Resolving Disks & Mergers in $z\sim2$ Heavily Reddened Quasars and their Companion Galaxies with ALMA.

We present sub-arcsecond resolution ALMA imaging of the CO(3-2) emission in two $z\sim2.5$ heavily reddened quasars (HRQs) - ULASJ1234+0907 and ULASJ2315+0143 - and their companion galaxies. Dynamical modeling of the resolved velocity fields enables us to constrain the molecular gas morphologies and host galaxy masses. Combining the new data with extensive multi-wavelength observations, we are able to study the relative kinematics of different molecular emission lines, the molecular gas fractions and the locations of the quasars on the M$_{\rm{BH}}$-M$_{\rm{gal}}$ relation. Despite having similar black-hole properties, the two HRQs display markedly different host galaxy properties and local environments. J1234 has a very massive host, M$_{\rm{dyn}} \sim 5 \times 10^{11}$M$_\odot$ and two companion galaxies that are similarly massive located within 200 kpc of the quasar. The molecular gas fraction is low ($\sim$6%). The significant ongoing star formation in the host galaxy is entirely obscured at rest-frame UV and optical wavelengths. J2315 is resolved into a close-separation major-merger ($\Delta$r=15 kpc; $\Delta$v=170 km/s) with a $\sim$1:2 mass ratio. The total dynamical mass is estimated to be $\lesssim$10$^{11}$M$_\odot$ and the molecular gas fraction is high ($>$45%). A new HSC image of the galaxy shows unobscured UV-luminous star-forming regions co-incident with the extended reservoir of cold molecular gas in the merger. We use the outputs from the Illustris simulations to track the growth of such massive black holes from $z\sim6$ to the present day. While J1234 is consistent with the simulated $z\sim2$ relation, J2315 has a black hole that is over-massive relative to its host galaxy.