Resulting Density Perturbations Research Articles

Coseismic and post-seismic gravity disturbance induced by seismic sources using a 2.5-D spectral element method

SUMMARYI present a prescription for computing free-air coseismic and post-seismic gravity changes induced by seismic sources in a viscoelastic earth model. I assume a spherical earth geometry and a 2.5-D calculation, that is, 3-D motions that satisfy the equations of quasi-static equilibrium on a 2-D viscoelastic structure. The prescription permits application to regional gravity computations where a 2-D structure adequately represents the structural heterogeneity. I use a hybrid approach where deformation is computed on a discretized domain and the resulting density perturbations are expanded with spherical harmonics to produce the free-air gravity field. Starting with a solution to the equations of quasi-static displacements in the Laplace transform domain for a given dislocation source, I solve Poisson’s equation using Lagrangian interpolation on spectral element nodes to compute the required deformation quantities that contribute to free-air gravity. A numerical inverse Laplace transform then yields time domain results. This methodology is tested with analytic solutions on a spherically stratified viscoelastic structure, then applied to evaluate the effect of a descending slab of relatively high viscosity on post-seismic gravity in a megathrust faulting setting.

MIGRATION TRAPS IN DISKS AROUND SUPERMASSIVE BLACK HOLES

ABSTRACT Accretion disks around supermassive black holes (SMBHs) in active galactic nuclei (AGNs) contain stars, stellar mass black holes, and other stellar remnants, which perturb the disk gas gravitationally. The resulting density perturbations exert torques on the embedded masses causing them to migrate through the disk in a manner analogous to planets in protoplanetary disks. We determine the strength and direction of these torques using an empirical analytic description dependent on local disk gradients, applied to two different analytic, steady-state disk models of SMBH accretion disks. We find that there are radii in such disks where the gas torque changes sign, trapping migrating objects. Our analysis shows that major migration traps generally occur where the disk surface density gradient changes sign from positive to negative, around 20–300R g, where R g = 2GM/c 2 is the Schwarzschild radius. At these traps, massive objects in the AGN disk can accumulate, collide, scatter, and accrete. Intermediate mass black hole formation is likely in these disk locations, which may lead to preferential gap and cavity creation at these radii. Our model thus has significant implications for SMBH growth as well as gravitational wave source populations.

Density perturbations from curvatons revisited

We investigate density perturbations sourced by a curvaton with a generic energy potential. The key feature of a curvaton potential which deviates from a quadratic is that the curvaton experiences a non–uniform onset of its oscillation. This sources additional contributions to the resulting density perturbations, and we especially find that curvaton potentials that are flatter compared to a quadratic lead to enhancement of the linear and second–order density perturbations, while steepened potentials can generate strongly scale–dependent non–Gaussianity. As such examples, we study pseudo–Nambu–Goldstone curvatons and self–interacting curvatons. Our analyses are analytic, and thus provide a systematic framework for studying curvatons in general. The discussion in this paper are based on [1, 2].

Runnings in the curvaton

We investigate the scale-dependence, or the runnings, of linear andsecond order density perturbations generated in various curvatonscenarios. We argue that the second order perturbations,i.e. non-Gaussianity, can strongly depend on the scale, even when thelinear perturbations are nearly scale-invariant. We present analyticformulae for the runnings from curvatons with general energypotentials, and clarify the conditions under which fNLbecomes strongly scale-dependent. From the point of view of thefNL running, curvaton potentials can be classified intoroughly two categories by whether the potential flattens or steepenscompared to a quadratic one. As such examples, we studypseudo-Nambu-Goldstone curvatons, and self-interacting curvatons,respectively. The dynamics of non-quadratic curvatons and thebehaviors of the resulting density perturbations are clarified byanalytical methods.Then we also study models where multiple source can beresponsible for density perturbations such as the multi-curvaton, andmixed curvaton and inflaton models where the running offNL can also be large due to their multi-source nature.We make quantitative analysis for each curvaton scenario and discussin what cases the scale-dependence, in particular, offNL can be large enough to be probed with future CMBexperiments.

