Red giant stars are perhaps the most important type of stars for Galactic and extra-galactic archaeology : they are luminous , occur in all stellar populations , and their surface temperatures allow precise abundance determinations for many different chemical elements .
Yet , the full star formation and enrichment history of a galaxy can be traced directly only if two key observables can be determined for large stellar samples - age and chemical composition .
While spectroscopy is a powerful method to analyse the detailed abundances of stars , stellar ages are the ” missing link in the chain ” , since they are not a direct observable .
However , spectroscopy should be able to estimate stellar masses , which for red giants directly infer ages provided their chemical composition is known .

Here we establish a new empirical relation between the shape of the hydrogen line in the observed spectra of red giants and stellar mass determined from asteroseismology .
The relation allows to determine stellar masses and ages with the accuracy of 10-15 % .
The method can be used with confidence for stars in the following range of stellar parameters : 4000 < T _ { eff } < 5000 K , 0.5 < \log g < 3.5 , -2.0 < [ Fe / H ] < 0.3 , and luminosities \log L / L _ { Sun } < 2.5 .
Our analysis provides observational evidence that the H _ { \alpha } spectral characteristics of red giant stars are tightly correlated with their mass and therefore their age .
We also show that the method samples well all stellar populations with ages above 1 Gyr .
Targeting bright giants , the method allows to obtain simultaneous age and chemical abundance information far deeper than would be possible with asteroseismology , extending the possible survey volume to remote regions of the Milky Way and even to neighbouring galaxies like Andromeda or the Magellanic Clouds already with present instrumentation , like VLT and Keck facilities .