Triaxial collapse and virialisation of dark-matter haloes

We reconsider the ellipsoidal-collapse model and extend it in two ways: We modify the treatment of the external gravitational shear field, introducing a hybrid model in between linear and non-linear evolution, and we introduce a virialisation criterion derived from the tensor virial theorem to replace the ad-hoc criterion employed so far. We compute the collapse parameters delta_c and Delta_v and find that they increase with ellipticity e and decrease with prolaticity p. We marginalise them over the appropriate distribution of e and p and show the marginalised results as functions of halo mass and virialisation redshift. While the hybrid model for the external shear gives results very similar to those obtained from the non-linear model, ellipsoidal collapse changes the collapse parameters typically by (20...50)%, in a way increasing with decreasing halo mass and decreasing virialisation redshift. We qualitatively confirm the dependence on mass and virialisation redshift of a fitting formula for delta_c, but find noticeable quantitative differences in particular at low mass and high redshift. The derived mass function is in good agreement with mass functions recently proposed in the literature.Comment: 9 pages, 9 figures, published in Astronomy and Astrophysics; slight modifications to match the published versio

中央銀行行動と東アジア地域の政治経済分析 : 金融政策の主権と独立性

公共政策プログラム / Public Policy Program政策研究大学院大学 / National Graduate Institute for Policy Studies論文審査委員: 吉野 直行（主査）, CHEY Hyoung-kyu, LEON-GONZALEZ, Roberto, 園部 哲史, 藤原 一平（慶應義塾大学大学院経済学研究科 教授

Constraints on Ωm\Omega_\mathrm{m} and σ8\sigma_8 from the potential-based cluster temperature function

The abundance of galaxy clusters is in principle a powerful tool to constrain cosmological parameters, especially $\Omega_\mathrm{m}$ and $\sigma_8$, due to the exponential dependence in the high-mass regime. While the best observables are the X-ray temperature and luminosity, the abundance of galaxy clusters, however, is conventionally predicted as a function of mass. Hence, the intrinsic scatter and the uncertainties in the scaling relations between mass and either temperature or luminosity lower the reliability of galaxy clusters to constrain cosmological parameters. In this article, we further refine the X-ray temperature function for galaxy clusters by Angrick et al., which is based on the statistics of perturbations in the cosmic gravitational potential and proposed to replace the classical mass-based temperature function, by including a refined analytic merger model and compare the theoretical prediction to results from a cosmological hydrodynamical simulation. Although we find already a good agreement if we compare with a cluster temperature function based on the mass-weighted temperature, including a redshift-dependent scaling between mass-based and spectroscopic temperature yields even better agreement between theoretical model and numerical results. As a proof of concept, incorporating this additional scaling in our model, we constrain the cosmological parameters $\Omega_\mathrm{m}$ and $\sigma_8$ from an X-ray sample of galaxy clusters and tentatively find agreement with the recent cosmic microwave background based results from the Planck mission at 1$\sigma$-level.Comment: 10 pages, 5 figures, 2 tables; accepted by MNRAS; some typos correcte

Global liquidity and monetary policy autonomy: An examination of open-economy policy constraints

