The artefact appears to be a combination of diffraction from the microlens array on the sensor and reflection from the inside surface of the coverglass. Other cameras using the same Panasonic sensor have shown similar patterns on bright stars.
I've not had to deal with this yet but my first approach would be to build a mask that isolates the worst of the artefact and then reduce the brightness with CurvesTransformation and maybe blur it a little with Convolution or one of the wavelet processes. For the mask try RangeSelection to grab middle brightnesses (you don't want the background or the core of the big star) and then multiply that mask by the original image. If the mask includes a lot of stuff you don'r want, draw a preview around the section you do want and then use the SubstituteWithPreview script to copy the preview into a black image (create with PixelMath "0".) It will probably take some messing around and experimentation to get the mask right.
Cheers,
Rick.