Shu (1977) gives the analytic predictions for a a singular isothermal sphere (SIS). To see if we recover the expected dependences, we have conducted synthetic \(^{13}\)CO observations of a simulation of a SIS. The scale of the data cube was 0.42 pc x 0.42 pc x +-6 km/s. The peak density is 10\(^5\) cm\(^{-3}\). A small amount of noise was added to the data post-radiative transfer. (nb: 2 smaller SIS’s were also examined (0.052 and 0.22 pc\(^3\)), and due to the higher densities leading to partial or complete depletion of CO, the structures we recover are correspondingly skewed).
TO DO: Compare the density and pressure profiles of the SIS to individual cores in the simulation and observation.