An MCMC Fitting Method for Triaxial Dark Matter Haloes

Measuring the 3D distribution of mass on galaxy cluster scales is a crucial test of the LCDM model, providing constraints on the behaviour of dark matter. Recent work investigating mass distributions of individual galaxy clusters (e.g. Abell 1689) using weak and strong gravitational lensing has revealed potential inconsistencies between the predictions of structure formation models relating halo mass to concentration and those relationships as measured in massive clusters. However, such analyses employ simple spherical halo models while a growing body of work indicates that triaxial 3D halo structure is both common and important in parameter estimates. The very strong assumptions about the symmetry of the lensing halo implied with circular or perturbative elliptical NFW models are not physically motivated and lead to incorrect parameter estimates with significantly underestimated error bars. We here introduce a Markov Chain Monte Carlo (MCMC) method to fit fully triaxial models to weak lensing data that gives parameter and error estimates that fully incorporate the true uncertainty present in nature. Applying the MCMC triaxial fitting method to a population of NFW triaxial lenses drawn from the shape distribution of structure formation simulations, we find that including triaxiality cannot explain a population of massive, highly concentrated clusters within the framework of LCDM, but easily explains rare cases of apparently massive, highly concentrated, very efficient lensing clusters. Our MCMC triaxial NFW fitting method is easily expandable to include constraints from additional data types, and its application returns model parameters and errors that more accurately capture the true (and limited) extent of our knowledge of the structure of galaxy cluster lenses. (abridged)Comment: 18 pages, 15 figures. Updated to match published versio

A New Look at Massive Clusters: weak lensing constraints on the triaxial dark matter halos of Abell 1689, Abell 1835, & Abell 2204

Measuring the 3D distribution of mass on galaxy cluster scales is a crucial test of the LCDM model, providing constraints on the nature of dark matter. Recent work investigating mass distributions of individual galaxy clusters (e.g. Abell 1689) using weak and strong gravitational lensing has revealed potential inconsistencies between the predictions of structure formation models relating halo mass to concentration and those relationships as measured in massive clusters. However, such analyses employ simple spherical halo models while a growing body of work indicates that triaxial 3D halo structure is both common and important in parameter estimates. We recently introduced a Markov Chain Monte Carlo (MCMC) method to fit fully triaxial models to weak lensing data that gives parameter and error estimates that fully incorporate the true shape uncertainty present in nature. In this paper we apply that method to weak lensing data obtained with the ESO/MPG Wide-Field Imager for galaxy clusters A1689, A1835, and A2204, under a range of Bayesian priors derived from theory and from independent X-ray and strong lensing observations. For Abell 1689, using a simple strong lensing prior we find marginalized mean parameter values M_200 = (0.83 +- 0.16)x10^15 M_solar/h and C=12.2 +- 6.7, which are marginally consistent with the mass-concentration relation predicted in LCDM. The large error contours that accompany our triaxial parameter estimates more accurately represent the true extent of our limited knowledge of the structure of galaxy cluster lenses, and make clear the importance of combining many constraints from other theoretical, lensing (strong, flexion), or other observational (X-ray, SZ, dynamical) data to confidently measure cluster mass profiles. (Abridged)Comment: 21 pages, 10 figures, accepted for publication in MNRA

Cosmology with the cluster mass function: mass estimators and shape systematics in large weak lensing surveys

