A simple numerical experiment on the dust temperature bias for Lyman break galaxies at z ≳ 5

Some studies suggest that the dust temperatures (T_d) in high-redshift (z ≳ 5) Lyman break galaxies (LBGs) are high. However, possible observational bias in T_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 Atacama Large Millimetre/submillimetre Array (ALMA) is biased in terms of T_d. We show that ALMA tends to miss high-T_d objects even at total dust luminosity L_IR > 10¹¹ L_⊙. 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_d and low dust abundance. For ALMA Band 6, there is no tendency of high-T_d LBGs being more easily detected in our experiment. Thus, we suggest that the observed trend of high T_d in z ≳ 5 LBGs is real. We also propose that the 450 $\rm{\mu m}$ band is useful in further clarifying the dust temperatures. To overcome the current shallowness of 450 $\rm{\mu m}$ observations, we examine a future Antarctic 30-m class telescope with a suitable atmospheric condition for wavelengths ${\lesssim}450~\rm{\mu m}$, where the detection is not confusion-limited. We find that, with this telescope, an L_IR-selected sample with log (L_IR/L_⊙) > 11 is constructed for z ≳ 5, and detection in the intermediate-M_⋆ (stellar mass) range [9 < log (M_⋆/M_⊙) < 9.5] is much improved, especially at high T_d.