GEMPIC: Geometric ElectroMagnetic Particle-In-Cell Methods

We present a novel framework for Finite Element Particle-in-Cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov-Maxwell system. We derive a semi-discrete Poisson bracket, which retains the defining properties of a bracket, anti-symmetry and the Jacobi identity, as well as conservation of its Casimir invariants, implying that the semi-discrete system is still a Hamiltonian system. In order to obtain a fully discrete Poisson integrator, the semi-discrete bracket is used in conjunction with Hamiltonian splitting methods for integration in time. Techniques from Finite Element Exterior Calculus ensure conservation of the divergence of the magnetic field and Gauss' law as well as stability of the field solver. The resulting methods are gauge invariant, feature exact charge conservation and show excellent long-time energy and momentum behaviour. Due to the generality of our framework, these conservation properties are guaranteed independently of a particular choice of the Finite Element basis, as long as the corresponding Finite Element spaces satisfy certain compatibility conditions.Comment: 57 Page

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

A New Einstein Cross: A Highly Magnified, Intrinsically Faint Lyman-Alpha Emitter at z=2.7

We report the discovery of a new Einstein cross at redshift z_S = 2.701 based on Lyman-alpha emission in a cruciform configuration around an SDSS luminous red galaxy (z_L = 0.331). The system was targeted as a possible lens based on an anomalous emission line in the SDSS spectrum. Imaging and spectroscopy from the W. M. Keck Observatory confirm the lensing nature of this system. This is one of the widest-separation galaxy-scale lenses known, with an Einstein radius of ~1.84 arcsec. We present simple gravitational lens models for the system and compute the intrinsic properties of the lensed galaxy. The total mass of the lensing galaxy within the 8.8 +/- 0.1 kpc enclosed by the lensed images is (5.2 +/- 0.1) x 10^11 M_sun. The lensed galaxy is a low mass galaxy (0.2 L*) with a high equivalent-width Lyman-alpha line (EW_Lya_rest = 46 +/- 5 Angstroms). Follow-up studies of this lens system can probe the mass structure of the lensing galaxy, and can provide a unique view of an intrinsically faint, high-redshift, star-forming galaxy at high signal-to-noise ratio.Comment: ApJ Letters, in pres

Gravitational Lenses With More Than Four Images: I. Classification of Caustics

We study the problem of gravitational lensing by an isothermal elliptical density galaxy in the presence of a tidal perturbation. When the perturbation is fairly strong and oriented near the galaxy's minor axis, the lens can produce image configurations with six or even eight highly magnified images lying approximately on a circle. We classify the caustic structures in the model and identify the range of models that can produce such lenses. Sextuple and octuple lenses are likely to be rare because they require special lens configurations, but a full calculation of the likelihood will have to include both the existence of lenses with multiple lens galaxies and the strong magnification bias that affects sextuple and octuple lenses. At optical wavelengths these lenses would probably appear as partial or complete Einstein rings, but at radio wavelengths the individual images could probably be resolved.Comment: 30 pages, including 12 postscript figures; accepted for publication in Ap

Testing a new analytic model for gravitational lensing probabilities

We study gravitational lensing with a multiple lens plane approach, proposing a simple analytical model for the probability distribution function (PDF) of the dark matter convergence, kappa, for the different lens planes in a given cosmology as a function of redshift and smoothing angle, theta. The model is fixed solely by the variance of kappa, which in turn is fixed by the amplitude of the power spectrum, sigma_8. We test the PDF against a high resolution Tree-Particle-Mesh simulation and find that it is far superior to the Gaussian or the lognormal, especially for small values of theta << 1 arcmin and at large values of kappa relevant to strong lensing. With this model, we predict the probabilities of strong lensing by a single plane or by multiple planes. We find that for theta ~ 10 arcsec, a single plane accounts for almost all (~ 98%) of the strong lensing cases for source redshift unity. However, for a more typical source redshift of 4, about 12% of the strong lensing cases will result from the contribution of a secondary clump of matter along the line of sight, introducing a systematic error in the determination of the surface density of clusters, typically overestimating it by about 2-5%. We also find that matter inhomogenieties introduce a dispersion in the value of the angular diameter distance about its cosmological mean. The probable error relative to the mean increases with redshift to a value of about 8% for z ~ 6 and theta ~ 10 arcsec.Comment: Accepted for publication in ApJ, 13 pages, 12 figures, revised version, references added, section 6 expande

