In a large Mongo collection, how do I retrieve only ID's (or any other specific property) using mongoose?

Let's say I have a Person collection, and a Car collection, and that all people have a single car, and the Person document stores the Id of the car.

Somewhere along the way, due to bad back-end validation, some Cars have been persisted to the DB, without any owners. I would like to delete all these 'orphan' cars.

My approach is probably not the most optimal, but here goes:

exports.cleanOrphanCars = (req, res) ->
  Car.find() #find all the cars
  .exec(err, cars) ->
    return res.send(StatusMessages.ERROR.code, { error: err }) if err?
    carIds = cars.map (car) => 
    #map the IDs to a new array for faster iteration
     return car._id
    Person.find()
    .exec(err, people) ->
      peoplesCarIds = (person) =>
        return person.carId
      for carId in carIds
        found = false
        for personsCarId in peoplesCarIds
          if personCarId is carId
            found = true
        if not found 
        #if no Person references this car, we can remove it
          Car.remove({_id : carId})

Getting all these Cars and Persons is too slow. Is there a way to fetch an array of IDs straight from mongo, without me having to map the IDs locally?

Also would it be possible to skip the prefetching and have just one query to remove any orphan Cars?