arXiv subjects

Charles R. Keeton

Publications and source records attributed to Charles R. Keeton.

At least 73 records · Page 4Linked to original sources

arXiv2006

Lensed Quasar Hosts

Gravitational lensing assists in the detection of quasar hosts by amplifying and distorting the host light away from the unresolved quasar core images. We present the results of HST observations of 30 quasar hosts at redshifts 1 < z < 4.5. The hosts are small in size (r_e <~ 6 kpc), and span a range of morphologies consistent with early-types (though smaller in mass) to disky/late-type. The ratio of the black hole mass (MBH, from the virial technique) to the bulge mass (M_bulge, from the stellar luminosity) at 1 1.7 is a factor of 3--6 higher than the local value. But, depending on the stellar content the ratio may decline at z>4 (if E/S0-like), flatten off to 6--10 times the local value (if Sbc-like), or continue to rise (if Im-like). We infer that galaxy bulge masses must have grown by a factor of 3--6 over the redshift range 3>z>1, and then changed little since z~1. This suggests that the peak epoch of galaxy formation for massive galaxies is above z~1. We also estimate the duty cycle of luminous AGNs at z>1 to be ~1%, or 10^7 yrs, with sizable scatter.

astro-ph↗

arXiv2006

Formalism for testing theories of gravity using lensing by compact objects. II: Probing Post-Post-Newtonian metrics

We study gravitational lensing by compact objects in gravity theories that can be written in a Post-Post-Newtonian (PPN) framework: i.e., the metric is static and spherically symmetric, and can be written as a Taylor series in m/r, where m is the gravitational radius of the compact object. Working invariantly, we compute corrections to standard weak-deflection lensing observables at first and second order in the ratio of the angular gravitational radius to the angular Einstein ring radius of the lens. We show that the first-order corrections to the total magnification and centroid position vanish universally for gravity theories that can be written in the PPN framework. This arises from some surprising, fundamental relations among the lensing observables in PPN gravity models. We derive these relations for the image positions, magnifications, and time delays. A deep consequence is that any violation of the universal relations would signal the need for a gravity model outside the PPN framework (provided that some basic assumptions hold). In practical terms, the relations will guide observational programs to test general relativity, modified gravity theories, and possibly the Cosmic Censorship conjecture. We use the new relations to identify lensing observables that are accessible to current or near-future technology, and to find combinations of observables that are most useful for probing the spacetime metric. We give explicit applications to the Galactic black hole, microlensing, and the binary pulsar J0737-3039.

gr-qc↗

arXiv2005

Formalism for Testing Theories of Gravity Using Lensing by Compact Objects. I: Static, Spherically Symmetric Case

We are developing a general, unified, and rigorous analytical framework for using gravitational lensing by compact objects to test different theories of gravity beyond the weak-deflection limit. In this paper we present the formalism for computing corrections to lensing observables for static, spherically symmetric gravity theories in which the corrections to the weak-deflection limit can be expanded as a Taylor series in one parameter, namely the gravitational radius of the lens object. We take care to derive coordinate-independent expressions and compute quantities that are directly observable. We compute first- and second-order corrections to the image positions, magnifications, and time delays. Interestingly, we find that the first-order corrections to the total magnification and centroid position vanish in all gravity theories that agree with general relativity in the weak-deflection limit, but they can remain nonzero in modified theories that disagree with GR in the weak-deflection limit. For the Reissner-Nordstrom metric and a related metric from heterotic string theory, our formalism reveals an intriguing connection between lensing observables and the condition for having a naked singularity, which could provide an observational method for testing the existence of such objects. We apply our formalism to the Galactic black hole and predict that the corrections to the image positions are at the level of 10 micro-arcseconds, while the correction to the time delay is a few hundredths of a second. These corrections would be measurable today if a pulsar were found to be lensed by the Galactic black hole; and they should be readily detectable with planned missions like MAXIM.

gr-qc↗

arXiv2005

Differential Microlensing of the Continuum and Broad Emission Lines in SDSS J0924+0219, the Most Anomalous Lensed Quasar

