Empress. III. morphology, stellar population, and dynamics of extremely metal poor galaxies (empgs): Are empgs local analogs of high-z young galaxies?

We present the morphology and stellar population of 27 extremely metal poor galaxies (EMPGs) at $z\sim0$ with metallicities of $0.01-0.1$ Z$_{\odot}$. We conduct multi-component surface brightness (SB) profile fitting for the deep Subaru/HSC $i$-band images of the EMPGs with the Galfit software, carefully removing the SB contributions of potential associated galaxies (PAGs). We find that the EMPGs with a median stellar mass of $\log(M_{*}/{\rm M}_{\odot})=5.77$ have a median Sersic index of $n=1.08$ and a median effective radius of $r_{\rm e}=176$ pc, suggesting that typical EMPGs are very compact disk galaxies. We compare the EMPGs with $z\sim 6$ galaxies and local galaxies on the size-mass ($r_{\rm e}$--$M_*$) diagram, and identify that the majority of the EMPGs have a $r_{\rm e}$--$M_*$ relation similar to $z\sim0$ star-forming galaxies rather than $z\sim6$ galaxies. Not every EMPG is a local analog of high-$z$ young galaxies in the $r_{\rm e}$--$M_*$ relation. We also study the PAGs of our galaxies, and find that 23 out of the 27 EMPGs show detectable PAGs within the projected distance of 10 kpc. The PAGs have median values of $n=0.93$, $r_{\rm e}=1.41$ kpc, and $\log(M_{*}/{\rm M}_{\odot})=7.47$ that are similar to those of local dwarf irregulars and ultra-diffuse galaxies. A spectrum of one EMPG-PAG system, so far available, indicates that the PAG is dynamically related to the EMPG with a median velocity difference of $\Delta V=96.1$ km s$^{-1}$. This moderately-large $\Delta V$ cannot be explained by the dynamics of the PAG, but likely by the infall on the PAG. EMPGs may form in infalling gas, and become part of PAG disks undergoing further metal enrichment.