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The stellar mass assembly of galaxies can be affected by both secular andenvironmental processes. In this study, for the first time, we investigate thestellar mass assembly of $\sim90,000$ low redshift, central galaxies selectedfrom SDSS group catalogues (M$_{\rm Stellar}\gtrsim10^{9.5}$M$_{\odot}$,M$_{\rm Halo}\gtrsim10^{12}$M$_{\odot}$) as a function of both stellar and halomass. We use estimates of the times at which 10, 50 and 90 per cent of thestellar mass was assembled from photometric spectral energy distributionfitting, allowing a more complete investigation than single stellar ages alone.We consider trends in both stellar and halo mass simultaneously, findingdependencies of all assembly times on both. We find that galaxies with higherstellar masses (at constant halo mass) have on average older lookback times,similar to previous studies of galaxy assembly. We also find that galaxies athigher halo mass (at constant stellar mass) have younger lookback times,possibly due to a larger reservoir of gas for star formation. An exception tothis is a sub sample with high stellar-to-halo mass ratios, which are likelymassive, field spirals. We compare these observed trends to those predicted bythe TNG300 simulation, finding good agreement overall as a function of eitherstellar or halo mass. However, some differences in the assembly times (of up to$\sim 3$ Gyr) appear when considering both stellar and halo masssimultaneously, noticeably at intermediate stellar masses (M$_{\rm Stellar}\sim 10^{11}$ M$_{\odot}$). These discrepancies are possibly linked to thequenched fraction of galaxies and the kinetic mode AGN feedback implemented inTNG300.

The Stellar Mass Assembly of Low Redshift, Massive, Central Galaxies in SDSS and the TNG300 simulation