Just bought an 09 Outback. The engine buzzes and rattles during the morning start up. However, once warmed up and during the day the noise is gone. I assume something is loose. What should I look for?
You should look for the booklet in the glove compartment titled Subaru Maintenance and Warranty Supplement.
Unless this car has unusually high odometer mileage, or unless it was not maintained properly by the previous owner, it is under multiple warranties (Bumper-to-Bumper, Powertrain, Emissions, Rust-Through).
Under no circumstances should you pay for repairs to the engine of this car since those multiple warranties put the financial onus on Subaru of America, through their agent, the local Subaru dealership. Take it to the dealership, describe (and hopefully demonstrate) the symptoms, and allow them to diagnose the problem.
All of that being said, I think that the most likely source of the problem is a loose or bent heat shield on the exhaust system. The symptoms that you describe are consistent with a loose heat shield–but the dealership will likely ignore any diagnosis that you offer, and will run their own diagnostic procedure.