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

Context. The density of the ambient medium around a supermassive black hole (SMBH) and the way it varies with distance plays an important role in our understanding of the inflow-outflow mechanisms in the Galactic centre (GC). This dependence is often fitted by spherical power-law profiles based on observations in the X-ray, infrared (IR), submillimetre (submm), and radio domains. Aims. Nevertheless, the density profile is poorly constrained at the intermediate scales of 1000 Schwarzschild radii (R_s). Here we independently constrain the spherical density profile using the stellar bow shock of the star S2 which orbits the SMBH at the GC with the pericentre distance of 14.4 mas (∼1500 R_s). Methods. Assuming an elliptical orbit, we apply celestial mechanics and the theory of bow shocks that are at ram pressure equilibrium. We analyse the measured IR flux density and magnitudes of S2 in the L′-band (3.8 micron) obtained over seven epochs in the years between 2004–2018. We put an upper limit on the emission from S2's associated putative bow shock and constrain the density profile of the ambient medium. Results. We detect no significant 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 the dust-extinction model, the upper limit on the number density at the S2 periapse is ∼1.87  ×  10⁹ cm⁻³, which yields a density slope of at most 3.20. Using the synchrotron bow-shock emission, we obtain the ambient density of ≲1.01  ×  10⁵ cm⁻³ and a slope of ≲1.47. These values are consistent with a wide variety of media from hot accretion flows to potentially colder and denser media comparable in properties to broad-line-region clouds. However, a standard thin disc can be excluded at the distance of S2's pericentre. Conclusions. With the current photometry sensitivity of 0.01 mag, we are not able to make stringent constraints on the density of the ambient medium in the GC using S2-star observations. We can distinguish between hot accretion flows and thin, cold discs, where the latter can be excluded at the scale of the S2 periapse. Future observations of stars in the S cluster using instruments such as Mid-IR Extremely Large Telescope Imager and Spectrograph at Extremely Large Telescope with the photometric sensitivity of as much as 10⁻³ mag will allow the GC medium to be probed at intermediate scales at densities as low as ∼700 cm⁻³ in case of non-thermal bow-shock emission. The new instrumentation, in combination with discoveries of stars with smaller pericentre distances, will help to independently constrain the density profile around Sagittarius A* (Sgr A*). [ABSTRACT FROM AUTHOR]