A galaxy's accretion history unveiled from its integrated spectrum

We present a new method of quantifying a galaxy's accretion history from its integrated spectrum alone. Using full spectral fitting and calibrated regularization techniques we show how we can accurately derive a galaxy's mass distribution in age-metallicity space and further separate this into stellar populations from different chemical enrichment histories. By exploiting the fact that accreted lower mass galaxies will exhibit an offset to lower metallicities at fixed age compared to the in-situ stellar population, we quantify the fraction of light that comes from past merger events, that are long since mixed in phase-space and otherwise indistinguishable. Empirical age-metallicity relations (AMRs) parameterized for different galaxy masses are used to identify the accreted stellar populations and link them back to the progenitor galaxy's stellar mass. This allows us to not only measure the host galaxy's total ex-situ mass fraction ($f_{acc}$), but also quantify the relative amount of accreted material deposited by satellite galaxies of different masses, i.e. the accreted satellite mass function in analogy to the subhalo mass function. Using mock spectra of simulated, present-day galaxies from the EAGLE suite we demonstrate that our method can recover the total accreted fraction to within $\approx 12 \%$, the stellar mass of the most massive accreted subhalo to within $\approx 26 \%$ and the slope of the accreted satellite mass function to within $\approx 16 \%$ of the true values from the EAGLE merger trees. Future application of this method to observations could potentially provide us accretion histories of hundreds of individual galaxies, for which deep integrated light spectroscopy is available.