The Ultimately Large Telescope -- what kind of facility do we need to detect Population III stars?

The launch of the James Webb Space Telescope will open up a new window for observations at the highest redshifts, reaching out to z~15. However, even with this new facility, the first stars will remain out of reach, as they are born in small minihalos with luminosities too faint to be detected even by the longest exposure times. In this paper, we investigate the basic properties of the Ultimately Large Telescope, a facility that can detect Population III star formation regions at high redshift. Observations will take place in the near-infrared and therefore a moon-based facility is proposed. An instrument needs to reach magnitudes as faint as 39mag$_mathrm{AB}$, corresponding to a primary mirror size of about 100m in diameter. Assuming JWST NIRCam filters, we estimate that Pop III sources will have unique signatures in a colour-colour space and can be identified unambiguously.