Comparing astronomical datacubes using level-set topology

We describe position-position-velocity data cubes derived from the star-forming interstellar medium (SFISM). The physical characteristics and evolution of the SFISM must be deduced from the incomplete information present in the observed data. Astrophysicists can simulate the evolution of the SFISM from first principles but the standard comparisons of simulated data with observations do not completely describe the SFISM. Given the hierarchical structure present in the emission, we forward the use of Reeb graphs as a tool for comparing data cubes. We describe the computation of a Reeb graph and show that the properties encoded in the Reeb graph highlight the deficiencies of simulations at capturing the structure of the SFISM.