Sounds like Red-tailed Hawk.

That's exactly what I thought Embothrium. How did you guess that based on my meager description?! Do other hawks have different cries?? I was listening to their cries on YouTube, but am not a birder of any kind (just a bird lover). What is absolutely amazing is how raptors are really make a big time comeback in the suburbs around NYC..., there are even expanding colonies of Red Tails on MANHATTAN (experts are not sure why; but gotta be a very positive environmental message!). Last year, I had flocks/gangs of Wild Turkeys in my yard (with attitude) no less. And though I have not seen them YET, a friend of mine told me of her awe in sighting bald eagles recently. Some good news for a change. Peace out.

BTW, do you know if Red Tails migrate or are permanent residents? (This is in Zone 7/NYC/NJ Metro Area.)

Dead trees are important to a lot of nesting birds (and insects of course too), maybe even bats. I had a dead river birch along my pond, and yellow tailed woodpeckers nested there for two years.

Well, the "untended" areas would be helpful for the beetle larvae. They like that kind of environment. What humans tend to think of as chaos :)

"Well, the "untended" areas would be helpful for the beetle larvae."

That's interesting. Maybe that was the factor and not the overabundance of cut lumber (maybe both?), because with the downed vegetation, I could not mow, weed, or even walk out back. It was a tangled mess of fallen branches, vines, giant "weeds", etc. (looked like a plane had crashed in the jungle!)

Red tailed hawks don't seem to migrate. A good place to see them in
winter is along the Thruway in Greene Co. They sit on dead trees,
waiting for the cars to do their hunting for them..We used to
have a lot of dead trees in the swamp. My guess was that they sprouted
during a severe drought in the 1960's, grew for about 10 years, then
were killed when the water table went back to normal. Most of them have
fallen over in the last ten years. The last one I heard, but it took me a
day or two to figure out which one was missing. Needless to say, there
aren't any buildings near this. The most important things in the line of
fire are a yellow buckeye and a Little Girl magnolia.

On falling over!

Yes, that is one thing that you DO have to worry about with sick, dying or dead trees..., at least with the BIG ONES! That's why you don't hesitate about removing the ones anywhere near the fall zone!

The Pileated woodpecker is one good reason to leave some dead wood and trees around your lot. The first one I ever saw was one pecking on the standpipe on the roof of my house. He made a terrific noise.

Since then I have seen them when we lived in Indiana and now in North Carolina. Once you see this crow sized woodpecker on a tree in your yard, you will never forget it.

https://en.wikipedia.org/wiki/Pileated_woodpecker

When you see him because of his head he is a quite primitive looking bird./

He is worth putting up with the ugliness of the dead tree.

Dead trees can be kinda neat in their own way. In most sanitoriums, err, subdivisions ppl manicure their grass like they should tend to their children. Guess it doesn't talk back lol.

In a natural place or tree line where it won't fall on my car or house, leave it

A dead standing tree is often referred to as a snag. At any given time, about 10 percent of the forest is dead trees (mostly already on the ground, but a few standing) and they are essential to the forest. Some plants like lady slippers seems to have a relationship with the fungus that grows off a rotting pine tree log.

In my backyard, I have removed one dead pine (too close to house) and let two other dead pines come crashing down (they were leaning away from house.) Each was about 8 to 10 inches in diameter. Also, I have several dead sweet gum saplings. Two are standing and one I pushed over last summer.

Of the two pines that have crashed, one I have let be in the yard, but I did cut one up until my chainsaw broke.

Before the trees fell, birds has hollowed nesting spots in them.

The sweet gum that I pushed over has some pretty cool mushrooms growing on it this summer. I think I will let it be.

Krnuttle we have one of those giant woodpeckers on our wooded cul de sac! They are quite awesome and they swoop and fly so quickly too.

Small (hairy and downy) woodpeckers were foraging on the snag that my neighbor in the back had until earlier this year. They could move up and down the snag as fast as the fastest squirrel, but unlike squirrels that move head down on 4 legs, woodpeckers move down with their heads up on their 2 legs and strong tails, it amused me every time I saw it :-)

I have learned that the cost of taking down dead trees is often far higher than the cost of repairing the damage of letting it fall, even on my house! If the wood isn't good for burning in my fireplace, I don't stack the logs but spread them around on the ground and plant ferns amongst them, line paths, make steps, fill hugelkultur beds.. Learned that a dead tree supports more life than a live one, which is a comforting thought in contemplating my own mortality.

Yeah, cemeteries have the best trees, even cemeteries of non-gardeners 8^/

Greenlawn Cemetery in Columbus is famous for its trees. It's also a great place for birding.

While they were doing other tree work I had the guys cut back the limbs of the the big dead ash but not to the trunk. I had started training a climbing hydrangea up it years before and damned if I was going to give it up just because its tree died. The climbing hydrangea loves it and covers the trunk and branches completely. It is not close to the house and if it falls it won't take out the house or us.

OTOH there's a 6 ft Satomi Dogwood right smack in middle of the front yard. It didn't make it through the winter. I was hoping it would green up, but it is dead. And Depressing. It has to go.