Star formation in the GC: observational constraints and theory

We review some observational aspects and theoretical models for the formation of the young massive stars in the central parsec of our Galaxy. It is concluded that an in-situ star formation model provides the best description of the data. One possible guess for the initial gas confguration is one circular and another eccentric gas discs, not necessarily coeval during their short lifetimes. The circular disc probably resulted from a mass deposition event long compared with the local orbital time, whereas the eccentric disc should have formed more dynamically. Based on X-ray observations of the GC, we argue that the initial mass function (IMF) of stars formed in these discs is top-heavy. Such top-heavy IMF is most likely a result of inefficiency with which these optically thick discs fragment, and thus may be a generic result for star-forming AGN discs. We also present preliminary results of numerical simulations of star forming discs, showing that stars with a top-heavy IMF can be formed in both circular and eccentric discs. However, the inner arcsecond ''S-stars'', and the massive star cluster IRS13E, do not naturally form in these star-forming discs, and still lack explanation.