The Top Ten List of Gravitational Lens Candidates from the HST Medium Deep Survey

A total of 10 good candidates for gravitational lensing have been discovered in the WFPC2 images from the HST Medium Deep Survey (MDS) and archival primary observations. These candidate lenses are unique HST discoveries, i.e. they are faint systems with sub-arcsecond separations between the lensing objects and the lensed source images. Most of them are difficult objects for ground-based spectroscopic confirmation or for measurement of the lens and source redshifts. Seven are ``strong lens'' candidates which appear to have multiple images of the source. Three are cases where the single image of the source galaxy has been significantly distorted into an arc. The first two quadruply lensed candidates were reported in Ratnatunga et al 1995 (ApJL, 453, L5) We report on the subsequent eight candidates and describe them with simple models based on the assumption of singular isothermal potentials. Residuals from the simple models for some of the candidates indicate that a more complex model for the potential will probably be required to explain the full structural detail of the observations once they are confirmed to be lenses. We also discuss the effective survey area which was searched for these candidate lens objects.Comment: 26 pages including 12 figures and 10 tables. AJ Vol. 117, No.

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

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

Shear and Ellipticity in Gravitational Lenses

Galaxies modeled as singular isothermal ellipsoids with an axis ratio distribution similar to the observed axis ratio distribution of E and S0 galaxies are statistically consistent with both the observed numbers of two-image and four-image lenses and the inferred ellipticities of individual lenses. However, no four-image lens is well fit by the model (typical $\chi^2/N_{dof} \sim 20$), the axis ratio of the model can be significantly different from that of the observed lens galaxy, and the major axes of the model and the galaxy may be slightly misaligned. We found that models with a second, independent, external shear axis could fit the data well (typical $\chi^2/N_{dof} \sim 1$), while adding the same number of extra parameters to the radial mass distribution does not produce such a dramatic improvement in the fit. An independent shear axis can be produced by misalignments between the luminous galaxy and its dark matter halo, or by external shear perturbations due to galaxies and clusters correlated with the primary lens or along the line of sight. We estimate that the external shear perturbations have no significant effect on the expected numbers of two-image and four-image lenses, but that they can be important perturbations in individual lens models. However, the amplitudes of the external shears required to produce the good fits are larger than our estimates for typical external shear perturbations (10-15% shear instead of 1-3% shear) suggesting that the origin of the extra angular structure must be intrinsic to the primary lens galaxy in most cases.Comment: 38 pages, 9 figures, submitted to Ap

Can Strong Gravitational Lensing Constrain Dark Energy?

We discuss the ratio of the angular diameter distances from the source to the lens, $D_{ds}$, and to the observer at present, $D_{s}$, for various dark energy models. It is well known that the difference of $D_s$s between the models is apparent and this quantity is used for the analysis of Type Ia supernovae. However we investigate the difference between the ratio of the angular diameter distances for a cosmological constant, $(D_{ds}/D_{s})^{\Lambda}$ and that for other dark energy models, $(D_{ds}/D_{s})^{\rm{other}}$ in this paper. It has been known that there is lens model degeneracy in using strong gravitational lensing. Thus, we investigate the model independent observable quantity, Einstein radius ($\theta_E$), which is proportional to both $D_{ds}/D_s$ and velocity dispersion squared, $\sigma_v^2$. $D_{ds}/D_s$ values depend on the parameters of each dark energy model individually. However, $(D_{ds}/D_s)^{\Lambda} - (D_{ds}/D_{s})^{\rm{other}}$ for the various dark energy models, is well within the error of $\sigma_v$ for most of the parameter spaces of the dark energy models. Thus, a single strong gravitational lensing by use of the Einstein radius may not be a proper method to investigate the property of dark energy. However, better understanding to the mass profile of clusters in the future or other methods related to arc statistics rather than the distances may be used for constraints on dark energy.Comment: 15 pages, 13 figures, Accepted in PR