Talks & Events
Ph.D. Thesis Defenses: 2008
DR21 Main: A collapsing cloud
The molecular cloud, DR21 Main, is an example of a large-scale gravitational collapse about an axis near the plane of the sky where the collapse is free of major disturbances due to rotation or other effects. Using flux maps, polarimetric maps, and measurements of the field inclination by comparing the line widths of ion and neutral species, we estimate the temperature, mass, magnetic field, and the turbulent kinetic, mean magnetic, and gravitational potential energies, and present a 3D model of the cloud and magnetic field.
3 + 1 Formulations of General Relativity
In this thesis we carry out a theoretical and numerical study of different 3+1 formulations of General Relativity (GR) which have direct applications to numerical relativity. In particular, we introduce a method to analyze the well- posedness of constrained evolution of the Einstein equations and show that the well-posedness of constrained evolution of the Arnowitt-Deser-Misner (ADM), Baumgarte-Shapiro-Shibata-Nakamura (BSSN) and formulations which resemble the Kidder-Scheel-Teukolsky (KST) one, depends entirely on the properties of the gauge. Driven by this result, we introduce two new well-posed formulations of GR. The first one is a parabolization of the ADM formulation, which we call the PADM formulation, and is derived by addition of combinations of the constraints and their derivatives to the RHS of the ADM evolution equations. The desirable property of PADM is that it turns the surface of constraints into a local attractor because its constraint propagation system becomes second-order parabolic independently of the gauge conditions employed. The PADM system may be classified as mixed hyperbolic--second-order parabolic (MHSP). The second formulation is a parabolization of the KST formulation, which we call the PKST formulation, and is a manifestly MHSP set of equations. We carry out a stability analysis of flat space and demonstrate that the PADM system exponentially damps and smoothes all constraint violating modes. Finally, we describe a numerical implementation of the PADM formulation and study its accuracy and stability in a series of standard numerical tests. We show that the PADM scheme is numerically stable, convergent and second-order accurate, and we compare its numerical properties with those of standard ADM and its hyperbolic KST extension. We demonstrate that PADM has better control of the constraint-violating modes than ADM and KST.
N-body simulations of modified gravity
We introduce the method and the implementation of a cosmological simulation of a class of metric-variation f ( R ) models that accelerate the cosmological expansion without a cosmological constant and evade solar-system bounds of small-field deviations to general relativity. Such simulations are shown to reduce to solving a non-linear Poisson equation for the scalar degree of freedom introduced by the f ( R ) modifications. We detail the method to efficiently solve the non-linear Poisson equation by using a Neton-Gauss-Seidel relaxation scheme coupled with multigrid method to accelerate the convergence. The simulations are shown to satisfy tests comparing the simulated outcome to analytical solutions for simple situations, and the dynamics of the simulations are tested with orbital and Zeldovich collapse tests. Finally, we present several static and dynamical simulations using realistic cosmological parameters to highlight the differences between standard physics and f ( R ) physics. In general, we find that the f ( R ) modifications result in stronger gravitational attraction that enhances the dark matter power spectrum by ~ 20% for large but observationally allowed f ( R ) modifications. More detailed study of the non-linear f ( R ) effects on the power spectrum are presented in a companion paper.
Revealing Dark Matter Substructure with Anisotropies in the Diffuse Gamma-Ray Background
The majority of gamma-ray emission from Galactic dark matter annihilation is likely to be detected as a contribution to the diffuse gamma-ray background. I show that dark matter substructure in the halo of the Galaxy induces characteristic anisotropies in the diffuse background that could be used to determine the small-scale dark matter distribution. I calculate the angular power spectrum of the emission from dark matter substructure for several models of the subhalo population, and show that features in the power spectrum can be used to infer the presence of substructure. The shape of the power spectrum is largely unaffected by the subhalo radial distribution and mass function, and for many scenarios I find that a measurement of the angular power spectrum by GLAST will be able to constrain the abundance of substructure. An anti-biased subhalo radial distribution is shown to produce emission that differs significantly in intensity and large-scale angular dependence from that of a subhalo distribution which traces the smooth dark matter halo, potentially impacting the detectability of the dark matter signal for a variety of targets and methods.
Phenomenology of Warped Extra Dimensions
In this thesis we analyze the phenomenology of a particular class of models which are an extension of the Standard Model of particle physics, and go by the name of warped extra dimensions. We show how this very simple framework, which is motivated by trying to find a solution to the hierarchy problem, is capable of leading to a vast and rich phenomenology not only in particle physics but also in cosmology. The flexibility of this framework has allowed us to learn about model building techniques in particle physics, collider phenomenology and furthermore to make a link with cosmology. Regarding the latter link, we see that when we combine warped extra dimensions with the other major new physics scenario supersymmetry, we are able to account for the excess of baryons over anti-baryons in the Universe. Furthermore, we show that once we have an extra spatial dimension we can accommodate the Higgs field as the fifth component of our gauge bosons. This leads to the models that go by the name of Gauge-Higgs Unification (GHU). We construct a particular model and calculate the Higgs potential at one-loop showing that all SM masses can be accommodated and we obtain a Higgs mass in the acceptable range between 115 GeV and 160 GeV. Lastly, we analyze the interesting collider phenomenology derived from this scenario and show the detection possibilities at the next Large Hadron Collider (LHC).
