in the docs for the open/close api it says
A closed index has almost no overhead on the cluster (except for maintaining its metadata)
I was wondering what meant by metadata and what is the overhead?
I'm asking because we had a bit too much confidence in the fact that we could put all synonyms in the mapping (turns out: too heavy, don't do it). We made a new index with all the synonyms tucked away in files but want to keep the old index for a while to see if we can trust the new one. We closed the old one but now I'm not sure if the mapping and settings of the closed index are still pumped around in the cluster because of that sentence in the docs 
The metadata/overhead are essentially the information stored in the cluster state. So this includes what nodes hold each shard in the index, the settings of the index, and importantly for your case, the mappings/analysis.
What's excluded are the various in-memory datastructures that are needed to actually search the index, such as the term dictionary, posting list, ordinals, etc etc.
So in your case, the synonym list will still be persistent in the cluster state, and still impose the performance tax on the master (and network transfer between nodes). You can verify this by calling: GET /_cluster/state, and you'll see that the big list of synonyms is still present for that index.
When you use file-based synonyms, those values are also loaded into the cluster state. But they are only loaded when the index is opened, so if you close them they are removed from the cluster state and you'll save a bit of work on the master node.
Thanks for that Zachary! Sorry for the late reply, I was on vacation but it helped the developers that were solving the problem 