"Closely" is modifying the verb "tied". Both are acceptable but sometimes choice will depend on the flow of the sentence or whether it sounds natural.
To illustrate, look at the following four sentences and see whether they have different meanings:-
1. He slowly eats his food. 2. Slowly, he eats his food. 3. He eats slowly his food. 4. He eats his food slowly.
To me, sentence 1 and sentence 4 sound more natural than the others.