SDSS J0924+0219 is the most glaring example of a gravitational lens with anomalous flux ratios: optical broad-band photometry shows image D to be a factor of 12 fainter than expected for smooth lens potentials. We report spectroscopy showing that the anomaly is present in the broad emission line flux ratios as well. There are differences between the emission line and continuum flux ratios: the A/D ratio is 10 in the broad Lyman-alpha line and 19 in the associated continuum. Known variability argues for the presence of microlensing. We show that microlensing can account for both the continuum and emission line flux ratios, if the broad emission line region is comparable in size to the Einstein radii of the microlenses. Specifically, we need the half-light radius of the broad-line region to be R_BLR <~ 0.4 Rein ~ 9$ lt-days, which is small but reasonable. If the broad-line region is that large, then stars can contribute only 15-20% of the surface mass density at the positions of the images. While we cannot exclude the possibility that millilensing by dark matter substructure is present as well, we conclude that microlensing is present and sufficient to explain existing data. Under this hypothesis, the A/D flux ratio should return to a value close to unity on a time scale of years rather than millennia.

astro-ph↗

arXiv2005

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 θ=3'' and ~200% at θ=5'', when we adopt a power-law source luminosity function Φ(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.

astro-ph↗

arXiv2005

Multipole Models of Four-Image Gravitational Lenses with Anomalous Flux Ratios

Anomalous radio flux ratios in four-image gravitational lens systems can be explained by adding a clumpy cold dark matter (CDM) component to the potential of the lens galaxy. Evans & Witt (2003) recently suggested that smooth multipole perturbations can provide a reasonable alternative to CDM substructure in some but not all cases. We generalize their method in two ways so as to determine whether multipole models can explain highly anomalous systems. We carry the multipole expansion to higher order, and also include external tidal shear as a free parameter. Fitting for the shear proves crucial to finding a physical (positive-definite density) model. For B1422+231, working to order k = 5 (and including shear) yields a model that is physical but implausible. Going to higher order (k >~ 9) reduces global departures from ellipticity at the cost of introducing small scale wiggles near the bright images. These localized undulations are more pronounced in B2045+265, where k ~ 17 multipoles are required to smooth out large scale deviations from elliptical symmetry. Such modes surely cannot be taken at face value; they must indicate that the models are trying to reproduce some other sort of structure. Our formalism naturally finds models that fit the data exactly, but we use B0712+472 to show that measurement uncertainties have little effect on our results. Finally, we consider the system B1933+503, where two sources are lensed by the same foreground galaxy. The additional constraints provided by the images of the second source render the multipole model unphysical. We conclude that external shear must be taken into account to obtain plausible models, and that a purely smooth angular structure for the lens galaxy does not provide a viable alternative to the prevailing CDM clump hypothesis.

astro-ph↗

arXiv2005

Identifying Lenses with Small-Scale Structure. II. Fold Lenses

When the source in a 4-image gravitational lens lies close to a "fold" caustic, two of the lensed images lie close together. If the lens potential is smooth on the scale of the separation between the two close images, then the difference between their fluxes should approximately vanish, Rfold = (F1-F2)/(F1+F2) \approx 0. Violations of this "fold relation" in observed lenses are thought to indicate the presence of structure on scales smaller than the separation between the close images. We study the fold relation and find it to be more subtle and rich than was previously realized. The degree to which Rfold can differ from zero for realistic smooth lenses depends not only on the distance of the source from the caustic, but also on its location along the caustic, and on the angular structure of the lens potential. Thus, it is impossible to say from Rfold alone whether observed flux ratios are anomalous or not. Instead, we must consider the full distribution of Rfold values that can be obtained from smooth potentials that reproduce the separation between the two close images and the distance to the next nearest image. We analyze the generic and specific features of this distribution, and then show that 5 of the 12 known lenses with fold configurations have flux ratio anomalies: B0712+472, SDSS 0924+0219, PG 1115+080, B1555+375, and B1933+503. Combining this with our previous analysis revealing anomalies in 3 of the 4 known lenses with cusp configurations, we conclude that at least half (8/16) of all 4-image lenses that admit generic, local analyses exhibit flux ratio anomalies indicative of small-scale structure. The fold and cusp relations do not reveal the nature of the implied small-scale structure, but do provide the formal foundation for substructure studies. [Abridged]

astro-ph↗

arXiv2005

Discovery of a Fifth Image of the Large Separation Gravitationally Lensed Quasar SDSS J1004+4112

