick together. The study confirms that the very old results of Fellhauer et al. (2002) are valid in this low number regime independent of the background potential ('They hit they stick').
The results of this new study do not imply that the study of Fellhauer et al. (2009) are wrong, they just can not be applied to those low number systems. The simulations of P. Assmann for part 1.2 of this project confirm these results, when applied to high mass star clusters trying to merge in a very strong background potential (there a strong DM halo).
In a study of star cluster systems around an early-type dwarf galaxy, which falls into a galaxy cluster environment, we show that due to harassment we first have to strip about 90% of the DM before we loose the star clusters around the dwarf or stars from the dwarf itself. Even though the system is highly disturbed the error in estimating the mass from the velocity distribution of the SCs stays within a factor of 2 until almost total destruction of the system (Smith et al. 2013b).
This project was performed as a PhD-thesis by P. Assmann, who graduated at the end of March 2012. Parts of the project are an international collaboration with Prof. P. Kroupa in Bonn, Germany.
We propose a new scenario to explain the formation of dSph galaxies, combining two very standard theories. The first ingredient is the LambdaCDM formation scenario of structure formation in the universe. In this scenario, as seen for example in the Millennium II simulation of Boylan-Kolchin et al. (2009), we see that small dark matter (DM) haloes form first and later merge into larger entities. As dSph galaxies are supposedly residing in the smallest haloes, which were able to retain gas and form stars, they are regarded the basic building blocks of larger galaxies.
At same time it became clear, that stars do not form evenly distributed over a galaxy (e.g. Lada and Lada 2003), but in clumpy, hierarchical structures spanning from associations, open clusters all the way to globular clusters. If the star formation efficiency is low then these newly formed star clusters are not able to survive - they dissolve and spread their stars inside the galaxy.
In our models we combine the two approaches and simulate dissolving star clusters inside a DM halo. With our models we are able to explain many of the unusual features presented with dSph galaxies.
We investigate if the unusual massive star cluster (GC1) of the dwarf elliptical galaxy Scl-dE1 (Sc22) in Sculptor, could reside in its own dark matter halo and has evolved out of the merging of several star clusters (Assmann et al. 2011a). For this reason we investigated the merging of 2 star clusters in a dark matter halo of either cusped or cored shaped. The result of this study was that to achieve the observed parameters the mass of the halo has to be that low that it is at maximum comparable to the luminous mass or even less. The results are in agreement with the assumption that the star cluster does not reside in a dark matter halo of its own.
Assmann et al. (2011b) investigate the rapid dissolution of a single massive star cluster (due to gas-expulsion) in the tidal field of a Milky Way like galaxy. We are able to interpret the thick disc of the Milky Way solely out of dissolved massive star clusters in the past. A number of mechanisms have been previously proposed to explain the formation of the Milky Way's thick disc. These include a violent merging history, dynamical friction of infalling satellites or simple secular evolution of the disc. A new mechanism is proposed; star clusters orbit in the tidal field of the Milky Way potential and dissolve as a result of gas-expulsion and tidal interactions. This alone can produce the thick disc of the Milky Way.
Furthermore P. Assmann discovered a resonant behaviour in the distribution of stars of the dissolved star cluster on their first few orbits around the Milky Way, which she calls the Christmas-tree effect, which needs further investigation, because this effect has been observed in the dynamics of Milky Way stars.
We show that our models provide easy explanations for various observations found with dSph galaxies around the MW. Our models explain distorted contours, density centres which are not exactly located in the geometrical centre of the dwarf, multiple centres of densities as well as elongations and tails. On the dynamical side we can explain with our models both raising and falling velocity dispersions in the centre and the same for the outer parts. Due to effects what we call fossil remnants of the formation process we are able to explain bumps and wiggles in the velocity dispersion profile, which were until now regarded as errors in the measurements and we see effects which could mimic a velocity gradient throughout the dwarf without the need of a real tidal field, destroying the satellite.
In Assmann et al. (2013a) we describe our fiducial model. It shows a surface brightness distribution similar to the ones found with the classical dSph. The long-term evolution has erased most of the sub-structure from the dissolving star clusters (SCs). The scale-length is about 500 pc and the profile is close to exponential. It also shows a flat velocity dispersion profile, with an over-all dispersion of about 9 km/s. To achieve these values we used an NFW-halo with a somewhat lower mass than deduced from observations of real dSph. While those have about 10^7 M_sun within 300 pc, our model has 10^ M_sun within 500 pc. We introduce a measure named delta = Delta(v_mean,max) / sigma_500pc to quantify the velocity 'anomalies' stemming from the dissolved SCs (dubbed fossil remnants).
