Direct Mapping of Massive Compact Objects in Extragalactic Dark Halos

A significant fraction of non-baryonic or baryonic dark matter in galactic halos may consist of MASsive Compact Objects (MASCOs) with mass M=10^{1-4}M_{sun}. Possible candidates for such compact objects include primordial black holes or remnants of primordial (Population III) stars. We propose a method for directly detecting MASCOs in extragalactic halos, using the VLBI techniques with extremely high resolution. If a galactic halo comprising a large number of MASCOs produces multiple images of a background radio-loud QSO by gravitational lensing, then a high-resolution radio map of each macro-lensed image should reveal microlensing effects by MASCOs. To assess their observational feasibility, we simulate microlensing of the radio-loud, four-image lensed QSO, B1422+231, assuming angular resolution of ~0.01 mas. MASCOs are represented by point masses. For comparison, we also simulate microlensing of B1422+231 by singular isothermal spheres. We find that the surface brightness of the macro-lensed images shows distinct spatial patterns on the scale of the Einstein radius of the perturbers. In the case of point-mass perturbers, many tiny dark spots also appear in the macro-lensed images associated with a decrease in the surface brightness toward the fringe of the original QSO image, whereas no such spots are available in the SIS models. Based on the size, position and magnified or demagnified patterns of images, we shall be able to determine the mass and density profile of a MASCO as well as its spatial distribution and abundance in a galactic halo.Comment: 4 pages, 3 figure

Constraints on the Inner Mass Profiles of Lensing Galaxies from Missing Odd Images

Most gravitational lens systems consist of two or four observable images. The absence of detectable odd images allows us to place a lower limit on the power-law slope of the inner mass profile of lensing galaxies. Using a sample of six two-image radio-loud lens systems and assuming a singular power-law surface density (Sigma proportional to r^{-beta}) for the inner several kpc of the mass distribution, we find that there is less than a 10% probability that the data are consistent with profile slopes beta < 0.80. Furthermore, individual mass modeling yields beta > 0.85 for B0739+366 and beta > 0.91 for B1030+074. Modeling central black holes as additional point masses changes the constraints in these systems to beta > 0.84 and beta > 0.83, respectively. The inner mass profiles of lensing galaxies are therefore not much shallower than isothermal.Comment: Final published version, minor typos corrected, 13 page

Three-dimensional Mapping of CDM Substructure at Submillimeter Wavelengths

The cold dark matter (CDM) structure formation model predicts that about 5-10 percent of a typical galactic halo of mass \sim 10^{12} \ms is in substructures with masses \lesssim 10^8 \ms. To directly detect such substructures, we propose to observe dust continuum emission from a strongly lensed QSO-host galaxy using a large submillimeter interferometer array with a high angular resolution of $\sim 0.01$arcsec such as the planned Atacama Large Submillimeter Array (ALMA). To assess their observational feasibility, we numerically simulate millilensing of an extended circular source by a CDM substructure modeled as a tidally truncated singular isothermal sphere (SIS) embedded in a typical QSO-galaxy lens system, B1422+231, modeled as a singular isothermal ellipsoid (SIE) with an external constant shear and a constant convergence. Assuming an angular resolution of 0.01arcsec, we find that the angular positions of \sim 10^8 \ms substructures at several kpc from the center of the macrolens halo can be directly measured if the size of the dust continuum emission region and the gradient of the surface brightness at the position of the perturber are sufficiently large. From the astrometric shift on a scale of a few times $10~$mas of an image perturbed by a subhalo with respect to an unperturbed macrolensed image, we can break the degeneracy between subhalo mass and distance provided that macrolensing parameters are determined from positions and fluxes of multiple images.Comment: 7 pages, 7 EPS files. An assessment of our assumption of constancy in shear and convergence has been included. Version accepted for publication in Ap

CFHT AO Imaging of the CLASS Gravitational Lens System B1359+154

We present adaptive optics imaging of the CLASS gravitational lens system B1359+154 obtained with the Canada-France-Hawaii Telescope (CFHT) in the infrared K band. The observations show at least three brightness peaks within the ring of lensed images, which we identify as emission from multiple lensing galaxies. The results confirm the suspected compound nature of the lens, as deduced from preliminary mass modeling. The detection of several additional nearby galaxies suggests that B1359+154 is lensed by the compact core of a small galaxy group. We attempted to produce an updated lens model based on the CFHT observations and new 5-GHz radio data obtained with the MERLIN array, but there are too few constraints to construct a realistic model at this time. The uncertainties inherent with modeling compound lenses make B1359+154 a challenging target for Hubble constant determination through the measurement of differential time delays. However, time delays will offer additional constraints to help pin down the mass model. This lens system therefore presents a unique opportunity to directly measure the mass distribution of a galaxy group at intermediate redshift.Comment: 12 pages including 3 figures; ApJL accepte

