One of the major advances in cosmology over the past three decades has been the theory of hierarchical structure formation. This model provides a way to understand how the structures we observe, such as galaxies and clusters of galaxies, came to be. Simulations predict that ~10% of the mass of galactic dark matter halos is in “clumps.” This translates to ~100 clumps for a halo of 1012 solar masses, typical of galaxies. However, the number of clumps actually seen in the Milky Way is closer to ten. The discrepancy is even greater for the Local Group as a whole. If the “missing satellites” actually exist, their presence should be detectable via strong gravitational lensing, where a distant quasar appears as multiple images due to a foreground galaxy along the line of sight.
A connection between lensing and substructure may already have been discovered. Simple lens models predict image fluxes that disagree with the observed values in many systems. Dalal & Kochanek (2002) that these anomalies can be explained if a few percent of the lensing galaxy's mass is contained in dark-matter clumps of roughly one million solar masses each. Since this result would have profound implications for cosmology, it is important to consider whether the anomalous flux ratios could also be explained by “smooth” perturbations to the gravitational potential of the lensing galaxy. Evans & Witt (2003) considered a simple multipole model for the lens potential, but its assumptions were too restrictive to draw reliable conclusions. In particular, they ignored tidal “shear” due to galaxies outside the main lensing galaxy. This simplification is problematic, since many lensing galaxies are not found in isolation, but rather in groups. In addition, the most-anomalous lens systems were not considered. We developed a more general multipole formalism, by allowing Fourier modes of arbitrary order, and including shear as a free parameter (Congdon & Keeton 2005). Making these changes leads to an underconstrained problem, and some care is required to choose the optimal solution. Noting that the lens galaxies in the systems we considered were early-type, we selected the solution with isodensity contours that deviated least from elliptical symmetry. We applied our formalism to all the relevant anomalous lens systems, and concluded that multipole models can be ruled out as an explanation for anomalous flux ratios, thus lending further support to hierarchical structure formation.
Looking for new ways to probe substructure has been the focus of my current work. In order to use flux ratios to constrain substructure, it is necessary to find a robust and reliable method to determine whether a given system is anomalous. For “cusp” or “fold” configurations, where a triplet or pair of bright images is produced, Keeton, Gaudi & Petters (2003, 2005) have developed mathematical relations that can determine whether the lens galaxy in such a system can be described by a smooth mass model. I have been working to develop an equivalent formalism for time delays. I have recently shown that the time delay between the bright images in a fold lens should scale with the third power of the image separation (Congdon et al., in preparation). If a lens system is observed to violate this scaling relation, we can use such a “time-delay anomaly” to establish the presence of substructure within the lensing galaxy. When this work is completed, we will have a powerful new tool for quantifying the importance of substructure in galactic CDM halos.
At optical wavelengths, anomalous flux ratios may be explained by
microlensing, since quasar optical emission regions have roughly the same
angular extent as the Einstein angle of stellar-mass objects in lensing
galaxies. Microlensing is inherently more complicated than substructure
lensing, since the density of stars at the position of a lensed image is much
greater than the density of CDM clumps. Therefore, simplifying assumptions are
often made in microlensing investigations. Two approaches have generally been
followed. In the first method, the lensed quasar is taken to be a point source,
and the distribution of stars in the lensing galaxy is described by a mass
function that accounts for the proportion of stars with different masses. In
the second approach, the lensed quasar is properly treated as an extended
source, but all stars in the lensing galaxy are assumed to have the same mass.
We generalized earlier work by considering a model that simultaneously includes an extended source and a stellar mass function for the lens (Congdon et al. 2007b). In addition, while previous studies all assumed quasar accretion disks to be viewed face-on, we allowed them to have arbitrary inclinations and studied how microlensing depends on the projected shape of the source. Our simulations revealed a couple of surprises. First, for images of negative parity, the dependence of microlensing on dark matter fraction varies strongly with source size; adding dark matter increases the flux variability for small sources and decreases it for large sources. Since accretion disks and broad-emission-line regions have different sizes, our result suggests that it may be possible to use observations of these regions to constrain the density of stars and dark matter at the positions of the lensed images. Second, we found that elliptical sources that are aligned with the direction of tidal shear experience greater magnification variability than sources with perpendicular alignment. This effect becomes more prominent as the ellipticity increases, which raises the prospect of using microlensing to probe source shape. Our finding may also provide an alternative to the idea that rapid microlensing variability is due to relativistic motion of objects within the source.
The general
theory of relativity is one of the pillars of modern physics, but its experimental
verification has been limited to Solar System tests, which are confined to the
weak-field regime. Gravitational lensing holds great promise for exploring the
predictions of general relativity under the more extreme conditions found in
the environments of black holes and other compact objects. For the case of strong lensing, where
multiple images of a background star are produced, the image positions, fluxes
and time delays provide important constraints on the spacetime metric (e. g.,
Keeton & Petters 2006). However, this information is only useful if
strong lensing can be detected. We have considered prospects for observing strong lensing by the supermassive black hole at
the Galactic center, Sgr A* (Congdon
et al. 2007a). We computed
the expected number of stars strongly lensed by Sgr A* using detailed models of
the stellar populations in the Galactic cusp, bulge and disk. For a K-band
magnitude limit of 17, we found
the expected number of detectable lensed stars to be 0.56, with the disk
providing the dominant contribution. If
the magnitude limit reaches K=21.5, we
expect to observe roughly 20 lensed stars. We have examined various systematic
uncertainties in our predictions, including extinction by dust.
We also considered massive black holes in other stellar systems. We found that the probability of observing effects due to strong lensing caused by an intermediate-mass black hole in a globular cluster is quite small. However, a supermassive black hole in a typical massive elliptical galaxy should lens ~100 stars in its host galaxy. This number could exceed 5,000 for a giant elliptical galaxy such as M87.
Using our results for Sgr A*, we considered
how strong lensing could be used to constrain theories of gravity. Since measuring PPN parameters requires a
time-varying source position, lensed cusp stars with orbital periods on the
order of a decade would be ideal for testing general relativity. We found that observations with a resolution
of order 10 microarcseconds would make this possible. Future instruments such
as the Space Interferometry Mission and the Global Astrometric
Interferometer for Astrophysics may attain this capability if they include
observing capabilities at infrared wavelengths.