The multi-scale environment of RS Cnc from CO and HI observations

We present a detailed study of the circumstellar gas distribution and kinematics of the semi-regular variable star RS Cnc on spatial scales ranging from ~1" (~150 AU) to ~6' (~0.25 pc). New modeling of CO1-0 and CO2-1 imaging observations leads to a revised characterization of RS Cnc's previously identified axisymmetric molecular outflow. Rather than a simple disk-outflow picture, we find that a gradient in velocity as a function of latitude is needed to fit the spatially resolved spectra, and in our preferred model, the density and the velocity vary smoothly from the equatorial plane to the polar axis. In terms of density, the source appears quasi-spherical, whereas in terms of velocity the source is axi-symmetric with a low expansion velocity in the equatorial plane and faster outflows in the polar directions. The flux of matter is also larger in the polar directions than in the equatorial plane. An implication of our model is that the stellar wind is still accelerated at radii larger than a few hundred AU, well beyond the radius where the terminal velocity is thought to be reached in an asymptotic giant branch star. The HI data show the previously detected head-tail morphology, but also supply additional detail about the atomic gas distribution and kinematics. We confirm that the `head' seen in HI is elongated in a direction consistent with the polar axis of the molecular outflow, suggesting that we are tracing an extension of the molecular outflow well beyond the molecular dissociation radius (up to ~0.05 pc). The 6'-long HI `tail' is oriented at a PA of 305{\deg}, consistent with the space motion of the star. We measure a total mass of atomic hydrogen ~0.0055 solar mass and estimate a lower limit to the timescale for the formation of the tail to be ~6.4x10^4 years. (abridged)