  We probed the surface environment of large ($>$80 km in diameter) T-type
asteroids, a taxonomic type relatively ill-constrained as an independent group,
and discussed their place of origin. We performed spectroscopic observations of
two T-type asteroids, (96) Aegle and (570) Kythera, over 2.8--4.0 $\mu$m using
the Subaru telescope. With other T-types' spectra available in the literature
and survey datasets, we strove to find commonalities and global trends in this
group. We also utilised the asteroids' polarimetric data and meteorite spectra
to constrain their surface texture and composition. Our targets exhibit red
$L$-band continuum slopes similar to (1) Ceres and 67P/Churyumov-Gerasimenko,
and have an OH-absorption feature with band centres $<$2.8 $\mu$m. (96) Aegle
hints at a shallow N--H band near 3.1 $\mu$m and C--H band of organic materials
over 3.4--3.6 $\mu$m, whereas no diagnostic bands of water ice and other
volatiles exceeding the noise of the data were seen for both asteroids. The
large T-type asteroids but (596) Scheila display similar spectral shapes to our
targets. $\sim$50 \% of large T-types contain an absorption band near 0.6--0.65
$\mu$m likely associated with hydrated minerals. For T-type asteroids (except
Jupiter Trojans) of all sizes, we found a weak correlation: the smaller the
diameter and the closer the Sun, the redder the visible slope. The 2.9-$\mu$m
band depths of large T-types suggest that they might have experienced aqueous
alteration comparable to Ch-types but more intense than most of the main-belt
asteroids. The polarimetric phase curve of the T-types is well described by a
particular surface structure and their 0.5--4.0 $\mu$m reflectance spectra
appear most similar to CI chondrites with grain sizes of $\sim$25--35 $\mu$m.
Taken as a whole, we propose that large T-type asteroids might be dislodged
roughly around 10 au in the early solar system.
