Statistical and systematic uncertainties in pixel-based source reconstruction algorithms for gravitational lensing

Gravitational lens modeling of spatially resolved sources is a challenging inverse problem with many observational constraints and model parameters. We examine established pixel-based source reconstruction algorithms for de-lensing the source and constraining lens model parameters. Using test data for four canonical lens configurations, we explore statistical and systematic uncertainties associated with gridding, source regularisation, interpolation errors, noise, and telescope pointing. Specifically, we compare two gridding schemes in the source plane: a fully adaptive grid that follows the lens mapping but is irregular, and an adaptive Cartesian grid. We also consider regularisation schemes that minimise derivatives of the source (using two finite difference methods) and introduce a scheme that minimises deviations from an analytic source profile. Careful choice of gridding and regularisation can reduce "discreteness noise" in the $\chi^2$ surface that is inherent in the pixel-based methodology. With a gridded source, some degree of interpolation is unavoidable, and errors due to interpolation need to be taken into account (especially for high signal-to-noise data). Different realisations of the noise and telescope pointing lead to slightly different values for lens model parameters, and the scatter between different "observations" can be comparable to or larger than the model uncertainties themselves. The same effects create scatter in the lensing magnification at the level of a few percent for a peak signal-to-noise ratio of 10, which decreases as the data quality improves.Comment: 20 pages, 18 figures, accepted to MNRAS, see http://physics.rutgers.edu/~tagoreas/papers/ for high resolution image

Biases in inferring dark matter profiles from dynamical and lensing measurements

The degeneracy between disc and halo contributions in spiral galaxy rotation curves makes it difficult to obtain a full understanding of the distribution of baryons and dark matter in disc galaxies like our own Milky Way. Using mock data, we study how constraints on dark matter profiles obtained from kinematics, strong lensing, or a combination of the two are affected by assumptions about the halo model. We compare four different models: spherical isothermal and Navarro-Frenk-White halos, along with spherical and elliptical Burkert halos. For both kinematics and lensing we find examples where different models fit the data well but give enclosed masses that are inconsistent with the true (i.e., input) values. This is especially notable when the input and fit models differ in having cored or cuspy profiles (such as fitting an NFW model when the underlying dark matter distribution follows a different profile). We find that mass biases are more pronounced with lensing than with kinematics, and using both methods can help reduce the bias and provide stronger constraints on the dark matter distributions.Comment: 13 pages, 8 figures, submitted for MNRAS publication Nov 15th 201

The Impact of Baryonic Cooling on Giant Arc Abundances

Using ray tracing for simple analytic profiles, we demonstrate that the lensing cross section for producing giant arcs has distinct contributions due to arcs formed through image distortion only, and arcs form from the merging of two or three images. We investigate the dependence of each of these contributions on halo ellipticity and on the slope of the density profile, and demonstrate that at fixed Einstein radius, the lensing cross section increases as the halo profile becomes steeper. We then compare simulations with and without baryonic cooling of the same cluster for a sample of six clusters, and demonstrate that cooling can increase the overall abundance of giant arcs by factors of a few. The net boost to the lensing probability for individual clusters is mass dependent, and can lower the effective low mass limit of lensing clusters. This last effect can potentially increase the number of lensing clusters by an extra 50%. While the magnitude of these effects may be overestimated due to the well known overcooling problem in simulations, it is evident that baryonic cooling has a non-negligible impact on the expected abundance of giant arcs, and hence cosmological constraints from giant arc abundances may be subject to large systematic errors.Comment: ApJ Submitte