Most likely you don't want to fadeOut completely as that will set the element to display: none. Also, you don't need to get headerImage again in the callback, use $(this). I would say this is probably better:
The speed of the transitions is given by 300 in the code above (300ms), if you want to make it faster or slower than change that number. The second number in the fadeTo function is the opacity that it's being faded to.
I've switched careers...
I'm NO LONGER a scientist,
but now a web developer...