Ph.D. Thesis Defenses: 2004
The instabilities of astrophysical flames
February 5, 2004 | Robert Rosner
Jonathan Dursi

Large-scale simulations of supernovae of Type Ia, which are essential for the ultimate understanding of the supernovae mechanism, need flame physics input at three stages: Ignition and early flame propagation, Large scale burning in a turbulent medium, and a transition to detonation, should one occur. The current state of the art in multidimensional calculations is to ignore the first point by simply imposing some already-ignited regions in the domain, and to treat large-scale burning by using a flame speed model which is based on scaling arguments. Very little rigorous work has been done on the third point, on discovering an astrophysically relevant mechanism for deflagration-to- detonation transitions (DDT). The state of terrestrial flame-turbulence research is greatly more sophisticated than the current astrophysical corpus, and we would like to begin placing astrophysical combustion research on the same rigorous footing as terrestrial combustion research. One aspect of our investigation of flame physics has been to examine the behavior of well-known flame instabilities such as Landau-Darrieus in the context of astrophysical flames and degenerate matter. These instabilities can distort and wrinkle the flame surface, increasing the amount of burning and thus the rate of energy input.

Can We See Lorentz-Violating Vector Fields in the CMB?
July 14, 2004
Eugene Lim

We investigate the perturbation theory of a fixed-norm, timelike Lorentz-violating vector field. After consistently quantizing the vector field to put constraints on its parameters, we compute the primordial spectra of perturbations generated by inflation in the presence of this vector field. We find that its perturbations are sourced by the perturbations of the inflaton; without the inflaton perturbation the vector field perturbations decay away leaving no primordial spectra of perturbations. Since the inflaton perturbation does not have a spin-1 component, the vector field generically does not generate any spin-1 "vector-type" perturbations. Nevertheless, it will modify the amplitude of both the spin-0 "scalar-type" and spin-2 "tensor-type" perturbation spectra, leading to violations of the inflationary consistency relationship.

Effects of instrumental noise on CMB lensing reconstruction
August 11, 2004 | Wayne Hu
Takemi Okamoto

Gravitational lensing of the cosmic microwave background results in the generation of higher-order correlations, which can be utilized to estimate the distribution of the intervening dark matter. Although techniques for constructing near-optimal estimators exist, an approach that takes issues related instrumental noise into account is necessary for a realistic assessment of the ability of future experiments to reconstruct gravitational lenses. We provide a quadratic estimator based on a likelihood approach that accounts for survey boundaries and inhomogeneous noise, and discuss the practical issues associated with implementing the estimator. We utilize the quadratic estimator to perform a preliminary study of the effects of survey boundaries and correlated noise on the reconstruction of lenses using the microwave background. We find that the presence of boundaries does not increase the bias in the reconstructed maps, and produce direction-dependent correlations between multipole moments separated by the fundamental mode of the region with missing data. We also examine a simple case of striping, and show that the method results in no additional bias. We conclude that the presence of non-ideal experimental noise does not significantly limit the ability to measure gravitational lensing in the cosmic microwave background.

Spectral Variability of Quasars in the Sloan Digital Sky Survey II. The C IV Line
September 21, 2004 | Richard G. Kron
Brian Wilhite

Sloan Digital Sky Survey (SDSS) repeat spectroscopic observations have resulted in multiple-epoch spectroscopy for ~2500 quasars observed more than 50 days apart. From this sample, calibrating against stars observed simultaneously, we identify 315 quasars that have varied significantly between observations. We create an ensemble difference spectrum (bright phase minus faint phase) covering rest-frame wavelengths from 1000 to 6000 . This average difference spectrum is bluer than the average single-epoch quasar spectrum; a power-law fit to the difference spectrum yields a spectral index a l = -2.00, compared to an index of a l = -1.35 for the single-epoch spectrum. The difference spectrum also exhibits very weak or absent emission line features. Due to the lack of variability of the lines, measured photometric color is not always bluer in brighter phases, but depends on redshift and the filters used. Lastly, the difference spectrum is bluer than the ensemble quasar spectrum only for l rest < 2500 , indicating that the variability cannot result from a simple scaling of the average quasar spectrum.

