Temperature, Mass and Turbulence: A Spatially Resolved Multi-Band Non-LTE Analysis of CS in TW~Hya

Observations of multiple rotational transitions from a single molecule allow for unparalleled constraints on the physical conditions of the emitting region. We present an analysis of CS in TW~Hya using the $J=7-6$, $5-4$ and $3-2$ transitions imaged at $\sim 0.5^{\prime\prime}$ spatial resolution, resulting in a temperature and column density profile of the CS emission region extending out to 230~au, far beyond previous measurements. In addition, the 15~kHz resolution of the observations and the ability to directly estimate the temperature of the CS emitting gas, allow for one of the most sensitive searches for turbulent broadening in a disk to date. Limits of $v_{\rm turb} \lesssim 0.1 c_s$ can be placed across the entire radius of the disk. We are able to place strict limits of the local H$_2$ density due to the collisional excitations of the observed transitions. From these we find that a minimum disk mass of $3 \times 10^{-4}~M_{\rm sun}$ is required to be consistent with the CS excitation conditions and can uniquely constrain the gas surface density profile in the outer disk.