Galaxy-halo size relation from Sloan Digital Sky Survey Data Release 7 and the ELUCID simulation

Based on galaxies in the Sloan Digital Sky Survey Data Release 7 (SDSS DR7) and dark matter haloes in the dark matter only, cosmological and constrained ELUCID simulation, we investigate the relation between the observed radii of central galaxies with stellar mass $\gtrsim 10^{8} h^{-2}{\rm M}_\odot$ and the virial radii of their host dark matter haloes with virial mass $\gtrsim 10^{10.5} h^{-1}{\rm M}_\odot$, and the dependence of galaxy-halo size relation on the halo spin and concentration. Galaxies in observation are matched to dark matter (sub-)haloes in the ELUCID simulation using a novel neighborhood subhalo abundance matching method. For galaxy 2D half-light radii $R_{50}$, we find that early- and late-type galaxies have the same power-law index 0.55 with $R_{50} \propto R_{\rm vir}^{0.55}$, although early-type galaxies have smaller 2D half-light radii than late-type galaxies at fixed halo virial radii. When converting the 2D half-light radii $R_{50}$ to 3D half-mass radii $r_{1/2}$, both early- and late-type galaxies display similar galaxy-halo size relations with $\log r_{1/2} = 0.55 \log (R_{\rm vir}/210 h^{-1}{\rm kpc}) + 0.39$. We find that the galaxy-halo size ratio $r_{1/2}/ R_{\rm vir}$ decreases with increasing halo mass. At fixed halo mass, there is no significant dependence of galaxy-halo size ratio on the halo spin or concentration.