We present statistical properties of diffuse Lyman-alpha halos (LAHs) around high-$z$ star-forming galaxies with large Subaru samples of Lyman-alpha emitters (LAEs) at $z=2.2$. We make subsamples defined by the physical quantities of LAEs central Lyman-alpha luminosities, UV magnitudes, Lyman-alpha equivalent widths, and UV slopes, and investigate LAHs radial surface brightness (SB) profiles and scale lengths $r_n$ as a function of these physical quantities. We find that there exist prominent LAHs around LAEs with faint Lyman-alpha luminosities, bright UV luminosities, and small Lyman-alpha equivalent widths in cumulative radial Lyman-alpha SB profiles. We confirm this trend with the anti-correlation between $r_n$ and Lyman-alpha luminosities (equivalent widths) based on the Spearmans rank correlation coefficient that is $rho=-0.9$ ($-0.7$) corresponding to the $96%$ ($93%$) confidence level, although the correlation between $r_n$ and UV magnitudes is not clearly found in the rank correlation coefficient. Our results suggest that LAEs with properties similar to typical Lyman-break galaxies (with faint Lyman-alpha luminosities and small equivalent widths) possess more prominent LAHs. We investigate scenarios for the major physical origins of LAHs with our results, and find that the cold stream scenario is not preferred, due to the relatively small equivalent widths up to $77$AA in LAHs that include LAEs central components. There remain two possible scenarios of Lyman-alpha scattering in circum-galactic medium and satellite galaxies that cannot be tested with our observational data.
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