Abstract
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 $ .
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