ner_tags: O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation O B-Citation I-Citation I-Citation I-Citation O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Model I-Model O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O B-Wavelength O O O O O B-Wavelength O O O O O O O O O O O B-Wavelength O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O B-Wavelength O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O B-Wavelength O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O
tokens: Fig. 7 ). Figure 7. The surface density profile (top panel) and the K -band luminosity function (bottom panel) of early- and late-type stars in the Galactic Centre. The points mark the stellar number counts in distance and magnitude bins, as indicated by the horizontal error bars, and the vertical error bars indicate Poisson standard errors of the bin counts. For model fitting, the unbinned values are used (see Section 4.2 ). We can reproduce and confirm the results of Buchholz et al. ( 2009 ) and other studies of the spatial distribution of stars in the Galactic Centre (e.g. Paumard et al. 2006 ; Bartko et al. 2009 ; Do et al. 2009 , 2013 ; Lu et al. 2009 ). Following Do et al. ( 2013 , appendix E), we determine the respective surface density profiles by means of Bayesian inference, using a power-law profile as a model (Σ ∝ R α ). This approach does not require binning the star counts, and allows taking into account the estimated class membership probabilities as weights. For the late-type stars, we find a rather flat density profile (α = −0.33 ± 0.05), which appears essentially core-like towards the very centre. This still presents a puzzle, because these stars are old enough to be relaxed and would be expected to form a significantly steeper Bahcall Wolf ( 1976 ) cusp in that case (−0.75 α −0.5, but see Gallego-Cano et al. 2018 ; Schödel et al. 2018 ). For the early-type stars, we find a broken power-law profile with a turnover radius at about 10 arcsec, which we interpret as the outer edge of the young stellar disc (see Støstad et al. 2015 ). Within that radius, the surface density profile has a well-defined index of α = −0.83 ± 0.10, or α = −1.00 ± 0.15 if we exclude the central S-star cluster (at R 1 arcsec). Beyond that radius, the number of early-type stars drops rapidly. We can also reproduce the results of previous studies focused on the stellar K -band luminosity function (KLF). For the late-type stars with K 14.5, i.e. if we exclude red clump stars, we find a KLF well-described by a relation N ∝ 10 β K with an index of β = 0.36 ± 0.02, which is similar to that of the Galactic bulge (e.g. Genzel et al. 2003 ; Buchholz et al. 2009 ). The KLF of the early-type stars appears to be top-heavy in the disc region (1 arcsec ≲ R ≲ 10 arcsec), as also found by Paumard et al. ( 2006 ), Buchholz et al. ( 2009 ), and Bartko et al. ( 2010 ). The question of whether the KLF of these stars is indeed flat or somewhat steeper at the faint end, as found by Do et al. ( 2013 ), can likely be answered conclusively only on the basis of spectroscopic observations with a high completeness for B-stars over the entire region, which is currently only reached by deep imaging observations (e.g. ). 5 CONCLUSIONS For a proof of concept, we have constructed a machine-trained, random forest classifier to identify early- and late-type stars in the environment of the Galactic Centre black hole, based on intermediate-band photometry using seven filters in the