Exploiting flux ratio anomalies to probe warm dark matter in future large-scale surveys

Flux ratio anomalies in strong gravitationally lensed quasars constitute a unique way to probe the abundance of non-luminous dark matter haloes, and hence the nature of dark matter. In this paper, we identify double-imaged quasars as a statistically efficient probe of dark matter, since they are 20 times more abundant than quadruply imaged quasars. Using N-body simulations that include realistic baryonic feedback, we measure the full distribution of flux ratios in doubly imaged quasars for cold (CDM) and warm dark matter (WDM) cosmologies. Through this method, we fold in two key systematics - quasar variability and line-of-sight structures. We find that WDM cosmologies predict a similar to 6 per cent difference in the cumulative distribution functions of flux ratios relative to CDM, with CDM predicting many more small ratios. Finally, we estimate that similar to 600 doubly imaged quasars will need to be observed in order to be able to unambiguously discern between CDM and the two WDM models studied here. Such sample sizes will be easily within reach of future large-scale surveys such as Euclid. In preparation for this survey data, we require discerning the scale of the uncertainties in modelling lens galaxies and their substructure in simulations, plus a strong understanding of the selection function of observed lensed quasars.

A Framework for Numerical Simulations of Structure Formation

Claude Becker

In the absence of a full analytical treatment of nonlinear structure formation in the universe, numerical simulations provide the critical link between the properties of the underlying model and the features of the observed structures. Currently N-body simulations are the main tool to study structure growth. We explore an alternative framework for numerical simulations of structure formation. The underlying idea is to replace the long-range gravitational force in the Vlasov-Poisson system by a purely local interaction. To this end we trade the classical phase space distribution for its quantum mechanical counterpart, the Wigner distribution function. Its dynamical equation is equivalent to the Schrödinger equation and reduces to the Vlasov equation in the formal semi-classical limit. The proposed framework allows in principle to simulate systems with arbitrary phase space distributions and could for instance be beneficial for simulations of warm dark matter, where the velocity dispersion is important. We discuss several methods to obtain a set of wavefunctions whose Wigner distribution is close to a given initial phase space distribution function. An auxiliary gauge field is introduced to mediate the gravitational interaction, thereby obtaining a local Schrödinger-Maxwell system. We also use the ideas of lattice gauge theories to obtain a fully gauge-invariant discretization of the equations of motion. Their iterative solution was implemented in a three-dimensional simulation code. We discuss its computational complexity and memory requirements. Several testbed simulations were performed with this method. We compared the gravitational collapse of a Gaussian wavefunction with an independent numerical solution of the spherically symmetric Schrödinger-Newton system. The results were found to be in good agreement. Finally, a simple example of the growth of cosmic perturbations is investigated within our framework. We conclude by outlining various possible directions to optimize and develop our method.

