Prospects for measuring supermassive black hole masses with future extremely large telescopes

The next generation of giant-segmented mirror telescopes ($>$ 20 m) will enable us to observe galactic nuclei at much higher angular resolution and sensitivity than ever before. These capabilities will introduce a revolutionary shift in our understanding of the origin and evolution of supermassive black holes by enabling more precise black hole mass measurements in a mass range that is unreachable today. We present simulations and predictions of the observations of nuclei that will be made with the Thirty Meter Telescope (TMT) and the adaptive optics assisted integral-field spectrograph IRIS, which is capable of diffraction-limited spectroscopy from $Z$ band (0.9 $\mu$m) to $K$ band (2.2 $\mu$m). These simulations, for the first time, use realistic values for the sky, telescope, adaptive optics system, and instrument, to determine the expected signal-to-noise ratio of a range of possible targets spanning intermediate mass black holes of $\sim10^4$ \msun to the most massive black holes known today of $>10^{10}$ $M_\odot$. We find that IRIS will be able to observe Milky Way-mass black holes out the distance of the Virgo cluster, and will allow us to observe many more brightest cluster galaxies where the most massive black holes are thought to reside. We also evaluate how well the kinematic moments of the velocity distributions can be constrained at the different spectral resolutions and plate scales designed for IRIS. We find that a spectral resolution of $\sim8000$ will be necessary to measure the masses of intermediate mass black holes. By simulating the observations of galaxies found in SDSS DR7, we find that over $10^5$ massive black holes will be observable at distances between $0.005 < z < 0.18$ with the estimated sensitivity and angular resolution provided by access to $Z$-band (0.9 $\mu$m) spectroscopy from IRIS and the TMT adaptive optics system. (Abridged)