The origin of the nebulosity around SN 1987A is investigated using two-dimensional, hydrodynamic calculations of the interaction of the progenitor's stellar winds. The collision of the final blue supergiant (BSG) wind with a highly flattened red supergiant (RSG) wind expelled earlier produces a double-lobed bubble of shocked BSG wind confined by a shell of shocked, swept-up RSG wind. Assuming the supernova ionizes a portion of this structure, we derive emission-measure images from our models. They provide a direct comparison between the interacting-winds model and the Hubble Space Telescope (HST) images, which reveal three elliptical rings of emission around SN 1987A. The similarity of the overall morphology of our images and the HST images suggests that the interacting-winds scenario is the correct explanation for these puzzling rings. This model is subsequently used to predict the nebula's appearance in the promptly reflected continuum light from the supernova. The simulated image for day 750 is consistent with a recently published 6120 Angstrom continuum image, but our day 1028 image does not resemble the observations as closely. The discrepancy is traced to a small difference in the extent of the bubble along the polar axis and can be resolved by increasing the pole-to-equator density gradient in the RSG wind. Finally, we present stellar evolution models for the progenitor of SN 1987A. The timescales of the late evolutionary stages correspond closely to hydrodynamic timescales in the interacting-winds model. We emphasize that the densest layers of the nebula are not well resolved in our calculations, and clumping on smaller scales will affect the emission. Hence, we compare the images quantitatively only to demonstrate the plausibility of the model and to motivate additional work on the clumping. The extreme asymmetries inferred for the RSG wind and the subtle discrepancies between the images are discussed to motivate further work with the interacting-winds model. In the Appendix, we illustrate how grid resolution affects the radiative cooling and discuss why it should be a concern in calculations of this type.
