Astronomy is still in public beta. We launch sites only when they've demonstrated the ability to sustain growth. For a rough idea of what we look for, see the Area 51 statistics. Like many sites in beta, Astronomy doesn't have the rate of new questions we are looking for yet. Every other measure signals this is a solid community that we are happy to have on our network. How long will the site have before it graduates? As long as necessary.
Besides the traffic and engagement numbers, we also look at the content quality. Last spring, we ran a self-evaluation so that you could tell us how things are going:
Let's get critical: Apr 2014 Site Self-Evaluation
When I reviewed the results, they looked fairly typical of a mid-stage beta: there are some things that can be improved, but the site is clearly accomplishing it's mission to provide expert answers to Astronomy questions.
Figuring out how to increase questions organically is a puzzle. So far, the best method I've found is the weekly topic challenge. If you want to help your site grow, this is something I'd encourage you to try out.
The mobile app doesn't really make a distinction between a graduated site and betas. The only real way to tell is to look at the icon in the site list. As long as Astronomy is in beta, it will have the generic speech bubble with a capital
A in it. When our designers create a skins for graduated sites, they'll change the icon too. (And personally I look forward to what they will do with the design of this site when it graduates!)