Lower Limits on Aperture Size for an ExoEarth-Detecting Coronagraphic Mission

The yield of Earth-like planets will likely be a primary science metric for future space-based missions that will drive telescope aperture size. Maximizing the exoEarth candidate yield is therefore critical to minimizing the required aperture. Here we describe a method for exoEarth candidate yield maximization that simultaneously optimizes, for the first time, the targets chosen for observation, the number of visits to each target, the delay time between visits, and the exposure time of every observation. This code calculates both the detection time and multi-wavelength spectral characterization time required for planets. We also refine the astrophysical assumptions used as inputs to these calculations, relying on published estimates of planetary occurrence rates as well as theoretical and observational constraints on terrestrial planet sizes and classical habitable zones. Given these astrophysical assumptions, optimistic telescope and instrument assumptions, and our new completeness code that produces the highest yields to date, we suggest lower limits on the aperture size required to detect and characterize a statistically-motivated sample of exoEarths.Comment: Accepted for publication in ApJ; 38 pages, 16 Figures, 3 Table

Phase statistics of seismic coda waves

We report the analysis of the statistics of the phase fluctuations in the coda of earthquakes recorded during a temporary experiment deployed at Pinyon Flats Observatory, California. The practical measurement of the phase is discussed and the main pitfalls are underlined. For large values, the experimental distributions of the phase first, second and third derivatives obey universal power-law decays whose exponents are remarkably well predicted by circular Gaussian statistics. For small values, these distributions are flat. The details of the transition between the plateau and the power-law behavior are governed by the wavelength. The correlation function of the first phase derivative along the array shows a simple algebro-exponential decay with the mean free path as the only length scale. Although only loose bounds are provided in this study, our work suggests a new method to estimate the degree of heterogeneity of the crComment: 4 figures, submitted to Physical Review Letter

A Two-Threshold Model for Scaling Laws of Non-Interacting Snow Avalanches

The sizes of snow slab failure that trigger snow avalanches are power-law distributed. Such a power-law probability distribution function has also been proposed to characterize different landslide types. In order to understand this scaling for gravity driven systems, we introduce a two-threshold 2-d cellular automaton, in which failure occurs irreversibly. Taking snow slab avalanches as a model system, we find that the sizes of the largest avalanches just preceeding the lattice system breakdown are power law distributed. By tuning the maximum value of the ratio of the two failure thresholds our model reproduces the range of power law exponents observed for land-, rock- or snow avalanches. We suggest this control parameter represents the material cohesion anisotropy.Comment: accepted PR

Fate of Kaluza-Klein Bubble

We numerically study classical time evolutions of Kaluza-Klein bubble space-time which has negative energy after a decay of vacuum. As the zero energy Witten's bubble space-time, where the bubble expands infinitely, the subsequent evolutions of Brill and Horowitz's momentarily static initial data show that the bubble will expand in terms of the area. At first glance, this result may support Corley and Jacobson's conjecture that the bubble will expand forever as well as the Witten's bubble. The irregular signatures, however, can be seen in the behavior of the lapse function in the maximal slicing gauge and the divergence of the Kretchman invariant. Since there is no appearance of the apparent horizon, we suspect an appearance of a naked singularity as the final fate of this space-time.Comment: 13 pages including 10 figures, RevTeX, epsf.sty. CGPG-99/12-8, RESCEU-6/00 and DAMTP-2000-30. To appear in Phys. Rev.

Black hole radiation with high frequency dispersion

We consider one model of a black hole radiation, in which the equation of motion of a matter field is modified to cut off high frequency modes. The spectrum in the model has already been analytically derived in low frequency range, which has resulted in the Planckian distributin of the Hawking temperature. On the other hand, it has been numerically shown that its spectrum deviates from the thermal one in high frequency range. In this paper, we analytically derive the form of the deviation in the high frequency range. Our result can qualitatively explain the nature of the numerically calculated spectrum. The origin of the deviation is clarified by a simple discussion.Comment: 9 pages, 10 figures, submitted to Phys.Rev.

