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Measuring the mass of the supermassive black hole of the lenticular galaxy NGC 4546

Most galaxies with a well-structured bulge host a supermassive black hole (SMBH) in their centre. Stellar kinematics models applied to adaptive optics (AO) assisted integral field unit observations are well-suited to measure the SMBH mass ($M_{BH}$) and also the total mass-to-light ratio [$(M/L)_{TOT}$] and possible anisotropies in the stellar velocity distribution in the central region of galaxies. In this work, we used new AO assisted Near-Infrared Integral Field Spectrometer (NIFS) observations and also photometric data from the Hubble Space Telescope Legacy Archive of the galaxy NGC 4546 in order to determine its SMBH mass. To do this, we applied the Jeans Anisotropic Modelling (JAM) method to fit the average second velocity moment in the line of sight $(\overline{v^2_{los}})$ of the stellar structure. In addition, we also obtained $(M/L)_{TOT}$ and the classical anisotropy parameter $β_z$=1--($σ_z$/$σ_R$)$^2$ for this object within a field of view of 200$\times$200 pc$^2$. Maps of the stellar radial velocity and of the velocity dispersion were built for this galaxy using the penalized pixel fitting ({\sc ppxf}) technique. We applied the Multi Gaussian Expansion procedure to fit the stellar brightness distribution. Using JAM, the best-fitting model for $\overline{v^2_{los}}$ of the stellar structure was obtained with $(M/L)_{TOT}$ = 4.34$\pm$0.07 (Johnson's R band), $M_{BH}$ = (2.56$\pm$0.16)$\times$10$^8$ M$_\odot$ and $β_z$ = --0.015$\pm$0.03 (3$σ$ confidence level). With these results, we found that NGC 4546 follows the $M_{BH}$ $\times$ $σ$ relation. We also measured the central velocity dispersion within a radius of 1 arcsec of this object as $σ_c$ = 241$\pm$2 km s$^{-1}$.