Quasar Microlensing: when compact masses mimic smooth matter

The magnification induced by gravitational microlensing is sensitive to the size of a source relative to the Einstein radius, the natural microlensing scale length. This paper investigates the effect of source size in the case where the microlensing masses are distributed with a bimodal mass function, with solar mass stars representing the normal stellar masses, and smaller masses (down to $8.5\times 10^{-5}$M$_\odot$) representing a dark matter component. It is found that there exists a critical regime where the dark matter is initially seen as individual compact masses, but with an increasing source size the compact dark matter acts as a smooth mass component. This study reveals that interpretation of microlensing light curves, especially claims of small mass dark matter lenses embedded in an overall stellar population, must consider the important influence of the size of the source.Comment: 6 pages, to appear in ApJ. As ever, quality of figures reduce

A Natural Formalism for Microlensing

If the standard microlensing geometry is inverted so that the Einstein ring is projected onto the observer plane rather than the source plane, then the relations between the observables (\theta_E,\tilde r_E) and the underlying physical quantities (M,\pi_rel) become immediately obvious. Here \theta_E and \tilde r_E are the angular and projected Einstein radii, M is the mass of the lens, and \pi_rel is the lens-source relative parallax. I recast the basic formalism of microlensing in light of this more natural geometry and in terms of observables. I then find that the relations between observable and physical quantities assume an exceptionally simple form. In an appendix, I propose a set of notational conventions for microlensing.Comment: 8 pages, 1 figure tells all. Interested parties are requested to vote on a proposed standard for microlensing notation given in the appendix. Submitted to Ap

Source Size Limitation from Variabilities of a Lensed Quasar

In the case of gravitationally-lensed quasars, it is well-known that there is a time delay between occurrence of the intrinsic variabilities in each split image. Generally, the source of variabilities has a finite size, and there are time delays even in one image. If the origin of variabilities is widely distributed, say over \gsim 100 pc as whole, variabilities between split images will not show a good correlation even though their origin is identical. Using this fact, we are able to limit the whole source size of variabilities in a quasar below the limit of direct resolution by today's observational instruments.Comment: 15 pages LaTeX, 3 figures, accepted to ApJ Letter. e-mail: [email protected]

A multipole-Taylor expansion for the potential of gravitational lens MG J0414+0534

We employ a multipole-Taylor expansion to investigate how tightly the gravitational potential of the quadruple-image lens MG J0414+0534 is constrained by recent VLBI observations. These observations revealed that each of the four images of the background radio source contains four distinct components, thereby providing more numerous and more precise constraints on the lens potential than were previously available. We expand the two-dimensional lens potential using multipoles for the angular coordinate and a modified Taylor series for the radial coordinate. After discussing the physical significance of each term, we compute models of MG J0414+0534 using only VLBI positions as constraints. The best-fit model has both interior and exterior quadrupole moments as well as exterior m=3 and m=4 multipole moments. The deflector centroid in the models matches the optical galaxy position, and the quadrupoles are aligned with the optical isophotes. The radial distribution of mass could not be well constrained. We discuss the implications of these models for the deflector mass distribution and for the predicted time delays between lensed components.Comment: 44 pages, 5 figures, 11 tables, accepted for publication in Ap

X-ray Detection of the Primary Lens Galaxy Cluster of the Gravitational Lens System Q0957+561

Analysis of several recent ROSAT HRI observations of the gravitationally lensed system Q0957+561 has led to the detection at the 3sigma level of the cluster lens containing the primary galaxy G1. The total mass was estimated by applying the equation of hydrostatic equilibrium to the detected hot intracluster gas for a range of cluster core radii, cluster sizes and for different values of the Hubble constant. X-ray estimates of the lensing cluster mass provide a means to determine the cluster contribution to the deflection of rays originating from the quasar Q0957+561. The present mass estimates were used to evaluate the convergence parameter kappa, the ratio of the local surface mass density of the cluster to the critical surface mass density for lensing. The convergence parameter, kappa, calculated in the vicinity of the lensed images, was found to range between 0.07 and 0.21, depending on the assumed cluster core radius and cluster extent. This range of uncertainty in kappa does not include possible systematic errors arising from the estimation of the cluster temperature through the use of the cluster luminosity-temperature relation and the assumption of spherical symmetry of the cluster gas. Applying this range of values of kappa to the lensing model of Grogin & Narayan (1996) for Q0957+561 but not accounting for uncertainties in that model yields a range of values for the Hubble constant:67<H_0<82 km s^-1 Mpc^-1, for a time delay of 1.1 years.Comment: Accepted for publication in ApJ, 25 pages, 9 figure

Measuring the Size of Quasar Broad-Line Clouds Through Time Delay Light-Curve Anomalies of Gravitational Lenses

