Ask HN: What is volume of login requests for services like FB, Twitter?

I am curious to see how many login requests (per second) are served by high traffic services like FB, Twitter, gmail, instagram. What is their architecture to achieve that login scale? Is login a scalability problem for them at all given that most of them have long term login sessions, even more so on mobile devices.

Please note that I am not looking for regular data request rates but purely login rate.

Also, I am curious to see if there are set times where the login volume spikes. For corporations typically the volume is highest between 8-10 when people come in to work. What will it be for these services?