Understanding how molecules and dust might have formed within a rapidly expanding young supernova remnant is important because of the obvious application to vigorous supernova activity at very high redshift. In previous papers, we have mapped the Crab nebula (the Crab) in a rotovibrational H2emission line, and then measured the molecular excitation temperature for a few of the brighter H2-emitting knots that we have found to be scattered throughout the Crab's filaments. We found that H2 emission is often quite strong, correlates with optical low-ionization emission lines and has a surprisingly high excitation temperature. Here, we study Knot 51, a representative, bright example. It is a spatially isolated structure for which we have available long-slit optical and near-infrared (NIR) spectra covering emission lines from ionized, neutral and molecular gas, as well asHubble Space Telescope visible and Southern Astrophysical Research telescope NIR narrow-band images. We present a series of CLOUDYsimulations to probe the excitation mechanisms, formation processes and dust content in environments that can produce the observed H2 emission. There is still considerable ambiguity about the geometry of Knot 51, so we do not try for an exact match between model and observations. Rather, we aim to explain how the bright H2 emission lines can be formed from within a cloud of the size of Knot 51 that also produces the observed optical emission from ionized and neutral gas. Our models that are powered only by the Crab's synchrotron radiation are ruled out because they are not able to reproduce the observed strong H2 emission coming from thermally populated levels. The simulations that come closest to fitting the observations (although they still have conspicuous discrepancies) have the core of Knot 51 almost entirely atomic with the H2 emission coming from just a trace molecular component, and in which there is extra heating. In this unusual environment, H2 forms primarily through H by radiative detachment rather than by grain catalysis. In this picture, the 55 H2-emitting cores that we have previously catalogued in the Crab have a total mass of about 0.1 M, which is about 5 per cent of the total mass of the system of filaments. We also explore the effect of varying the dust abundance. We discuss possible future observations that could further elucidate the nature of these H2 knots.

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Published in Monthly Notices of the Royal Astronomical Society, v. 430, issue 2, p. 1257-1279.

This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society ©: 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.

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