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

On the morphology of the electron-positron annihilation emission as seen by SPI/INTEGRAL

The 511 keV positron annihilation emission remains a mysterious component of the high energy emission of our Galaxy. Its study was one of the key scientific objective of the SPI spectrometer on-board the INTEGRAL satellite. In fact, a lot of observing time has been dedicated to the Galactic disk with a particular emphasis on the central region. A crucial issue in such an analysis concerns the reduction technique used to treat this huge quantity of data, and more particularly the background modeling. Our method, after validation through a variety of tests, is based on detector pattern determination per ~6 month periods, together with a normalisation variable on a few hour timescale. The Galactic bulge is detected at a level of ~70 sigma allowing more detailed investigations. The main result is that the bulge morphology can be modelled with two axisymmetric Gaussians of 3.2 deg. and 11.8 deg. FWHM and respective fluxes of 2.5 and 5.4 x 10^-4 photons/(cm^2.s^1). We found a possible shift of the bulge centre towards negative longitude at l=-0.6 +/- 0.2 degrees. In addition to the bulge, a more extended structure is detected significantly with flux ranging from 1.7 to 2.9 x10^-3 photons/(cm^2.s^1) depending on its assumed geometry (pure disk or disk plus halo). The disk emission is also found to be symmetric within the limits of the statistical errors.Comment: This paper has 12 pages and 14 figures. Accepted for publication by the Astrophysical Journa

Projection and Galaxy Clustering Fourier Spectra

Second order perturbation theory predicts a specific dependence of the bispectrum, or three-point correlation function in the Fourier transform domain, on the shape of the configuration of its three wave vector arguments, which can be taken as a signature of structure formed by gravitational instability. Comparing this known dependence on configuration shape with the weak shape dependence of the galaxy bispectrum has been suggested as an indication of bias in the galaxy distribution. However, to interpret results obtained from projected catalogs, we must first understand the effects of projection on this shape dependence. We present expressions for the projected power spectrum and bispectrum in both Cartesian and spherical geometries, and we examine the effects of projection on the predicted bispectrum with particular attention to the dependence on configuration shape. Except for an overall numerical factor, for Cartesian projection with characteristic depth \Dstar there is little effect on the shape dependence of the bispectrum for wavelengths small compared to \Dstar or projected wavenumbers q \Dstar \gg 1 . For angular projection, a scaling law is found for spherical harmonic index $\ell \gg 1$, but there is always a mixing of scales over the range of the selection function. For large $\ell$ it is sufficient to examine a small portion of the sky.Comment: aastex, 7 figure

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

The FIR/submm window on galaxy formation

Our view on the deep universe has been so far biased towards optically bright galaxies. Now, the measurement of the Cosmic Infrared Background in FIRAS and DIRBE residuals, and the observations of FIR/submm sources by the ISOPHOT and SCUBA instruments begin unveiling the ``optically dark side'' of galaxy formation. Though the origin of dust heating is still unsolved, it appears very likely that a large fraction of the FIR/submm emission is due to heavily-extinguished star formation. Consequently, the level of the CIRB implies that about 2/3 of galaxy/star formation in the universe is hidden by dust shrouds. In this review, we introduce a new modeling of galaxy formation and evolution that provides us with specific predictions in FIR/submm wavebands. These predictions are compared with the current status of the observations. Finally, the capabilities of current and forthcoming instruments for all-sky and deep surveys of FIR/submm sources are briefly described.Comment: 10 pages, Latex, 5 postscript figures, to appear in ``The Birth of Galaxies'', 1999, B. Guiderdoni, F.R. Bouchet, T.X. Thuan & J. Tran Thanh Van (eds), Editions Frontiere

