The distribution of stars around the Milky Way's central black hole II. Diffuse light from sub-giants and dwarfs

Context. This is the second of three papers that search for the predicted stellar cusp around the Milky Way's central black hole, Sagittarius A*, with new data and methods. Aims. We aim to infer the distribution of the faintest stellar population currently accessible through observations around Sagittarius A*. Methods. We used adaptive optics assisted high angular resolution images obtained with the NACO instrument at the ESO VLT. Through optimised PSF fitting we removed the light from all detected stars above a given magnitude limit. Subsequently we analysed the remaining, diffuse light density. Systematic uncertainties were constrained by the use of data from different observing epochs and obtained with different filters. We show that it is necessary to correct for the diffuse emission from the mini-spiral, which would otherwise lead to a systematically biased light density profile. We used a Paschen alpha map obtained with the Hubble Space Telescope for this purpose. Results. The azimuthally averaged diffuse surface light density profile within a projected distance of R less than or similar to 0.5 pc from Sagittarius A* can be described consistently by a single power law with an exponent of Gamma = 0.26 +/- 0.02(stat) +/- 0.05(sys), similar to what has been found for the surface number density of faint stars in Paper I. Conclusions. The analysed diffuse light arises from sub-giant and main-sequence stars with K-s approximate to 19 22 with masses of 0.8-1.5 M-circle dot. These stars can be old enough to be dynamically relaxed. The observed power-law profile and its slope are consistent with the existence of a relaxed stellar cusp around the Milky Way's central black hole. We find that a Nuker law provides an adequate description of the nuclear cluster's intrinsic shape (assuming spherical symmetry). The 3D power-law slope near Sgr A* is gamma = 1.13 +/- 0.03(model) +/- 0.05(sys). The stellar density decreases more steeply beyond a break radius of about 3 pc, which corresponds roughly to the radius of influence of the massive black hole. At a distance of 0.01 pc from the black hole, we estimate a stellar mass density of 2.6 +/- 0.3 x 10(7) M-circle dot pc(-3) and a total enclosed stellar mass of 180 +/- 30 M circle dot. These estimates assume a constant mass-to-light ratio and do not take stellar remnants into account. The fact that a flat projected surface density is observed for old giants at projected distances R less than or similar to 0.3 pc implies that some mechanism may have altered their appearance or distribution.