[sunshinesnacks]

I think the section “Atmospheric refraction and the solar limb” near the end of the article addresses this.

[madcaptenor]

Not exactly; even after the sun is fully below the horizon there's some light. See the interactive graph - the times aren't long enough for twilight. But you can use a larger value of "a" in the equation above it to make that change.

[sunshinesnacks]

Yeah, you’re right. Something like civil twilight, as you mentioned above, should get it closer to what is being discussed here.