Splitting the lentils: Clues to galaxy/black hole coevolution from the discovery of offset relations for non-dusty versus dusty (wet-merger-built) lenticular galaxies in the $M_{\rm bh}$-$M_{\rm *,spheroid}$ diagram

This work advances the (galaxy morphology)-dependent (black hole mass, $M_{\rm bh}$)-(spheroid/galaxy stellar mass, $M_*$) scaling relations by introducing `dust bins' for lenticular (S0) galaxies. Doing so has led to the discovery of $M_{\rm bh}$-$M_{\rm *,sph}$ and $M_{\rm bh}$-$M_{\rm *,gal}$ relations for dusty S0 galaxies - built by major wet mergers and comprising half the S0 sample - offset from the distribution of dust-poor S0 galaxies. The situation is reminiscent of how major dry mergers of massive S0 galaxies have created an offset population of ellicular and elliptical galaxies. For a given $M_{\rm bh}$, the dust-rich S0 galaxies have 3 to 4 times higher $M_{\rm *,sph}$ than the dust-poor S0 galaxies, and the steep distributions of both populations in the $M_{\rm bh}$-$M_{\rm *,sph}$ diagram bracket the $M_{\rm bh} \propto M_{\rm *,sph}^{2.27+/-0.48}$ relation defined by the spiral galaxies, themselves renovated through minor mergers. The new relations offer refined means to estimate $M_{\rm bh}$ in other galaxies and should aid with: (i) constructing (galaxy morphology)-dependent black hole mass functions; (ii) estimating the masses of black holes associated with tidal disruption events; (iii) better quantifying evolution in the scaling relations via improved comparisons with high-$z$ data by alleviating the pickle of apples versus oranges; (iv) mergers and long-wavelength gravitational wave science; (v) simulations of galaxy/black hole coevolution and semi-analytic works involving galaxy speciation; plus (vi) facilitating improved extrapolations into the intermediate-mass black hole landscape. The role of the galaxy's environment is also discussed, and many potential projects that can further explore the morphological divisions are mentioned.