Bird and Hawk

For those of you that are squeamish, be aware that this is a study of a dead bird that
I found it in the backyard lying on its back.

I ran for my sketchbook because this subject was the perfect model, he wasn't going to move. I once saw Cathy Johnson include a sketch of something dead in her book and decided this was one of those great opportunities for a nature sketch.

The bird looks young and I am thinking it may be in the Thrush family with it's coloring and long pointy beak. I could not see any evidence of obvious injury and am not sure what killed it.

However, I saw this young hawk bathing in my ground-set birdbath right near where I found the dead bird. My husband said a hawk would not just kill something unless they eat it.
Does anyone know what kind of hawk this is?

I am thinking it is a Cooper's Hawk.