We also examine the variability of the high-ionizaton C IVl1549 line in a sample of 105 quasars observed at multiple epochs. We find a strong correlation between the change in the C IV line flux and the change in the line width, but no correlations between the change in flux and changes in line center and skewness. The relation between line flux change and line width change is consistent with a model in which a broad line base varies with greater amplitude than the line core. Using moment analysis line-fitting techniques, we measure line fluxes, centers, widths and skewnesses for the C IV line at two epochs for each object. The well-known Baldwin Effect is seen for these objects, with a slope b = -0.12. The sample has a median intrinsic Baldwin Effect slope of b int = -0.86; the C IV lines in these high-luminosity quasars appear to be less responsive to continuum variations than those in lower luminosity objects. Additionally, we find no evidence for variability of the well known blueshift of the C IV line with respect to the low-ionization Mg IIl2798 line in the highest flux objects, indicating that this might be useful as a measure of orientation.

The dynamics of radiative shock waves: Linear and nonlinear evolution
September 23, 2004 | Robert Rosner
Andrea Mignone

The stability properties of one-dimensional radiative shocks with a power-law cooling function of the form L 0( r 2 T a are the main subject of this work. The linear analysis originally presented by Chevalier & Imamura, is thoroughly reviewed for several values of the cooling index a and higher overtone modes. Consistently with previous results, it is shown that the spectrum of the linear operator consists in a series of modes with increasing oscillation frequency. For each mode a critical value of the cooling index, a c , can be defined so that modes with a < a c are unstable, while modes with a > a c are stable.

The perturbative analysis is complemented by several numerical simulations to follow the time-dependent evolution of the system for different values of a. Particular attention is given to the comparison between numerical and analytical results (during the early phases of the evolution) and to the role played by different boundary conditions. It is shown that an appropriate treatment of the lower boundary yields results that closely follow the predicted linear behavior. During the nonlinear regime, the shock oscillations saturate at a finite amplitude and tend to a quasi-periodic cycle. The modes of oscillations during this phase do not necessarily coincide with those predicted by linear theory, but may be accounted for by mode-mode coupling.

On the generation of gravity waves in astrophysical environments
December 15, 2004 | Robert Rosner
Alexandros Alexakis

Typical ejecta of classical nova explosions (thermonuclear runaways of accreted H/He envelopes on the surfaces of a white dwarfs) are enriched in CNO and Ne, elements that are not product of the nuclear reactions involved. We investigate how this enrichment might originate from mixing of the white dwarf material (mainly composed of CNO&Ne) to the He/H envelope, due to large-scale flow and gravity wave interaction, prior to the explosion. In our simplified mixing model shear flow amplifies the waves, which eventually form cusps and break. This wave breaking injects a spray of C/O into the superincumbent H/He forming a layer with mixed material. Material from this layer are mixed through out the white dwarfs envelope by convective motions. We perform an extensive study of the interaction shear flows with interfacial gravity modes by (a)examining the stability properties of such flows using linear theory, (b)investigating the evolution of marginally unstable modes using weakly non-linear theory and (c)using two-dimensional numerical simulations to follow the non-linear evolution of the system. Our results allow us to formulate a quantitative expression for the amount of C/O per unit area that can be entrained into the H/He. The fraction of the envelope that is enriched depends on the horizontal distribution of shear velocity and the density contrast between the C/O white dwarf and the H/He layer. Using this parameterization to model the mixed mass, we then perform several one- dimensional Lagrangian calculations of an accreting white dwarf envelope. Our final results indicate that the envelope can be enriched by 25% of C/O by mass (consistent with that observed in some ejecta) for shear velocities, over the surface, with Mach numbers 0.4.