The non-Gaussianity of the cosmic shear likelihood - or: How odd is the Chandra Deep Field South?

(abridged) We study the validity of the approximation of a Gaussian cosmic shear likelihood. We estimate the true likelihood for a fiducial cosmological model from a large set of ray-tracing simulations and investigate the impact of non-Gaussianity on cosmological parameter estimation. We investigate how odd the recently reported very low value of $\sigma_8$ really is as derived from the \textit{Chandra} Deep Field South (CDFS) using cosmic shear by taking the non-Gaussianity of the likelihood into account as well as the possibility of biases coming from the way the CDFS was selected. We find that the cosmic shear likelihood is significantly non-Gaussian. This leads to both a shift of the maximum of the posterior distribution and a significantly smaller credible region compared to the Gaussian case. We re-analyse the CDFS cosmic shear data using the non-Gaussian likelihood. Assuming that the CDFS is a random pointing, we find $\sigma_8=0.68_{-0.16}^{+0.09}$ for fixed $\Omega_{\rm m}=0.25$. In a WMAP5-like cosmology, a value equal to or lower than this would be expected in $\approx 5$ of the times. Taking biases into account arising from the way the CDFS was selected, which we model as being dependent on the number of haloes in the CDFS, we obtain $\sigma_8 = 0.71^{+0.10}_{-0.15}$. Combining the CDFS data with the parameter constraints from WMAP5 yields $\Omega_{\rm m} = 0.26^{+0.03}_{-0.02}$ and $\sigma_8 = 0.79^{+0.04}_{-0.03}$ for a flat universe.Comment: 18 pages, 16 figures, accepted for publication in A&A; New Bayesian treatment of field selection bia

GaBoDS: The Garching-Bonn Deep Survey VIII. Lyman-break galaxies in the ESO Deep Public Survey

Aims. The clustering properties of a large sample of U-dropouts are investigated and compared to very precise results for B-dropouts from other studies to identify a possible evolution from z=4 to z=3. Methods. A population of ~8800 candidates for star-forming galaxies at z=3 is selected via the well-known Lyman-break technique from a large optical multicolour survey (the ESO Deep Public Survey). The selection efficiency, contamination rate, and redshift distribution of this population are investigated by means of extensive simulations. Photometric redshifts are estimated for every Lyman-break galaxy (LBG) candidate from its UBVRI photometry yielding an empirical redshift distribution. The measured angular correlation function is deprojected and the resulting spatial correlation lengths and slopes of the correlation function of different subsamples are compared to previous studies. Results. By fitting a simple power law to the correlation function we do not see an evolution in the correlation length and the slope from other studies at z=4 to our study at z=3. In particular, the dependence of the slope on UV-luminosity similar to that recently detected for a sample of B-dropouts is confirmed also for our U-dropouts. For the first time number statistics for U-dropouts are sufficient to clearly detect a departure from a pure power law on small scales down to ~2" reported by other groups for B-dropouts.Comment: 10 pages, 11 figures, accepted by A&A, full resolution version available at http://www.astro.uni-bonn.de/~hendrik/5880.pd

An effective Hamiltonian for phase fluctuations on a lattice: an extended XY model

We derive an effective Hamiltonian for phase fluctuations in an s-wave superconductor starting from the attractive Hubbard model on a square lattice. In contrast to the common assumption, we find that the effective Hamiltonian is not the usual XY model but is of an extended XY type. This extended feature is robust and leads to essential corrections in understanding phase fluctuations on a lattice. The effective coupling in the Hamiltonian varies significantly with temperature.Comment: 2 figure

Constrained simulations of the Antennae Galaxies: Comparison with Herschel-PACS observations

