Radiative Transfer Modeling of the Accretion Flow onto a Star-forming Core in W51

We present an analysis of the temperature, density, and velocity of the molecular gas in the star-forming core around W51 e2. We summarize the kinematic evidence that implies that the core around e2 is contracting onto a young massive star. The current paper presents a technique for modeling the three-dimensional structure of the core by simulating spectral line images of the source and comparing those images with observed data. The primary conclusions of this work are that the molecular gas in e2 is radially contracting at about 5 km s^-1 and that the temperature and density of the gas decrease outward over 0.15 pc scales. The simple model of the collapse of the singular isothermal sphere for low-mass star formation is an inadequate description of this high-mass molecular core; better models have temperature ~r^-0.6, density ~r^-2, and velocity ~r^+0.1. The core appears to be spherical rather than disklike at the scale of these observations, 0.3 pc. In this paper we show how a series of models of gradually increasing complexity can be used to investigate the sensitivity of the model to its parameters. Major sources of uncertainty for this method and this data set are the interdependence of temperature and density, the assumed NH₃ abundance, the distance uncertainty, and the flux calibration of the data.