Which sources would those be?

You'll see on the net various charts of the family. Most of them come, at least originally, from people that have compiled them over on the Real Deal forum. As far as simply listing made members go, the charts are usually as "up to date" as possible - unless someone dies.

However, listing captains can be tricky because sometimes there are ones that were captains at one time but not now. I'd be willing to bet the above names are a good example. Although all of those guys have been identified as captains at one time, I'd be surprised if the Providence faction needed 4 captains at this point. 4 captains is probably what the family needs total. 4 captains seems to be about what the New Jersey, Philadelphia, and Chicago families have now and they are similar in size to New England.