Accurate measurement of the cluster mass function is a crucial element in efforts to constrain structure formation models, the normalisation of the matter power spectrum and the cosmological matter density, and the nature and evolution of dark energy. Large weak lensing surveys of ~20,000 galaxy clusters and groups will be key tools in the observational pursuit of that goal. These weak lensing studies often proceed by stacking the lensing signals of many clusters and groups binned by mass-correlated observables such as richness and luminosity; typically such analyses ignore the triaxial structure of dark matter halos on the assumption that the averaging of many shear signals within each mass bin makes its effects (as large as factors of two in mass model parameter estimates from individual clusters) negligible. We test this assumption and find that triaxiality can bias 3D virial mass estimates compared to those for a spherical population by a few percent if suboptimal mass estimators are used. This bias affects not only direct lensing constraints on the mass function but can also affect the scatter and normalization of the mass-observable relations derived from lensing that are so crucial to constraining the cluster mass function with large samples. However, we demonstrate that a careful choice of mass estimator can remove the bias very effectively if the lensing signals from a sufficient number of triaxial halos are averaged together, and further quantify that sufficient number for adequate shape averaging. We thus show that by choosing observable bins to contain an adequate number of halos and by utilizing a carefully chosen 3D mass estimator stacked weak-lensing analyses can give unbiased constraints on the triaxial mass function.Comment: 10 pages, 7 figures, accepted for publication in MNRA

The Hubble constant from galaxy lenses: impacts of triaxiality and model degeneracies

The Hubble constant can be constrained using the time delays between multiple images of gravitationally lensed sources. In some notable cases, typical lensing analyses assuming isothermal galaxy density profiles produce low values for the Hubble constant, inconsistent with the result of the HST Key Project (72 +- 8 km/s/Mpc). Possible systematics in the values of the Hubble constant derived from galaxy lensing systems can result from a number of factors, e.g. neglect of environmental effects, assumption of isothermality, or contamination by line-of-sight structures. One additional potentially important factor is the triaxial structure of the lensing galaxy halo; most lens models account for halo shape simply by perturbing the projected spherical lensing potential, an approximation that is often necessary but that is inadequate at the levels of triaxiality predicted in the CDM paradigm. To quantify the potential error introduced by this assumption in estimates of the Hubble parameter, we strongly lens a distant galaxy through a sample of triaxial softened isothermal halos and use an MCMC method to constrain the lensing halo profile and the Hubble parameter from the resulting multiple image systems. We explore the major degeneracies between the Hubble parameter and several parameters of the lensing model, finding that without a way to accurately break these degeneracies accurate estimates of the Hubble parameter are not possible. Crucially, we find that triaxiality does not significantly bias estimates of the Hubble constant, and offer an analytic explanation for this behaviour in the case of isothermal profiles. Neglected triaxial halo shape cannot contribute to the low Hubble constant values derived in a number of galaxy lens systems.Comment: Minor revisions to match version published in MNRAS. 13 pages, 11 figure

Marine Microalgae: Climate, Energy, and Food Security From the Sea

Climate, energy, and food security are three of the greatest challenges society faces this century. Solutions for mitigating the effects of climate change often conflict with solutions for ensuring society’s future energy and food requirements. For example, BioEnergy with Carbon Capture and Storage (BECCS) has been proposed as an important method for achieving negative CO2 emissions later this century while simultaneously producing renewable energy on a global scale. However, BECCS has many negative environmental consequences for land, nutrient, and water use as well as biodiversity and food production. In contrast, large-scale industrial cultivation of marine microalgae can provide society with a more environmentally favorable approach for meeting the climate goals agreed to at the 2015 Paris Climate Conference, producing the liquid hydrocarbon fuels required by the global transportation sector, and supplying much of the protein necessary to feed a global population approaching 10 billion people

Marine Microalgae CLIMATE, ENERGY, AND FOOD SECURITY FROM THE SEA

Climate, energy, and food security are three of the greatest challenges society faces this century. Solutions for mitigating the effects of climate change often conflict with solutions for ensuring society\u27s future energy and food requirements. For example, BioEnergy with Carbon Capture and Storage (BECCS) has been proposed as an important method for achieving negative CO2 emissions later this century while simultaneously producing renewable energy on a global scale. However, BECCS has many negative environmental consequences for land, nutrient, and water use as well as biodiversity and food production. In contrast, large-scale industrial cultivation of marine microalgae can provide society with a more environmentally favorable approach for meeting the climate goals agreed to at the 2015 Paris Climate Conference, producing the liquid hydrocarbon fuels required by the global transportation sector, and supplying much of the protein necessary to feed a global population approaching 10 billion people