15 watts would be about 1 amp (or 1,000 mA) at 15 volts, in the brightest sunlight available.
After your battery reaches a full state of charge, it's only going to require a few dozen mA to keep it fully charged (assuming it's not sulfated or otherwise in poor condition).
Forcing an amp through it for 4-6 hours a day is probably going to overcharge it.
Measure the voltage across the battery, after it's fully charged and has had the panel connected to it for the good part of a day in bright sunlight. If the voltage measures much above 13.5 volts (which is considered to be the ideal long-term "maintenance" voltage), it'll lose water quick, and will die prematurely - in which case you either need to disconnect the panel manually, or install a charge controller.
BTW, since your panel is only capable of supplying about 1 amp, you would only need a controller that's capable of handling at least 1 amp.