We analyze an extremely deep 450-$\mu$m image ($1\sigma=0.56$\,mJy\,beam$^{-1}$) of a $\simeq 300$\,arcmin$^{2}$ area in the CANDELS/COSMOS field as part of the SCUBA-2 Ultra Deep Imaging EAO Survey (STUDIES). We select a robust (signal-to-noise ratio $\geqslant 4$) and flux-limited ($\geqslant 4$\,mJy) sample of 164 sub-millimeter galaxies (SMGs) at 450-$\mu$m that have $K$-band counterparts in the COSMOS2015 catalog identified from radio or mid-infrared imaging. Utilizing this SMG sample and the 4705 $K$-band-selected non-SMGs that reside within the noise level $\leqslant 1$\,mJy\,beam$^{-1}$ region of the 450-$\mu$m image as a training set, we develop a machine-learning classifier using $K$-band magnitude and color-color pairs based on the thirteen-band photometry available in this field. We apply the trained machine-learning classifier to the wider COSMOS field (1.6\,deg$^{2}$) using the same COSMOS2015 catalog and identify a sample of 6182 450-$\mu$m SMG candidates with similar colors. The number density, radio and/or mid-infrared detection rates, redshift and stellar mass distributions, and the stacked 450-$\mu$m fluxes of these SMG candidates, from the S2COSMOS observations of the wide field, agree with the measurements made in the much smaller CANDELS field, supporting the effectiveness of the classifier. Using this 450-$\mu$m SMG candidate sample, we measure the two-point autocorrelation functions from $z=3$ down to $z=0.5$. We find that the 450-$\mu$m SMG candidates reside in halos with masses of $\simeq (2.0\pm0.5) \times10^{13}\,h^{-1}\,\rm M_{\odot}$ across this redshift range. We do not find evidence of downsizing that has been suggested by other recent observational studies.

中文翻译：

---

SCUBA-2 超深成像 EAO 调查（研究）。四、亚毫米星系的空间聚集和晕质量

我们分析了 $\simeq 300$\,arcmin$^{2}$ 的极深 450-$\mu$m 图像（$1\sigma=0.56$\,mJy\,beam$^{-1}$）作为 SCUBA-2 超深成像 EAO 调查 (STUDIES) 的一部分，CANDELS/COSMOS 领域的区域。我们选择了 450-$\mu$m 的 164 个亚毫米星系 (SMG) 的稳健（信噪比 $\geqslant 4$）和通量限制（$\geqslant 4$\,mJy）样本在 COSMOS2015 目录中具有通过无线电或中红外成像识别的 $K$ 波段对应物。利用此 SMG 样本和位于 450-$\mu$ 噪声水平 $\leqslant 1$\,mJy\,beam$^{-1}$ 区域内的 4705 $K$-band-selected non-SMGs m 图像作为训练集，我们基于该领域可用的 13 波段光度测量，使用 $K$ 波段幅度和颜色-颜色对开发了一个机器学习分类器。我们使用相同的 COSMOS2015 目录将经过训练的机器学习分类器应用于更广泛的 COSMOS 领域 (1.6\,deg$^{2}$)，并识别具有相似颜色的 6182 450-$\mu$m SMG 候选样本。这些 SMG 候选对象的数密度、射电和/或中红外探测率、红移和恒星质量分布以及堆积的 450-$\mu$m 通量，来自 S2COSMOS 宽视场的观测，与所做的测量一致在更小的 CANDELS 字段中，支持分类器的有效性。使用这个 450-$\mu$m SMG 候选样本，我们测量了从 $z=3$ 到 $z=0.5$ 的两点自相关函数。我们发现 450-$\mu$m SMG 候选者位于光晕中，质量为 $\simeq (2.0\pm0.5) \times10^{13}\,h^{-1}\,\rm M_{\ odot}$ 在这个红移范围内。