Rank-Ordering Statistics of Extreme Events: Application to the Distribution of Large Earthquakes

Rank-ordering statistics provides a perspective on the rare, largest elements of a population, whereas the statistics of cumulative distributions are dominated by the more numerous small events. The exponent of a power law distribution can be determined with good accuracy by rank-ordering statistics from the observation of only a few tens of the largest events. Using analytical results and synthetic tests, we quantify the systematic and the random errors. We also study the case of a distribution defined by two branches, each having a power law distribution, one defined for the largest events and the other for smaller events, with application to the World-Wide (Harvard) and Southern California earthquake catalogs. In the case of the Harvard moment catalog, we make more precise earlier claims of the existence of a transition of the earthquake magnitude distribution between small and large earthquakes; the $b$-values are $b_2 = 2.3 \pm 0.3$ for large shallow earthquakes and $b_1 = 1.00 \pm 0.02$ for smaller shallow earthquakes. However, the cross-over magnitude between the two distributions is ill-defined. The data available at present do not provide a strong constraint on the cross-over which has a $50\%$ probability of being between magnitudes $7.1$ and $7.6$ for shallow earthquakes; this interval may be too conservatively estimated. Thus, any influence of a universal geometry of rupture on the distribution of earthquakes world-wide is ill-defined at best. We caution that there is no direct evidence to confirm the hypothesis that the large-moment branch is indeed a power law. In fact, a gamma distribution fits the entire suite of earthquake moments from the smallest to the largest satisfactorily. There is no evidence that the earthquakes of the Southern California catalog have a distribution with tw

Torsional nodeless vibrations of quaking neutron star restored by combined forces of shear elastic and magnetic field stresses

Within the framework of Newtonian magneto-solid-mechanics, relying on equations appropriate for a perfectly conducting elastic continuous medium threaded by a uniform magnetic field, the asteroseismic model of a neutron star undergoing axisymmetric global torsional nodeless vibrations under the combined action of Hooke's elastic and Lorentz magnetic forces is considered with emphasis on a toroidal Alfv\'en mode of differentially rotational vibrations about the dipole magnetic moment axis of the star. The obtained spectral equation for frequency is applied to $\ell$-pole identification of quasi-periodic oscillations (QPOs) of X-ray flux during the giant flares of SGR 1806-20 and SGR 1900+14. Our calculations suggest that detected QPOs can be consistently interpreted, within the framework of this model, as produced by global torsional nodeless vibrations of quaking magnetar if they are considered to be restored by the joint action of bulk forces of shear elastic and magnetic field stresses.Comment: 18 pages, 5 figures; accepted in Ap

A trick for passing degenerate points in Ashtekar formulation

We examine one of the advantages of Ashtekar's formulation of general relativity: a tractability of degenerate points from the point of view of following the dynamics of classical spacetime. Assuming that all dynamical variables are finite, we conclude that an essential trick for such a continuous evolution is in complexifying variables. In order to restrict the complex region locally, we propose some `reality recovering' conditions on spacetime. Using a degenerate solution derived by pull-back technique, and integrating the dynamical equations numerically, we show that this idea works in an actual dynamical problem. We also discuss some features of these applications.Comment: 9 pages by RevTeX or 16 pages by LaTeX, 3 eps figures and epsf-style file are include

Adjusted ADM systems and their expected stability properties: constraint propagation analysis in Schwarzschild spacetime

In order to find a way to have a better formulation for numerical evolution of the Einstein equations, we study the propagation equations of the constraints based on the Arnowitt-Deser-Misner formulation. By adjusting constraint terms in the evolution equations, we try to construct an "asymptotically constrained system" which is expected to be robust against violation of the constraints, and to enable a long-term stable and accurate numerical simulation. We first provide useful expressions for analyzing constraint propagation in a general spacetime, then apply it to Schwarzschild spacetime. We search when and where the negative real or non-zero imaginary eigenvalues of the homogenized constraint propagation matrix appear, and how they depend on the choice of coordinate system and adjustments. Our analysis includes the proposal of Detweiler (1987), which is still the best one according to our conjecture but has a growing mode of error near the horizon. Some examples are snapshots of a maximally sliced Schwarzschild black hole. The predictions here may help the community to make further improvements.Comment: 23 pages, RevTeX4, many figures. Revised version. Added subtitle, reduced figures, rephrased introduction, and a native checked. :-

Finding the Needles in the Haystacks: High-Fidelity Models of the Modern and Archean Solar System for Simulating Exoplanet Observations

We present two state-of-the-art models of the solar system, one corresponding to the present day and one to the Archean Eon 3.5 billion years ago. Each model contains spatial and spectral information for the star, the planets, and the interplanetary dust, extending to 50 AU from the sun and covering the wavelength range 0.3 to 2.5 micron. In addition, we created a spectral image cube representative of the astronomical backgrounds that will be seen behind deep observations of extrasolar planetary systems, including galaxies and Milky Way stars. These models are intended as inputs to high-fidelity simulations of direct observations of exoplanetary systems using telescopes equipped with high-contrast capability. They will help improve the realism of observation and instrument parameters that are required inputs to statistical observatory yield calculations, as well as guide development of post-processing algorithms for telescopes capable of directly imaging Earth-like planets.Comment: Accepted for publication in PAS