Algebraic Correlation Function and Anomalous Diffusion in the HMF model

In the quasi-stationary states of the Hamiltonian Mean-Field model, we numerically compute correlation functions of momenta and diffusion of angles with homogeneous initial conditions. This is an example, in a N-body Hamiltonian system, of anomalous transport properties characterized by non exponential relaxations and long-range temporal correlations. Kinetic theory predicts a striking transition between weak anomalous diffusion and strong anomalous diffusion. The numerical results are in excellent agreement with the quantitative predictions of the anomalous transport exponents. Noteworthy, also at statistical equilibrium, the system exhibits long-range temporal correlations: the correlation function is inversely proportional to time with a logarithmic correction instead of the usually expected exponential decay, leading to weak anomalous transport properties

Formation and dynamics of self-sustained neutron haloes in disk accreting sources

It has been recognized long ago that the presence of hot plasma in the inner accretion disks around black holes could lead to the neutron production via dissociation of helium nuclei. We show that, for a broad range of accretion parameters, neutrons effectively decouple from protons and pile up in the inner disk leading to the formation of self-sustained halo. This means that new neutrons in the halo are supplied mainly by the splitting of helium nuclei in their collisions with existing neutrons. Once formed, such a halo can exist even if the proton temperature is much lower than the energy threshold of helium dissociation. We show that neutron haloes can be the natural source of relativistic electrons and positrons, providing characteristic comptonization spectra and hard spectral tails observed in many black hole candidates, and also giving rise to relativistic outflows. Deuterium gamma-ray line at 2.2 MeV resulting from neutron capture is also expected at a level detectable by future INTEGRAL mission. Furthermore, the presence of a neutron halo strongly affects the dynamics of accretion and leads to the rich variety of transient dynamical regimes.Comment: 10 pages, submitted to Astronomy and Astrophysic

Observational Constraints on Higher Order Clustering up to $z\simeq 1

Constraints on the validity of the hierarchical gravitational instability theory and the evolution of biasing are presented based upon measurements of higher order clustering statistics in the Deeprange Survey, a catalog of $\sim710,000$ galaxies with $I_{AB} \le 24$ derived from a KPNO 4m CCD imaging survey of a contiguous $4^{\circ} \times 4^{\circ}$ region. We compute the 3-point and 4-point angular correlation functions using a direct estimation for the former and the counts-in-cells technique for both. The skewness $s_3$ decreases by a factor of $\simeq 3-4$ as galaxy magnitude increases over the range $17 \le I \le 22.5$ ($0.1 \lesssim z \lesssim 0.8$). This decrease is consistent with a small {\it increase} of the bias with increasing redshift, but not by more than a factor of 2 for the highest redshifts probed. Our results are strongly inconsistent, at about the $3.5-4 \sigma$ level, with typical cosmic string models in which the initial perturbations follow a non-Gaussian distribution - such models generally predict an opposite trend in the degree of bias as a function of redshift. We also find that the scaling relation between the 3-point and 4-point correlation functions remains approximately invariant over the above magnitude range. The simplest model that is consistent with these constraints is a universe in which an initially Gaussian perturbation spectrum evolves under the influence of gravity combined with a low level of bias between the matter and the galaxies that decreases slightly from $z \sim 0.8$ to the current epoch.Comment: 28 pages, 4 figures included, ApJ, accepted, minor change

Kinetic theory for non-equilibrium stationary states in long-range interacting systems

We study long-range interacting systems perturbed by external stochastic forces. Unlike the case of short-range systems, where stochastic forces usually act locally on each particle, here we consider perturbations by external stochastic fields. The system reaches stationary states where external forces balance dissipation on average. These states do not respect detailed balance and support non-vanishing fluxes of conserved quantities. We generalize the kinetic theory of isolated long-range systems to describe the dynamics of this non-equilibrium problem. The kinetic equation that we obtain applies to plasmas, self-gravitating systems, and to a broad class of other systems. Our theoretical results hold for homogeneous states, but may also be generalized to apply to inhomogeneous states. We obtain an excellent agreement between our theoretical predictions and numerical simulations. We discuss possible applications to describe non-equilibrium phase transitions.Comment: 11 pages, 2 figures; v2: small changes, close to the published versio