  In this study, galaxy samples have been generated using mock observation
techniques based on the results of TNG100-1 simulations to investigate three
forms of intrinsic alignment: satellite-central alignment between the
orientation of the brightest group galaxies (BGG) and the spatial distribution
of their satellites, radial alignment between the satellites' orientation and
the direction towards their BGG, as well as direct alignment between the
orientation of BGG and that of its satellites. Overall, the predictions of
galaxy alignment generally align with observations, although minor
discrepancies have been identified. For satellite-central alignment, the
alignment strength and color-dependence trends are well replicated by the mock
observations. Regarding radial alignment, the signals are weak but discernible,
with no apparent color dependence. As for direct alignment, no signal is
detected, nor is there any color dependence. We also investigate the alignment
dependencies on halo or the BGG properties, and proximity effect. For
satellite-central alignment, the predicted alignment signal shows a positive
correlation with halo and BGG mass, consistent with observations and previous
predictions. Similar correlations have also been observed with the BGG age and
metallicity, which merit future observational analysis for confirmation.
Proximity effects have been observed for all three types of alignment, with
satellites closer to the BGG exhibiting stronger alignment signals. The
influence of galaxy definition and shape determination on alignment studies is
also analyzed. This study underscores the importance of employing mock
observation techniques for a fair comparison between predictions and
observations.
