Nickel(II) & Copper(II) Complexes of 5(3)-Methyl-pyrazole-3(5)-carboxamide

744-74

Maximum Entropy for Gravitational Wave Data Analysis: Inferring the Physical Parameters of Core-Collapse Supernovae

The gravitational wave signal arising from the collapsing iron core of a Type II supernova progenitor star carries with it the imprint of the progenitor's mass, rotation rate, degree of differential rotation, and the bounce depth. Here, we show how to infer the gravitational radiation waveform of a core collapse event from noisy observations in a network of two or more LIGO-like gravitational wave detectors and, from the recovered signal, constrain these source properties. Using these techniques, predictions from recent core collapse modeling efforts, and the LIGO performance during its S4 science run, we also show that gravitational wave observations by LIGO might have been sufficient to provide reasonable estimates of the progenitor mass, angular momentum and differential angular momentum, and depth of the core at bounce, for a rotating core collapse event at a distance of a few kpc.Comment: 44 pages, 12 figures; accepted version scheduled to appear in Ap J 1 April 200

On the streaming motions of haloes and galaxies

A simple model of how objects of different masses stream towards each other as they cluster gravitationally is described. The model shows how the mean streaming velocity of dark matter particles is related to the motions of the parent dark matter haloes. It also provides a reasonably accurate description of how the pairwise velocity dispersion of dark matter particles differs from that of the parent haloes. The analysis is then extended to describe the streaming motions of galaxies. This shows explicitly that the streaming motions measured in a given galaxy sample depend on how the sample was selected, and shows how to account for this dependence on sample selection. In addition,we show that the pairwise dispersion should also depend on sample type. Our model predicts that, on small scales, redshift space distortions should affect red galaxies more strongly than blue.Comment: 10 pages, submitted to MNRA

Statistics of Gravitational Microlensing Magnification. I. Two-Dimensional Lens Distribution

(Abridged) In this paper we refine the theory of microlensing for a planar distribution of point masses. We derive the macroimage magnification distribution P(A) at high magnification (A-1 >> tau^2) for a low optical depth (tau << 1) lens distribution by modeling the illumination pattern as a superposition of the patterns due to individual ``point mass plus weak shear'' lenses. We show that a point mass plus weak shear lens produces an astroid- shaped caustic and that the magnification cross-section obeys a simple scaling property. By convolving this cross-section with the shear distribution, we obtain a caustic-induced feature in P(A) which also exhibits a simple scaling property. This feature results in a 20% enhancement in P(A) at A approx 2/tau. In the low magnification (A-1 << 1) limit, the macroimage consists of a bright primary image and a large number of faint secondary images formed close to each of the point masses. Taking into account the correlations between the primary and secondary images, we derive P(A) for low A. The low-A distribution has a peak of amplitude ~ 1/tau^2 at A-1 ~ tau^2 and matches smoothly to the high-A distribution. We combine the high- and low-A results and obtain a practical semi-analytic expression for P(A). This semi-analytic distribution is in qualitative agreement with previous numerical results, but the latter show stronger caustic-induced features at moderate A for tau as small as 0.1. We resolve this discrepancy by re-examining the criterion for low optical depth. A simple argument shows that the fraction of caustics of individual lenses that merge with those of their neighbors is approx 1-exp(-8 tau). For tau=0.1, the fraction is surprisingly high: approx 55%. For the purpose of computing P(A) in the manner we did, low optical depth corresponds to tau << 1/8.Comment: 35 pages, including 6 figures; uses AASTeX v4.0 macros; submitted to Ap

Cluster-Cluster Microlensing as a Probe of Intracluster Stars, MACHOs, and Remnants of the First Generation Stars

The galaxy cluster Abell 2152 is recently found to be forming a cluster-cluster system with another, more distant cluster whose core is almost perfectly aligned to that of A2152. We discuss the detectability of microlensing events where a single star in the source cluster behind A2152 is extremely magnified by an intracluster compact object in A2152. We show that a search with an 8m-class telescope with a wide field of view, such as the Subaru/Suprime-Cam, can probe intracluster compact objects with a wide mass range of m_{co} ~ 10^{-5}-10^{10} M_sun, including ranges that have not yet been constrained by any past observations. We expect that the event rate is biased for the background cluster than the foreground cluster (A2152), which would be a unique signature of microlensing, making this experiment particularly powerful. The sensitivity of this experiment for the mass fraction of compact objects would be 1-10% in the total dark matter of the cluster, which is roughly constant against m_{co}, with a reasonable telescope time for large telescopes (~10 nights). Therefore any compact objects in this mass range can be detected or rejected as the dominant component of the dark matter. About 10 events are expected if 20% of the cluster mass is in a form of compact objects with M ~ 1 M_sun, as claimed by the MACHO collaboration for the Milky Way halo. Other possibly detectable targets include intracluster stars stripped by galaxy interactions, and hypothetical very massive black holes (M >~ 100 M_sun) produced as remnants of the first generation stars, which might be responsible for the recently reported excess of the cosmic infrared background radiation that seems impossible to explain by normal galactic light.Comment: 14 pages, 6 figures, to appear in ApJ. Some minor corrections, and references adde

