Abstract
In this work I use astrometric and spectroscopic data on the S2 star at the Galactic centre (GC) up to 2016 to derive specific constraints on the size of a dark matter (DM) spike around the central supermassive black hole Sgr A*. These limits are the best direct constraints on a DM spike at the GC for non-annihilating dark matter and exclude a spike with radius greater than a few tens of parsecs for cuspy outer halos and a few hundred parsecs for cored outer halos.