Compound gravitational lensing as a probe of dark matter substructure within galaxy halos

We show how observations of multiply-imaged quasars at high redshift can be used as a probe of dark matter clumps (subhalos with masses ~ 10^9 solar masses) within the virialized extent of more massive lensing halos. A large abundance of such satellites is predicted by numerical simulations of galaxy formation in cold dark matter (CDM) cosmogonies. Small-scale structure within galaxy halos affects the flux ratios of the images without appreciably changing their positions. We use numerical simulations to quantify the effect of dark matter substructure on the distribution of magnifications, and find that the magnification ratio of a typical image pair will deviate significantly from the value predicted by a smooth lensing potential if, near the Einstein radius, only a few percent of the lens surface density is contained in subhalos. The angular size of the continuum source dictates the range of subclump masses that can have a detectable effect: to avoid confusion with gravitational microlensing caused by stars in the lens galaxy, the background source must be larger than the optical continuum-emitting region of a QSO. We also find that substructure will cause distortions to images on milli-arcsecond scales and bias the distribution of QSO magnification ratios -- two other possible methods of detection.Comment: accepted for publication in ApJ, 21 pages, 10 figure

GLAMER Part I: A Code for Gravitational Lensing Simulations with Adaptive Mesh Refinement

A computer code is described for the simulation of gravitational lensing data. The code incorporates adaptive mesh refinement in choosing which rays to shoot based on the requirements of the source size, location and surface brightness distribution or to find critical curves/caustics. A variety of source surface brightness models are implemented to represent galaxies and quasar emission regions. The lensing mass can be represented by point masses (stars), smoothed simulation particles, analytic halo models, pixelized mass maps or any combination of these. The deflection and beam distortions (convergence and shear) are calculated by modified tree algorithm when halos, point masses or particles are used and by FFT when mass maps are used. The combination of these methods allow for a very large dynamical range to be represented in a single simulation. Individual images of galaxies can be represented in a simulation that covers many square degrees. For an individual strongly lensed quasar, source sizes from the size of the quasar's host galaxy (~ 100 kpc) down to microlensing scales (~ 10^-4 pc) can be probed in a self consistent simulation. Descriptions of various tests of the code's accuracy are given.Comment: 13 pages, 9 figures, submitted to MNRAS, corrected some typos, replaced figure 9 after problem with numerical precision was discovere

Lensed: a code for the forward reconstruction of lenses and sources from strong lensing observations

Robust modelling of strong lensing systems is fundamental to exploit the information they contain about the distribution of matter in galaxies and clusters. In this work, we present Lensed, a new code which performs forward parametric modelling of strong lenses. Lensed takes advantage of a massively parallel ray-tracing kernel to perform the necessary calculations on a modern graphics processing unit (GPU). This makes the precise rendering of the background lensed sources much faster, and allows the simultaneous optimisation of tens of parameters for the selected model. With a single run, the code is able to obtain the full posterior probability distribution for the lens light, the mass distribution and the background source at the same time. Lensed is first tested on mock images which reproduce realistic space-based observations of lensing systems. In this way, we show that it is able to recover unbiased estimates of the lens parameters, even when the sources do not follow exactly the assumed model. Then, we apply it to a subsample of the SLACS lenses, in order to demonstrate its use on real data. The results generally agree with the literature, and highlight the flexibility and robustness of the algorithm.Comment: v2: major revision; accepted by MNRAS; lens reconstruction code available at http://glenco.github.io/lensed

Zooming into the Cosmic Horseshoe: new insights on the lens profile and the source shape

The gravitational lens SDSS J1148+1930, also known as the Cosmic Horseshoe, is one of the biggest and of the most detailed Einstein rings ever observed. We use the forward reconstruction method implemented in the lens fitting code Lensed to investigate with great detail the properties of the lens and of the background source. We model the lens with different mass distributions, focusing in particular on the determination of the slope of the dark matter component. The inherent degeneracy between the lens slope and the source size can be broken when we can isolate separate components of each lensed image, as in this case. For an elliptical power law model, $\kappa(r) \sim r^{-t}$, the results favour a flatter-than-isothermal slope with a maximum-likelihood value t = 0.08. Instead, when we consider the contribution of the baryonic matter separately, the maximum-likelihood value of the slope of the dark matter component is t = 0.31 or t = 0.44, depending on the assumed Initial Mass Function. We discuss the origin of this result by analysing in detail how the images and the sources change when the slope t changes. We also demonstrate that these slope values at the Einstein radius are not inconsistent with recent forecast from the theory of structure formation in the LambdaCDM model.Comment: 13 pages, 9 figures, accepted for publication in MNRA

A Fundamental Test of the Nature of Dark Matter

Dark matter may consist of weakly interacting elementary particles or of macroscopic compact objects. We show that the statistics of the gravitational lensing of high redshift supernovae strongly discriminate between these two classes of dark matter candidates. We develop a method of calculating the magnification distribution of supernovae, which can be interpreted in terms of the properties of the lensing objects. With simulated data we show that >~ 50 well measured type Ia supernovae (\Delta m ~ 0.2 mag) at redshifts ~1 can clearly distinguish macroscopic from microscopic dark matter if \Omega_o \simgt 0.2 and all dark matter is in one form or the other.Comment: 8 pages, 2 figures, AASTeX, replaced to conform to the version to be published in ApJL. It is now more clearly written and addresses some possible systematic uncertaintie

GLAMER Part II: Multiple Plane Gravitational Lensing

We present an extension to multiple planes of the gravitational lensing code {\small GLAMER}. The method entails projecting the mass in the observed light-cone onto a discrete number of lens planes and inverse ray-shooting from the image to the source plane. The mass on each plane can be represented as halos, simulation particles, a projected mass map extracted form a numerical simulation or any combination of these. The image finding is done in a source oriented fashion, where only regions of interest are iteratively refined on an initially coarse image plane grid. The calculations are performed in parallel on shared memory machines. The code is able to handle different types of analytic halos (NFW, NSIE, power-law, etc.), haloes extracted from numerical simulations and clusters constructed from semi-analytic models ({\small MOKA}). Likewise, there are several different options for modeling the source(s) which can be distributed throughout the light-cone. The distribution of matter in the light-cone can be either taken from a pre-existing N-body numerical simulations, from halo catalogs, or are generated from an analytic mass function. We present several tests of the code and demonstrate some of its applications such as generating mock images of galaxy and galaxy cluster lenses.Comment: 14 pages, 10 figures, submitted to MNRA

Lattice softening effects at the Mott critical point of Cr-doped V2_2O3_3

We have performed sound velocity measurements in (V$_{1-x}$Cr$_x$)$_2$O$_3$ in the vicinity of the critical point of the first order Mott transition line. The pressure sweeps at constant temperature reveal a large dip in the $c_{33}$ compression modulus, this dip sharpens as the critical point is approached. We do not observe signs of criticality on the shear modulus $c_{44}$ which is consistent with a transition governed by a scalar order parameter, in accordance with the DMFT description of the transition. However, the amplitude of the effect is an order of magnitude smaller than the one obtained from DMFT calculations for a single band Hubbard model. We analyze our results using a simple model with the electronic response function obtained from the scaling relations for the conductivity