  We present observational evidence for a stellar Fundamental Metallicity
Relation (FMR), a smooth relation between stellar mass, star-formation rate
(SFR) and the light-weighted stellar metallicity of galaxies (analogous to the
well-established gas-phase FMR). We use the flexible, non-parametric software
pPXF to reconstruct simultaneously the star-formation and chemical-enrichment
history of a representative sample of galaxies from the local MaNGA survey. We
find that (i) the metallicity of individual galaxies increases with cosmic time
and (ii) at all stellar masses, the metallicity of galaxies is progressively
higher, moving from the star-burst region above the main sequence (MS) towards
the passive galaxies below the MS, manifesting the stellar FMR. These findings
are in qualitative agreement with theoretical expectations from IllustrisTNG,
where we find a mass-weighted stellar FMR. The scatter is reduced when
replacing the stellar mass $M_{*}$ with $M_{*}/R_{\rm e}$ (with $R_{\rm e}$
being the effective radius), in agreement with previous results using the
velocity dispersion $\sigma_{\rm e}$, which correlates with $M_{*}/R_{\rm e}$.
Our results point to starvation as the main physical process through which
galaxies quench, showing that metal-poor gas accretion from the
intergalactic/circumgalactic medium -- or the lack thereof -- plays an
important role in galaxy evolution by simultaneously shaping both their
star-formation and their metallicity evolutions, while outflows play a
subordinate role. This interpretation is further supported by the additional
finding of a young stellar FMR, tracing only the stellar populations formed in
the last 300 Myr. This suggests a tight co-evolution of the chemical
composition of both the gaseous interstellar medium and the stellar
populations, where the gas-phase FMR is continuously imprinted onto the stars
over cosmic times.
