In Alaska, they hang out mostly in lakes ( https://www.adfg.alaska.gov/index.cfm?adfg=arcticchar.main ).
"In Alaska, all known populations of Arctic char appear to spend their entire lives in lakes and do not migrate. Anadromous populations of Arctic char have not been observed in Alaska, although anadromous forms of the species do exist in on the Chukchi Peninsula and Kamchatka in far east Russia."
Yes, this was also my opinion, but last summer I have found a dwarf stock of brook-resident Arctic-type char with no lakes in the vicinity. It is sitting in the area rich with springs, above a large aufeis.
Hmmmm ... would the warm period of the freeze / thaw cycle of the aufeis allow time for the spawning process to complete? Basically providing a temporary 'lake' environment where the char take refuge in the brooks?
By August the aufeis surface becomes smaller; the "braided" brook above it forms numerous shallow channels (no lake-type habitats are present). The water temperature was 4*C; in the nearby river it was 6*C (the day was cold).