We report the discovery of a fifth image in the large separation lensed quasar system SDSS J1004+4112. A faint point source located 0.2'' from the center of the brightest galaxy in the lensing cluster is detected in images taken with the Advanced Camera for Surveys (ACS) and the Near Infrared Camera and Multi-Object Spectrometer (NICMOS) on the Hubble Space Telescope. The flux ratio between the point source and the brightest lensed component in the ACS image is similar to that in the NICMOS image. The location and brightness of the point source are consistent with lens model predictions for a lensed image. We therefore conclude that the point source is likely to be a fifth image of the source quasar. In addition, the NICMOS image reveals the lensed host galaxy of the source quasar, which can strongly constrain the structure of the lensing critical curves and thereby the mass distribution of the lensing cluster.

astro-ph↗

arXiv2005

Finite Source Effects in Strong Lensing: Implications for the Substructure Mass Scale

Flux ratio `anomalies' in quadruply-imaged gravitational lenses can be explained with galactic substructure of the sort predicted by CDM, but the strength and uniqueness of that hypothesis needs to be further assessed. A good way to do that is to use the physical scale associated with the size of the source quasar, and its dependence on wavelength. We develop an analytic toy model to study finite source effects in substructure lensing and identify general principles. We find that image positions and magnifications are basically independent of source size until the source is large enough to intersect a substructure caustic. Even sources that are much larger than the substructure Einstein radius can be perturbed at a detectable level. A tremendous amount could be learned by comparing image positions and magnifications at wavelengths that correspond to different source sizes. In a separate analysis, we carefully study four observed radio lenses to determine which of the images are anomalous. In B0712+472, if the flux ratio anomaly is real it is probably in image C. In B1422+231, the anomaly is in image A. Interestingly, B2045+265 and B1555+375 both appear to have two anomalous images. It remains to be seen whether CDM predicts enough substructure to explain multiple anomalies in multiple lenses. When we join our modeling results and substructure theory, we obtain lower bounds on the masses of the substructures responsible for the observed anomalies. The mass bounds are broadly consistent with expectations for CDM. Perhaps more importantly, we outline various systematic effects in the mass bounds; poor knowledge of whether the substructure lies within the main lens galaxy or elsewhere along the line of sight appears to be the dominant systematic. [Abridged]

astro-ph↗

arXiv2004

Gravitational lensing magnification without multiple imaging

Gravitational lensing can amplify the apparent brightness of distant sources. Images that are highly magnified are often part of multiply-imaged systems, but we consider the possibility of having large magnifications without additional detectable images. In rare but non-negligible situations, lensing can produce a singly highly magnified image; this phenomenon is mainly associated with massive cluster-scale halos (>~1e13.5 Msun). Alternatively, lensing can produce multiply-imaged systems in which the extra images are either unresolved or too faint to be detectable. This phenomenon is dominated by galaxies and lower-mass halos (<~1e12 Msun), and is very sensitive to the inner density profile of the halos. Although we study the general problem, we customize our calculations to four quasars at redshift z~6 in the Sloan Digital Sky Survey (SDSS), for which Richards et al. (2004) have ruled out the presence of extra images down to an image splitting of 0.3" and a flux ratio of f=0.01. We predict that 9-29% of all z~6 quasars that are magnified by a factor of mu>10 would lack detectable extra images, with 5-10% being true singly-imaged systems. The maximum of 29% is reached only in the unlikely event that all low-mass (<~1e10 Msun) halos have highly concentrated (isothermal) profiles. In more realistic models where dwarf halos have flatter (NFW) inner profiles, the maximum probability is ~10%. We conclude that the probability that all four SDSS quasars are magnified by a factor of 10 is <~1e-4. The only escape from this conclusion is if there are many (>10) multiply-imaged z~6 quasars in the SDSS database that have not yet been identified, which seems unlikely. In other words, lensing cannot explain the brightnesses of the z~6 quasars, and models that invoke lensing to avoid having billion-Msun black holes in the young universe are not viable.

