We analyse and report in detail new near-infrared (1.45 - 2.45 microns) observations of the Dusty S-cluster Object (DSO/G2) during its approach to the black hole at the center of the Galaxy that were carried out with ESO VLT/SINFONI between February and September 2014. Before May 2014 we detect spatially compact Br-gamma and Pa-alpha line emission from the DSO at about 40mas east of SgrA*. The velocity of the source, measured from the red-shifted emission, is 2700+-60 km/s. No blue-shifted emission above the noise level is detected at the position of SgrA* or upstream the presumed orbit. After May we find spatially compact Br-gamma blue-shifted line emission from the DSO at about 30mas west of SgrA* at a velocity of -3320+-60 km/s and no indication for significant red-shifted emission. We do not detect any significant extension of velocity gradient across the source. We find a Br-gamma-line full width at half maximum of 50+-10 Angstroem before and 15+-10 Angstroem after the peribothron transit, i.e. no significant line broadening with respect to last year is observed. Br-gamma line maps show that the bulk of the line emission originates from a region of less than 20mas diameter. This is consistent with a very compact source on an elliptical orbit with a peribothron time passage in 2014.39+-0.14. For the moment, the flaring activity of the black hole in the near-infrared regime has not shown any statistically significant increment. Increased accretion activity of SgrA* may still be upcoming. We discuss details of a source model according to which the DSO is rather a young accreting star than a coreless gas and dust cloud.
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