<p> It is shown that at sufficiently large radii dark energy modifies the behavior of (a) bound orbits around a galaxy, and (b) virialized gas in a cluster of galaxies. In (a), there exists a maximum circular orbit beyond which periodic motion is no longer possible, and the evolution of orbits near critical binding is analytically calculable using an adiabatic invariant integral. The finding may have application to wide galaxy pairs. In (b), dark energy necessitates the use of the generalized Virial Theorem to describe gas at the outskirts of a cluster. As a result, gas at a radius of 4 Mpc or above will readily escape. A simple model indicates that this mechanism can lead to mass loss via an outflow.</p>

<p> QPOs (Quasi-Periodic Oscillations) are time oscillations that appear in the light curve of observational data in x-ray bands. They are of mysterious origin although they are believed to be a result of the intense gravity around neutron stars and black holes and emit x-rays from accretion disks. I investigate a derived ratio between two periods has been found in the QPO data. The two periods, which appear as peaks in the power density spectrum have been found to be in a 3:2 ratio and can possibly distinguish theoretical models. In the work presented here, two physical approaches are developed that can explain the integer resonance ratio. One is a cusp layer model, which is based on a boundary layer model that uses the physical conditions at opposite sides of said layer to explore the magnitude of the vertical versus radial epicyclic frequencies and confirm the anticipated scales of the observed frequencies. It also happens to recreate a 3:2 resonance ratio for the Keplerian angular frequencies at the ISCO, taken as the preferred radius for the boundary layer model. </p><p> A toy model was recreated and utilized to emulate the Alfven radius due to the accretion disk's innate magnetic field and explore how it serves as a disruption radius and impacts the accretion of mass and the effective inner edge of the disk. The simulations show that there is no significance deviation from the ISCO as an effective inner edge for the accretion disk due to the magnetospheric influence of the disk alone. </p><p> I also invoke a parameter to handle the coupling between the vertical and radial epicyclical frequencies and relate it to the pressure within the disk. I show the coupling is strongest at the equatorial plane where pressure is at its maximum value. </p><p> A model I utilize is a relativistic resonance model, combined with a helioseismological approach to explore the pulsation of the inner edge of the accretion disk that imparts the resonance of the accreting matter moving along the Kerr space-time orbits. The helioseismological model gives a characteristic frequency for small perturbations in the stellar matter within the atmosphere of a star. The diskoseismological model extends that principle to material within an accretion disk. I take it to the same extent that the QPO frequencies are due to small perturbations along the marginally stable circular orbit, in the vertical and radial directions and use it as a probe into the inner disk and what information it yields. The inner disk edge, per the model, is treated as a vibrating surface that yields the radial and vertical epicyclic frequencies as characteristic features of the vibration. The epicyclical frequencies found using the physical parameters of the model within the cusp layer inside the disk could explain the physical context of the phenomenon responsible for the creation of the QPOs. An approach within the diskoseismological model uses the cylindrical reference frame of a disk in terms of the distribution of mass in combination with the strong gravity of the central object and the Keplerian velocity and sonic speed to yield a natural resonance ratio of 3/2 as well. </p><p> The model can be used as a diagnostic tool to explore the physical phenomena of the material orbits and the disk itself. Most importantly, the model can be used to determine and constrain the ratio of spin to mass of the compact object itself. It yields new information as previously undetermined by any earlier model; the adiabatic index at a specific radius within the accretion disk, which serves to lend insight into the innate phenomena of accretion disks at large. It establishes what were previously unknown information, such as the mass density distribution at a specific radius and outward, the radius of influence in terms of the sonic radius, the accretion rate, and the temperature distribution at the same radius for the accretion disk, as all are dependent on the adiabatic index. In all previous literature, the adiabatic index is taken as an assumptive estimate, and the models build on that assumed value of the adiabatic index. This model allows us to obtain an actual value of the adiabatic index at the ISCO and use it as an establishing feature to refine models on for more physically realistic observations.</p>