We present a spatially resolved spectroscopic analysis of the young Galactic supernova remnant Kes 75 (SNR G29.7-0.3) using the Chandra X-ray Observatory. Kes 75 is one of an increasing number of examples of a shell-type remnant with a central pulsar powering an extended radio/X-ray core. We are able to pinpoint the location of the recently discovered pulsar, PSR J1846−0258, and confirm that X-rays from the remnant's core component are consistent with non-thermal power-law emission from both the pulsar and its surrounding wind nebula. We find that the spectrum of the pulsar is significantly harder than that of the wind nebula. Fainter, diffuse emission is detected from throughout the volume delineated by the radio shell with a surface brightness distribution strikingly similar to the radio emission. The presence of strong lines attributable to ionized Mg, Si, and S indicate that at least some of this emission is thermal in nature. However, when we characterize the emission using a model of an underionized plasma with non-solar elemental abundances, we find we require an additional diffuse high-energy component. We show that a significant fraction of this emission is an X-ray scattering halo from the pulsar and its wind nebula, although a nonthermal contribution from electrons accelerated in the shock cannot be excluded.

We examine the evolution of an almost-circular Keplerian orbit interacting with unbound perturbers. We calculate the change in eccentricity and angular momentum that results from a single encounter, assuming that the timescale for the interaction is shorter than the orbital period. The orbital perturbations are incorporated into a Boltzmann equation that allows for eccentricity dissipation. We present an analytic solution to the Boltzmann equation that describes the distribution of orbital eccentricity and relative inclination as a function of time. The eccentricity and inclination of the binary do not evolve according to a normal random walk but perform a Lévy flight. The slope of the mass spectrum of perturbers dictates whether close gravitational scatterings are more important than distant tidal ones. When close scatterings are important, the mass spectrum sets the slope of the eccentricity and inclination distribution functions. We use this general framework to understand the eccentricities of several Kuiper belt systems: Pluto, 2003 EL 61 , and Eris. We use the model of Tholen et al. to separate the non-Keplerian components of the orbits of Pluto's outer moons Nix and Hydra from the motion excited by interactions with other Kuiper belt objects. Our distribution is consistent with the observations of Nix, Hydra, and the satellites of 2003 EL 61 and Eris. We address applications of this work to objects outside of the solar system, such as extra-solar planets around their stars and millisecond pulsars.

We examine the effects of passing field stars on the angular momentum of a nearly radial orbit of an Oort cloud comet bound to the Sun. We derive the probability density function (PDF) of the change in angular momentum from one stellar encounter, assuming a uniform and isotropic field of perturbers. We show that the total angular momentum follows a Lévy flight, and determine its distribution function. If there is an asymmetry in the directional distribution of perturber velocities, the marginal probability distribution of each component of the angular momentum vector can be different. The constant torque attributed to Galactic tides arises from a non-cancellation of perturbations with an impact parameter of order the semimajor axis of the comet. When the close encounters are rare, the angular momentum is best modeled by the stochastic growth of stellar encounters. If trajectories passing between the comet and sun occur frequently, the angular momentum exhibits the coherent growth attributed to the Galactic tides.

The velocity dispersion, or eccentricity distribution, of protoplanets interacting with planetesimals is set by a balance between dynamical friction and viscous stirring. We calculate analytically the eccentricity distribution function of protoplanets embedded in a cold, shear-dominated planetesimal swarm. We find a distinctly non-Rayleigh distribution with a simple analytical form. The peak of the distribution lies much lower than the rms value, indicating that while most of the bodies have similarly small eccentricities, a small subset of the population contains most of the thermal energy. We also measure the shear-dominated eccentricity distribution using numerical simulations. The numerical code treats each protoplanet explicitly and adds an additional force term to each body to represent the dynamical friction of the planetesimals. Without fitting any parameters, the eccentricity distribution of protoplanets in the N-body simulation agrees with the analytical results. This distribution function provides a useful tool for testing hybrid numerical simulations of late-stage planet formation.

We examine the growth of eccentricities of a population of particles with initially circular orbits around a central massive body. Successive encounters between pairs of particles increase the eccentricities in the disk on average. As long as the epicyclic motions of the particles are small compared to the shearing motion between Keplerian orbits, there is no preferred scale for the eccentricities. The simplification due to this self-similarity allows us to find an analytic form for the distribution function; full numerical integrations of a disk with 200 planetesimals verify our analytical self-similar distribution. The shape of this non-equilibrium profile is identical to the equilibrium profile of a shear-dominated population whose mutual excitations are balanced by dynamical friction or Epstein gas drag.