We present the redshift evolution of the radial surface brightness (SB) profile of the rest-frame UV and optical stellar continua for 9119 Lya emitters (LAEs) at z~0-8 and 0-2, respectively. Using Hubble Space Telescope data and the LAE catalogs taken from the literature, we derive the structural quantities of the 9119 LAEs and ~180,000 comparison galaxies of photo-z star-forming galaxies (SFGs) and Lyman break galaxies (LBGs) by the well-tested profile fitting. From 936 well-fitted LAEs, we carefully define the homogeneous sample of LAEs falling in the same ranges of UV-continuum luminosity and Lya equivalent width over z~0-8, and evaluate the redshift evolution. We find that the effective radius r_e distribution is represented by a log-normal function, and that the median Sersic index is almost constant at n~1-1.5 for the LAEs over z~0-7, suggesting that typical LAEs have a stellar-disk morphology. The size-luminosity relation of the LAEs monotonically decreases towards high-z, following size-luminosity relations of SFGs and LBGs. The median r_e values of the LAEs significantly evolve as r_e~(1+z)^-1.37, similar to those of the SFGs and LBGs in the same luminosity range, in contrast with the claims of no evolution made by previous studies whose LAE samples are probably biased to faint sources at low-z. The r_e distribution, star-formation rate surface densities, and stellar-to-halo size ratios of the LAEs are comparable with those of the SFGs and LBGs, indicating that LAEs have stellar components similar to SFGs and LBGs with a Lya emissivity controlled by the non-stellar physics such as geometry, kinematics, and ionization states of the inter-stellar/circum-galactic medium.
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