Neighbors SUCK! I feel your pain. Assuming you've already talked to neighbors, manager &/or landlord, who do nothing to improve situation, I'd check w/ local police to see about local laws. Write down time of noise disturbance, what kind of noise, & by whom, if you know. Never know when you might need the info.

I'm not sure about car noise, but most cities have an ordinance in which you have to remain reasonably quiet after a certain time (usually between 9pm until 7am - or around that). Really, besides talking with the neighbor, apartment manager, or local police officials, there is nothing you can really do. One problem with contacting the police is that by the time the officer gets to your house, the neighbor could be gone. (Hence no police report to write up).

I would definitey keep a running log of when, where, how long - especially if the city had a noise/disturbance ordinance.

There is nothing the police or apartment folks will be able to do for you. The person has a right to come and go at whatever hours he chooses. If you live in a colder climate it is also reasonable for him to let his car warm up. Living in an apartment comes with it's "concessions of comfort" and unfortunately this is one of them.

If the car is street legal, really not much can be done. However, if the manager gets enough written complaints, and depending on local and state law, the landlord may be able or decide to terminate them once the lease has expired.