On the energetics, initiation of detonations, and nucleosynthesis of Type Ia supernovae in the gravitationally confined detonation model
A sophisticated scheme to capture the effects of weak interactions and change in composition of matter burned to nuclear statistical equilibrium in hydrodynamic explosion simulations of Type Ia supernovae is developed. Coupled to a flame model, the scheme is applied to two dimensional axisymmetric simulations of Type Ia supernovae. The explosions are simulated in the gravitationally confined detonation paradigm, where a near Chandrasekhar-mass carbon-oxygen white dwarf ignites in a single "bubble" within the first ~100 km off center, and the subsequent evolution of the bubble (rise, growth, and break-out through the stellar surface) is thought to lead to the initiation of a detonation at the antipodal point of break-out. Increasingly higher- resolution simulations of the region where the detonation is purportedly initiated are presented, and detonations are indeed observed to form via the gradient mechanism in most cases. To support the validity of the initiation of a detonation in the under-resolved full star simulations, and to quantify the uncertainties and dependences of successful initiation on details of its environment (such as composition, density, peak - and background temperature, functional form of the temperature inhomogeneity), a suite of one dimensional reactive hydrodynamics calculations determining the smallest sizes of hot-spots leading to a detonation are performed for a range of conditions that might obtain in the surface layers of white dwarf stars. Finally, a novel, computationally inexpensive method to obtain full isotopic yield information of material that was burned by fusion processes to nuclear statistical equilibrium during the detonation phase of the supernova explosion is developed and applied to the aforementioned supernova simulations.
The effects of neglecting reduced shear on dark energy constraints from three-dimensional weak lensing methods
The weak gravitational lensing of distant galaxies by large-scale structure is expected to become a powerful probe of dark energy. By measuring the ellipticities of large numbers of background galaxies, the subtle gravitational distortion called "cosmic shear" can be measured and used to constrain dark energy parameters. The observed galaxy ellipticities, however, are induced not by shear but by reduced shear, which also accounts for slight magnifications of the images. This distinction is negligible for present weak lensing surveys, but it will become more important as we improve our ability to measure and understand small-angle cosmic shear modes. I calculate the discrepancy between shear and reduced shear in the context of power spectra and cross spectra, finding the difference could be as high as 10% on the smallest accessible angular scales. I estimate how this difference will bias dark energy parameters obtained from two types of 3D weak lensing methods: weak lensing tomography and the shear ratio method known as offset-linear scaling. For weak lensing tomography, ignoring the effects of reduced shear will cause future surveys such as the Dark Energy Survey, Large Synoptic Survey Telescope, or Joint Dark Energy Mission to bias their dark energy parameters by amounts that are comparable to their error bars. I advocate that reduced shear be properly accounted for in these surveys, and I provide a semi-analytic formula for doing so. For a space telescope such as the Joint Dark Energy Mission, the offset- linear scaling method is insensitive to reduced shear for modes l <= 3000, but the method becomes invalid when including modes with l >= 5000. Reduced shear could have important consequences for other observables such as the weak lensing of the cosmic microwave background.
Type Ia supernova rate studies from the SDSS-II Supernova Study
I present new measurements of the type Ia SN rate from the SDSS-II Supernova Survey. The SDSS-II Supernova Survey was carried out during the Fall months (Sept.-Nov.) of 2005-2007 and discovered [approximate]500 spectroscopically confirmed SNe Ia with densely sampled (once every [approximate] 4 days), multi- color light curves. Additionally, the SDSS-II Supernova Survey has discovered several hundred SNe Ia candidates with well-measured light curves, but without spectroscopic confirmation of type. This total, achieved in 9 months of observing, represents [approximate] 15-20% of the total SNe Ia discovered worldwide since 1885. I describe some technical details of the SN Survey observations and SN search algorithms that contributed to the extremely high- yield of discovered SNe and that are important as context for the SDSS-II Supernova Survey SN Ia rate measurements.
I describe 3 separate SN Ia studies: (1) A precise measurement of the SN Ia rate at low-redshift ( z < 0.12) based on a highly pure sample of SNe Ia with a well measured selection function. (2) A measurement of the type Ia SN rate to a redshift limit z [Special characters omitted.] 0.3, based on [approximate] 350 SNe Ia. (3) A measurement of the type Ia SN rate in galaxy clusters in the redshift range 0.03 < z < 0.30.
