The Impact of Galaxy-halo Size Relations on Galaxy Clustering Signals

Galaxies come in different sizes and morphologies, and these differences are thought to correlate with properties of their underlying dark matter halos. However, identifying the specific halo property that controls the galaxy size is a challenging task, especially because most halo properties depend on one another. In this work, we demonstrate this challenge by studying how the galaxy-halo size relations impact the galaxy clustering signals. We investigate the reason that a simple linear relation model, which prescribes that the galaxy size is linearly proportional to the dark matter halo’s virial radius, can still produce clustering signals that match the observational data reasonably well. We find that this simple linear relation model for galaxy sizes, when combined with the subhalo abundance matching technique, introduces an implicit dependence on the halo formation history. As a result, the effect of halo assembly bias enters the resulting galaxy clustering, especially at lower stellar masses, producing a clustering signal that resembles the observed one. At higher stellar masses, the effect of halo assembly bias weakens and is partially canceled out by the effect of halo bias, and the clustering of large and small galaxies becomes more similar. This combined effect implies that small and large galaxies not only occupy halos of different masses, but they must also occupy halos of different assembly histories. Our study highlights the challenge of identifying a particular halo property that controls galaxy sizes through constraints from galaxy clustering alone.