Probing Dark Matter Substructure in Lens Galaxies

We investigate the effects of numerous dark matter subhalos in a galaxy-sized halo on the events of strong lensing, to assess their presence as expected from the cold dark matter scenario. Lens galaxies are represented by a smooth ellipsoid in an external shear field and additional cold dark matter subhalos taken from Monte Carlo realizations which accord with recent N-body results. We also consider other possible perturbers, globular clusters and luminous dwarf satellites, for comparison. We then apply the models to the particular lens systems with four images, B1422+231 and PG1115+080, for which smooth lens models are unable to reproduce both the positions of the images and their radio flux ratios or dust-free optical flux ratios simultaneously. We show that the perturbations by both globular clusters and dwarf satellites are too small to change the flux ratios, whereas cold dark matter subhalos are most likely perturbers to reproduce the observed flux ratios in a statistically significant manner. This result suggests us the presence of numerous subhalos in lens galaxies, which is consistent with the results of cosmological N-body simulations.Comment: 19 pages, including 5 figures, ApJ in pres

Analytic Cross Sections for Substructure Lensing

The magnifications of the images in a strong gravitational lens system are sensitive to small mass clumps in the lens potential; this effect has been used to infer the amount of substructure in galaxy dark matter halos. I study the theory of substructure lensing to identify important general features, and to compute analytic cross sections that will facilitate further theoretical studies. I show that the problem of a clump anywhere along the line of sight to a lens can be mapped onto an equivalent problem of a clump in a simple convergence and shear field; clumps at arbitrary redshifts are therefore not hard to handle in calculations. For clumps modeled as singular isothermal spheres (SIS), I derive simple analytic estimates of the cross section for magnification perturbations of a given strength. The results yield two interesting conceptual points. First, lensed images with positive parity are always made brighter by SIS clumps; images with negative parity can be brightened but are much more likely to be dimmed. Second, the clumps need not lie within the lens galaxy; they can be moved in redshift by several tenths and still have a significant lensing effect. Isolated small halos are expected to be common in hierarchical structure formation models, but it is not yet known whether they are abundant enough compared with clumps inside lens galaxies to affect the interpretation of substructure lensing.Comment: accepted in ApJ; minor text changes from original versio

The Quintuple Quasar: Mass Models and Interpretation

The strange morphology of the six-component gravitational lens PMN J0134-0931 has resisted explanation. We present the first successful quantitative models for the system, based on the idea that there are two lens galaxies and two components of the background source. One source is quintuply imaged and corresponds to the five brightest observed radio components. The other source is triply imaged and corresponds to the sixth component, along with two others too faint to have been detected. The models reproduce the observed image positions and fluxes, and make falsifiable predictions about other properties of the system. Some of these predictions have been confirmed by high-resolution radio and optical observations, as described in the companion paper by Winn et al. (2003). Although we cannot determine the lens model uniquely with current data, we predict that the lens galaxies are spiral galaxies with roughly equal velocity dispersions sigma~120km/s and a projected separation of only 0.4" (2/h kpc at z_l=0.76). This system is the first known lens with five images of a single quasar, and the second with more than four images.Comment: ApJ, in press. 22 pp, 9 fig

The Importance of Lens Galaxy Environments

While many strong gravitational lens galaxies are suspected to lie in groups or clusters of galaxies, environmental effects in lens models are often unconstrained and sometimes ignored. We show that this creates significant biases in a variety of lensing applications, by creating mock lenses associated with each of 13 galaxies in a realistic model group, and then analyzing them with standard techniques. We find that standard models of double lenses, which neglect environment, grossly overestimate the ellipticity of the lens galaxy (de/e~0.5) and the Hubble constant (dh/h~0.22). Standard models of quad lenses, which approximate the environment as a tidal shear, recover the ellipticity reasonably well (|de/e|<~0.24) but overestimate the Hubble constant (dh/h~0.15), and have significant (~30%) errors in the millilensing analyses used to constrain the amount of substructure in dark matter halos. For both doubles and quads, standard models slightly overestimate the velocity dispersion of the lens galaxy (d(sigma)/sigma~0.06), and underestimate the magnifications of the images (d(mu)/mu ~ -0.25). Standard analyses of lens statistics overestimate Omega_Lambda (by 0.05-0.14), and underestimate the ratio of quads to doubles (by a factor of 2). These biases help explain some long-standing puzzles (such as the high observed quad/double ratio), but aggravate others (such as the low value of H_0 inferred from lensing). Most of the biases are caused by neglect of the convergence from the mass associated with the environment, but additional uncertainty is introduced by neglect of higher-order terms. Fortunately, we show that directly observing and modeling lens environments should make it possible to remove the biases and reduce the uncertainties associated with environments to the few percent level. (Abridged)Comment: 14 emulateapj pages; accepted in Ap

Analytic Time Delays and H_0 Estimates for Gravitational Lenses

We study gravitational lens time delays for a general family of lensing potentials, which includes the popular singular isothermal elliptical potential and singular isothermal elliptical density distribution but allows general angular structure. Using a novel approach, we show that the time delay can be cast in a very simple form, depending only on the observed image positions. Including an external shear changes the time delay proportional to the shear strength, and varying the radial profile of the potential changes the time delay approximately linearly. These analytic results can be used to obtain simple estimates of the time delay and the Hubble constant in observed gravitational lenses. The naive estimates for four of five time delay lenses show surprising agreement with each other and with local measurements of H_0; the complicated Q 0957+561 system is the only outlier. The agreement suggests that it is reasonable to use simple isothermal lens models to infer H_0, although it is still important to check this conclusion by examining detailed models and by measuring more lensing time delays.Comment: 16 pages with 2 embedded figures; submitted to Ap