Convexity and Robustness of Dynamic Traffic Assignment and Freeway Network Control

We study the use of the System Optimum (SO) Dynamic Traffic Assignment (DTA) problem to design optimal traffic flow controls for freeway networks as modeled by the Cell Transmission Model, using variable speed limit, ramp metering, and routing. We consider two optimal control problems: the DTA problem, where turning ratios are part of the control inputs, and the Freeway Network Control (FNC), where turning ratios are instead assigned exogenous parameters. It is known that relaxation of the supply and demand constraints in the cell-based formulations of the DTA problem results in a linear program. However, solutions to the relaxed problem can be infeasible with respect to traffic dynamics. Previous work has shown that such solutions can be made feasible by proper choice of ramp metering and variable speed limit control for specific traffic networks. We extend this procedure to arbitrary networks and provide insight into the structure and robustness of the proposed optimal controllers. For a network consisting only of ordinary, merge, and diverge junctions, where the cells have linear demand functions and affine supply functions with identical slopes, and the cost is the total traffic volume, we show, using the maximum principle, that variable speed limits are not needed in order to achieve optimality in the FNC problem, and ramp metering is sufficient. We also prove bounds on perturbation of the controlled system trajectory in terms of perturbations in initial traffic volume and exogenous inflows. These bounds, which leverage monotonicity properties of the controlled trajectory, are shown to be in close agreement with numerical simulation results

Constraining galaxy cluster temperatures and redshifts with eROSITA survey data

The nature of dark energy is imprinted in the large-scale structure of the Universe and thus in the mass and redshift distribution of galaxy clusters. The upcoming eROSITA mission will exploit this method of probing dark energy by detecting roughly 100,000 clusters of galaxies in X-rays. For a precise cosmological analysis the various galaxy cluster properties need to be measured with high precision and accuracy. To predict these characteristics of eROSITA galaxy clusters and to optimise optical follow-up observations, we estimate the precision and the accuracy with which eROSITA will be able to determine galaxy cluster temperatures and redshifts from X-ray spectra. Additionally, we present the total number of clusters for which these two properties will be available from the eROSITA survey directly. During its four years of all-sky surveys, eROSITA will determine cluster temperatures with relative uncertainties of Delta(T)/T<10% at the 68%-confidence level for clusters up to redshifts of z~0.16 which corresponds to ~1,670 new clusters with precise properties. Redshift information itself will become available with a precision of Delta(z)/(1+z)<10% for clusters up to z~0.45. Additionally, we estimate how the number of clusters with precise properties increases with a deepening of the exposure. Furthermore, the biases in the best-fit temperatures as well as in the estimated uncertainties are quantified and shown to be negligible in the relevant parameter range in general. For the remaining parameter sets, we provide correction functions and factors. The eROSITA survey will increase the number of galaxy clusters with precise temperature measurements by a factor of 5-10. Thus the instrument presents itself as a powerful tool for the determination of tight constraints on the cosmological parameters.Comment: accepted for publication in A&A; 17 pages, 20 figure

XMM-Newton and Chandra Cross Calibration Using HIFLUGCS Galaxy Clusters: Systematic Temperature Differences and Cosmological Impact

Cosmological constraints from clusters rely on accurate gravitational mass estimates, which strongly depend on cluster gas temperature measurements. Therefore, systematic calibration differences may result in biased, instrument-dependent cosmological constraints. This is of special interest in the light of the tension between the Planck results of the primary temperature anisotropies of the CMB and Sunyaev-Zel'dovich plus X-ray cluster counts analyses. We quantify in detail the systematics and uncertainties of the cross-calibration of the effective area between five X-ray instruments, EPIC-MOS1/MOS2/PN onboard XMM-Newton and ACIS-I/S onboard Chandra, and the influence on temperature measurements. Furthermore, we assess the impact of the cross calibration uncertainties on cosmology. Using the HIFLUGCS sample, consisting of the 64 X-ray brightest galaxy clusters, we constrain the ICM temperatures through spectral fitting in the same, mostly isothermal, regions and compare them. Our work is an extension to a previous one using X-ray clusters by the IACHEC. Performing spectral fitting in the full energy band we find that best-fit temperatures determined with XMM-Newton/EPIC are significantly lower than Chandra/ACIS temperatures. We demonstrate that effects like multitemperature structure and different relative sensitivities of the instruments at certain energy bands cannot explain the observed differences. We conclude that using XMM-Newton/EPIC, instead of Chandra/ACIS to derive full energy band temperature profiles for cluster mass determination results in an 8% shift towards lower OmegaM values and <1% shift towards higher sigma8 values in a cosmological analysis of a complete sample of galaxy clusters. Such a shift is insufficient to significantly alleviate the tension between Planck CMB anisotropies and SZ plus XMM-Newton cosmological constraints.Comment: Accepted by A&A; Python-Script for modification of XMM-Newton/EPIC and Chandra/ACIS effective areas according to the stacked residual ratios: https://wikis.mit.edu/confluence/display/iachec/Data

Scaling relations for galaxy clusters: properties and evolution

Well-calibrated scaling relations between the observable properties and the total masses of clusters of galaxies are important for understanding the physical processes that give rise to these relations. They are also a critical ingredient for studies that aim to constrain cosmological parameters using galaxy clusters. For this reason much effort has been spent during the last decade to better understand and interpret relations of the properties of the intra-cluster medium. Improved X-ray data have expanded the mass range down to galaxy groups, whereas SZ surveys have openened a new observational window on the intracluster medium. In addition,continued progress in the performance of cosmological simulations has allowed a better understanding of the physical processes and selection effects affecting the observed scaling relations. Here we review the recent literature on various scaling relations, focussing on the latest observational measurements and the progress in our understanding of the deviations from self similarity.Comment: 38 pages. Review paper. Accepted for publication in Space Science Reviews (eds: S. Ettori, M. Meneghetti). This is a product of the work done by an international team at the International Space Science Institute (ISSI) in Bern on "Astrophysics and Cosmology with Galaxy Clusters: the X-ray and Lensing View

XMM Observations of Metal Abundances in Galaxy Clusters

The hot gas that fills the space between galaxies in clusters is rich in metals. Due to their large potential well, galaxy clusters accumulate metals over the whole history of the cluster, and retain important information on cluster formation and evolution.We derive detailed metallicity maps for a sample of 5 clusters, observed with XMM-Newton, to study the distribution of metals in the Intra-Cluster Medium (ICM). We show that even in relaxed clusters the distribution of metals shows many inhomogeneities with several maxima separated by low metallicity regions. We also found a deviation from the expected temperature-metallicity relation