We present results of the cross-correlation Lyα intensity mapping with Subaru/Hyper Suprime-Cam (HSC) ultra-deep narrowband images and Lyα emitters (LAEs) at z = 5.7 and 6.6 in a total area of 4 deg2. Although an overwhelming amount of data quality controls have been performed for the narrowband images, we further conduct extensive analyses evaluating systematics of large-scale point-spread function wings, sky subtractions, and unknown errors based on physically uncorrelated signals and sources found in real HSC images and object catalogs, respectively. Removing the systematics, we carefully calculate cross-correlations between Lyα intensity of the narrowband images and the LAEs. We tentatively identify very diffuse Lyα emission with the ≃3σ (≃2σ) significance at ⪆100 comoving kiloparsecs (ckpc) far from the LAEs at z = 5.7 (6.6), around and probably even beyond a virial radius of star-forming galaxies with M h ∼ 1011 M o˙. The diffuse Lyα emission possibly extends up to 1000 ckpc with the surface brightness of 10-20-10-19 erg s-1 cm-2 arcsec-2. We confirm that the small-scale (<150 ckpc) Lyα radial profiles of LAEs are consistent with those obtained by recent Multi-Unit Spectroscopic Explorer observations. Comparisons with numerical simulations suggest that the large-scale (∼150-1000 ckpc) Lyα emission are not explained by unresolved faint neighboring galaxies including satellites, but by a combination of Lyα photons emitted from the central LAE and other unknown sources, such as cold-gas streams and galactic outflow. We find no evolution in the Lyα radial profiles of our LAEs from z = 5.7 to 6.6, where theoretical models predict a flattening of the profile slope made by cosmic reionization, albeit with our moderately large observational errors.
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