Breaking the law: the M_{bh}-M_{spheroid} mass relations for core-Sersic and Sersic galaxies

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 > 2x10^8 M_Sun 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 ~ (M_sph)^2 among the (non-pseudobulge) lower-mass systems: specifically, log[M_bh/M_Sun] = (1.92+/-0.38)log[M_sph/7x10^{10}M_Sun] + (8.38+/-0.17). `Classical' spheroids hosting a 10^6 M_Sun black hole will have M_bh/M_sph ~ 0.025%. These new relations (i) bring consistency to the relation M_bh ~ sigma^5 and the fact that L ~ sigma^x with exponent x equal to 5 and 2 for bright (M_B < -20.5 mag) and faint spheroids, respectively, (ii) mimic the non-(log-linear) behavior in the M_bh-(Sersic n) diagram, (iii) necessitate the existence of a previously over-looked M_bh ~ L^{2.5} relation for Sersic (i.e.\ not core-Sersic) 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 for `classical' spheroids will have a host of important implications that relate to (i) galaxy/black hole formation theories, (ii) searches for the fundamental 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.