We study the radio and optical properties of the brightest group galaxies (BGGs) in a sample of galaxy groups from the Sloan Digital Sky Survey (SDSS) DR7. The luminosity difference between the BGG and the second-ranked galaxy in the group (known as the luminosity, or magnitude, gap) has been used as a probe for the level of galaxy interaction for the BGG within the group. We study the properties of BGGs with magnitude gaps in the range of 0–2.7 mag, in order to investigate any relation between the luminosity gap and the radio properties of the BGG. In order to eliminate selection biases, we ensure that all variations in stellar mass are accounted for. We then confirm that, at fixed stellar mass, there are no significant variations in the optical properties of the BGGs over the full range of luminosity gaps studied. We compare these optical results with the Evolution and Assembly of GaLaxies and their Environments (EAGLE) hydrodynamical simulations and find broad consistency with the observational data. Using EAGLE we also confirm that no trends begin to arise in the simulated data at luminosity gaps beyond our observational limits. Finally, we find that, at a fixed stellar mass, the fraction of BGGs that are radio-loud also shows no trend as a function of luminosity gap. We examine how the BGG offset from the center of the group may affect the radio results and find no significant trend for the fraction of radio-loud BGGs with a magnitude gap in either the BGG samples with greater or less than 100 kpc offset from the center of the group.

我们研究了来自斯隆数字巡天 (SDSS) DR7 的星系群样本中最亮星系群 (BGG) 的射电和光学特性。BGG 与组中排名第二的星系之间的光度差异（称为光度或星等、间隙）已被用作该组内 BGG 星系相互作用水平的探针。我们研究了具有 0 至 2.7 mag 幅度差距的 BGG 的特性，以研究光度差距与 BGG 的射电特性之间的任何关系。为了消除选择偏差，我们确保将恒星质量的所有变化都考虑在内。然后我们确认，在固定的恒星质量下，在所研究的整个光度间隙范围内，BGG 的光学特性没有显着变化。我们将这些光学结果与星系及其环境的演化和组装 (EAGLE) 流体动力学模拟进行比较，并发现与观测数据的广泛一致性。使用 EAGLE，我们还确认在超出我们观察极限的光度差距处的模拟数据中没有开始出现趋势。最后，我们发现，在固定的恒星质量下，射电响亮的 BGG 部分也没有显示出作为光度差距函数的趋势。我们研究了 BGG 与组中心的偏移如何影响无线电结果，并发现在与中心偏移大于或小于 100 kpc 的 BGG 样本中，具有幅度差距的无线电响度 BGG 的比例没有显着趋势组的。