Dynamical flows through Dark Matter Haloes II: one and two points statistics at the virial radius

In a serie of three papers, the dynamical interplay between environments and dark matter haloes is investigated, while focussing on the dynamical flows through their virial sphere. Our method relies on both cosmological simulations, to constrain the environments, and an extension to the classical matrix method to derive the response of the halo (see Pichon & Aubert (2006), paper I). The current paper focuses on the statistical characterisation of the environments surrounding haloes, using a set of large scale simulations. Our description relies on a `fluid' halocentric representation where the interactions between the halo and its environment are investigated in terms of a time dependent external tidal field and a source term characterizing the infall. The method is applied to 15000 haloes, with masses between 5 x 10^12 Ms and 10^14 Ms evolving between z = 1 and z = 0. The net accretion at the virial radius is found to decrease with time, resulting from both an absolute decrease of infall and from a growing contribution of outflows. Infall is found to be mainly radial and occurring at velocities ~ 0.75 V200. Outflows are also detected through the virial sphere and occur at lower velocities ~ 0.6 V200 on more circular orbits. The external tidal field is found to be strongly quadrupolar and mostly stationnary, possibly reflecting the distribution of matter in the halo's near environment. The coherence time of the small scale fluctuations of the potential hints a possible anisotropic distribution of accreted satellites. The flux density of mass on the virial sphere appears to be more clustered than the potential while the shape of its angular power spectrum seems stationnary.Comment: 34 pages, 29 figures, accepted for publication in MNRA

Vorticity generation in large-scale structure caustics

A fundamental hypothesis for the interpretation of the measured large-scale line-of-sight peculiar velocities of galaxies is that the large-scale cosmic flows are irrotational. In order to assess the validity of this assumption, we estimate, within the frame of the gravitational instability scenario, the amount of vorticity generated after the first shell crossings in large-scale caustics. In the Zel'dovich approximation the first emerging singularities form sheet like structures. Here we compute the expectation profile of an initial overdensity under the constraint that it goes through its first shell crossing at the present time. We find that this profile corresponds to rather oblate structures in Lagrangian space. Assuming the Zel'dovich approximation is still adequate not only at the first stages of the evolution but also slightly after the first shell crossing, we calculate the size and shape of those caustics and their vorticity content as a function of time and for different cosmologies. The average vorticity created in these caustics is small: of the order of one (in units of the Hubble constant). To illustrate this point we compute the contribution of such caustics to the probability distribution function of the filtered vorticity at large scales. We find that this contribution that this yields a negligible contribution at the 10 to 15 $h^{-1}$Mpc scales. It becomes significant only at the scales of 3 to 4 $h^{-1}$Mpc, that is, slightly above the galaxy cluster scales.Comment: 25 pages 16 figures; accepted for publication by A&A vol 342 (1999

Dynamical flows through Dark Matter Haloes: Inner perturbative dynamics, secular evolution, and applications

We investigate statistically the dynamical consequences of cosmological fluxes of matter and related moments on progenitors of today's dark matter haloes. Their dynamics is described via canonical perturbation theory which accounts for two types of perturbations: the tidal field corresponding to fly-bys and accretion of dark matter through the halo's outer boundary. he dynamical equations are solved linearly, order by order, projecting on a biorthogonal basis to consistently satisfy the field equation. Since our solution of the Boltzmann Poisson equations is explicit, it allows statistical predictions for the ensemble distribution of the inner dynamical features of haloes. The secular evolution of open galactic haloes is investigated: we derive the kinetic equation which governs the quasi-linear evolution of dark matter profile induced by infall and its corresponding gravitational correlations. This yields a Fokker Planck-like equation for the angle-averaged underlying distribution function. We show how these extensions to the classical theory could be used to (i) observationally constrain the statistical nature of the infall (ii) predict the observed distribution and correlations of substructures in upcoming surveys, (iii) predict the past evolution of the observed distribution of clumps, and finally (iv) weight the relative importance of the intrinsic (via the unperturbed distribution function) and external (tidal and/ or infall) influence of the environment in determining the fate of galaxies.Comment: 35 pages, 12 Postscript figures, accepted for publication by MNRA

Lipschitz normal embedding among superisolated singularities

Any germ of a complex analytic space is equipped with two natural metrics: the outer metric induced by the hermitian metric of the ambient space and the inner metric, which is the associated riemannian metric on the germ. A complex analytic germ is said Lipschitz normally embedded (LNE) if its outer and inner metrics are bilipschitz equivalent. LNE seems to be fairly rare among surface singularities; the only known LNE surface germs outside the trivial case (straight cones) are the minimal singularities. In this paper, we show that a superisolated hypersurface singularity is LNE if and only if its projectivized tangent cone has only ordinary singularities. This provides an infinite family of LNE singularities which is radically different from the class of minimal singularities.Comment: 17 pages, 8 figures. Minor errors and misprints corrected. Comments are welcome

Non parametric reconstruction of distribution functions from observed galactic disks

A general inversion technique for the recovery of the underlying distribution function for observed galactic disks is presented and illustrated. Under the assumption that these disks are axi-symmetric and thin, the proposed method yields the unique distribution compatible with all the observables available. The derivation may be carried out from the measurement of the azimuthal velocity distribution arising from positioning the slit of a spectrograph along the major axis of the galaxy. More generally, it may account for the simultaneous measurements of velocity distributions corresponding to slits presenting arbitrary orientations with respect to the major axis. The approach is non-parametric, i.e. it does not rely on a particular algebraic model for the distribution function. Special care is taken to account for the fraction of counter-rotating stars which strongly affects the stability of the disk. An optimisation algorithm is devised -- generalising the work of Skilling & Bryan (1984) -- to carry this truly two-dimensional ill-conditioned inversion efficiently. The performances of the overall inversion technique with respect to the noise level and truncation in the data set is investigated with simulated data. Reliable results are obtained up to a mean signal to noise ratio of~5 and when measurements are available up to $4 R_{e}$. A discussion of the residual biases involved in non parametric inversions is presented. Prospects of application to observed galaxies and other inversion problems are discussed.Comment: 11 pages, 13 figures; accepted for publication by MNRA

Curve segmentation using directional information, relation to pattern detection

©2005 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.Presented at the 2005 International Conference on Image Processing (ICIP)September 11-14, 2005, Genova, Italy.DOI: 10.1109/ICIP.2005.1530175We propose an extension of the conformal (or geodesic) active contour framework in which the conformal factor depends not only on the position of the curve but also on the direction of its tangent. We describe several properties for variational curve segmentation schemes that justify the construction of optimal conformal factors (i.e., learning) in strong connection with pattern matching. The determination of optimal curves (i.e., segmentation) can be performed using either the calculus of variations or dynamic programming. The technique is illustrated on a road detection problem for different signal to noise ratios