The MBHBM* Project - II. Molecular gas kinematics in the lenticular galaxy NGC 3593 reveal a supermassive black hole

As part of the Measuring Black Holes in below Milky Way-mass (M*) galaxies (MBHBM*) Project, we present a dynamical measurement of the supermassive black hole (SMBH) mass in the nearby lenticular galaxy NGC 3593, using cold molecular gas 12CO(2-1) emission observed at an angular resolution of approximate to 0.'' 3 (approximate to 10 pc) with the Atacama Large Millimeter/submillimeter Array (ALMA). Our ALMA observations reveal a circumnuclear molecular gas disc (CND) elongated along the galaxy major axis and rotating around the SMBH. This CND has a relatively low-velocity dispersion (less than or similar to 10 km s(-1)) and is morphologically complex, with clumps having higher integrated intensities and velocity dispersions (less than or similar to 25 km s(-1)). These clumps are distributed along the ridges of a two-arm/bi-symmetric spiral pattern surrounded by a larger ring-like structure (radius r approximate to 10 arcsec or approximate to 350 pc). This pattern likely plays an important role to bridge the molecular gas reservoirs in the CND and beyond (10 less than or similar to r less than or similar to 35 arcsec or 350 pc less than or similar to r less than or similar to 1.2 kpc). Using dynamical modelling, the molecular gas kinematics allow us to infer an SMBH mass M-BH = 2.40(-1.05)(+1.87) x 10(6) M-circle dot (only statistical uncertainties at the 3 sigma level). We also detect a massive core of cold molecular gas (CMC) of mass MCMC = (5.4 +/- 1.2) x 10(6) M-circle dot and effective (half-mass) radius r(CMC,e) = 11.2 +/- 2.8 pc, co-spatial with a nuclear star cluster (NSC) of mass M-NSC = (1.67 +/- 0.48) x 10(7) M-circle dot and effective radius r(NSC,e) = 5.0 +/- 1.0 pc (or 0.'' 15 +/- 0 '' 03). The mass profiles of the CMC and NSC are well described by Sersic functions with indices 1-1.4. Our M-BH and MNSC estimates for NGC 3593 agree well with the recently compiled M-BH-MNSC scaling relation. Although the MNSC uncertainty is twice the inferred M-BH, the rapid central rise of the rotation velocities of the CND (as the radius decreases) clearly suggests an SMBH. Indeed, our dynamical models show that even if MNSC is at the upper end of its allowed range, the evidence for a BH does not vanish, but remains with a lower limit of M-BH > 3 x 10(5) M-circle dot.