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the central parsec of the galaxy harbors more than one hundred young massive stars ( see * ? ? ? * ; * ? ? ? * ; * ? ? ? * and references therein ) .
this is highly surprising , since the tidal forces from the central four million solar mass black hole should make formation of stars by gravitational collapse from a cold interstellar cloud very difficult , if not impossible @xcite .
most of the wr - stars and o - stars ( dwarfs , giants , and supergiants ) dominating the luminosity of the early - type population were formed in a well defined single event @xmath36 myrs ago , perhaps as the result of the infall of a gas cloud followed by an in - situ star formation event . about half of these wr / o - stars between 0.8  and 12  from sgra * reside in a well defined but highly warped and eccentric disk that rotates clockwise on the sky .
there exists a significant ( @xmath5 ) counter - clockwise structure of wr / o stars @xcite , perhaps a second disk in a dissolving state . within about 1  of sgra * there is a sharp cutoff in the density of wr / o - stars .
instead there is a concentration of fainter stars ( b dwarfs ) with randomly oriented and eccentric orbits : the so - called s - star cluster @xcite .
( red triangles , scaled by a factor 0.05 ) , @xmath6 ( blue points ) and @xmath7 ( black asterisks)._,title="fig : " ]   ( red triangles , scaled by a factor 0.05 ) , @xmath6 ( blue points ) and @xmath7 ( black asterisks)._,title="fig : " ]    [ fig1 ]    figure [ fig1 ] ( left ) shows the projected , completeness and coverage corrected surface density profiles for various stellar populations .
the radial surface density of the clockwise wr / o - stars follows a power law @xmath8 between 0.8  and 15  .
the surface density distribution of the counter - clockwise wr / o - stars is flat between 0.8  and 15  with a larger central hole than the one of the clockwise stars and a shallow maximum at around 4.5  .
the radial surface density profile of b - dwarfs in the magnitude interval @xmath9 drops smoothly from the central 0.8  , where the s - stars reside , out to about 25  .
the distribution is similar to the clockwise wr / o - stars with a best - fitting power law of @xmath10 . in strong contrast to the early - type stars , late - type stars with @xmath11 exhibit a flat surface density distribution inside of 10 
( see also * ? ? ?
* ; * ? ? ?
figure [ fig1 ] ( right ) shows the completeness corrected k - band luminosity functions of early - type stars in three radial intervals together with three theoretical model luminosity functions based on different imfs , computed with the population synthesis code stars @xcite .
we assumed a cluster age of 6 myrs , and an exponentially decaying star burst with an @xmath12 time - scale of 1 myrs .
this is the best - fitting age and duration of a single star formation event derived from the hertzsprung - russell diagram distribution of the o / b - stars and the ratios of various sub - types of wr - stars @xcite .
the klf in the radial interval @xmath6 can be fitted by a power - law imf of @xmath2 ( the salpeter imf is @xmath13 ) .
the imf found by @xcite for their @xmath14 cloud simulation fits our data reasonably well .
the imf of the field early - type stars beyond 12  and the s - stars within 0.8  can be fitted by @xmath4 .
these latter klfs can also be fitted by salpeter / kroupa imfs and continuous star formation histories with moderate ages ( @xmath15 myrs ) .
most of the stars with @xmath16 are b dwarfs , the brighter magnitude bins contain o dwarfs , giants and wr stars .
the main sequence ends at about @xmath17 , corresponding to stars with initial masses of about @xmath18 with main - sequence lifetimes of 6 myr .
an @xmath19 early - type star for a 6 myr old population corresponds approximately to a b5v main sequence star with a zams mass of about @xmath20 ( see figure [ fig1 ] right ) .
the most massive stars with individual mass estimates have zams masses of at least @xmath21 @xcite .
our estimated imf slope of the stellar disks ( @xmath2 ) is therefore at least valid over the mass interval @xmath22 .
50 out of 110 stars with @xmath23 have an angular offset to the local average angular momentum direction of the clockwise system @xcite , below @xmath24 and 8 out of 15 stars with @xmath25 have offsets below @xmath24 .
in contrast , only one out of 11 stars fainter than @xmath26 is compatible with the clockwise disk .
this may be an indication that most of the few later b - dwarfs observed in the region of the disks do not belong to the clockwise system , but rather to the background population seen at projected distances beyond 12  , which has a more standard imf .
the observations suggest that the two wr / o / b - star disks ( or planar sets of streamers ) between 0.8  and 12  are structurally and dynamically distinct from both the s - star cluster and the outer region .
the properties of these warped disks , including in particular their steep surface density distribution , their top - heavy imf ( see also * ? ? ?
* ) , and their relatively low total stellar masses all strongly favor an in situ star formation model @xcite and broadly agree with the findings of recent hydrodynamical simulations @xcite of star formation triggered by infalling gas clouds . the sharp transition at 0.8  between disk zone and s - star cluster , both in terms of dynamics and mass function , in our opinion also strongly disfavors migration scenarios from the disks for the origin of the s - star cluster .
in turn , this sharp transition supports injection and capture scenarios ( e.g. * ? ? ? * ; * ? ? ? * ) .
the large central core @xcite of late - type stars is puzzling and currently not understood .
there are a number of possible interpretations , none of which at present offers a compelling explanation : equilibrium mass segregation by itself can not account for this distribution @xcite .
physical collisions with main - sequence stars and stellar black holes can remove moderately bright giants in the central arcsecond , but not over a much larger region , nor to @xmath27 @xcite .
tidal disruption of stars may play a role in the immediate vicinity of the massive black hole @xcite , but most likely can not be an explanation for the lack of an old cusp on the  0.5 pc scale .
the in - spiral of an intermediate mass black hole can plausibly gouge out a large enough core in the stellar distribution @xcite but no direct evidence for such a second black hole was found @xcite .
if the two - body relaxation time scale is significantly longer than the age of the galactic center star cluster ( and the hubble time ) throughout the central parsec @xcite the observed large core may reflect the initial conditions of the galactic center nuclear cluster , but the dynamics of the old star cluster is consistent with a relaxed , fully phase - mixed system @xcite .
in addition , there may be relaxation processes much faster than the standard two - body rate @xcite .
the top - heavy imf discussed here ( if applicable to earlier star formation episodes ) would obviously also lead to a lack of old low mass giants in the core , but the imf probably would have to depend strongly on radius .
the remarkable properties of the galactic center nuclear star cluster remain puzzling and continue to give us food for thought and further work .
we summarize our latest observations of the nuclear star cluster in the central parsec of the galaxy with the adaptive optics assisted , integral field spectrograph sinfoni on the eso / vlt , which result in a total sample of 177 bona fide early - type stars . 
 we find that most of these wolf rayet ( wr ) , o- and b- stars reside in two strongly warped eccentric ( @xmath0 ) disks between 0.8  and 12  from sgra * , as well as a central compact concentration ( the s - star cluster ) centered on sgra*. the later type b stars ( @xmath1 ) in the radial interval between 0.8  and 12  seem to be in a more isotropic distribution outside the disks . 
 we observe a dearth of late - type stars in the central few arcseconds , which is puzzling . 
 the stellar mass function of the disk stars is extremely top - heavy with a best fit power law of @xmath2 . since at least the wr / o - stars were formed in situ in a single star formation event @xmath36 myrs ago , this mass function probably reflects the initial mass function ( imf ) . 
 the mass functions of the s - stars inside 0.8  and of the early - type stars at distances beyond 12  differ significantly from the disk imf ; they are compatible with a standard salpeter / kroupa imf ( best fit power law of @xmath4 ) .