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.
