  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 Spearman's 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.
