Presence of a Fundamental Acceleration Scale in Galaxy Clusters

An acceleration scale of order $10^{-10}\mathrm{m/s^2}$ is implicit in the baryonic Tully-Fisher and baryonic Faber-Jackson relations, independently of any theoretical preference or bias. We show that the existence of this scale in the baryonic Faber-Jackson relation is most apparent when data from pressure supported systems of vastly different scales including globular clusters, elliptical galaxies, and galaxy clusters are analyzed together. This suggests the relevance of the acceleration scale $10^{-10}\mathrm{m/s^2}$ to structure formation processes at many different length scales and could be pointing to a heretofore unknown property of dark matter.