Might be wrong but it looks like the aura is being created by your sharpening process you can get them on a high contrast edges, maybe refine the selection edge around the bird and reduce it by 1 pixel don't know if you have PS but the refine edge tool lets you do that fairly easily.
It's either that or contrast. I increased contrast on the whole shot instead of solely the bird as I normally do. That might have created this difference between the bird and sky.