For a density that is not too sharply peaked towards the center , the local tidal field becomes compressive in all three directions .
Available gas can then collapse and form a cluster of stars in the center , including or even being dominated by a central black hole .
We show that for a wide range of ( deprojected ) Sérsic profiles in a spherical potential , the tidal forces are compressive within a region which encloses most of the corresponding light of observed nuclear clusters in both late-type and early-type galaxies .
In such models , tidal forces become disruptive nearly everywhere for relatively large Sérsic indices n \gtrsim 3.5 .
We also show that the mass of a central massive object ( CMO ) required to remove all radial compressive tidal forces scales linearly with the mass of the host galaxy .
If CMOs formed in ( progenitor ) galaxies with n \sim 1 , we predict a mass fraction of \sim 0.1 - 0.5 % , consistent with observations of nuclear clusters and super-massive black holes .
While we find that tidal compression possibly drives the formation of CMOs in galaxies , beyond the central regions and on larger scales in clusters disruptive tidal forces might contribute to prevent gas from cooling .