The galaxy-halo size relation of low-mass galaxies in FIRE

Galaxy sizes correlate closely with the sizes of their parent dark matter haloes, suggesting a link between halo formation and galaxy growth. However, the precise nature of this relation and its scatter remains to be understood fully, especially for low-mass galaxies. We analyse the galaxy-halo size relation for low-mass ($M_\star \sim 10^{7-9} {\rm M_\odot}$) central galaxies over the past 12.5 billion years with the help of cosmological volume simulations (FIREbox) from the Feedback in Realistic Environments (FIRE) project. We find a nearly linear relationship between the half-stellar mass galaxy size $R_{1/2}$ and the parent dark matter halo virial radius $R_{\rm vir}$. This relation evolves only weakly since redshift $z = 5$: $R_{1/2} {\rm kpc} = (0.053\pm0.002)(R_{\rm vir}/35 {\rm kpc})^{0.934\pm0.054}$, with a nearly constant scatter $\langle \sigma \rangle = 0.084 [{\rm dex}]$. Whilst this ratio is similar to what is expected from models where galaxy disc sizes are set by halo angular momentum, the low-mass galaxies in our sample are not angular momentum supported, with stellar rotational to circular velocity ratios $v_{\rm rot} / v_{\rm circ} \sim 0.15$. Introducing redshift as another parameter to the GHSR does not decrease the scatter. Furthermore, this scatter does not correlate with any of the halo properties we investigate -- including spin and concentration -- suggesting that baryonic processes and feedback physics are instead critical in setting the scatter in the galaxy-halo size relation. Given the relatively small scatter and the weak dependence of the galaxy-halo size relation on redshift and halo properties for these low-mass central galaxies, we propose using galaxy sizes as an independent method from stellar masses to infer halo masses.