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The density profile of the ambient medium around a supermassive black holeplays an important role in understanding the inflow-outflow mechanisms in theGalactic Centre. We constrain the spherical density profile using the stellarbow shock of the star S2 which orbits the supermassive black hole at theGalactic Centre with the pericentre distance of 14.4 mas ($\sim$ 1500R$_\text{s}$). Assuming an elliptical orbit, we apply celestial mechanics andthe theory of bow shocks that are at ram pressure equilibrium. We analyse themeasured infrared flux density and magnitudes of S2 in the L'-band (3.8 micron)obtained over seven epochs in the years between 2004-2018. We detect nosignificant change in S2 flux density until the recent periapse in May 2018.The intrinsic flux variability of S2 is at the level of 2 - 3%. Based on thedust-extinction model, the upper limit on the number density at the S2 periapseis $\sim$1.87$\times$10$^9$ cm$^{-3}$, which yields a density slope of at most3.20. Using the synchrotron bow-shock emission, we obtain an ambient density of$\leq$ 1.01$\times$10$^5$ cm$^{-3}$ and a slope of $\leq$ 1.47. These valuesare consistent with a wide variety of media from hot accretion flows topotentially colder and denser media comparable in properties to broad-lineregion clouds. A standard thin disc can be, however, excluded at the distanceof the S2 pericentre. Based on our sensitivity of 0.01 mag, we can distinguishbetween hot accretion flows and thin, cold discs, where the latter can beexcluded at the scale of the S2 periapse. Future observations of stars withsmaller pericentre distances in the S cluster using instruments such asMETIS@ELT with a photometric sensitivity of as much as 10$^{-3}$ mag will allowto probe the Galactic Centre medium at intermediate scales at densities as lowas $\sim$ 700 cm$^{-3}$ in case of non-thermal bow-shock emission.

Constraining the accretion flow density profile near Sgr A* using the $L'$-band emission of the S2 star