This work aims to investigate the fundamental plane, the Kormendy, the Faber-Jackson, and the size-luminosity relations for two galaxy samples (brightest cluster galaxies (BCGs) and isolated elliptical galaxies (IEs)) in different environments. These relations are investigated in different wavelength bands, griz, of the Sloan Digital Sky Survey (SDSS). We constructed a sample of 2002 BCGs from the redMaPPer clusters catalog with spectroscopic redshifts in the range ( $0.076 \leqslant \textit{z} \leqslant 0.394$ ). The sample of IEs consists of 550 objects and is extracted from the catalog of isolated galaxies (SDSS-based Isolated Galaxies, SIG) with spectroscopic redshifts range ( $0.01 \leqslant \textit{z} \leqslant 0.08$ ). In general, we found that slopes of all studied scaling relations are waveband dependent except for the Faber-Jackson relation. The fundamental plane (FP) for both samples steepens as one moves from shorter to longer wavelengths. We found that BCGs lie on a different FP from that of IEs. In average the coefficient a of BCGs is larger than that of IEs by about 5 $\sigma $ , while the coefficient b is larger by about 11 $\sigma $ . By studying the Kormendy relation (KR), we found that its slope varies through the waveband for both samples. Also, the slope of BCGs is smaller than that of IEs by about 7 $\sigma $ , while the intercept is smaller by about 12 $\sigma $ . We also examined the Faber-Jackson (FJ) relation and found that its slope is similar for all wavebands for both samples. BCGs defines a steeper FJ relation than IEs such that $\mbox{L} \varpropto \sigma ^{6.25}$ for BCGs and $\mbox{L} \varpropto \sigma ^{2.63}$ for IEs. We also studied the size-luminosity relation and found that its slope is decreasing slightly with waveband for both samples. We also found that BCGs define a steeper size-luminosity relation than IEs, in average the slope of BCGs is greater than that of IEs by $\sim 7\sigma $ .

中文翻译：

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最亮星团星系和孤立椭圆星系的基本平面

这项工作旨在研究不同环境下两个星系样本（最亮的星系团（BCG）和孤立的椭圆星系（IE））的基本平面、Kormendy、Faber-Jackson 和大小-光度关系。这些关系在斯隆数字巡天 (SDSS) 的不同波段 griz 中进行了研究。我们从 redMapPer 集群目录中构建了一个 2002 BCG 样本，光谱红移范围为 ($0.076 \leqslant \textit{z} \leqslant 0.394$)。IE 的样本由 550 个对象组成，并从具有光谱红移范围 ( $0.01 \leqslant \textit{z} \leqslant 0.08$ ) 的孤立星系目录（基于 SDSS 的孤立星系，SIG）中提取。一般来说，我们发现除了 Faber-Jackson 关系之外，所有研究的标度关系的斜率都依赖于波段。随着波长从较短到较长，两种样品的基面 (FP) 都变得陡峭。我们发现 BCG 位于与 IE 不同的 FP 上。平均而言，BCG 的系数 a 比 IE 的系数大约 5 $\sigma $ ，而系数 b 大约 11 $\sigma $ 。通过研究 Kormendy 关系 (KR)，我们发现它的斜率在两个样本的整个波段内变化。此外，BCG 的斜率比 IE 的斜率小约 7 $\sigma $ ，而截距小约 12 $\sigma $ 。我们还检查了 Faber-Jackson (FJ) 关系，发现两个样本的所有波段的斜率都相似。BCG 定义了比 IE 更陡峭的 FJ 关系，使得 $\mbox{L} \varpropto \sigma ^{6.25}$ 用于 BCG，$\mbox{L} \varpropto \sigma ^{2.63}$ 用于 IE。我们还研究了尺寸-光度关系，发现两个样品的斜率随波段略有下降。我们还发现 BCG 定义了比 IE 更陡峭的尺寸-亮度关系，平均而言，BCG 的斜率比 IE 的斜率大 $\sim 7\sigma $ 。