The Confluent System Formalism: I.The Mass Function of Objects in the Peak Model

This is the first paper of a series of two devoted to develop a practical method to describe the growth history of bound virialized objects in the gravitational instability scenario without resorting to $N$-body simulations. Here we present the basic tool of this method, ``the confluent system formalism'', which allows us to follow the filtering evolution of peaks in a random Gaussian field of density fluctuations. This is applied to derive the theoretical mass function of objects within the peak model framework. Along the process followed for the derivation of this function, we prove that the Gaussian window is the only one consistent with the peak model ansatz. We also give a well justified derivation of the density of peaks with density contrast upcrossing a given threshold in infinitesimal ranges of scale and correct this scale function for the cloud-in-cloud effect. Finally, we characterize the form of the mass vs. scale and the critical overdensity vs. collapse time relations which are physically consistent with the peak model in an Einstein-de Sitter universe with density field endowed with different power spectra. The result is a fully justified semianalytical mass function which is close to the Press \& Schechter (1974) one giving good fits to $N$-body simulations. But the interest of the confluent system formalism is not merely formal. It allows us to distinguish between accretion and merger events, which is essential for the detailed modelling of the clustering process experienced by objects.Comment: 24 pages, uuencoded compressed postscript file including 4 figures (164 kb). To be published in ApJ, 1st November issu

Are the HI deficient galaxies on the outskirts of Virgo recent arrivals?

The presence on the Virgo cluster outskirts of spiral galaxies with gas deficiencies as strong as those of the inner galaxies stripped by the intracluster medium has led us to explore the possibility that some of these peripheral objects are not newcomers. A dynamical model for the collapse and rebound of spherical shells under the point mass and radial flow approximations has been developed to account for the amplitude of the motions in the Virgo I cluster (VIC) region. According to our analysis, it is not unfeasible that galaxies far from the cluster, including those in a gas-deficient group well to its background, went through its core a few Gyr ago. The implications would be: (1) that the majority of the HI-deficient spirals in the VIC region might have been deprived of their neutral hydrogen by interactions with the hot intracluster medium; and (2) that objects spending a long time outside the cluster cores might keep the gas deficient status without altering their morphology.Comment: Accepted for publication in ApJ. 4 pages, 3 figures. Uses emulateapj

The Effects of the Peak-Peak Correlation on the Peak Model of Hierarchical Clustering

In two previous papers a semi-analytical model was presented for the hierarchical clustering of halos via gravitational instability from peaks in a random Gaussian field of density fluctuations. This model is better founded than the extended Press-Schechter model, which is known to agree with numerical simulations and to make similar predictions. The specific merger rate, however, shows a significant departure at intermediate captured masses. The origin of this was suspected as being the rather crude approximation used for the density of nested peaks. Here, we seek to verify this suspicion by implementing a more accurate expression for the latter quantity which accounts for the correlation among peaks. We confirm that the inclusion of the peak-peak correlation improves the specific merger rate, while the good behavior of the remaining quantities is preserved.Comment: ApJ accepted. 15 pages, including 4 figures. Also available at ftp://pcess1.am.ub.es/pub/ApJ/effectpp.ps.g

Merger vs. Accretion and the Structure of Dark Matter Halos

High-resolution N-body simulations of hierarchical clustering in a wide variety of cosmogonies show that the density profiles of dark matter halos are universal, with low mass halos being denser than their more massive counterparts. This mass-density correlation is interpreted as reflecting the earlier typical formation time of less massive objects. We investigate this hypothesis in the light of formation times defined as the epoch at which halos experience their last major merger. Such halo formation times are calculated by means of a modification of the extended Press & Schechter formalism which includes a phenomenological frontier, Delta_m, between tiny and notable relative mass captures leading to the distinction between merger and accretion. For Delta_m=0.6, we confirm that the characteristic density of halos is essentially proportional to the mean density of the universe at their time of formation. Yet, proportionality with respect to the critical density yields slightly better results for open universes. In addition, we find that the scale radius of halos is also essentially proportional to their virial radius at the time of formation. We show that these two relations are consistent with the following simple scenario. Violent relaxation caused by mergers rearranges the structure of halos leading to the same density profile with universal values of the dimensionless characteristic density and scale radius. Between mergers, halos grow gradually through the accretion of surrounding layers by keeping their central parts steady and expanding their virial radius as the critical density of the universe diminishes.Comment: ApJ, accepted. 14 pages, including 3 figures and 1 table. Also available at http://pcess1.am.ub.es/pub/ApJ/halostruc.ps.g

The nature of dark matter and the density profile and central behavior of relaxed halos