This paper examines the monetary policy constraints facing economies on a fixed peg or managed float regime, contrasting the Mundell-Fleming Trilemma view against the Compensation view commonly found at central banks. While the former holds that foreign exchange inflows and outflows affect the domestic money base, constraining monetary policy under non-floating regimes unless capital controls are adopted, the latter purports that endogenous sterilisation of foreign exchange flows invalidates this trade-off. The predictions of both theories are empirically evaluated for five East Asian economies using central bank balance sheets, vector error correction models and impulse response functions. The findings indicate that the dynamics for the economies studied correspond more closely to the Compensation view than the Trilemma view, suggesting that it is a sustained loss of foreign ex-change reserves that imposes a relevant constraint on autonomy rather than the adoption of a non-floating exchange rate regime.Die vorliegende Arbeit untersucht, welchen geldpolitischen Einschränkungen Ökonomien mit festen oder eingeschränkt schwankenden Wechselkursen unterworfen sind. Hierbei wird das Mundell-Fleming-Trilemma der Kompensations-Hypothese gegenübergestellt, welche häufig in Zentralbanken vertreten wird. Die erste Sichtweise unterstellt, dass Währungszuflüsse und -abflüsse sich auf die inländische Geldbasis auswirken und damit den geldpolitischen Handlungsspielraum einschränken, es sei denn Kapitalverkehrskontrollen werden eingeführt. Die zweite Sichtweise hingegen behauptet, dass endogene Sterilisation von Währungsströmen diesen Mechanismus außer Kraft setzt. Anhand von Bilanzdaten für fünf ostasiatische Ökonomien und mit Hilfe von Vektor-Fehlerkorrekturmodellen und Impulsantworten werden die Prognosen beider Theorien empirisch überprüft. Die Ergebnisse zeigen, dass die Zusammenhänge eher der Kompensations-Hypothese entsprechen. Dies deutet darauf hin, dass geldpolitische Autonomie durch einen anhaltenden Abfluss von Währungsreserven wesentlicher eingeschränkt wird als durch die Einführung eines nicht-flexiblen Wechselkurssystems

An analytic approach to number counts of weak-lensing peak detections

We develop and apply an analytic method to predict peak counts in weak-lensing surveys. It is based on the theory of Gaussian random fields and suitable to quantify the level of spurious detections caused by chance projections of large-scale structures as well as the shape and shot noise contributed by the background galaxies. We compare our method to peak counts obtained from numerical ray-tracing simulations and find good agreement at the expected level. The number of peak detections depends substantially on the shape and size of the filter applied to the gravitational shear field. Our main results are that weak-lensing peak counts are dominated by spurious detections up to signal-to-noise ratios of 3--5 and that most filters yield only a few detections per square degree above this level, while a filter optimised for suppressing large-scale structure noise returns up to an order of magnitude more.Comment: 9 pages, 5 figures, submitted to A&

Ellipticity and prolaticity of the initial gravitational-shear field at the position of density maxima

Dark-matter haloes are supposed to form at the positions of maxima in the initial matter density field. The gravitational-shear field's ellipticity and prolaticity that serve as input for the ellipsoidal-collapse model, however, are derived from a distribution that does not take the additional maximum constraint into account. In this article, I quantify the variations of the most probable and the expected values of the ellipticity and the prolaticity when considering this additional constraint as well as the implications for the ellipsoidal-collapse model. Based on the statistics of Gaussian random fields, it is possible to set up a joint distribution for the eigenvalues of the gravitational-shear tensor and the matter density that incorporates the maximum constraint by invoking a vanishing first derivative and a negative definite second derivative of the density field into the calculation. In the density range relevant for cosmological structure formation, both the most probable and the expected value of the ellipticity calculated from the standard distribution used in the literature are about 3-8 per cent higher compared to the ones calculated under the additional assumption of a density maximum. Additionally, the analogous quantities for the prolaticity do not vanish but acquire slightly positive values in the range of $10^{-3}$-$10^{-2}$. For large overdensities, the predictions from both distributions converge. The values for $\delta_\mathrm{c}$ and $\Delta_\mathrm{v}$ derived from the ellipsoidal-collapse model using the standard distribution for the initial ellipticity and prolaticity are up to 4 and 6 per cent higher, respectively, than those obtained taking the additional maximum constraint into account in the range of $10^{13}$-$10^{15}~h^{-1}~\mathrm{M}_\odot$ in mass and 0-2 in redshift.Comment: 11 pages, 4 figures, 1 table; typos corrected to match the version published in MNRA

The formation of CDM haloes I: Collapse thresholds and the ellipsoidal collapse model

