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S62 and S4711: Indications of a population of faint fast moving stars inside the S2 orbit -- S4711 on a 7.6 year orbit around Sgr~A*

We present high-pass filtered NACO and SINFONI images of the newly discovered stars S4711-S4715 between 2004 and 2016. Our deep H+K-band (SINFONI) and K-band (NACO) data show the S-cluster star S4711 on a highly eccentric trajectory around Sgr~A* with an orbital period of 7.6 years and a periapse distance of 144 AU to the super massive black hole (SMBH). S4711 is hereby the star with the shortest orbital period and the smallest mean distance to the SMBH during its orbit to date. The used high-pass filtered images are based on co-added data sets to improve the signal to noise. The spectroscopic SINFONI data let us determine detailed stellar properties of S4711 like the mass and the rotational velocity. The faint S-cluster star candidates, S4712-S4715, can be observed in a projected distance to Sgr~A* of at least temporarily $\leq$ 120 mas. From these stars, S4714 is the most prominent one with an orbital period of 12 years and an eccentricity of 0.985. The stars S4712-S4715 show similar properties with comparable magnitudes and stellar masses to S4711. The MCMC simulations determine confidently precise uncertainties for the orbital elements of S62 and S4711-S4715. The presence of S4711 in addition to S55, S62, and the also newly found star S4714 implies a population of faint stars that can be found at distances to Sgr~A* that are comparable to the size of our solar system. These short orbital time period stars in the dense cluster around the SMBH in the center of our Galaxy are perfect candidates to observe gravitational effects such as the periapse shift.