astro-ph↗

arXiv2004

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)

astro-ph↗

arXiv2004

Effects of Triaxiality on the Statistics of Large-Separation Gravitational Lenses

We study the statistics of large-separation gravitational lens systems produced by non-spherical halos in the Cold Dark Matter (CDM) model. Specifically, we examine how the triaxiality of CDM halos affects the overall lensing probabilities and the relative numbers of different image configurations (double, quadruple, and naked cusp lenses). We find that triaxiality significantly enhances lensing probabilities by a factor of ~2-4, so it cannot be ignored. If CDM halos have central density slopes alpha<~1.5, we predict that a significant fraction (>~20%) of large-separation lenses should have naked cusp image configurations; this contrasts with lensing by isothermal (α~2) galaxies where naked cusp configurations are rare. The image multiplicities depend strongly on the inner density slope α: for α=1, the naked cusp fraction is >~60%; while for α=1.5, quadruple lenses are actually the most probable. Thus, the image multiplicities in large-separation lenses offer a simple new probe of the inner density profiles of dark matter halos. We also compute the expected probabilities and image multiplicities for lensed quasars in the Sloan Digital Sky Survey, and argue that the recent discovery of the large-separation quadruple lens SDSS J1004+4112 is consistent with expectations for CDM.

astro-ph↗

arXiv2004

Microlensing of the Broad Emission Line Region in the Quadruple Lens SDSS J1004+4112

We present seven epochs of spectroscopy on the quadruply imaged quasar SDSS J1004+4112, spanning observed-frame time delays from 1 to 322 days. The spectra reveal differences in the emission lines between the lensed images. Specifically, component A showed a strong enhancement in the blue wings of several high-ionization lines relative to component B, which lasted at least 28 days (observed frame) then faded. Since the predicted time delay between A and B is <30 days, our time coverage suggests that the event was not intrinsic to the quasar. We attribute these variations to microlensing of part of the broad emission line region of the quasar, apparently resolving structure in the source plane on a scale of ~10^{16} cm at z=1.734. In addition, we observed smaller differences in the emission line profiles between components A and B that persisted throughout the time span, which may also be due to microlensing or millilensing. Further spectroscopic monitoring of this system holds considerable promise for resolving the structure of the broad emission line region in quasars.

astro-ph↗

arXiv2003

(Lack of) lensing constraints on cluster dark matter profiles

Using stellar dynamics and strong gravitational lensing as complementary probes, Sand et al. (2002, 2003) have recently claimed strong evidence for shallow dark matter density profiles in several lensing clusters, which may conflict with predictions of the Cold Dark Matter paradigm. However, systematic uncertainties in the analysis weaken the constraints. By re-analyzing their data, we argue that the tight constraints claimed by Sand et al., were driven by prior assumptions. Relaxing the assumptions, we find that no strong constraints may be derived on the dark matter inner profile from the Sand et al. data; we find satisfactory fits (with reasonable parameters) for a wide range of inner slopes 0 < beta < 1.4. Useful constraints on the mass distributions of lensing clusters can still be obtained, but they require moving beyond mere measurements of lensing critical radii into the realm of detailed lens modeling.

astro-ph↗

arXiv2003

Identifying Lenses with Small-Scale Structure. I. Cusp Lenses

The inability of standard models to explain the flux ratios in many 4-image gravitational lenses has been cited as evidence for significant small-scale structure in lens galaxies. That claim has generally relied on detailed lens modeling, so it is both model dependent and somewhat difficult to interpret. We present a more robust and generic method for identifying lenses with small-scale structure. For a close triplet of images associated with a source near a cusp caustic, the sum of the signed magnifications should approximately vanish. We derive realistic upper bounds on the sum, and argue that lenses with flux ratios that significiantly violate the bounds can be said to have structure in the lens potential on scales smaller than the image separation. Five observed lenses have such flux ratio ``anomalies'': B2045+265, 1RXS J1131-1231, and SDSS J0924+0219 have strong anomalies; B0712+472 has a strong anomaly at optical/near-IR wavelengths and a marginal anomaly at radio wavelengths; and RX J0911+0551 appears to have an anomaly, but this conclusion is subject to uncertainties about octopole modes in early-type galaxies. Analysis of the cusp relation does not identify the known anomaly in B1422+231, so methods that are more sophisticated (and less generic) than the cusp relation may be necessary to uncover flux ratio anomalies in some systems. Although these flux ratio anomalies might represent milli- or micro-lensing, we cannot identify the cause; we can only conclude that the lenses have significant structure in the potential on scales smaller than the separation between the images. Additional arguments must be invoked to specify the nature of this small-scale structure. [Abridged]

