Not all hard-wired detectors have backup batteries. The rectangular-ish piece on the right looks like the holder for a 9v battery but I can't see any connectors so it may be that they used the same assembly for models with and without batteries.
It could be beeping because it has failed (I could read any date on it) but hard to know how to interpret beeps without the owner's manual.
If all else fails, replace the unit - better to be safe than sorry.
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