Wavefronts, Caustic Sheets, and Caustic Surfing in Gravitational Lensing

Very little attention has been paid to the properties of optical wavefronts and caustic surfaces due to gravitational lensing. Yet the wavefront-based point of view is natural and provides insights into the nature of the caustic surfaces on a gravitationally lensed lightcone. We derive analytically the basic equations governing the wavefronts, lightcones, caustics on wavefronts, and caustic surfaces on lightcones in the context of weak-field, thin-screen gravitational lensing. These equations are all related to the potential of the lens. In the process, we also show that the standard single-plane gravitational lensing map extends to a new mapping, which we call a wavefront lensing map. Unlike the standard lensing map, the Jacobian matrix of a wavefront lensing map is not symmetric. Our formulas are then applied to caustic ``surfing.'' By surfing a caustic surface, a space-borne telescope can be fixed on a gravitationally lensed source to obtain an observation of the source at very high magnification over an extended time period, revealing structure about the source that could not otherwise be resolved. Using our analytical expressions for caustic sheets, we present a scheme for surfing a caustic sheet of a lensed source in rectilinear motion. Detailed illustrations are also presented of the possible types of wavefronts and caustic sheets due to nonsingular and singular elliptical potentials, and singular isothermal spheres, including an example of caustic surfing for a singular elliptical potential lens.Comment: To appear in J. Math. Phys., 31 pages, 15 figure

The Spin of the Near-Extreme Kerr Black Hole GRS 1915+105

Based on a spectral analysis of the X-ray continuum that employs a fully relativistic accretion-disk model, we conclude that the compact primary of the binary X-ray source GRS 1915+105 is a rapidly-rotating Kerr black hole. We find a lower limit on the dimensionless spin parameter of a* greater than 0.98. Our result is robust in the sense that it is independent of the details of the data analysis and insensitive to the uncertainties in the mass and distance of the black hole. Furthermore, our accretion-disk model includes an advanced treatment of spectral hardening. Our data selection relies on a rigorous and quantitative definition of the thermal state of black hole binaries, which we used to screen all of the available RXTE and ASCA data for the thermal state of GRS 1915+105. In addition, we focus on those data for which the accretion disk luminosity is less than 30% of the Eddington luminosity. We argue that these low-luminosity data are most appropriate for the thin alpha-disk model that we employ. We assume that there is zero torque at the inner edge of the disk, as is likely when the disk is thin, although we show that the presence of a significant torque does not affect our results. Our model and the model of the relativistic jets observed for this source constrain the distance and black hole mass and could thus be tested by determining a VLBA parallax distance and improving the measurement of the mass function. Finally, we comment on the significance of our results for relativistic-jet and core-collapse models, and for the detection of gravitational waves.Comment: 58 pages, 18 figures. Accepted for publication in ApJ. New in this version is a proposed observational test of our spin model and the kinematic model of the radio jet

Mathematics of Gravitational Lensing: Multiple Imaging and Magnification

The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds in the case of single and multiple lens planes. We discuss recent advances in the mathematics of stochastic lensing, discussing a general formula for the global expected number of minimum lensed images as well as asymptotic formulas for the probability densities of the microlensing random time delay functions, random lensing maps, and random shear, and an asymptotic expression for the global expected number of micro-minima. Multiple imaging in optical geometry and a spacetime setting are treated. We review global magnification relation results for model-dependent scenarios and cover recent developments on universal local magnification relations for higher order caustics.Comment: 25 pages, 4 figures. Invited review submitted for special issue of General Relativity and Gravitatio

Dark Energy and Gravity

I review the problem of dark energy focusing on the cosmological constant as the candidate and discuss its implications for the nature of gravity. Part 1 briefly overviews the currently popular `concordance cosmology' and summarises the evidence for dark energy. It also provides the observational and theoretical arguments in favour of the cosmological constant as the candidate and emphasises why no other approach really solves the conceptual problems usually attributed to the cosmological constant. Part 2 describes some of the approaches to understand the nature of the cosmological constant and attempts to extract the key ingredients which must be present in any viable solution. I argue that (i)the cosmological constant problem cannot be satisfactorily solved until gravitational action is made invariant under the shift of the matter lagrangian by a constant and (ii) this cannot happen if the metric is the dynamical variable. Hence the cosmological constant problem essentially has to do with our (mis)understanding of the nature of gravity. Part 3 discusses an alternative perspective on gravity in which the action is explicitly invariant under the above transformation. Extremizing this action leads to an equation determining the background geometry which gives Einstein's theory at the lowest order with Lanczos-Lovelock type corrections. (Condensed abstract).Comment: Invited Review for a special Gen.Rel.Grav. issue on Dark Energy, edited by G.F.R.Ellis, R.Maartens and H.Nicolai; revtex; 22 pages; 2 figure