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Buteo platypterus
Emma, they said they see up to 100,000 a day sometimes!! look up "river of raptors Costa Rica" and "Kekoldi raptor viewing" in Costa Rica...there's a viewing tower and a 360 degree view! I should post my pics from there but it doesn't do it justice!
I would definitely go with what Liam says, Thanks for adding on that you saw 10,000 at a time. That makes it even more possible.
Liam suggested Broad-Winged Hawks above (trust him!)...I know Swainson's Hawks migrate in groups like this...we have them here in Colo. I saw the fall migration in Costa Rica and we saw probably 10,000 turkey vultures in 2 hours...riding the thermals just like this! Great spotting!
usually birds of prey do collect in great numbers in the sky. I have seen turkey vultures , at least 20.
this seems to be a really large number! 70 at least! Wings is a big clue!