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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 asignificant correction. Core galaxies, typically with M_bh > 2x10^8 M_Sun andthought to be formed in dry merger events, are shown to be well described by alinear relation for which the median black hole mass is 0.36% - roughly doublethe old value of constancy. Of greater significance is that M_bh ~ (M_sph)^2among 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' spheroidshosting a 10^6 M_Sun black hole will have M_bh/M_sph ~ 0.025%. These newrelations (i) bring consistency to the relation M_bh ~ sigma^5 and the factthat 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 inthe M_bh-(Sersic n) diagram, (iii) necessitate the existence of a previouslyover-looked M_bh ~ L^{2.5} relation for Sersic (i.e.\ not core-Sersic)galaxies, and (iv) resolve past conflicts (in mass prediction) with theM_bh-sigma relation at the low-mass end. Furthermore, the bent nature of theM_bh-M_sph relation for `classical' spheroids will have a host of importantimplications that relate to (i) galaxy/black hole formation theories, (ii)searches for the fundamental black hole scaling relation, (iii) black hole masspredictions in other galaxies, (iv) alleged pseudobulge detections, (v)estimates of the black hole mass function and mass density based on luminosityfunctions, (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 andcalibrations matching inactive black hole masses with low-mass AGN data, andmore.

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