We present detailed morphological properties of Lyman alpha emitters (LAEs) at z~ 5.7 in the COSMOS field, based on {it Hubble Space Telescope} Advanced Camera for Surveys (ACS) data. The ACS imaging in the F814W filter covered 85 LAEs of the 119 LAEs identified in the full two square degree field, and 47 LAEs of them are detected in the ACS images. Nearly half of them are spatially extended with a size larger than 0.15 arcsec (~0.88 kpc at z=5.7) up to 0.4 arcsec (~2.5 kpc at z=5.7). The others are nearly unresolved compact objects. Two LAEs show double-component structures, indicating interaction or merging of building components to form more massive galaxies. By stacking the ACS images of all the detected sources, we obtain a Sersic parameter of n~0.7 with a half-light radius of 0.13 arcsec (0.76 kpc), suggesting that the majority of ACS detected LAEs have not spheroidal-like but disk-like or irregular light profiles. Comparing ACS F814W magnitudes (I_814) with Subaru/Suprime-Cam magnitudes in the NB816, i, and z bands, we find that the ACS imaging in the F814W band mainly probes UV continuum rather than Lyman alpha line emission. UV continuum sizes tend to be larger for LAEs with larger Lyalpha emission regions as traced by the NB816 imaging. The non-detection of 38 LAEs in the ACS images is likely due to the fact that their surface brightness is even too low both in the UV continuum and Lyalpha emission. Estimating I_814 for the LAEs with ACS non-detection from the z and NB816 magnitudes, we find that 16 of these are probably LAEs with a size larger than 0.15 arcsec in UV continuum. All these results suggest that our LAE sample contains systematically larger LAEs in UV continuum size than those previously studied at z~6.
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