Solving the cooling flow problem in cool-core galaxy clusters is critical to under- standing the largest structures in the universe. In addition, cool-core systems are the only places where we have observed direct evidence of AGN feedback, and thus provide the unique opportunity to test models of AGN feedback and various other physical processes. In this thesis we study the influence of momentum-driven AGN feedback on cool-core clusters using high-resolution adaptive mesh refinement (AMR) simulations. We find that run-away cooling first happens only in the central 50 pc region while no local instability develops outside the very center of the cluster. The gas is accreted onto the super-massive black hole (SMBH) which powers AGN jets at an increasing rate as the entropy continues to decrease in the core. The ICM first cools into clumps along the propagation direction of the AGN jets due to the non-linear perturbation. As the jet power increases, gas condensation occurs isotropically, forming spatially extended (up to a few tens kpc) structures that resemble the observed Hα filaments in Perseus and many other cool-core cluster. Jet heating elevates the gas entropy and cooling time, halting clump formation. The cold gas that is not accreted onto the SMBH settles into a rotating disk. In the last few Gyr, the ICM cools onto the disk directly while the innermost region of the disk continues to accrete onto the SMBH, powering the AGN jets to achieve a thermal balance. The mass cooling rate averaged over 7 Gyr is &sim 30 solarmass/yr, an order of magnitude lower than the classic cooling flow value (which we obtain in runs without the AGN). Owing to its self-regulating mechanism, AGN feedback can successfully balance cooling with a wide range of model parameters. Besides suppressing cooling, our model produces cold structures in early stages (up to &sim 2 Gyr) that are in good agreement with the observations. However, the long-lived massive cold disk is unrealistic, suggesting that additional physical processes are still needed. Our recent investigation shows that star formation may play an important role.

The oldest open clusters within 250 pc of the Sun, the Hyades and Praesepe, are important benchmarks for calibrating stellar properties such as rotation and magnetic activity. As they have the same age and roughly solar metallicity, these clusters serve as an ideal laboratory for testing the agreement between theoretical and empirical rotation-activity relations at ~650 Myr. The re-purposed Kepler mission, K2, has allowed me to measure rotation periods for dozens of Hyads and hundreds of Praesepe members, including the first periods measured for fully convective Hyads. These data have enabled new tests of models describing the evolution of stellar rotation; discrepancies with these models imply that we still do not fully understand how magnetic fields affect stellar spin-down. I show how we can compare the dependence of H-alpha and X-ray emission on rotation in order to test theories of magnetic field topology and stellar dynamos. These tests inform models of stellar wind-driven angular momentum loss and the age-rotation-activity relation. I also present rotation periods measured for 48 Hyads and 677 Praesepe members with K2, and discuss the impact of unresolved binaries on the study of rotational evolution.

Over two hundred extrasolar planets have been discovered to date with various methods. This thesis reports on searching for extrasolar planets and characterising them by simulating their atmospheres. We used open clusters as targets for deep transit searches, with specific emphasis on the University of St. Andrews Planet Search at the Isaac Newton Telescope. We reduced CCD photometry and described the algorithm we used to search for transits. We estimated the number of transits we expect from our data. We then reduced photometry for the open cluster NGC 6940. From that data we found 18 low-amplitude, short-duration events, though none are transiting planets. They are all eclipsing binary stars. However, our null result constrains the number of planets around M dwarfs, the most numerous stars in our sample. In order to characterise reflected light from extrasolar planets, we built a three-dimensional Monte Carlo based radiation transfer model of extrasolar planetary atmospheres. We detailed the input parameters of the model, and show results of various models, focusing especially on the fractal nature of the clouds of our models, because these are the first three dimensional radiation transfer models of extrasolar planet atmospheres. We found very low geometric albedos in our simulations. Using data specific to the transiting planet HD 209458b, we built a model atmosphere with Rayleigh-scattering hydrogen gas and clouds of enstatite and iron. We show in several models the rarity of a bright HD 209458b, and conclude with some explanations on why extrasolar planets are likely dark and not detected with reflected light.

In this work, the efficiency of the LUMBA UVES pipeline for processing of spectroscopic observations is tested by use on 23 high-resolution spectra of the open star cluster M67. An abundance trend discovered by Gavel et al. (2019) concerning iron abundances of giant and sub-giant stars of that cluster is examined. An initial run for a set of ”Gaia FGK benchmark stars”, as described in Blanco-Cuaresma et al. (2014) and Heiter et al. (2015) helps inspect the structure, method and output of the pipeline. Through Python language programming, processes are greatly automatized and the pipeline is run for a total of 460 weak and strong iron lines of our 23-star sample. The line fitting and efficiency of the pipeline is appreciated by statistically analyzing the results and looking into individual discrepant ones. The abundance trend is reproduced while using FeI lines, unlike runs using FeII lines. Trends in abundance over line strength plots also hint at bias through the Gaia-Eso Survey (GES) microturbulence relation. Using internal Data Release 6 (iDR6) and LUMBA-derived starting parameters, log(g) - Teff plots of our sample stars agree with a previously established 4.3 Gyr cluster age. An alternate run is performed for those stars, using LUMBA-derived starting parameters. The choice of starting parameters does impact abundance derivation, but is not the primary source of persistent systematic discrepancies.