Fourier Modeling of the Radio Torus Surrounding Supernova 1987A
  We present detailed Fourier modeling of the radio remnant of Supernova 1987A, using high-resolution 9 GHz and 18 GHz data taken with the Australia Telescope Compact Array over the period 1992 to 2008. We develop a parameterized three-dimensional torus model for the expanding radio shell, in which the emission is confined to an inclined equatorial belt; our model also incorporates both a correction for light travel-time effects and an overall east-west gradient in the radio emissivity. By deriving an analytic expression for the two-dimensional Fourier transform of the projected three-dimensional brightness distribution, we can fit our spatial model directly to the interferometric visibility data. This provides robust estimates to the radio morphology at each epoch. The best-fit results suggest a constant remnant expansion at 4000 +/- 400 km/s over the 16-year period covered by the observations. The model fits also indicate substantial mid-latitude emission, extending to 40 degree on either side of the equatorial plane. This likely corresponds to the extra-planar structure seen in H$\alpha$ and Ly$\alpha$ emission from the supernova reverse shock, and broadly supports hydrodynamic models in which the complex circumstellar environment was produced by a progression of interacting winds from the progenitor. Our model quantifies the clear asymmetry seen in the radio images: we find that the eastern half of the radio remnant is consistently ~40 brighter than the western half at all epochs, which may result from an asymmetry in the ejecta distribution between these two hemispheres. 
C.-Y. Ng, B. M. Gaensler, L. Staveley-Smith, R. N. Manchester, M. J.   Kesteven, L. Ball, A. K. Tzioumis