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We investigate the collapse of primordial gas in a minihalo withthree-dimensional radiation hydrodynamics simulations that accurately model thetransfer of H2 line emission. For this purpose, we have implemented amultiline, multifrequency ray-tracing scheme in the moving-mesh code Arepo thatis capable of adaptively refining rays based on the Healpix algorithm, as wellas a hybrid equilibrium/non-equilibrium primordial chemistry solver. We findthat a multifrequency treatment of the individual H2 lines is essential, sincefor high optical depths the smaller cross-section in the wings of the linesgreatly increases the amount of energy that can escape. The influence ofDoppler shifts due to bulk velocities is comparatively small, since systematicvelocity differences in the cloud are typically smaller than the sound speed.During the initial collapse phase, the radially averaged escape fraction agreesrelatively well with the fit of Ripamonti & Abel. However, in general it is notadvisable to use a simple density-dependent fitting function, since the escapefraction depends on many factors and does not capture the suppression ofdensity perturbations due to the diffusion of radiation. The Sobolev methodoverestimates the escape fraction by more than an order of magnitude, since theproperties of the gas change on scales smaller than the Sobolev length.

Multifrequency radiation hydrodynamics simulations of H2 line emission in primordial, star-forming clouds