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tokens: the same is not necessarily true for the standoff radius. In Fig. 3 we plot the standoff radius versus orbital radius. The standoff radius near the pericentre may not be resolvable, although at larger distances from Sgr A* the likelihood for resolving the source increases. It is also worth noting that we calculated the thermal free–free emission around Sgr A* and concluded that it is not detectable. Figure 3. Left: the standoff radius for S2 ( R o ) versus the orbital radius ( R ⋆ in units of 10 −3 pc). We see that the value is always less than unity, as expected. Right: angular diameter of the standoff radius (θ o ) versus the angular diameter of the orbital radius (θ ⋆ ). Around pericentre it may be difficult to resolve the finite size of the standoff radius. However, S2 should still be detectable via synchrotron emission. 4 CONCLUSIONS AND FUTURE OBSERVATIONS The innermost stars orbiting Sgr A* (such as the S-stars) produce a bow shock. Although this shock will likely not be detectable via thermal emission, we have shown that stars such as S2 may be detectable via synchrotron emission. Fig. 1 shows that the contrast of synchrotron flux relative to Sgr A* is maximized around the 1.4 GHz band. However, due to scattering we will need to use a higher frequency, around 10 GHz, if we are to resolve our star. If a star such as S2 emits strong synchrotron emission, the combined signal from the star and Sgr A* may exceed the quiescent radio emission from the black hole. As was the case with G2 (see next paragraph) it is not clear that any additional synchrotron emission will be observable. Arguably, it is best to resolve the synchrotron emission from any star orbiting Sgr A*, such as S2. At apoapse S2 is ∼0.23 arcsec from Sgr A* while at periapse it is only ∼0.015 arcsec away. Thus, to detect a star such as S2 requires both good sensitivity and resolution. VLBI can provide submilliarcsec observations of Sgr A* (e.g. Lu et al. 2011 ) and thus the required precision. S2 is an ideal test case since the star will reach periapse in 2017 or early 2018. Recently, gas cloud G2 was observed orbiting Sgr A*, and was approximately 3100 Schwarzschild radii from the black hole at pericentre. It was predicted that the bow shock from this encounter would displace the quiescent radio emission of Sgr A* by ∼33 mas (Narayan, Özel Sironi 2012 ; Sadowski et al. 2013 ). However, observations across the spectrum showed no apparent variability during the periastron passage of G2 (Bower et al. 2015 ; Valencia-S et al. 2015 ). It is unclear why a bow shock was not detected. One possibility is that at the centre of G2 is low-mass star with wind velocity ∼100 km s −1 (Crumley Kumar 2013 ; Scoville Burkert 2013 ). Synchrotron emission from such a small v w would be extremely difficult to detect. Star S2 is massive, and thus the winds are likely an order of magnitude larger. If synchrotron emission is not detected for S2 it may be that our value for ε nt is too large. It