Non-Gaussianity from curvatons revisited

We investigate density perturbations sourced by a curvaton with a generic energy potential. The key feature of a curvaton potential which deviates from a quadratic is that the curvaton experiences a nonuniform onset of its oscillation. This sources additional contributions to the resulting density perturbations, and we especially find that the non-Gaussianity parameter ${f}_{\mathrm{NL}}$ can become large with either sign no matter whether the curvaton dominates or subdominates the universe when it decays. Such nonquadratic curvaton potentials are required in order to produce a red-tilted density perturbation spectrum (without invoking large-field inflation), and are also motivated by explicit curvaton models based on microscopic physics. We further apply our generic results to the case where the curvaton is a pseudo-Nambu-Goldstone boson of a broken U(1) symmetry, and show that the resulting density perturbations are strongly enhanced towards the hilltop region of the energy potential, accompanied by a mild increase of the non-Gaussianity. Such hilltop Nambu-Goldstone curvatons can produce observationally suggested density perturbations under wide ranges of inflation/reheating scales, and further predict the non-Gaussianity of the density perturbations to lie within the range $10\ensuremath{\lesssim}{f}_{\mathrm{NL}}\ensuremath{\lesssim}30$.

Quantum cosmology: expectations and results

We study cosmologies based on low-energy effective string theory with higher-order string corrections to a tree-level action and with a modulus scalar field (dilaton or compactification modulus). In the presence of such corrections it is possible to construct nonsingular cosmological solutions in the context of Pre-Big-Bang and Ekpyrotic universes. We review the construction of nonsingular bouncing solutions and resulting density perturbations in Pre-Big-Bang and Ekpyrotic models. We also discuss the effect of higher-order string corrections on a dark energy universe and show several interesting possibilities of the avoidance of future singularities.

Cosmologies from higher‐order string corrections

AbstractWe study cosmologies based on low‐energy effective string theory with higher‐order string corrections to a tree‐level action and with a modulus scalar field (dilaton or compactification modulus). In the presence of such corrections it is possible to construct nonsingular cosmological solutions in the context of Pre‐Big‐Bang and Ekpyrotic universes. We review the construction of nonsingular bouncing solutions and resulting density perturbations in Pre‐Big‐Bang and Ekpyrotic models. We also discuss the effect of higher‐order string corrections on a dark energy universe and show several interesting possibilities of the avoidance of future singularities.

Construction of nonsingular pre-big-bang and ekpyrotic cosmologies and the resulting density perturbations

We consider the construction of nonsingular pre-big-bang and ekpyrotic type cosmological models realized by the addition to the action of specific higher-order terms stemming from quantum corrections. We study models involving general relativity coupled to a single scalar field with a potential motivated by the ekpyrotic scenario. We find that the inclusion of the string loop and quantum correction terms in the string frame makes it possible to obtain solutions of the variational equations which are nonsingular and bouncing in the Einstein frame, even when a negative exponential potential is present, as is the case in the ekpyrotic scenario. This allows us to discuss the evolution of cosmological perturbations without the need to invoke matching conditions between two Einstein universes, one representing the contracting branch, the second the expanding branch. We analyze the spectra of perturbations produced during the bouncing phase and find that the spectrum of curvature fluctuations in the model proposed originally to implement the ekpyrotic scenario has a large blue tilt ${(n}_{\mathcal{R}}=3).$ Except for instabilities introduced on small scales, the result agrees with what is obtained by imposing continuity of the induced metric and of the extrinsic curvature across a constant scalar field (up to ${k}^{2}$ corrections equal to the constant energy density) matching surface between the contracting and the expanding Einstein universes. We also discuss nonsingular cosmological solutions obtained when a Gauss-Bonnet term with a coefficient suitably dependent on the scalar matter field is added to the action in the Einstein frame with a potential for the scalar field present. In this scenario, nonsingular solutions are found which start in an asymptotically flat state, undergo a period of superexponential inflation, and end with a graceful exit. The spectrum of fluctuations is also calculated in this case.

Analysis and interpretation of high‐resolution topography and gravity of Ishtar Terra, Venus

