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tokens: least three distinct components, when stars are grouped by their spectral types and kinematics (e.g. Genzel et al. 2010 , section II). We choose to examine the limiting case of a Bahcall–Wolf cusp with γ = 0, which is analytically tractable and roughly matches the observed, slightly flatter density profile of the entire visible stellar population (e.g. Genzel et al. 2003 ; Bartko et al. 2010 ), as well as the observed distribution of diffuse light (e.g. Schödel et al. 2017 ), emanating from stars that could plausibly be old enough to be dynamically relaxed. Figure 3. The on-sky trajectories of the stars S1, S2, S9, and S13 over the time of simulated observations (solid and dashed lines), starting in the year 2000 and covering exactly one orbital period of S2 [approx. 16 yr, see Gillessen et al. ( 2017 ) for measurements of the orbital elements], overlaid on a snapshot of a sample realization of the distribution of background stars (shown as points) and their average light distribution (shown in colour). In the inner region of the nuclear cluster, stars move to good approximation like test particles in a point mass potential Φ( r ) = − GM 0 / r created by the central supermassive black hole, which has a canonical mass of M 0 ≈ 4 × 10 6 M ⊙ , and is located at a distance of R 0 ≈ 8 kpc from the Sun. To be in a stable configuration, these stars must be on bound, effectively Keplerian orbits, which can be defined by six orbital elements. The required distribution of the semi-major axes a = GM 0 /2ε of the background stars, to generate a realization of a Keplerian Bahcall–Wolf cusp, is (Schödel et al. 2003 ; Alexander 2005 ) The corresponding number density profile is . To ensure numerically that in our simulations the correct surface density profile is reproduced within the central square arcsecond, an upper cut-off of this distribution at a = 2 arcsec is sufficient. Any stars with larger semi-major axes are unlikely to be found very close to the central black hole, even in projection. We do not impose a strict lower cut-off, but exclude very few stars with a minimum (pericentre) distance r p = a (1 − e ) r t from the black hole, where r t is the approximate tidal radius of a typical observed B-type star in the Galactic Centre (e.g. Habibi et al. 2017 ): The required distributions of the eccentricity e , the inclination of the orbital plane i , the angle of the ascending node Ω, and the argument of pericentre ω, the specific forms of which encode the assumption of isotropy for the stellar velocities and positions, are the following: The time of pericentre has to be sampled uniformly over the duration of one orbital period, which, in turn, depends on the semi-major axis: The reference epoch t 0 = 2000 is arbitrary, but chosen to coincide roughly with the beginning of Galactic Centre observations using advanced high-resolution observing techniques, specifically adaptive optics imaging and integral field spectroscopy. Magnitudes are assigned to the