Interpreting the High Frequency QPO Power Spectra of Accreting Black Holes

In the context of a relativistic hot spot model, we investigate different physical mechanisms to explain the behavior of quasi-periodic oscillations (QPOs) from accreting black holes. The locations and amplitudes of the QPO peaks are determined by the ray-tracing calculations presented in Schnittman & Bertschinger (2004a): the black hole mass and angular momentum give the geodesic coordinate frequencies, while the disk inclination and the hot spot size, shape, and overbrightness give the amplitudes of the different peaks. In this paper additional features are added to the existing model to explain the broadening of the QPO peaks as well as the damping of higher frequency harmonics in the power spectrum. We present a number of analytic results that closely agree with more detailed numerical calculations. Four primary pieces are developed: the addition of multiple hot spots with random phases, a finite width in the distribution of geodesic orbits, Poisson sampling of the detected photons, and the scattering of photons from the hot spot through a corona of hot electrons around the black hole. Finally, the complete model is used to fit the observed power spectra of both type A and type B QPOs seen in XTE J1550-564, giving confidence limits on each of the model parameters.Comment: 30 pages, 5 figures, submitted to Ap

A Hot Spot Model for Black Hole QPOs

In at least two black hole binary systems, the Rossi X-Ray Timing Explorer has detected high frequency quasi-periodic oscillations (HFQPOs) with a 2:3 frequency commensurability. We propose a simple hot spot model to explain the positions, amplitudes, and widths of the HFQPO peaks. Using the exact geodesic equations for the Kerr metric, we calculate the trajectories of massive test particles, which are treated as isotropic, monochromatic emitters in their rest frames. By varying the hot spot parameters, we are able to explain the different features observed in ``Type A'' and ``Type B'' QPOs from XTE J1550-564. In the context of this model, the observed power spectra allow us to infer values for the black hole mass and angular momentum, and also constrain the parameters of the model.Comment: 4 pages, 2 figures, to be published in X-Ray Timing 2003: Rossi and Beyond, ed. P. Kaaret, F. K. Lamb, & J. H. Swank (Melville, NY: American Institute of Physics

Ray casting implicit fractal surfaces with reduced affine arithmetic

A method is presented for ray casting implicit surfaces defined by fractal combinations of procedural noise functions. The method is robust and uses affine arithmetic to bound the variation of the implicit function along a ray. The method is also efficient due to a modification in the affine arithmetic representation that introduces a condensation step at the end of every non-affine operation. We show that our method is able to retain the tight estimation capabilities of affine arithmetic for ray casting implicit surfaces made from procedural noise functions while being faster to compute and more efficient to store

Shape and Trajectory Tracking of Moving Obstacles

This work presents new methods and algorithms for tracking the shape and trajectory of moving reflecting obstacles with broken rays, or rays reflecting at an obstacle. While in tomography the focus of the reconstruction method is to recover the velocity structure of the domain, the shape and trajectory reconstruction procedure directly finds the shape and trajectory of the obstacle. The physical signal carrier for this innovative method are ultrasonic beams. When the speed of sound is constant, the rays are straight line segments and the shape and trajectory of moving objects will be reconstructed with methods based on the travel time equation and ellipsoid geometry. For variable speed of sound, we start with the eikonal equation and a system of differential equations that has its origins in acoustics and seismology. In this case, the rays are curves that are not necessarily straight line segments and we develop algorithms for shape and trajectory tracking based on the numerical solution of these equations. We present methods and algorithms for shape and trajectory tracking of moving obstacles with reflected rays when the location of the receiver of the reflected ray is not known in advance. The shape and trajectory tracking method is very efficient because it is not necessary for the reflected signal to traverse the whole domain or the same path back to the transmitter. It could be received close to the point of reflection or far away from the transmitter. This optimizes the energy spent by transmitters for tracking the object, reduces signal attenuation and improves image resolution. It is a safe and secure method. We also present algorithms for tracking the shape and trajectory of absorbing obstacles. The new methods and algorithms for shape and trajectory tracking enable new applications and an application to one-hop Internet routing is presented.Comment: 22 pages, 2 figures, 2 table

Designing Volumetric Truss Structures

We present the first algorithm for designing volumetric Michell Trusses. Our method uses a parametrization approach to generate trusses made of structural elements aligned with the primary direction of an object's stress field. Such trusses exhibit high strength-to-weight ratios. We demonstrate the structural robustness of our designs via a posteriori physical simulation. We believe our algorithm serves as an important complement to existing structural optimization tools and as a novel standalone design tool itself