Three-Point Statistics from a New Perspective

Multipole expansion of spatial three-point statistics is introduced as a tool for investigating and displaying configuration dependence. The novel parametrization renders the relation between bi-spectrum and three-point correlation function especially transparent as a set of two-dimensional Hankel transforms. It is expected on theoretical grounds, that three-point statistics can be described accurately with only a few multipoles. In particular, we show that in the weakly non-linear regime, the multipoles of the reduced bispectrum, $Q_l$, are significant only up to quadrupole. Moreover, the non-linear bias in the weakly non-linear regime only affects the monopole order of these statistics. As a consequence, a simple, novel set of estimators can be constructed to constrain galaxy bias. In addition, the quadrupole to dipole ratio is independent of the bias, thus it becomes a novel diagnostic of the underlying theoretical assumptions: weakly non-linear gravity and perturbative local bias. To illustrate the use of our approach, we present predictions based on both power law, and CDM models. We show that the presently favoured SDSS-WMAP concordance model displays strong ``baryon bumps'' in the $Q_l$'s. Finally, we sketch out three practical techniques estimate these novel quantities: they amount to new, and for the first time edge corrected, estimators for the bispectrum.Comment: 5 pages 6 figures, ApL accepte

Separation of foregrounds from cosmic microwave background observations with the MAP satellite

Simulated observations of a 10\dg \times 10\dg field by the Microwave Anisotropy Probe (MAP) are analysed in order to separate cosmic microwave background (CMB) emission from foreground contaminants and instrumental noise and thereby determine how accurately the CMB emission can be recovered. The simulations include emission from the CMB, the kinetic and thermal Sunyaev-Zel'dovich (SZ) effects from galaxy clusters, as well as Galactic dust, free-free and synchrotron. We find that, even in the presence of these contaminating foregrounds, the CMB map is reconstructed with an rms accuracy of about 20 $\mu$K per 12.6 arcmin pixel, which represents a substantial improvement as compared to the individual temperature sensitivities of the raw data channels. We also find, for the single 10\dg \times 10\dg field, that the CMB power spectrum is accurately recovered for \ell \la 600.Comment: 7 pages, 7 figures, MNRAS submitte

Simulations of the Microwave Sky and of its ``Observations''

Here follows a preliminary report on the construction of fake millimeter and sub-millimeter skies, as observed by virtual instruments, e.g. the COBRA/SAMBA mission, using theoretical modeling and data extrapolations. Our goal is to create maps as realistic as possible of the relevant physical contributions which may contribute to the detected signals. This astrophysical modeling is followed by simulations of the measurement process itself by a given instrumental configuration. This will enable a precise determination of what can and cannot be achieved with a particular experimental configuration, and provide a feedback on how to improve the overall design. It is a key step on the way to define procedures for the separation of the different physical processes in the future observed maps. Note that this tool will also prove useful in preparing and analyzing current (\eg\ balloon borne) Microwave Background experiments. Keywords: Cosmology -- Microwave Background Anisotropies.Comment: 6 pages of uuencoded compressed postscript (1.2 Mb uncompressed), to appear in the proceedings of the meeting "Far Infrared and Sub-millimeter Space Missions in the Next Decade'', Paris, France, Eds. M. Sauvage, Space Science Revie

Ensemble inequivalence, bicritical points and azeotropy for generalized Fofonoff flows

We present a theoretical description for the equilibrium states of a large class of models of two-dimensional and geophysical flows, in arbitrary domains. We account for the existence of ensemble inequivalence and negative specific heat in those models, for the first time using explicit computations. We give exact theoretical computation of a criteria to determine phase transition location and type. Strikingly, this criteria does not depend on the model, but only on the domain geometry. We report the first example of bicritical points and second order azeotropy in the context of systems with long range interactions.Comment: 4 pages, submitted to Phys. Rev. Let

Dessins, their delta-matroids and partial duals

Given a map $\mathcal M$ on a connected and closed orientable surface, the delta-matroid of $\mathcal M$ is a combinatorial object associated to $\mathcal M$ which captures some topological information of the embedding. We explore how delta-matroids associated to dessins d'enfants behave under the action of the absolute Galois group. Twists of delta-matroids are considered as well; they correspond to the recently introduced operation of partial duality of maps. Furthermore, we prove that every map has a partial dual defined over its field of moduli. A relationship between dessins, partial duals and tropical curves arising from the cartography groups of dessins is observed as well.Comment: 34 pages, 20 figures. Accepted for publication in the SIGMAP14 Conference Proceeding

Quasi-local evolution of cosmic gravitational clustering in the weakly non-linear regime

