tokens: We thank Maxim Makukov, Chingis Omarov, Emmanuil Y. Vilkoviskij and Ari Laor for valuable comments, discussion, support and supervision. We also thank the anonymous referee for useful comments and suggestions. This work has benefitted very much from funding of exchange and collaboration between Germany and Kazakhstan by Volkswagen Foundation under the project ‘STARDISK – Simulating Dense Star-Gas Systems in Galactic Nuclei using special hardware’ (I/81 396). GRAPE and GPU hardware at Fesenkov Astrophysical Institute in Kazakhstan used for this work have been supported by the STARDISK project too. We acknowledge support from the Strategic Priority Research Program ‘The Emergence of Cosmological Structure’ of the Chinese Academy of Sciences (No. XDB09000000) (Pilot B programme). We acknowledge support by Chinese Academy of Sciences through the Silk Road Project at NAOC, through the Chinese Academy of Sciences Visiting Professorship for Senior International Scientists, Grant Number 2009S1-5 (RS), and through the ‘Qianren’ special foreign experts programme of China. RS has also been partially supported by NSFC (National Natural Science Foundation of China), grant no. 11073025. GK acknowledges a Chinese Academy of Sciences Young International Postdoctoral Fellowship Grant No. 2011Y2JB09. YM acknowledges support from the China Postdoctoral Science Foundation through grant no. 2015T80011 and from excellence initiative at the University of Heidelberg, through mobility measures for international research collaborations project no. 7.1.47, and the European Research Council under the European Union's Horizon 2020 Programme, ERC-2014-STG grant GalNUC 638435. PB acknowledges the special support by the NASU under the Main Astronomical Observatory GRID/GPU computing cluster project. The special GPU accelerated supercomputer laohu at the Center of Information and Computing at National Astronomical Observatories, Chinese Academy of Sciences, funded by Ministry of Finance of People's Republic of China under the grant ZDYZ2008-2, has been used for some of the largest simulations. We also used smaller GPU clusters titan , hydra and kepler , funded under the grants I/80041-043 and I/84678/84680 of the Volkswagen Foundation and grants 823.219-439/30 and /36 of the Ministry of Science, Research and the Arts of Baden-Württemberg, Germany.
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