Effect of an isotropic outflow from the Galactic centre on the bow-shock evolution along the orbit

Motivated by the observations of several infrared-excess bow-shock sources and proplyd-like objects near the Galactic centre, we analyse the effect of a potential outflow from the centre on bow shock properties. We show that due to the non-negligible isotropic central outflow the bow-shock evolution along the orbit becomes asymmetric between the pre-peribothron and post-peribothron phases. This is demonstrated by the calculation of the bow-shock size evolution, the velocity along the shocked layer, the surface density of the bow-shock, and by emission-measure maps close to the peribothron passage. Within the ambient velocity range of $\lesssim 2000\,{\rm km\, s^{-1}}$ the asymmetry is profound and the changes are considerable for different outflow velocities. As a case study we perform model calculations for the Dusty S-cluster Object (DSO/G2) as a potential young stellar object that is currently being monitored and has passed the pericentre at $\sim 2000$ Schwarzschild radii from the supermassive black hole (Sgr A*) in 2014. We show that the velocity field of the shocked layer can contribute to the observed increasing line width of the DSO source up to the peribothron. Subsequently, supposing that the line emission originates in the bow shock, a decrease of the line width is expected. Furthermore, the decline of the bow-shock emission measure in the post-peribothron phase could help to reveal the emission of the putative star. The dominant contribution of circumstellar matter (either inflow or outflow) is consistent with the observed stable luminosity and compactness of the DSO/G2 source during its pericentre passage.