We present a set of hydro-dynamical numerical simulations of the Antennae galaxies in order to understand the origin of the central overlap starburst. Our dynamical model provides a good match to the observed nuclear and overlap star formation, especially when using a range of rather inefficient stellar feedback efficiencies (0.01 < q_EoS < 0.1). In this case a simple conversion of local star formation to molecular hydrogen surface density motivated by observations accounts well for the observed distribution of CO. Using radiative transfer post-processing we model synthetic far-infrared spectral energy distributions (SEDs) and two-dimensional emission maps for direct comparison with Herschel-PACS observations. For a gas-to-dust ratio of 62:1 and the best matching range of stellar feedback efficiencies the synthetic far-infrared SEDs of the central star forming region peak at values of ~65 - 81 Jy at 99 - 116 um, similar to a three-component modified black body fit to infrared observations. Also the spatial distribution of the far-infrared emission at 70 um, 100 um, and 160 um compares well with the observations: >50% (> 35%) of the emission in each band is concentrated in the overlap region while only < 30% (< 15%) is distributed to the combined emission from the two galactic nuclei in the simulations (observations). As a proof of principle we show that parameter variations in the feedback model result in unambiguous changes both in the global and in the spatially resolved observable far-infrared properties of Antennae galaxy models. Our results strengthen the importance of direct, spatially resolved comparative studies of matched galaxy merger simulations as a valuable tool to constrain the fundamental star formation and feedback physics.Comment: 17 pages, 8 figures, 4 tables, submitted to MNRAS, including revisions after first referee report, comments welcom

Mean eigenvalues for simple, simply connected, compact Lie groups

We determine for each of the simple, simply connected, compact and complex Lie groups SU(n), Spin$(4n+2)$ and $E_6$ that particular region inside the unit disk in the complex plane which is filled by their mean eigenvalues. We give analytical parameterizations for the boundary curves of these so-called trace figures. The area enclosed by a trace figure turns out to be a rational multiple of $\pi$ in each case. We calculate also the length of the boundary curve and determine the radius of the largest circle that is contained in a trace figure. The discrete center of the corresponding compact complex Lie group shows up prominently in the form of cusp points of the trace figure placed symmetrically on the unit circle. For the exceptional Lie groups $G_2$, $F_4$ and $E_8$ with trivial center we determine the (negative) lower bound on their mean eigenvalues lying within the real interval $[-1,1]$. We find the rational boundary values -2/7, -3/13 and -1/31 for $G_2$, $F_4$ and $E_8$, respectively.Comment: 12 pages, 8 figure

Intermediate range chemical ordering of cations in simple molten alkali halides

The presence of first sharp diffraction peaks in the partial structure factors is investigated in computer simulations of molten mixtures of alkali halides. An intermediate range ordering appears for the Li+ ions only, which is associated with clustering of this species and is not reflected in the arrangement of other ions. This ordering is surprising in view of the simplicity of the interionic interactions in alkali halides. The clustering reflects an incomplete mixing of the various species on a local length scale, which can be demonstrated by studying the complementary sub-space of cations in the corresponding pure alkali halides by means of a void analysis.Comment: 5 pages, 5 figure

A Semi-Classical Analysis of Order from Disorder

We study in this paper the Heisenberg antiferromagnet with nearest neighbours interactions on the Husimi cactus, a system which has locally the same topology as the Kagom\'e lattice. This system has a huge classical degeneracy corresponding to an extensive number of degrees of freedom.We show that unlike thermal fluctuations, quantum fluctuations lift partially this degeneracy and favour a discrete subset of classical ground states. In order to clarify the origin of these effects, we have set up a general semi-classical analysis of the order from disorder phenomenon and clearly identified the differences between classical and quantum fluctuations. This semi-classical approach also enables us to classify various situations where a selection mechanism still occurs. Moreover, once a discrete set of ground states has been preselected, our analysis suggests that tunelling processes within this set should be the dominant effect underlying the strange low energy spectrum of Kagom\'e-like lattices.Comment: 49 pages, Latex, 12 PS figure

Spectroscopic analysis of finite size effects around a Kondo quantum dot

We consider a simple setup in which a small quantum dot is strongly connected to a finite size box. This box can be either a metallic box or a finite size quantum wire.The formation of the Kondo screening cloud in the box strongly depends on the ratio between the Kondo temperature and the box level spacing. By weakly connecting two metallic reservoirs to the quantum dot, a detailed spectroscopic analysis can be performed. Since the transport channels and the screening channels are almost decoupled, such a setup allows an easier access to the measure of finite-size effects associated with the finite extension of the Kondo cloud.Comment: contribution to Les Houches proceeding, ``Quantum magnetism'' 200