The apparent depth of compensation (ADC) of the topography of Venus, determined on a global scale using the Airy isostasy model, shows that the topography specified by the spherical harmonics of degree lower than 10 is compensated at depths greater than 150 km, that of degree higher than about 35 is compensated at a constant depth of about 35 km, and the compensation depths of the harmonics of degree 10–35 shoal as the harmonic degree increases. Based on these characteristics of the globally determined ADC, three different maps of the topography and gravitational potential of the Greater Ishtar Terra are derived using the harmonics of degree 1–75 (LW), 10–75 (IW), and 30–75 (SW), respectively. The LW maps of the topography and potential do not correlate well, but the IW and SW maps show good correlation, emphasizing that the long‐wavelength components of the gravitational potential over the Ishtar Terra have contributions from sources broader than the Terra. The energy of the gravitational potential of the topography is about an order of magnitude greater than that of the observed potential, indicating that the topography is strongly compensated. The ADC of the topography is estimated by both spectral and space domain analysis. In the spectral domain, three independent procedures, the energy spectrum, the statistical method, and the wavelength‐dependent method, are employed. The first two yield a mean ADC value for the entire spectrum, whereas the last one calculates the ADC for different wavelengths. The ADC decreases as the longer‐wavelength components are excluded. The mean ADC values determined for the LW, IW, and SW maps by the energy spectrum method are 115, 65, and 40 km, respectively. Those calculated through the statistical method are 85, 55, and 34 km, respectively. These values reflect the upper and lower limits, because the energy spectrum method overestimates and the statistical method underestimates the ADC. The wavelength‐dependent method shows that the ADCs of the wavelengths 500–1350 km are similar for all the maps but those of the longer wavelengths significantly differ among the maps. The mean ADC values also differ from the ADC of local topographic features. For example, the ADC of Maxwell Montes is about 55 km in both the LW and IW maps. In the space domain, the ADC is determined for Pratt and Airy isostasy models through fitting a linear and a quadratic function to the geoid height versus topography data, respectively. The ADC values determined show good agreement with the above‐mentioned values. In addition, the relationship between the high‐resolution topography and the line‐of‐sight acceleration residuals of the western Ishtar Terra specified by wavelengths of 300–500 km suggests that the high‐resolution topography is compensated at a depth of about 25 km. We also determine the lateral density perturbations inside a surface layer so that together with the topography of the Greater Ishtar Terra they give rise to the observed gravitational potential over the Terra. Three layer thicknesses of 50, 100, and 200 km are examined. The resulting density perturbations are too large to be interpreted in terms of lateral temperature variations alone. This suggests lateral variations in the rock type; the crust beneath the mountain belts may contain considerable amounts of low‐density material.

Open inflation with an arbitrary false vacuum mass.

We calculate the power spectrum of adiabatic density perturbations in an open inflationary model in which inflation occurs in two stages. First an epoch of old inflation creates a large, smooth universe, solving the horizon and homogeneity problems. Then an open universe emerges through the nucleation of a single bubble, with constant density hypersurfaces inside the bubble having constant negative spatial curvature. An epoch of `slow roll' inflation, shortened to give $\Omega _0<1$ today, occurs within the bubble, which contains our entire observable universe. In this paper we compute the resulting density perturbations in the same `new thin wall' approximation used in a previous paper, but for an arbitrary positive mass of the inflaton field in the false vacuum.

Dependence of density perturbations on the coupling constant in a simple model of inflation.

In the standard inflationary scenario with inflaton potential {ital V}({Phi})={ital M}{sup 4}{minus}1/4{lambda}{Phi}{sup 4}, the resulting density perturbations {delta}{rho}/{rho} are proportional to {lambda}{sup 1/2}. Upper bounds on {delta}{rho}/{rho} require {lambda}{approx lt}10{sup {minus}13}. Ratra has shown that an alternative treatment of reheating results in {delta}{rho}/{rho}{proportional to}{lambda}{sup {minus}1}, so that an upper bound on {delta}{rho}/{rho} does not put an obvious upper bound on {lambda}. We verify that {delta}{rho}/{rho}{proportional to}{lambda}{sup {minus}1} is indeed a possibility, but show that {lambda}{approx lt}10{sup {minus}13} is still required.

Bubble growth and droplet decay in the quark-hadron phase transition in the early Universe.

When the Universe was about 10 \ensuremath{\mu}sec old, it underwent a phase transition in which the quarks and gluons condensed into hadrons. We assume that this phase transition was of first order and study how the Universe evolved through the mixed phase in a scenario with small initial supercooling and monotonically growing hadronic bubbles. Nucleation of bubbles, collisions of shock fronts preceding the bubbles, arrestation of bubble growth by the reheating due to these collisions, subsequent slow growth of the bubbles to fill the entire Universe, condensation of baryon number, death of the remaining quark matter droplets, and the resulting density perturbations are discussed. A (1+1)-dimensional approximation is frequently used to make analytic calculations possible.