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Scaling relations between supermassive black hole mass, M_BH, and host galaxyproperties are a powerful instrument for studying their coevolution. A completepicture involving all of the black hole scaling relations, in which eachrelation is consistent with the others, is necessary to fully understand theblack hole-galaxy connection. The relation between M_BH and the central lightconcentration of the surrounding bulge, quantified by the S\'ersic index n, maybe one of the simplest and strongest such relations, requiring onlyuncalibrated galaxy images. We have conducted a census of literature S\'ersicindex measurements for a sample of 54 local galaxies with directly measuredM_BH values. We find a clear M_BH - n relation, despite an appreciable level ofscatter due to the heterogeneity of the data. Given the current M_BH - L_sphand the L_sph - n relations, we have additionally derived the expected M_BH - nrelations, which are marginally consistent at the 2 sigma level with theobserved relations. Elliptical galaxies and the bulges of disc galaxies areeach expected to follow two distinct bent M_BH - n relations due to theS\'ersic/core-S\'ersic divide. For the same central light concentration, wepredict that M_BH in the S\'ersic bulges of disc galaxies are an ordermagnitude higher than in S\'ersic elliptical galaxies if they follow the sameM_BH - L_sph relation.

The supermassive black hole mass - S\'ersic index relations for bulges and elliptical galaxies