In the excursion set approach to structure formation initially spherical regions of the linear density field collapse to form haloes of mass $M$ at redshift $z_{\rm id}$ if their linearly extrapolated density contrast, averaged on that scale, exceeds some critical threshold, $\delta_{\rm c}(z_{\rm id})$. The value of $\delta_{\rm c}(z_{\rm id})$ is often calculated from the spherical or ellipsoidal collapse model, which provide well-defined predictions given auxiliary properties of the tidal field at a given location. We use two cosmological simulations of structure growth in a $\Lambda$ cold dark matter scenario to quantify $\delta_{\rm c}(z_{\rm id})$, its dependence on the surrounding tidal field, as well as on the shapes of the Lagrangian regions that collapse to form haloes at $z_{\rm id}$. Our results indicate that the ellipsoidal collapse model provides an accurate description of the mean dependence of $\delta_{\rm c}(z_{\rm id})$ on both the strength of the tidal field and on halo mass. However, for a given $z_{\rm id}$, $\delta_{\rm c}(z_{\rm id})$ depends strongly on the halo's characteristic formation redshift: the earlier a halo forms, the higher its initial density contrast. Surprisingly, the majority of haloes forming $today$ fall below the ellipsoidal collapse barrier, contradicting the model predictions. We trace the origin of this effect to the non-spherical shapes of Lagrangian haloes, which arise naturally due to the asymmetry of the linear tidal field. We show that a modified collapse model, that accounts for the triaxial shape of protohaloes, provides a more accurate description of the measured minimum overdensities of recently collapsed objects.Comment: MNRAS in pres

Intracluster medium of the merging cluster Abell 3395

We present a detailed imaging and spectral analysis of the merging environment of the bimodal cluster A3395 using X-ray and radio observations. X-ray images of the cluster show five main constituents of diffuse emission : A3395 NE, A3395 SW, A3395 NW, A3395 W, and a filament connecting NE to W. X-ray surface-brightness profiles of the cluster did not show any shock fronts in the cluster. Temperature and entropy maps show high temperature and high entropy regions in the W, the NW, the filament and between the NE and SW subclusters. The NE, SW and W components have X-ray bolometric luminosities similar to those of rich clusters of galaxies but have relatively higher temperatures. Similarly, the NW component has X-ray bolometric luminosity similar to that of isolated groups but with much higher temperature. It is, therefore, possible that all the components of the cluster have been heated by the ongoing mergers. The NE subcluster is the most massive and luminous constituent and other subclusters are found to be gravitationally bound to it. The W component is most probably either a clump of gas stripped off the SW due to ram pressure or a separate subcluster that has merged or is merging with the SW. No X-ray cavities are seen associated with the Wide Angle Tailed (WAT) radio source near the centre of the SW subcluster. Minimum energy pressure in the radio emission-peaks of the WAT galaxy is comparable with the external thermal pressure. The radio spectrum of the WAT suggests a spectral age of ~10Myr

On the derivation of an X-ray temperature function without reference to mass and the prediction of weak-lensing number counts from the statistics of Gaussian random fields

We present a novel approach for the derivation of the X-ray temperature function for galaxy clusters, which is based on the statistics of Gaussian random fields applied to the cosmic gravitational potential. It invokes only locally defined quantities so that no reference to the cluster's mass is made. To relate linear and non-linear potential and to take into account only structures that have collapsed, we include either spherical- or ellipsoidal-collapse dynamics and compare both resulting models to temperature functions derived from a numerical simulation. Since deviations from the theoretical prediction are found in the simulation for high redshifts, we develop an analytic model to include the effects of mergers in our formalism. We jointly determine the cosmological parameters Omega_m0 and sigma_8 from two different cluster samples for different temperature definitions and find good agreement with constraints from WMAP5. Introducing theoretically a refined detection definition based on the upcrossing criterion, we reformulate our analytic approach for 2D and use it to predict the number density of spurious detections caused by large-scale structure and shot noise in filtered weak-lensing convergence maps. Agreement with a numerical simulation is found at the expected level

Hannah Arendt's Ghosts:Reflections on the Disputable Path from Windhoek to Auschwitz

Historians on both sides of the Atlantic are currently engaged in a controversy about the allegedly genocidal nature of western colonialism and its connections with the mass violence unleashed by Nazi Germany between 1939 and 1945. The debate touches upon some of the most “sensitive” issues of twentieth-century history: the violent “dark side” of modern western civilization, the impact of colonial massacres on the European societies that generated this violence and, perhaps most controversially, the origins and uniqueness of the Holocaust