Constraints on Galaxy Density Profiles from Strong Gravitational Lensing: The Case of B 1933+503

We consider a wide range of parametric mass models for B 1933+503, a ten-image radio lens, and identify shared properties of the models with the best fits. The approximate rotation curves varies by less than 8.5% from the average value between the innermost and the outermost image (1.5h^{-1} kpc to 4.1h^{-1} kpc) for models within 1 \sigma of the best fit, and the radial dependence of the shear strength and angle also have common behavior for the best models. The time delay between images 1 and 6, the longest delay between the radio cores, is \Delta t = (10.6^{+2.4}_{-1.1})h^{-1} days (\Omega_0=0.3, \lambda_0=0.7) including all the modeling uncertainties. Deeper infrared observations, to more precisely register the lens galaxy with the radio images and to measure the properties of the Einstein ring image of the radio source's host galaxy, would significantly improve the model constraints and further reduce the uncertainties in the mass distribution and time delay.Comment: 24 pages, 10 figures, final version to appear in ApJ. Some minor corrections (e.g. constraint on central unseen image was stronger than intended earlier, now agrees with text, conventions on angles fixed in text/plots). Resulting model fits have some change in chi squareds and best parameters (e.g. cores, flatness of rotation curve) have some changes. Properties of model families and trends for best fitting models very close to earlier results; general conclusions the sam

Limits on a Stochastic Background of Gravitational Waves from Gravitational Lensing

We compute the effects of a stochastic background of gravitational waves on multiply imaged systems or on weak lensing. There are two possible observable effects, a static relative deflection of images or shear, and an induced time dependent shift or proper motion. We evaluate the rms magnitude of these effects for a COBE normalized, scale-invariant spectrum, which is an upper limit on spectra produced by inflation. Previous work has shown that large-scale structure may cause a relative deflection large enough to affect observations, but we find that the corresponding effect of gravity waves is smaller by $\sim 10^4$ and so cannot be observed. This results from the oscillation in time as well as the redshifting of the amplitude of gravity waves. We estimate the magnitude of the proper motion induced by deflection of light due to large-scale structure, and find it to be $\sim 10^{-8}$ arcsec per year. This corresponds to $\sim 50$ km/s at cosmological distances, which is quite small compared to typical peculiar velocities. The COBE normalized gravity wave spectrum produces motions smaller still by $\sim 10^2$. We conclude that light deflection due to these cosmological perturbations cannot produce observable proper motions of lensed images. On the other hand, there are only a few known observational limits on a stochastic background of gravity waves at shorter, astrophysical wavelengths. We calculate the expected magnitudes of the effects of lensing by gravity waves of such wavelengths, and find that they are too small to yield interesting limits on the energy density of gravity waves.Comment: 14 pages, LaTex + 1 PS Figure, accepted version to be published in Phys. Rev. D15, Dec. 1996. An incorrect assumption was removed, also various other minor change

Gravitational lensing on the Cosmic Microwave Background by gravity waves

We study the effect of a stochastic background of gravitational waves on the gravitational lensing of the Cosmic Microwave Background (CMB) radiation. It has been shown that matter density inhomogeneities produce a smoothing of the acoustic peaks in the angular power spectrum of the CMB anisotropies. A gravitational wave background gives rise to an additional smoothing of the spectrum. For the most simple case of a gravitational wave background arising during a period of inflation, the effect results to be three to four orders of magnitude smaller than its scalar counterpart, and is thus undetectable. It could play a more relevant role in models where a larger background of gravitational waves is produced.Comment: 6 pages, RevTeX file, 1 figur

The impact of lens galaxy environments on the image separation distribution

We study the impact of lens galaxy environments on the image separation distribution of lensed quasars. We account for both environmental convergence and shear, using a joint distribution derived from galaxy formation models calibrated by galaxy-galaxy lensing data and number counts of massive elliptical galaxies. We find that the external field enhances lensing probabilities, particularly at large image separations; the increase is ~30% at \theta=3'' and ~200% at \theta=5'', when we adopt a power-law source luminosity function \Phi(L) \propto L^-2.1. The enhancement is mainly driven by convergence, which boosts both the image separation and magnification bias (for a fixed lens galaxy mass). These effects have been neglected in previous studies of lens statistics. Turning the problem around, we derive the posterior convergence and shear distributions and point out that they are strong functions of image separation; lens systems with larger image separations are more likely to lie in dense environments.Comment: 8 pages, 10 figures, accepted for publication in MNRA

Determination of Inflationary Observables by Cosmic Microwave Background Anisotropy Experiments

Inflation produces nearly Harrison-Zel'dovich scalar and tensor perturbation spectra which lead to anisotropy in the cosmic microwave background (CMB). The amplitudes and shapes of these spectra can be parametrized by $Q_S^2$, $r\equiv Q_T^2/Q_S^2$, $n_S$ and $n_T$ where $Q_S^2$ and $Q_T^2$ are the scalar and tensor contributions to the square of the CMB quadrupole and $n_S$ and $n_T$ are the power-lawspectral indices. Even if we restrict ourselves to information from angles greater than one third of a degree, three of these observables can be measured with some precision. The combination $130^{1-n_S}Q_S^2$ can be known to better than $\pm 0.3\%$. The scalar index $n_S$ can be determined to better than $\pm 0.02$. The ratio $r$ can be known to about $\pm 0.1$ for $n_S \simeq 1$ and slightly better for smaller $n_S$. The precision with which $n_T$ can be measured depends weakly on $n_S$ and strongly on $r$. For $n_S \simeq 1$ $n_T$ can be determined with a precision of about $\pm 0.056(1.5+r)/r$. A full-sky experiment with a $20'$beam using technology available today, similar to those being planned by several groups, can achieve the above precision. Good angular resolution is more important than high signal-to-noise ratio; for a given detector sensitivity and observing time a smaller beam provides significantly more information than a larger beam. The uncertainties in $n_S$ and $r$ are roughly proportional to the beam size. We briefly discuss the effects of uncertainty in the Hubble constant, baryon density, cosmological constant and ionization history.Comment: 28 pages of uuencoded postscript with 8 included figures. A postscript version is also available by anonymous ftp at ftp://astro.uchicago.edu/pub/astro/knox/fullsim.p

Reconstructing the Inflaton Potential --- an Overview

We review the relation between the inflationary potential and the spectra of density (scalar) perturbations and gravitational waves (tensor perturbations) produced, with particular emphasis on the possibility of reconstructing the inflaton potential from observations. The spectra provide a potentially powerful test of the inflationary hypothesis; they are not independent but instead are linked by consistency relations reflecting their origin from a single inflationary potential. To lowest-order in a perturbation expansion there is a single, now familiar, relation between the tensor spectral index and the relative amplitude of the spectra. We demonstrate that there is an infinite hierarchy of such consistency equations, though observational difficulties suggest only the first is ever likely to be useful. We also note that since observations are expected to yield much better information on the scalars than on the tensors, it is likely to be the next-order version of this consistency equation which will be appropriate, not the lowest-order one. If inflation passes the consistency test, one can then confidently use the remaining observational information to constrain the inflationary potential, and we survey the general perturbative scheme for carrying out this procedure. Explicit expressions valid to next-lowest order in the expansion are presented. We then briefly assess the prospects for future observations reaching the quality required, and consider a simulated data set that is motivated by this outlook.Comment: 69 pages standard LaTeX plus 4 postscript figures. Postscript version of text in landscape format (35 pages) available at http://star-www.maps.susx.ac.uk/papers/infcos_papers.html Modifications are a variety of updates to discussion and reference