astro-ph↗

arXiv2003

SDSS J0903+5028: A New Gravitational Lens

We report the discovery of a new gravitationally lensed quasar from the Sloan Digital Sky Survey, SDSS J090334.92+502819.2. This object was targeted for SDSS spectroscopy as a Luminous Red Galaxy (LRG), but manual examination of the spectrum showed the presence of a quasar at z= 3.6 in addition to a red galaxy at z=0.388, and the SDSS image showed a second possible quasar image nearby. Follow-up imaging and spectroscopy confirmed the lensing hypothesis. In images taken at the ARC 3.5-meter telescope, two quasars are separated by 2.8 arc-seconds; the lensing galaxy is clearly seen and is blended with one of the quasar images. Spectroscopy taken at the Keck II telescope shows that the quasars have identical redshifts of z=3.6 and both show the presence of the same broad absorption line-like troughs. We present simple lens models which account for the geometry and magnifications. The lens galaxy lies near two groups of galaxies and may be a part of them. The models suggest that the groups may contribute considerable shear and may have a strong effect on the lens configuration.

astro-ph↗

arXiv2003

Lensing Optical Depth for Substructure and Isolated Dark Matter Halos

Multiply-imaged quasar lenses can be used to constrain the substructure mass fraction in galaxy-sized dark matter halos via anomalous flux ratios in lensed images. The flux ratios, however, can be affected by both the substructure in the lens halo and by isolated small-mass halos along the entire line-of-sight to the lensed source. While lensing by dark matter clumps near the lens galaxy is more efficient than elsewhere, the cumulative effect of all objects along the line-of-sight could be significant. Here we estimate the potential contribution of isolated clumps to the substructure lensing signal using a simple model motivated by cosmological simulations. We find that the contribution of isolated clumps to the total lensing optical depth ranges from a few to tens percent, depending on assumptions and the particular configuration of the lens. Therefore, although the contribution of isolated clumps to the lensing signal is not dominant, it should not be neglected in detailed analyses of substructure lensing. For the currently favored Lambda-CDM model, the total calculated optical depth for lensing is high, tau ~ 0.2-20 and could, therefore, naturally explain the high frequency of anomalous flux ratios in observed lenses. The prediction, however, is highly sensitive to the spatial distribution of substructure halos in the innermost regions of the lens halo, which is still very uncertain. Therefore, constraints on the properties of the substructure population or accurate cosmological constraints, such as the mass of the warm dark matter particle, are difficult if not impossible to derive at this point.

astro-ph↗

arXiv2003

The Quintuple Quasar: Radio and Optical Observations

We present results from high-resolution radio and optical observations of PMN J0134-0931, a gravitational lens with a unique radio morphology and an extremely red optical counterpart. Our data support the theory of Keeton & Winn (2003): five of the six observed radio components are multiple images of a single quasar, produced by a pair of lens galaxies. Multi-frequency VLBA maps show that the sixth and faintest component has a different radio spectrum than the others, confirming that it represents a second component of the background source rather than a sixth image. The lens models predict that there should be additional faint images of this second source component, and we find evidence for one of the predicted images. The previously-observed large angular sizes of two of the five bright components are not intrinsic (which would have excluded the possibility that they are lensed images), but are instead due to scatter broadening. Both the extended radio emission observed at low frequencies, and the intrinsic image shapes observed at high frequencies, can be explained by the lens models. The pair of lens galaxies is marginally detected in HST images. The differential extinction of the quasar images suggests that the extreme red color of the quasar is at least partly due to dust in the lens galaxies.

astro-ph↗