This is a behavior known as mobbing. Smaller birds, such as crows, jays, chickadees, and blackbirds will harass hawks, owls, cats, and other predators to chase them away. Mobbing behavior includes diving at the predator, pecking it, very loud and continuous warning calls, and defecating on the predator. The loud squawking ruins the predator's chance of sneaking up on prey, and it is also a great way for nature photographers to locate hawks and owls. The screaming of blue jays is a good sign that they have spotted a predator to torment.