Intensive monitoring campaigns have recently attempted to measure the time delays between multiple images of gravitational lenses. Some of the resulting light-curves show puzzling low-level, rapid variability which is unique to individual images, superimposed on top of (and concurrent with) longer time-scale intrinsic quasar variations which repeat in all images. We demonstrate that both the amplitude and variability time-scale of the rapid light-curve anomalies, as well as the correlation observed between intrinsic and microlensed variability, are naturally explained by stellar microlensing of a smooth accretion disk which is occulted by optically-thick broad-line clouds. The rapid time-scale is caused by the high velocities of the clouds (~5x10^3 km/s), and the low amplitude results from the large number of clouds covering the magnified or demagnified parts of the disk. The observed amplitudes of variations in specific lenses implies that the number of broad-line clouds that cover ~10% of the quasar sky is ~10^5 per 4 pi steradian. This is comparable to the expected number of broad line clouds in models where the clouds originate from bloated stars.Comment: 19 pages, 9 figures. Submitted to Ap

Lensing Degeneracies Revisited

This paper shows that the mass-sheet degeneracy and other degeneracies in lensing have simple geometrical interpretations: they are mostly rescalings of the arrival-time surface. Different degeneracies appear in Local Group lensing and in cosmological lensing, because in the former the absolute magnification is measured but the image structure is not resolved, whereas in the latter the reverse usually applies. The most dangerous of these is a combination we may call the `mass-disk degeneracy' in multiply-imaging galaxy lenses, which may lead to large systematic uncertainties in estimates of cosmological parameters from these systems.Comment: To appear in AJ (circa Oct 2000

Spectroscopy of the Lens Galaxy of Q0957+561A,B. Implications of a possible central massive dark object

We present new long-slit William Herschel Telescope spectroscopic observations of the lens galaxy G1 associated with the double-imaged QSO 0957+561A,B. The obtained central stellar velocity dispersion, sigma_l = 310 +/- 20 km/s, is in reasonable agreement with other measurements of this dynamical parameter. Using all updated measurements of the stellar velocity dispersion in the internal region of the galaxy (at angular separations < 1".5) and a simple isotropic model, we discuss the mass of a possible central massive dark object. It is found that the data of Falco et al. (1997) suggest the existence of an extremely massive object of (0.5-2.1) x 10E10/h M_\odot (80% confidence level), whereas the inclusion of very recent data (Tonry & Franx 1998, and this paper) substantially changes the results: the compact central mass must be $\le$ 6 x10E9/h M_\odot at the 90% confidence level. We note that, taking into account all the available dynamical data, a compact nucleus with a mass of 10E9/h M_\odot (best fit) cannot be ruled out.Comment: 20 pages, 10 figures ApJ, in pres

Distances and Cosmology From Galaxy Cluster CMB Data

The measurement of angular diameter distance to galaxy clusters, through combined Sunyaev-Zel'dovich (SZ) effect data with X-ray emission observations, is now a well-known probe of cosmology. Using a combination of SZ data and a map of the lensed CMB anisotropies by the galaxy cluster potential, we propose an alternative geometric technique to measure distance information primarily through cluster related multi-frequency CMB measurements. We discuss necessary requirements to implement this measurement, potential errors including systematic biases, and the extent to which cosmological parameters can be extracted. While individual cluster distances are not likely to be precise, with upcoming subarcminute resolution wide-area CMB observations, useful information on certain cosmological parameters, such as the equation of state of dark energy, can be obtained from a large sample of galaxy clusters.Comment: 4 pages, 2 figure

New Modeling of the Lensing Galaxy and Cluster of Q0957+561: Implications for the Global Value of the Hubble Constant

The gravitational lens 0957+561 is modeled utilizing recent observations of the galaxy and the cluster as well as previous VLBI radio data which have been re-analyzed recently. The galaxy is modeled by a power-law elliptical mass density with a small core while the cluster is modeled by a non-singular power-law sphere as indicated by recent observations. Using all of the current available data, the best-fit model has a reduced chi-squared of approximately 6 where the chi-squared value is dominated by a small portion of the observational constraints used; this value of the reduced chi-squared is similar to that of the recent FGSE best-fit model by Barkana et al. However, the derived value of the Hubble constant is significantly different from the value derived from the FGSE model. We find that the value of the Hubble constant is given by H_0 = 69 +18/-12 (1-K) and 74 +18/-17 (1-K) km/s/Mpc with and without a constraint on the cluster's mass, respectively, where K is the convergence of the cluster at the position of the galaxy and the range for each value is defined by Delta chi-squared = reduced chi-squared. Presently, the best achievable fit for this system is not as good as for PG 1115+080, which also has recently been used to constrain the Hubble constant, and the degeneracy is large. Possibilities for improving the fit and reducing the degeneracy are discussed.Comment: 22 pages in aaspp style including 6 tables and 5 figures, ApJ in press (Nov. 1st issue