Is Osteospermum the flower that opens in sun and closes without sun?

Yes, basically - it opens when the light levels are high enough and closes when the day is dull or in late afternoon.

As Spritzhenry says to a certain extent, but the flowers that realy close as soon as the sun goes in are Dimorphotheca which come in lovely colours and Aptenia (Mesembryanthemum) as I new them. We had a very hot South west facing Court yard in the old house which used to get very hot they used to be a picture there but no good if there is little sun.