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 \lesssim 0.5 pc from Sagittarius A* can be described consistently by a single power law with an exponent of \Gamma = 0.26 \pm 0.02 _ { stat } \pm 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 } \approx 19 - 22 with masses of 0.8 - 1.5 M _ { \odot } .
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 \pm 0.03 _ { model } \pm 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 \pm 0.3 \times 10 ^ { 7 } M _ { \odot } pc ^ { -3 } and a total enclosed stellar mass of 180 \pm 30 M _ { \odot } .
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 \lesssim 0.3 pc implies that some mechanism may have altered their appearance or distribution .