What I saw after the sun had set was really remarkable. The sky was very clear, and above the horizon I started noticing an expansive dark area with a pretty sharp edge, gradually consuming the sky. I soon realized that what I was seeing was the shadow of the Earth in the atmosphere. Inside the shadow, the sun had already set, but in the brighter area above the shadow, the sun would have still been directly visible.
I am able to replicate this effect in my sky renderer.
Here's a render at twilight, from the ground, facing away from the sun. You can clearly see the shadow of the Earth in the lower part of the image above the horizon (the ground is the sharp, rectangular, solid-colored area at the bottom). You can even see the anti-twilight arch!
away from sun.
And below is my earlier twilight render, looking in the direction of the sun, for comparison. The exposure on this image is three stops lower than the shadow image above. I raised the exposure on the image above because the sky was much darker in the direction opposite the sun.