The redshift of a galaxy directly relates to that galaxy's age. As the Universe expands, ancient light traveling through the universe will get stretched. This ‘light-stretching' is known as redshift. The higher the redshift, the further the light has traveled, so the older it is.
Therefore, from the redshift measurements of this small collection of galaxies in the UDF, the researchers have found that a definite spiral galaxy structure begins to form for galaxies at redshift 1.8, which equates to approximately 3.7 billion years after the Big Bang. However, these are only the embryos of spiral galaxies, the "woolly"-type galaxies with very basic structures smeared with nebulous clouds of star formation. It's not until approximately 8 billion years after the Big Bang (redshift 0.6) that more complex, multi-arm spiral structures form.
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"The observations of different spiral types are consistent with the interpretation that clumpy disks form first and then transition to spirals as the accretion rate and gas velocity dispersion decrease, and the growing population of old fast-moving stars begins to dominate the disk mass," they write.