What is the minimum power of signal at 10 billion light years away we can detect?

Answer 1

The Hubble Space Telescope detected the aggregate power of 1000 suns (order of magnitude) after a 1 million second integration onto the far-field CCD array, at that distance (order of magnitude) -- in the Hubble "ultra-deep-field" picture.

The ~1000 suns would be an estimate of a small portion of one of the furthest galaxies that integrated onto 1 pixel of the CCD array.

That's about as close an estimate as I can come up with.

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