The popular log-linear relation between supermassive black hole mass , M _ { bh } , and the dynamical mass of the host spheroid , M _ { sph } , is shown to require a significant correction .
Core galaxies , typically with M _ { bh } \gtrsim 2 \times 10 ^ { 8 } M _ { \odot } and thought to be formed in dry merger events , are shown to be well described by a linear relation for which the median black hole mass is 0.36 % — roughly double the old value of constancy .
Of greater significance is that M _ { bh } \propto M _ { sph } ^ { 2 } among the ( non-pseudobulge ) lower-mass systems : specifically , \log [ M _ { bh } / M _ { \odot } ] = ( 1.92 \pm 0.38 ) \log [ M _ { sph } / 7 \times 10 ^ { 10 } M _ { % \odot } ] + ( 8.38 \pm 0.17 ) .
‘ Classical ’ spheroids hosting a 10 ^ { 6 } M _ { \odot } black hole will have M _ { bh } / M _ { sph } \sim 0.025 % .
These new relations presented herein ( i ) bring consistency to the relation M _ { bh } \propto \sigma ^ { 5 } and the fact that L \propto \sigma ^ { x } with exponents of 5 and 2 for bright ( M _ { B } \lesssim - 20.5 mag ) and faint spheroids , respectively , ( ii ) mimic the non- ( log-linear ) behavior known to exist in the M _ { bh } – ( Sérsic n ) diagram , ( iii ) necessitate the existence of a previously over-looked M _ { bh } \propto L ^ { 2.5 } relation for Sérsic ( i.e .
not core-Sérsic ) galaxies , and ( iv ) resolve past conflicts ( in mass prediction ) with the M _ { bh } – \sigma relation at the low-mass end .
Furthermore , the bent nature of the M _ { bh } – M _ { sph } relation reported here for ‘ classical ’ spheroids will have a host of important implications that , while not addressed in this paper , relate to ( i ) galaxy/black hole formation theories , ( ii ) searches for the fundamental , rather than secondary , black hole scaling relation , ( iii ) black hole mass predictions in other galaxies , ( iv ) alleged pseudobulge detections , ( v ) estimates of the black hole mass function and mass density based on luminosity functions , ( vi ) predictions for space-based gravitational wave detections , ( vii ) connections with nuclear star cluster scaling relations , ( viii ) evolutionary studies over different cosmic epochs , ( ix ) comparisons and calibrations matching inactive black hole masses with low-mass AGN data , and more .