Self-similarity and scaling behavior of scale-free gravitational clustering

We measure the scaling properties of the probability distribution of the smoothed density field in $N$-body simulations of expanding universes with scale-free initial power-spectra, with particular attention to the predictions of the stable clustering hypothesis. We concentrate our analysis on the ratios $S_Q(\ell)\equiv {\bar \xi}_Q/{\bar \xi}_2^{Q-1}$, $Q \leq 5$, where ${\bar \xi}_Q$ is the averaged $Q$-body correlation function over a cell of radius $\ell$. The behavior of the higher order correlations is studied through that of the void probability distribution function. As functions of ${\bar \xi}_2$, the quantities $S_Q$, $3 \leq Q \leq 5$, exhibit two plateaus separated by a smooth transition around ${\bar \xi}_2 \sim 1$. In the weakly nonlinear regime, {\bar \xi}_2 \la 1, the results are in reasonable agreement with the predictions of perturbation theory. In the nonlinear regime, ${\bar \xi}_2 > 1$, the function $S_Q({\bar \xi}_2)$ is larger than in the weakly nonlinear regime, and increasingly so with $-n$. It is well-fitted by the expression $S_Q= ({\bar \xi}_2/100)^{0.045(Q-2)}\ {\widetilde S}_Q$for all$n. This weak dependence on scale proves {\em a small, but significant departure from the stable clustering predictions} at least for n=0$and$n=+1$. The analysis of$P_0$confirms that the expected scale-invariance of the functions$S_Q$is not exactly attained in the part of the nonlinear regime we probe, except possibly for$n=-2$and marginally for$n=-1$. In these two cases, our measurements are not accurate enough to be discriminant.Comment: 31 pages, postscript file, figure 1 missing. Postscript file including figure 1 available at ftp://ftp-astro-theory.fnal.gov:/pub/Publications/Pub-95-256-

Error estimation for the MAP experiment

We report here the first full sky component separation and CMB power spectrum estimation using a Wiener filtering technique on simulated data from the upcoming MAP experiment, set to launch in early 2001. The simulations included contributions from the three dominant astrophysical components expected in the five MAP spectral bands, namely CMB radiation, Galactic dust, and synchrotron emission. We assumed a simple homogeneous and isotropic white noise model and performed our analysis up to a spherical harmonic multipole lmax=512 on the fraction of the sky defined by b>20 degrees. We find that the reconstruction errors are reasonably well fitted by a Gaussian with an rms of 24 $\mu$K, but with significant deviations in the tails. Our results further support the predictions on the resulting CMB power spectrum of a previous estimate by Bouchet and Gispert (1999), which entailed a number of assumptions this work removes.Comment: 5 pages, 3 color figures, version accepted in A&A Letter

Extended Perturbation Theory for the Local Density Distribution Function

Perturbation theory makes it possible to calculate the probability distribution function (PDF) of the large scale density field in the small variance limit. For top hat smoothing and scale-free Gaussian initial fluctuations, the result depends only on the linear variance, sigma_linear, and its logarithmic derivative with respect to the filtering scale -(n_linear+3)=dlog sigma_linear^2/dlog L (Bernardeau 1994). In this paper, we measure the PDF and its low-order moments in scale-free simulations evolved well into the nonlinear regime and compare the results with the above predictions, assuming that the spectral index and the variance are adjustable parameters, n_eff and sigma_eff=sigma, where sigma is the true, nonlinear variance. With these additional degrees of freedom, results from perturbation theory provide a good fit of the PDFs, even in the highly nonlinear regime. The value of n_eff is of course equal to n_linear when sigma << 1, and it decreases with increasing sigma. A nearly flat plateau is reached when sigma >> 1. In this regime, the difference between n_eff and n_linear increases when n_linear decreases. For initial power-spectra with n_linear=-2,-1,0,+1, we find n_eff ~ -9,-3,-1,-0.5 when sigma^2 ~ 100.Comment: 13 pages, 6 figures, Latex (MN format), submitted to MNRA

The spectral catalogue of INTEGRAL gamma-ray bursts: results of the joint IBIS/SPI spectral analysis

We present the updated INTEGRAL catalogue of gamma-ray bursts (GRBs) observed between December 2002 and February 2012. The catalogue contains the spectral parameters for 59 GRBs localized by the INTEGRAL Burst Alert System (IBAS). We used the data from the two main instruments on board the INTEGRAL satellite: the spectrometer SPI (SPectrometer on INTEGRAL) nominally covering the energy range 18 keV - 8 MeV, and the imager IBIS (the Imager on Board the INTEGRAL Satellite) operating in the range from 15 keV to 10 MeV. For the spectral analysis we applied a new data extraction technique, developed in order to explore the energy regions of highest sensitivity for both instruments, SPI and IBIS. It allowed us to perform analysis of the GRB spectra over a broad energy range and to determine the bursts' spectral peak energies. The spectral analysis was performed on the whole sample of GRBs triggered by IBAS, including all the events observed in period December 2002 - February 2012. The catalogue contains the trigger times, burst coordinates, positional errors, durations and peak fluxes for 28 unpublished GRBs observed between September 2008 and February 2012. The light curves in 20 - 200 keV energy band of these events were derived using IBIS data. We compare the prompt emission properties of the INTEGRAL GRB sample with the BATSE and Fermi samples.Comment: 16 pages, 40 figures, accepted for publication in Astronomy & Astrophysic

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

On the Minimum Degree up to Local Complementation: Bounds and Complexity

The local minimum degree of a graph is the minimum degree reached by means of a series of local complementations. In this paper, we investigate on this quantity which plays an important role in quantum computation and quantum error correcting codes. First, we show that the local minimum degree of the Paley graph of order p is greater than sqrt{p} - 3/2, which is, up to our knowledge, the highest known bound on an explicit family of graphs. Probabilistic methods allows us to derive the existence of an infinite number of graphs whose local minimum degree is linear in their order with constant 0.189 for graphs in general and 0.110 for bipartite graphs. As regards the computational complexity of the decision problem associated with the local minimum degree, we show that it is NP-complete and that there exists no k-approximation algorithm for this problem for any constant k unless P = NP.Comment: 11 page

Stability criteria of the Vlasov equation and quasi-stationary states of the HMF model

We perform a detailed study of the relaxation towards equilibrium in the Hamiltonian Mean-Field (HMF) model, a prototype for long-range interactions in $N$-particle dynamics. In particular, we point out the role played by the infinity of stationary states of the associated $N ~$ Vlasov dynamics. In this context, we derive a new general criterion for the stability of any spatially homogeneous distribution, and compare its analytical predictions with numerical simulations of the Hamiltonian, finite $N$, dynamics. We then propose and verify numerically a scenario for the relaxation process, relying on the Vlasov equation. When starting from a non stationary or a Vlasov unstable stationary initial state, the system shows initially a rapid convergence towards a stable stationary state of the Vlasov equation via non stationary states: we characterize numerically this dynamical instability in the finite $N$ system by introducing appropriate indicators. This first step of the evolution towards Boltzmann-Gibbs equilibrium is followed by a slow quasi-stationary process, that proceeds through different stable stationary states of the Vlasov equation. If the finite $N$ system is initialized in a Vlasov stable homogenous state, it remains trapped in a quasi-stationary state for times that increase with the nontrivial power law $N^{1.7}$. Single particle momentum distributions in such a quasi-stationary regime do not have power-law tails, and hence cannot be fitted by the $q$-exponential distributions derived from Tsallis statistics.Comment: To appear in Physica

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