Assessing the Dark Matter Content of Two Quasar Host Galaxies at z ∼ 6 through Gas Kinematics

We conduct a study of the gas kinematics of two quasar host galaxies at z ≳ 6 traced by the [C ii] emission line using the Atacama Large Millimeter/submillimeter Array. By combining deep observations at both low and high resolution, we recover the diffuse emission, resolve its structure, and measure the rotation curves from the inner region of the galaxy to its outskirts using DysmalPy and 3DBarolo. Assuming that both galaxies exhibit disk rotation driven by the gravitational potential of the galaxy, we find that the best-fit disk models have a Vrot/σ ≈ 2 and inferred circular velocities out to ∼6-8 kpc scales, well beyond the likely stellar distribution. We then determine the mass profiles of each component (stars, gas, dark matter) with priors on the baryon and dark matter properties. We find relatively large dark matter fractions within their effective radii (fDM(R < Re) = 0.61 − 0.08 + 0.08 and 0.53 − 0.23 + 0.20 , respectively), which are significantly larger than those extrapolated from lower redshift studies and remain robust under different input parameters verified by Monte Carlo simulations. The large fDM(R < Re) corresponds to halo masses of ∼1012.5−1012.8 M⊙, thus representative of the most massive halos at these redshifts. Notably, while the masses of these supermassive black holes (SMBHs) are approximately 1 dex higher than the low-redshift relationship with stellar mass, the closer alignment of SMBH and halo masses with a local relationship may indicate that the early formation of these SMBHs is linked to their dark matter halos, providing insights into the coevolution of galaxies and black holes in the early Universe.