The low-redshift SN Ia rate measurement includes 17 SNe Ia at redshift z <= 0.12. Assuming a flat cosmology with O m = 0.3 = 1 - O L , we find a volumetric SN Ia rate of [Special characters omitted.] SNe Mpc -3 [Special characters omitted.] year -1 , at a volume-weighted mean redshift of 0.09. This result is consistent with previous measurements of the SN Ia rate in a similar redshift range. The systematic errors are well controlled, resulting in the most precise measurement of the SN Ia rate in this redshift range. We use a maximum likelihood method to fit SN rate models to the SDSS-II Supernova Survey data in combination with other rate measurements, thereby constraining models for the redshift-evolution of the SN Ia rate. Fitting the combined data to a simple power-law evolution of the volumetric SN Ia rate, r V 0( (1 + z ) b , we obtain a value of b = 1.5 � 0.6, i.e. the SN Ia rate is determined to be an increasing function of redshift at the ~ 2.5s level. Fitting the results to a model in which the volumetric SN rate, r V = Ar(t) + B[Special characters omitted.] (t), where r(t) is the stellar mass density and [Special characters omitted.] (t) is the star formation rate, we find A = (2.8 � 1.2) � 10^-14 SNe [Special characters omitted.] year -1 , B = [Special characters omitted.] SNe [Special characters omitted.] .
The SN rate measurement to a redshift limit z [Special characters omitted.] 0.3 provides an order of magnitude improvement in the statistics for SN Ia rate measurement in this redshift range. Although systematic uncertainties on the SN rate for 0.2 < z < 0.3 are significant, the SN rate is determined precisely for z [Special characters omitted.] 0.2 based on a sample of [approximate] 132 SNe Ia, with the majority being spectroscopically confirmed. The large sample of SNe Ia included in this study allow us to place constraints on the redshift dependence of the SN Ia rate in the redshift range covered by the SDSS-II Supernova Survey, based on the SDSS-II Supernova Survey data alone.
Non-linear Structure in Modified Action Theories of Gravity
We study the effects and carry out a suite of cosmological simulations of modified action f(R) models where cosmic acceleration arises from an alteration of gravity instead of dark energy. These models introduce an extra scalar degree of freedom which enhances the force of gravity below the Compton scale of the scalar. The simulations exhibit the so-called chameleon mechanism, necessary for satisfying local constraints on gravity, where this scale depends on environment, in particular the depth of the local gravitational potential. We find that the chameleon mechanism can substantially suppress the enhancement of power spectrum in the non-linear regime if the background field value is comparable to or smaller than the depth of the gravitational potentials of typical structures. Nonetheless power spectrum enhancements at intermediate scales remain at a measurable level even when the expansion history is indistinguishable from a cosmological constant, cold dark matter model. We also investigate the effects of the modified dynamics on halo properties such as their abundance and clustering. We find that the f(R) effects on the halo mass- function and bias depend mostly on the linear power spectrum modifications, but that the chameleon mechanism suppresses the modifications at high-mass halos with deep potential wells. The f(R) modifications also affect the threshold density for collapse, or similarly the overdensity for virialization and therefore can change halo definitions from those of ACDM. As a result, simple scaling relations that take the linear matter power spectrum into a non-linear spectrum fail to capture the modifications of f(R) due to the change in collapsed structures, the chameleon mechanism, and the time evolution of the modifications. A quantification of these effects, including modifications on halo profiles, is necessary to accurately describe halo properties and potentially construct a halo model of the non-linear power spectrum.
Cross-Calibration of Cluster Mass-Observables and Dark Energy
This paper is a first step towards developing a formalism to optimally extract dark energy information from number counts using multiple cluster observation techniques. We use a Fisher matrix analysis to study the improvements in the joint dark energy and cluster mass-observables constraints resulting from combining cluster counts and clustering abundances measured with different techniques. We use our formalism to forecast the constraints in O DE and w from combining optical and sz cluster counting on a 4000 sq. degree patch of sky. We find that this joint "self-calibration" yields ~ 41-64% better constraints on O DE and w compared to simply adding the Fisher matrices of the individually self-calibrated counts. The joint constraints are less sensitive to variations in the mass threshold or maximum redshift range. A by-product of our technique is that the correlation between different mass-observables is well constrained without the need of additional priors on its value. Finally, we compare results from combining optical and sz surveys to two sz-like surveys and find that combining surveys with different properties yields the best constraints.
Correlating Optical and Sunyaev-Zel'dovich Measurements of Galaxy Clusters in the SZA Survey
The interferometric cm-wave data from the Sunyaev-Zel'dovich Array survey were cross-correlated with galaxy clusters identified in a companion R and z ' optical imaging program conducted at Kitt Peak National Observatory with the Mosaic-1 camera on the 4m Mayall telescope. These optical data were reduced using pipelines designed for the similar data set of the RCS survey to produce a catalog of clusters. The average SZ signal correlated with this set of clusters and several sub-samples was measured. A negative correlation between the optical and radio data of the Sunyaev-Zel'dovich Array survey was measured at the 1-sigma level. Based on the optical mass proxies of detection significance and richness, the estimated average mass of the cluster samplea is approximately 1 x 10 14 solar masses. The average correlated SZ signal is consistent with this estimate, as is the temperature decrement measurement recovered from an MCMC analysis of a beta-model fit to the low-richness clusters. In all, there is a consistent picture of the average SZ signal being able to be recovered for an ensemble of clusters despite the mass of all systems individually being below the detection threshold of the SZA survey.