EPFL2011

Astrophysical applications of gravitationally lensed quasars

Alexander Eigenbrod

Gravitational lensing describes how light is deflected as it passes in the vicinity of a mass distribution. The amplitude of the deflection is proportional to the mass of the deflector, called "gravitational lens", and is generally weak, even for large masses. The faintness of this phenomenon explains why gravitational lensing remained essentially unobserved until the late 1970s (only gravitational lensing by the Sun has been observed during the solar eclipse of 1919). Before that time, gravitational lensing was considered merely as a theoretical curiosity. However, the situation dramatically changed with the discovery of the first extragalactic gravitational lens in 1979. Since then, together with the technological progress of astronomical instruments, gravitational lensing has turned from a curiosity into a powerful tool to address important astrophysical and cosmological questions. The present thesis focuses on applications related to gravitationally lensed quasars. Quasars are active galactic nuclei, where matter is heated up as it spirals down onto the central supermassive black hole. When a galaxy is located on the line of sight to a distant quasar, it acts as a gravitational lens and produces multiple images of this background source. The light of the quasar follows different paths for each of its images. Thus, variations of the intrinsic quasar luminosity are observed at different times in each image. The time delays between the images can be used to determine the Hubble constant H0, because they are inversely proportional to H0. This constant describes the current expansion rate of the Universe, and is one of the fundamental parameters of cosmological models. Many efforts have been spent over the years to determine H0, but its value is still poorly constrained. Gravitational lensing has the potential to noticeably decrease the uncertainty of H0. In practice, this requires regular and long-term monitoring of lensed quasars. We have run a series of numerical simulations to both optimize the available telescope time, and measure the time delays with an accuracy of a few percent. The results of these simulations are presented in the form of compact plots to be used to optimize the observational strategy of present and future monitoring programs. Once the time delays are measured, one can infer estimates of H0, provided several other observational constraints are available. A key element to accurately convert time delays into H0 is the redshift of the lensing galaxy. These redshift measurements are difficult because lensing galaxies are generally hidden in the glare of the much brighter quasar images. As a consequence, lens redshifts are often poorly constrained or even completely unknown. We have acquired spectroscopic data of sixteen lensing galaxies with the Very Large Telescope located in Chile. In combination with a powerful deconvolution algorithm, we determine the redshift of these sixteen lensing galaxies, which represents about 25% of all currently known quasar lensing galaxies. These results are useful for both H0 determinations and statistical studies of gravitational lenses, which can be used to provide new constraints on cosmological parameters. While the first part of this thesis focuses on the acquisition of observational constraints for the lens models, the main part consists in using the phenomenon of microlensing to determine the energy profile (or spatial structure) of quasar accretion disks. Microlensing is produced by the stars located in the lensing galaxy. These stars act as secondary lenses, and are called microlenses. Since the stars are moving in the galaxy, they induce flux and color variations in the images of the lensed quasar. These effects can be used as a natural telescope to probe the still mysterious inner structures of quasars with a spatial resolution about ten thousand times better than the capacities of current astronomical instruments, including the Very Large Telescope Interferometer. We present a three-year long spectrophotometric monitoring of the lensed quasar QSO 2237+0305, also known as the Einstein Cross, conducted at the Very Large Telescope. This monitoring reveals significant microlensing-induced variations in the spectra of the quasar images. In a subsequent analysis, we find that the source responsible for the optical and ultraviolet continuum has an energy profile well reproduced by a power-law R α λζ with ζ = 1.2 ± 0.3, where R is the size of the source emitting at wavelength λ. This agrees with the predictions of the standard thin accretion disk model and is, so far, the most accurate determination of a quasar energy profile. As a complement to our microlensing study, we have obtained high spectral and spatial resolution observations of the lensing galaxy of QSO 2237+0305. Our spectroscopic data are acquired with the SINFONI, FLAMES, and FORS2 spectrographs of the Very Large Telescope. We describe the reduction of these data, and provide the currently best and most complete determination of the kinematics of a gravitational lens. The comparison of our data with previously published dynamical models suggests that those may have overestimated the mass of the galaxy bulge. Thus, new and more sophisticated models are required. These models, combined with gravitational lensing, will provide two independent constraints on the mass distribution. This will allow to better determine the quantity and distribution of dark matter in this lensing galaxy, and especially in its extended halo.

EPFL2008

Looking for dark matter trails in colliding galaxy clusters

David Richard Harvey, Jean-Paul Richard Kneib, Richard Massey

If dark matter interacts, even weakly, via non-gravitational forces, simulations predict that it will be preferentially scattered towards the trailing edge of the halo during collisions between galaxy clusters. This will temporarily create a non-symmetric mass profile, with a trailing overdensity along the direction of motion. To test this hypothesis, we fit (and subtract) symmetric haloes to the weak gravitational data of 72 merging galaxy clusters observed with the Hubble Space Telescope. We convert the shear directly into excess. and project in to a one-dimensional profile. We generate numerical simulations and find that the one-dimensional profile is well described with simple Gaussian approximations. We detect the weak lensing signal of trailing gas at a 4 sigma confidence, finding a mean gas fraction of M-gas/M-dm = 0.13 +/- 0.035. We find no evidence for scattered dark matter particles with an estimated scattering fraction of f = 0.03 +/- 0.05. Finally, we find that if we can reduce the statistical error on the positional estimate of a single dark matter halo to < 2.5 arcsec, then we will be able to detect a scattering fraction of 10 per cent at the 3 sigma level with current surveys. This potentially interesting new method can provide an important independent test for other complimentary studies of the self-interaction cross-section of dark matter.