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We present the first comparison of observed stellar continuum spectra ofhigh-redshift galaxies and mock galaxy spectra generated from hydrodynamicalsimulations. The mock spectra are produced from the IllustrisTNG TNG100simulation combined with stellar population models and take into account dustattenuation and realistic observational effects (aperture effects and noise).We compare the simulated $D_n4000$ and EW(H$\delta$) of galaxies with $10.5\leq \log(M_\ast/M_\odot) \leq 11.5$ at $0.6 \leq z \leq 1.0$ to the observeddistributions from the LEGA-C survey. TNG100 globally reproduces the observeddistributions of spectral indices, implying that the age distribution ofgalaxies in TNG100 is generally realistic. Yet there are small but significantdifferences. For old galaxies, TNG100 shows small $D_n4000$ when compared toLEGA-C, while LEGA-C galaxies have larger EW(H$\delta$) at fixed $D_n4000$.There are several possible explanations: 1) LEGA-C galaxies have overall olderages combined with small contributions (a few percent in mass) from younger($<1$~Gyr) stars, while TNG100 galaxies may not have such youngsub-populations; 2) the spectral mismatch could be due to systematicuncertainties in the stellar population models used to convert stellar ages andmetallicities to observables. In conclusion, the latest cosmological galaxyformation simulations broadly reproduce the global age distribution of galaxiesat $z\sim1$ and, at the same time, the high quality of the latest observed andsimulated datasets help constrain stellar population synthesis models as wellas the physical models underlying the simulations.

Towards precise galaxy evolution: a comparison between spectral indices of $z\sim1$ galaxies in the IllustrisTNG simulation and the LEGA-C survey