Designated electrical circuit for smoke detectors?

Is there supposed to be a designated electrical circuit for the smoke detectors?
It looks like the smoke detectors are connected together properly. But the lights are also on the same circuit? Please reference any codes that may help me better understand.
Thank you for your help.

No requirement for a separate circuit for the alarms.
See IRC R314. If there is commercial power they must be wired to it, but no dedicated circuit req.