Old house--no neutral wire for Nest Protect?
Which Nest Protect should I get?
Just check the smoke alarm you have now. If it connects to [line voltage] wires, you’ll want Nest Protect (Wired 120V). If it doesn’t, you should get Nest Protect (Battery).

Those colored wires in your ceiling look like 24 gauge thermostat wires, unsuitable for line voltage. I surmise your old smoke directors ran on 24 volts. You need the battery version or you'll have to pull some new wire.
However:
The two brown wires look thicker though, more like 14awg. Do you get 120v across them? If you do, I'd assume the neutral is the one with a stripe.
The red, black, yellow and green wires should NOT be hooked to line voltage (and you shouldn't use them as 'interconnecting wires' if the detector is going to send 120v through them). Get the two brown wires separated from all the others and test them.
Utter guesswork that you'll need to confirm with the proper test equipment:
Black to solid brown. White to brown w/ stripe.