I could easily be mistaken here, but wouldn't applying any dark matter theory to a binary system require it to have its own dark matter halo and core? I can u

I could easily be mistaken here, but wouldn't applying any dark matter theory to a binary system require it to have its own dark matter halo and core? I can understand how things like superfluid DM might help explain galactic rotations, but I'm having a harder time applying it to things like wide binaries.