A simple numerical experiment on the dust temperature bias for Lyman
  break galaxies at $z\gtrsim 5$
  Some studies suggest that the dust temperatures ($T_\mathrm{d}$) in
high-redshift ($z\gtrsim 5$) Lyman break galaxies (LBGs) are high. However,
possible observational bias in $T_\mathrm{d}$ is yet to be understood. Thus, we
perform a simple test using random realizations of LBGs with various stellar
masses, dust temperatures, and dust-to-stellar mass ratios, and examine how the
sample detected by ALMA is biased in terms of $T_\mathrm{d}$. We show that ALMA
tends to miss high-$T_\mathrm{d}$ objects even at total dust luminosity. LBGs
are, however, basically selected by the stellar UV luminosity. The
dust-temperature bias in a UV-selected sample is complicated because of the
competing effects between high $T_\mathrm{d}$ and low dust abundance. For ALMA
Band 6, there is no tendency of high-$T_\mathrm{d}$ LBGs being more easily
detected in our experiment. Thus, we suggest that the observed trend of high
$T_\mathrm{d}$ in $z\gtrsim 5$ LBGs is real. We also propose that the 450
$\mu$m band is useful in further clarifying the dust temperatures. To overcome
the current shallowness of 450 $\mu$m observations, we examine a future
Antarctic 30-m class telescope with a suitable atmospheric condition for
wavelengths $\lesssim 450~\mu$m, where the detection is not confusion-limited.
We find that, with this telescope, an $L_\mathrm{IR}$-selected sample with
$\log(L_\mathrm{IR}/\mathrm{L}_{\odot})>11$ is constructed for $z\gtrsim 5$,
and detection in the intermediate-$M_\star$ (stellar mass) range [$9<\log
(M_\star /M_{\odot})<9.5$] is much improved, especially at high $T_\mathrm{d}$.
