Galaxy formation and evolution have been one of the most challenging problems in astrophysics. A single galaxy has various components (stars, atomic and molecular gas, a supermassive black hole, and dark matter) and has interacted with its cosmic environment throughout its history. A key issue in understanding galaxy evolution is to find the dominant physical processes in the interactions between the components of a galaxy and between a galaxy and its environment. AGN feedback has been proposed as a key process to suppress late star formation in massive elliptical galaxies and as a general consequence of galaxy mergers and interactions. In this thesis, I investigate feedback effects from active galactic nuclei (AGN) using a new simulation code and data from the Sloan Digital Sky Survey.

In the first chapter, I test purely mechanical AGN feedback models via a nuclear wind around the central SMBH in elliptical galaxies by comparing simulation results to four well-defined observational constraints: the mass ratio between the SMBH and its host galaxy, the lifetime of the quasar phase, the X-ray luminosity from the hot interstellar medium, and the mass fraction of young stars. Even though purely mechanical AGN feedback is commonly assumed in cosmological simulations, I find that it is inadequate, and cannot reproduce all four observational constraints simultaneously. This result suggests that both mechanical and radiative feedback modes are important physical processes. In the second chapter, I simulate the coevolution of the SMBH and its host galaxy under different environments, represented by different amounts of gas stripping. Though the connection between environment and galaxy evolution has been well-studied, environmental effects on the growth of the SMBH have not been answered yet. I find that strong gas stripping, which satellite galaxies might experience, highly suppresses SMBH mass accretion and AGN activity. Moreover, the suppression of the SMBH growth is stronger than the decrease in star formation. This results in a deviation of the SMBH to host galaxy mass ratio in satellite galaxies from the average ratio. In addition to simulations with AGN feedback models, I test AGN feedback in galaxy evolution by using the data from the Sloan Digital Sky Survey. Third, I analyze stellar populations and optical emission lines of green galaxies, defined in the (u – r) versus M_r color-magnitude diagram. Green galaxies have been suspected to be a transition phase between blue and red branches resulting from galaxy mergers or AGN feedback. However, I find that the average star formation and metallicity histories of green galaxies are simply the extensions of a continuous trend from blue and red branches, correlated mainly with the change in stellar mass. This implies that most green galaxies are not in the transition phase but are shaped by the same physical processes as the blue and red branches. Fourth, I examine radio emission from post-starburst galaxies. Radio-mode AGN feedback via jets has enough mechanical energy that can be deposited into interstellar medium to truncate star formation, leading to the post-starburst phase. While radio luminosity in the sample of post-starburst galaxies shows a positive correlation with stellar mass, the mass of recently formed stars is not related to the mechanical energy of the radio-mode AGN feedback. Because of the difference in time scale between the post-starburst phase (1 Gyr) and the lifetime of radio jets (0.01 to 0.1 Gyr), our results do not support the connection between the end of star formation and the radio-mode AGN feedback.