Radial density profiles of time-delay lensing galaxies

We present non-parametric radial mass profiles for ten QSO strong lensing galaxies. Five of the galaxies have profiles close to $\rho(r)\propto r^{-2}$, while the rest are closer to r^{-1}, consistent with an NFW profile. The former are all relatively isolated early-types and dominated by their stellar light. The latter --though the modeling code did not know this-- are either in clusters, or have very high mass-to-light, suggesting dark-matter dominant lenses (one is a actually pair of merging galaxies). The same models give H_0^{-1} = 15.2_{-1.7}^{+2.5}\Gyr (H_0 = 64_{-9}^{+8} \legacy), consistent with a previous determination. When tested on simulated lenses taken from a cosmological hydrodynamical simulation, our modeling pipeline recovers both H_0 and $\rho(r)$ within estimated uncertainties. Our result is contrary to some recent claims that lensing time delays imply either a low H_0 or galaxy profiles much steeper than r^{-2}. We diagnose these claims as resulting from an invalid modeling approximation: that small deviations from a power-law profile have a small effect on lensing time-delays. In fact, as we show using using both perturbation theory and numerical computation from a galaxy-formation simulation, a first-order perturbation of an isothermal lens can produce a zeroth-order change in the time delays.Comment: Replaced with final version accepted for publication in ApJ; very minor changes to text; high resolution figures may be obtained at justinread.ne

The Mean Number of Extra Micro-Image Pairs for Macro-Lensed Quasars

When a gravitationally lensed source crosses a caustic, a pair of images is created or destroyed. We calculate the mean number of such pairs of micro-images for a given macro-image of a gravitationally lensed point source, due to microlensing by the stars of the lensing galaxy. This quantity was calculated by Wambsganss, Witt & Schneider (1992) for the case of zero external shear, $\gamma=0$, at the location of the macro-image. Since in realistic lens models a non-zero shear is expected to be induced by the lensing galaxy, we extend this calculation to a general value of $\gamma$. We find a complex behavior of as a function of $\gamma$ and the normalized surface mass density in stars $\kappa_*$. Specifically, we find that at high magnifications, where the average total magnification of the macro-image is $=|(1-\kappa_*)^2-\gamma^2|^{-1}\gg 1$, $$becomes correspondingly large, and is proportional to$$. The ratio $/$ is largest near the line $\gamma=1-\kappa_*$ where the magnification $$becomes infinite, and its maximal value is 0.306. We compare our semi-analytic results for$$ to the results of numerical simulations and find good agreement. We find that the probability distribution for the number of extra image pairs is reasonably described by a Poisson distribution with a mean value of $$, and that the width of the macro-image magnification distribution tends to be largest for $\sim 1$.Comment: As accepted for publication in ApJ. 11 pages, 4 figures, minor change

Gravitational Lens Time Delays and Gravitational Waves

Using Fermat's principle, we analyze the effects of very long wavelength gravitational waves upon the images of a gravitationally lensed quasar. We show that the lens equation in the presence of gravity waves is equivalent to that of a lens with different alignment between source, deflector, and observer in the absence of gravity waves. Contrary to a recent claim, we conclude that measurements of time delays in gravitational lenses cannot serve as a method to detect or constrain a stochastic background of gravitational waves of cosmological wavelengths, because the wave-induced time delay is observationally indistinguishable from an intrinsic time delay due to the lens geometry.Comment: 22 pages in REVTEX 3.0 (previous versions may not have TeXed due to Unix mailer problems

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

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

Signalling plasticity and energy saving in a tropical bushcricket

Males of the tropical bushcricket Mecopoda elongata synchronize their acoustic advertisement signals (chirps) in interactions with other males. However, synchrony is not perfect and distinct leader and follower roles are often maintained. In entrainment experiments in which conspecific signals were presented at various rates, chirps displayed as follower showed notable signal plasticity. Follower chirps were shortened by reducing the number and duration of syllables, especially those of low and medium amplitude. The degree of shortening depended on the time delay between leader and follower signals and the sound level of the entraining stimulus. The same signal plasticity was evident in male duets, with the effect that the last syllables of highest amplitude overlapped more strongly. Respiratory measurements showed that solo singing males producing higher chirp rates suffered from higher metabolic costs compared to males singing at lower rates. In contrast, respiratory rate was rather constant during a synchronous entrainment to a conspecific signal repeated at various rates. This allowed males to maintain a steady duty cycle, associated with a constant metabolic rate. Results are discussed with respect to the preference for leader signals in females and the possible benefits males may gain by overlapping their follower signals in a chorus