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There is a growing array of supermassive black hole and nuclear star clusterscaling relations with their host spheroid, including a bent (black holemass)-(host spheroid mass) M_bh-M_sph relation and different (massive compactobject mass)-(host spheroid velocity dispersion) M_mco-sigma relations forblack holes and nuclear star clusters. By combining the observed M_bh ~sigma^(5.5) relation with the observed M_nc ~ sigma^(1.6--2.7) relation, wederive the expression M_bh ~ (M_nc)^(2--3.4), which should hold until thenuclear star clusters are eventually destroyed in the larger core-Sersicspheroids. This new mass scaling relation helps better quantify the rapidevolutionary growth of massive black holes in dense star clusters, and therelation is consistently recovered when coupling the observed M_nc ~(M_sph)^(0.6--1.0) relation with the recently observed quadratic relation M_bh~ (M_sph)^2 for Sersic spheroids.

Black hole and nuclear cluster scaling relations: M_bh ~ M_nc^{2.7+/-0.7}