https://doi.org/10.1140/epja/s10050-026-01838-z
Review
The time-delay model and its applications to galactic archaeology
1
Department of Physics, Trieste University, Via Fabio Valerio 2, 34143, Trieste, Friuli-Venezia-Giulia, Italy
2
Osservatorio Astronomico di Trieste, INAF, Via G.B. Tiepolo, 11, 34131, Trieste, Friuli-Venezia-Giulia, Italy
3
Sezione di Trieste, INFN, Via Fabio Valerio, 2, 34143, Trieste, Friuli-Venezia-Giulia, Italy
4
IFPU, Institute for the Fundamental Physics of the Universe, Via Beirut, 2, 34151, Trieste, Friuli-Venezia-Giulia, Italy
a
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Received:
2
December
2025
Accepted:
16
March
2026
Published online:
27
April
2026
Abstract
The time-delay model is the way we interpret the diagram [X/Fe] vs. [Fe/H], where X is the abundance of a generic element from carbon to uranium. This interpretation is based on the lifetimes of stars of different masses producing different elements. The abundance of Fe ([Fe/H]) traces the “stellar metallicity” and is due to supernovae Type Ia, which are believed to be the major producers of Fe, and in part to supernovae core-collapse. In particular, if X is an 
-element, produced on short timescales from massive stars, the ratio [/Fe] will show an overabundance of the -elements relative to Fe at low metallicity. In fact, the bulk of Fe is produced with a time delay relative to -elements, since Type Ia supernovae are white dwarfs in binary systems and they can have lifetimes as long as the age of the Universe. In this paper, I will show how powerful is the time-delay model in order to interpret the abundance patterns observed in stars and interstellar gas, since it allows us to put constraints on stellar nucleosynthesis as well as on the star formation histories of galaxies. I will present some applications of the time-delay model, in particular to the chemical evolution of the Milky Way and galaxies of different morphological type as well as to the identification of high redshift objects by means of their abundances.
Communicated by Maria Borge.
© The Author(s) 2026
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