In Assmann et al. (2013b) we publish a parameter study and show how our initial parameters influence the results of the simulations. We see that the scale-length of the halo mainly influences the central brightness of our models, while the scale-length of the SC distribution influences the scale-length of the luminous component. We explore in which part of parameter space we see the largest velocity anomalies and identify which parameters lead to SCs surviving in the central areas of the luminous component.
At the same time M. Fellhauer was involved in an international cooperation with the group of Prof. P. Kroupa in Bonn, Germany. One joint project was the investigation of different mass-functions on the mass-loss, gas-expulsion and expansion rates for massive SCs leading to objects similar to UCDs (Dabringhausen et al. 2010).
M. Fellhauer was/is co-adviser in the PhD-project of C. Bruens (Bonn, Germany), dealing with merging and expanding SCs, forming faint fuzzy SCs (Bruens et al. 2009) and UCDs (Bruens et al. 2011). Even though C. Bruens has yet to finish her PhD, the parts of co-advising through M. Fellhauer are finalised.
M. Fellhauer was also part of the spectroscopic confirmation of the new dSph galaxy Bootes~II (Koch et al. 2009).
Recent observational data (deep images) shows that there seems no real connection between Ursa Major II and the Orphan Stream. Also measurements of the velocity dispersion of UMa II revealed a strong velocity gradient inside the dwarf galaxy. This could be a sign of rotation or a signal for tidal disruption. If it is the latter case this gives us new constraints for the orbit of the dwarf galaxy and new models without dark matter are needed to show if we can still reproduce the properties of the dwarf galaxy today. We find new sets of possible orbits, abandoning the possible connection to the Orphan Stream, Fellhauer et al. (2007) used in their models. Our model does reproduce the high velocity dispersion and the velocity gradient inside of UMa II. Furthermore, we match the shape and luminosity of the observed dwarf. We focused on a dark matter free progenitor as already Fellhauer et al. 2007 pointed out that with a dwarf embedded in an dark matter halo we loose all restricting parameters for the orbit. In such a case the elongation of UMa II must be due to intrinsic rotation and is not necessarily aligned with the orbit of the dwarf. We investigated further if our results are just possible because of a very lucky instant we see the dwarf or if it is a more general feature. We show in (Smith et al. 2013c) that there is regular boosting of the velocity dispersion around the apo-galacticon. A first version of the paper was submitted earlier but then withdrawn in the light of new results.
M. Blana ('topico project') investigated the minimal possible mass required to have Leo IV and Leo V forming a bound pair. Our results show that the minimum mass required for the pair to be bound is rather high - ranging from 2 x 10^9 M_sun to 4.5 x 10^10 M_sun (within the virial radius). Computing the mass in dark matter within the standard optical radius of 300 pc shows that our models are well within the predicted range of dark matter content for satellites that faint. We therefore conclude that it is indeed possible that the two galaxies form a bound pair (M. Blana et al.\ 2012).
M. Blana ('titulo' project) investigated models for the Hercules dSph galaxies using the orbit determined by Martin and Jin (2010). Through an error committed by misreading a figure in that paper, we could not find a suitable model at first. Finally, we found a suitable model which fits total magnitude, surface brightness, scale-length, velocity dispersion and velocity gradient and have submitted the manuscript (Blana et al. 2013). This paper for the first time investigates a larger parameter space and shows how the different parameter can be fitted by different regions in parameter space.
M. Fellhauer was part of an observational campaign to investigate the elongation of the Hercules dwarf (Deason et al. 2012a) together with the observational group in Cambridge, UK.
In the many models of P. Assmann's PhD thesis we find enough cases to explain all features of the classical dSph galaxies of the MW. We find tilted contours, off-centre density centres, multiple density centres, surviving star clusters orbiting the dwarf, wiggles and bumps in the velocity dispersion profile and are able to make predictions about future high-resolution observations. Still the data has to be analyzed more carefully and direct models matching each dwarf in detail have to be found. This is partly addressed in Assmann et al. (2013b) but this topic leaves room for much more interesting research.
This work is/was supported by the following grants: