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 {\sc Galfit} software,
carefully removing the SB contributions of tails. We find that the EMPGs with a
median stellar mass of $\log(M_{*}/{\rm M}_{\odot})=6.0$ have a median
S{\'e}rsic index of $n=1.1$ and a median effective radius of $r_{\rm e}=200$
pc, suggesting that typical EMPGs have very compact disk. We compare the EMPGs
with $z\sim6$ 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. A spectrum of one pair of EMPG and tail, so far
available, indicates that the tail is dynamically related to the EMPG with a
median velocity difference of $\Delta V=101\pm32$ km s$^{-1}$. This
moderately-large $\Delta V$ cannot be explained by the dynamics of the tail,
but likely by the infall on the tail. For the first time, we may identify the
metal-poor star-forming system just now infalling into the tail.