We show that the two basic assumptions of the model recently proposed by Manrique and coworkers for the universal density profile of cold dark matter (CDM) halos, namely that these objects grow inside out in periods of smooth accretion and that their mass profile and its radial derivatives are all continuous functions, are both well understood in terms of the very nature of CDM. Those two assumptions allow one to derive the typical density profile of halos of a given mass from the accretion rate characteristic of the particular cosmology. This profile was shown by Manrique and coworkers to recover the results of numerical simulations. In the present paper, we investigate its behavior beyond the ranges covered by present-day N-body simulations. We find that the central asymptotic logarithmic slope depends crucially on the shape of the power spectrum of density perturbations: it is equal to a constant negative value for power-law spectra and has central cores for the standard CDM power spectrum. The predicted density profile in the CDM case is well fitted by the 3D S\'ersic profile over at least 10 decades in halo mass. The values of the S\'ersic parameters depend on the mass of the structure considered. A practical procedure is provided that allows one to infer the typical values of the best NFW or S\'ersic fitting law parameters for halos of any mass and redshift in any given standard CDM cosmology.Comment: 9 pages, 6 figures, to appear in the ApJ vol. 647, september 20, 2007. Minor changes to match the published versio

Theoretical dark matter halo kinematics and triaxial shape

In a recent paper, Salvador-Sol\'e et al. (2012) have derived the typical inner structure of dark matter haloes from that of peaks in the initial random Gaussian density field, determined by the power-spectrum of density perturbations characterising the hierarchical cosmology under consideration. In the present paper, we extend this formalism to the typical kinematics and triaxial shape of haloes. Specifically, we establish the link between such halo properties and the power-spectrum of density perturbations through the typical shape of peaks. The trends of the predicted typical halo shape, pseudo phase-space density and anisotropy profiles are in good agreement with the results of numerical simulations. Our model sheds light on the origin of the power-law-like pseudo phase-space density profile for virialised haloes.Comment: 18 pages, 6 figures. Published in MNRA

Galaxy And Mass Assembly (GAMA) : refining the local galaxy merger rate using morphological information

KRVS acknowledges the Science and Technology Facilities Council (STFC) for providing funding for this project, as well as the Government of Catalonia for a research travel grant (ref. 2010 BE-00268) to begin this project at the University of Nottingham. PN acknowledges the support of the Royal Society through the award of a University Research Fellowship and the European Research Council, through receipt of a Starting Grant (DEGAS-259586).We use the Galaxy And Mass Assembly (GAMA) survey to measure the local Universe mass-dependent merger fraction and merger rate using galaxy pairs and the CAS (concentration, asymmetry, and smoothness) structural method, which identifies highly asymmetric merger candidate galaxies. Our goals are to determine which types of mergers produce highly asymmetrical galaxies and to provide a new measurement of the local galaxy major merger rate. We examine galaxy pairs at stellar mass limits down to M* = 108 M⊙ with mass ratios of 4:1) the lower mass companion becomes highly asymmetric, whereas the larger galaxy is much less affected. The fraction of highly asymmetric paired galaxies which have a major merger companion is highest for the most massive galaxies and drops progressively with decreasing mass. We calculate that the mass-dependent major merger fraction is fairly constant at ∼1.3–2 per cent within 109.5 < M* < 1011.5 M⊙, and increases to ∼4 per cent at lower masses. When the observability time-scales are taken into consideration, the major merger rate is found to approximately triple over the mass range we consider. The total comoving volume major merger rate over the range 108.0 < M* < 1011.5 M⊙ is (1.2 ± 0.5) × 10−3 h370 Mpc−3 Gyr−1.Publisher PDFPeer reviewe

On the Origin of the Inner Structure of Halos

We calculate by means of the Press-Schechter formalism the density profile developed by dark-matter halos during accretion, i.e., the continuous aggregation of small clumps. We find that the shape of the predicted profile is similar to that shown by halos in high-resolution cosmological simulations. Furthermore, the mass-concentration relation is correctly reproduced at any redshift in all the hierarchical cosmologies analyzed, except for very large halo masses. The role of major mergers, which can cause the rearrangement of the halo structure through violent relaxation, is also investigated. We show that, as a result of the boundary conditions imposed by the matter continuously infalling into the halo during the violent relaxation process, the shape of the density profile emerging from major mergers is essentially identical to the shape the halo would have developed through pure accretion. This result explains why, according to high-resolution cosmological simulations, relaxed halos of a given mass have the same density profile regardless of whether they have had a recent merger or not, and why both spherical infall and hierarchical assembly lead to very similar density profiles. Finally, we demonstrate that the density profile of relaxed halos is not affected either by the capture of clumps of intermediate mass.Comment: 14 pages, 8 figures, accepted for publication in ApJ. Minor changes, matches the published version. To appear in the ApJ August 10, 2003 issu