We investigate the weakly non-linear evolution of cosmic gravitational clustering in phase space by looking at the Zel'dovich solution in the discrete wavelet transform (DWT) representation. We show that if the initial perturbations are Gaussian, the relation between the evolved DWT mode and the initial perturbations in the weakly non-linear regime is quasi-local. That is, the evolved density perturbations are mainly determined by the initial perturbations localized in the same spatial range. Furthermore, we show that the evolved mode is monotonically related to the initial perturbed mode. Thus large (small) perturbed modes statistically correspond to the large (small) initial perturbed modes. We test this prediction by using QSO Ly$\alpha$ absorption samples. The results show that the weakly non-linear features for both the transmitted flux and identified forest lines are quasi-localized. The locality and monotonic properties provide a solid basis for a DWT scale-by-scale Gaussianization reconstruction algorithm proposed by Feng & Fang (Feng & Fang, 2000) for data in the weakly non-linear regime. With the Zel'dovich solution, we find also that the major non-Gaussianity caused by the weakly non-linear evolution is local scale-scale correlations. Therefore, to have a precise recovery of the initial Gaussian mass field, it is essential to remove the scale-scale correlations.Comment: 22 pages, 13 figures. Accepted for publication in the Astrophysical Journa

The effect of point sources on satellite observations of the cosmic microwave background

We study the effect of extragalactic point sources on satellite observations of the cosmic microwave background (CMB). In order to separate the contributions due to different foreground components, a maximum-entropy method is applied to simulated observations by the Planck Surveyor satellite. In addition to point sources, the simulations include emission from the CMB and the kinetic and thermal Sunyaev-Zel'dovich (SZ) effects from galaxy clusters, as well as Galactic dust, free-free and synchrotron emission. We find that the main input components are faithfully recovered and, in particular, that the quality of the CMB reconstruction is only slightly reduced by the presence of point sources. In addition, we find that it is possible to recover accurate point source catalogues at each of the Planck Surveyor observing frequencies.Comment: 12 pages, 9 figures, submitted to MNRA

The Bispectrum of IRAS Galaxies

We compute the bispectrum for the galaxy distribution in the IRAS QDOT, 2Jy, and 1.2Jy redshift catalogs for wavenumbers 0.05<k<0.2 h/Mpc and compare the results with predictions from gravitational instability in perturbation theory. Taking into account redshift space distortions, nonlinear evolution, the survey selection function, and discreteness and finite volume effects, all three catalogs show evidence for the dependence of the bispectrum on configuration shape predicted by gravitational instability. Assuming Gaussian initial conditions and local biasing parametrized by linear and non-linear bias parameters b_1 and b_2, a likelihood analysis yields 1/b_1 = 1.32^{+0.36}_{-0.58}, 1.15^{+0.39}_{-0.39} and b_2/b_1^2=-0.57^{+0.45}_{-0.30}, -0.50^{+0.31}_{-0.51}, for the for the 2Jy and 1.2Jy samples, respectively. This implies that IRAS galaxies trace dark matter increasingly weakly as the density contrast increases, consistent with their being under-represented in clusters. In a model with chi^2 non-Gaussian initial conditions, the bispectrum displays an amplitude and scale dependence different than that found in the Gaussian case; if IRAS galaxies do not have bias b_1> 1 at large scales, \chi^2 non-Gaussian initial conditions are ruled out at the 95% confidence level. The IRAS data do not distinguish between Lagrangian or Eulerian local bias.Comment: 30 pages, 11 figure

Passive Evolution: Are the Faint Blue Galaxy Counts Produced by a Population of Eternally Young Galaxies?

A constant age population of blue galaxies, postulated in the model of Gronwall & Koo (1995), seems to provide an attractive explanation of the excess of very blue galaxies in the deep galaxy counts. Such a population may be generated by a set of galaxies with cycling star formation rates, or at the other extreme, be maintained by the continual formation of new galaxies which fade after they reach the age specified in the Gronwall and Koo model. For both of these hypotheses, we have calculated the luminosity functions including the respective selection criteria, the redshift distributions, and the number counts in the B_J and K bands. We find a substantial excess in the number of galaxies at low redshift (0 < z < 0.05) over that observed in the CFH redshift survey (Lilly et al. 1995) and at the faint end of the Las Campanas luminosity function (Lin et al. 1996). Passive or mild evolution fails to account for the deep galaxy counts because of the implications for low redshift determinations of the I-selected redshift distribution and the r-selected luminosity function in samples where the faded counterparts of the star-forming galaxies would be detectable.Comment: 11 pages, LaTeX type (aaspp4.sty), 3 Postscript figures, submitted to ApJ Letter