A little more clarity from me and much thanks...
I probably should have clarified a bit that I was just trying to come close, but thank you so much for the direction you all gave me.
What I ended up doing, I did in Illy. I took the original graphic and outlined a rough shape of the burst. I then put an outer glow effect on that shape and expanded the appearance separating the effect from the object. I just pasted the resulting object (formally the effect) into the new Illustration and gave it a good helping of opacity. Not exact, but pretty close.
Thanks again for all the responses.
Ben