The (black hole mass)-(color) relations for early- and late-type galaxies: red and blue sequences

[Abridged] Tight correlations between supermassive black hole (SMBH) mass ($M_{\mathrm{B}\mathrm{H}}$) and the properties of the host galaxy have useful implications for our understanding of the growth of SMBHs and evolution of galaxies. Here, we present newly observed correlations between $M_{\mathrm{B}\mathrm{H}}$ and the host galaxy total UV$-$ [3.6] color (${\mathcal{C}}_{\mathrm{U}\mathrm{V},\mathrm{t}\mathrm{o}\mathrm{t}}$, Pearson’s r = $0.6-0.7$) for a sample of 67 galaxies (20 early-type galaxies and 47 late-type galaxies) with directly measured $M_{\mathrm{B}\mathrm{H}}$ in the GALEX/S${}^4$G survey. The colors are carefully measured in a homogeneous manner using the galaxies’ FUV, NUV and 3.6 $\text{micron}$ magnitudes and their multi-component structural decompositions in the literature. We find that more massive SMBHs are hosted by (early- and late-type) galaxies with redder colors, but the $M_{\rm BH}- \mathcal{C_{\rm UV,tot}}$relationsforthetwomorphologicaltypeshaveslopesthatdifferat$\sim 2 \sigma$level\mathrm{.}Early-typegalaxiesdefinearedsequenceinthe$M_{\rm BH}- ${\mathcal{C}}_{\mathrm{U}\mathrm{V},\mathrm{t}\mathrm{o}\mathrm{t}}$$ diagrams, while late-type galaxies trace a blue sequence. Within the assumption that the specific star formation rate of a galaxy (sSFR) is well traced by $L_{\mathrm{U}\mathrm{V}}\mathrm{/}{L}_{3.6}$, it follows that the SMBH masses for late-type galaxies exhibit a steeper dependence on sSFR than those for early-type galaxies. The $M_{\mathrm{B}\mathrm{H}}-{\mathcal{C}}_{\mathrm{U}\mathrm{V},\mathrm{t}\mathrm{o}\mathrm{t}}$ and $M_{\mathrm{B}\mathrm{H}}-L_{3.6,\mathrm{t}\mathrm{o}\mathrm{t}}$ relations for the sample galaxies reveal a comparable level of vertical scatter in the log $M_{\mathrm{B}\mathrm{H}}$ direction, roughly $5\mathrm{\%}-27\mathrm{\%}$ more than the vertical scatter of the $M_{\mathrm{B}\mathrm{H}}-\sigma$ relation. Our $M_{\mathrm{B}\mathrm{H}}-{\mathcal{C}}_{\mathrm{U}\mathrm{V},\mathrm{t}\mathrm{o}\mathrm{t}}$ relations suggest different channels of SMBH growth for early- and late-type galaxies, consistent with their distinct formation and evolution scenarios.