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I don't understand why a strong absorption line H$\delta$ indicates a young star population. First of all, a strong H$\delta$ line just means that I have more A-type stars, doesn't it? Where is the connection to the age of a galaxy?

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A-stars have a main sequence lifetime of < a billion years and are much more numerous in a burst of star formation than the higher mass, and much more luminous O/B stars. The Balmer lines, particularly H$\delta$ are particularly prominent in A-stars compared with both hotter and cooler stars.

Lots of H$\delta$ tells you that the light is being dominated by main-sequence stars that are aged between about 200 Myr (after which the more luminous OB stars have died) and 1 Gyr, after which the A-stars will have died and H$\delta$ would be considerably weaker in cooler, longer-lived stars.

This simple argument applies to a single burst of star formation - a simple, single stellar population. Prolonged, or multiple epochs, of star formation will confuse the issue and require more detailed modelling.

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