I'm using solar panels at home, so have a little experience in this arena.
Your location will have an impact on how well a solar panel works, as well as its view of the Southern sky, time of year, angle of the panel, etc.
Also things like detectors eat battery power day & night, whether on or off (never really off). Suggest installing a battery disconnect switch.
If your batteries are already charged, you can get away with a smaller panel. Some claim they do fine with a 5 Watt panel ($39 on sale at Harbor Freight), but I'd recommend a 15 Watt panel ($79 on sale at Northern Tool).
Power (Watts) = I (Current in Amps) x E (Volts). I=P/E, current for the 5 Watt panel is 5/12, or 0.42 Amps during the peak of the day in ideal conditions. That's not much! The 15 Watt panel is 15/12, or 1.25 Amps, a safe trickle charge amount.
You only get usuable sun during a 4-5 hour stretch, depending on your location. A 15 Watt panel will keep your battery topped up. If you decide to add more panels to recharge, not just maintain your battery(s), you should invest in a solar controller too. Also available at Northern Tool for a few more sheckles.
Here's what the 15 Watt panel looks like:
Note, the store price for this panel is $99. Print out the online price of $79, and they will honor it in the store.