The Mass Function of Cosmic Structures with Non-Spherical Collapse

Non-spherical dynamical approximations and models for the gravitational collapse are used to extend the well-known Press \& Schechter (PS) approach, in order to determine analytical expressions for the mass function of cosmic structures. The problem is rigorously set up by considering the intrinsic Lagrangian nature of the mass function. The Lagrangian equations of motion of a cold and irrotational fluid in single-stream regime show that the shear, which is non-locally determined by all the matter field, is the quantity which characterizes non-spherical perturbations. The Zel'dovich approximation, being a self-consistent first-order Lagrangian and local one, is used as a suitable guide to develop realistic estimates of the collapse time of a mass clump, starting from the local initial values of density and shear. Both Zel'dovich-based \an\ and models and the homogeneous ellipsoidal model predict that more large-mass objects are expected to form than the usual PS relation. In particular, the homogeneous ellipsoid model is consistent at large masses with a Press \& Schechter mass function with a lower value of the \dc\ parameter, in the range 1.4$\div$1.6. This gives a dynamical explanation of why lower \dc\ values have been found to fit the results of several N-body simulations. When more small-scale structure is present, highly non-linear dynamical effects can effectively slow down the collapse rate of a perturbation, increasing the effective value of \dc. This may have interesting consequences on the abundance of large-mass high-redshift objects.Comment: 16 pages+5 figures, uuencoded postscript file, submitted to Ap

Observational Support for the Gurzadyan-Kocharyan Relation in Clusters of Galaxies

We show that observational data for four Abell clusters of galaxies support the Gur\-za\-dyan-Kocharyan relation between the Hausdorff dimension and the dynamical properties of a galaxy system. The Hausdorff dimension is calculated using the two-point correlation function, while the dynamical parameters are estimated using available data and reasonable assumptions on the mass function of galaxies. This result can have essential consequences in the understanding of the dynamical mechanisms that determine the fractal distribution of galaxies.Comment: 5 pages, uuencoded postscript file with figures, SISSA Preprint 72/94/A, A&A Letters in pres

A Lagrangian Dynamical Theory for the Mass Function of Cosmic Structures: I Dynamics

A new theory for determining the mass function of cosmic structures is presented. It relies on a realistic treatment of collapse dynamics. Gravitational collapse is analyzed in the Lagrangian perturbative framework. Lagrangian perturbations provide an approximation of truncated type, i.e. small-scale structure is filtered out. The collapse time is suitably defined as the instant at which orbit crossing takes place. The convergence of the Lagrangian series in predicting the collapse time of a homogeneous ellipsoid is demonstrated; it is also shown that third-order calculations are necessary in predicting collapse. Then, the Lagrangian prediction, with a correction for quasi-spherical perturbations, can be used to determine the collapse time of a homogeneous ellipsoid in a fast and precise way. Furthermore, ellipsoidal collapse can be considered as a particular truncation of the Lagrangian series. Gaussian fields with scale-free power spectra are then considered. The Lagrangian series for the collapse time is found to converge when the collapse time is not large. In this case, ellipsoidal collapse gives a fast and accurate approximation of the collapse time; spherical collapse is found to poorly reproduce the collapse time, even in a statistical sense. Analytical fits of the distribution functions of the inverse collapse times, as predicted by the ellipsoid model and by third-order Lagrangian theory, are given. These will be necessary for a determination of the mass function, which will be given in paper II.Comment: 18 pages, Latex, uses mn.sty and psfig, 7 postscript figures (fig. 2 and 3 not complete). Revised version, stylistic changes. MNRAS, in pres

The Cosmological Mass Function with 1D Gravity

The cosmological mass function problem is analyzed in full detail in the case of 1D gravity, with analytical, semi-analytical and numerical techniques. The extended Press & Schechter theory is improved by detailing the relation between smoothing radius and mass of the objects. This is done by introducing in the formalism the concept of a growth curve for the objects. The predictions of the extended Press & Schechter theory are compared to large N-body simulations of flat expanding 1D universes with scale-free power spectra of primordial perturbations. The collapsed objects in the simulations are located with a clump-finding algorithm designed to find regions that have undergone orbit crossing or that are in the multi-stream regime (these are different as an effect of the finite size of the multi-stream regions). It is found that the semi-analytical mass function theory, which has no free parameters, is able to recover the properties of collapsed objects both statistically and object by object. In particular, the predictions of regions in orbit crossing are optimized by the use of Gaussian filtering, while the use of sharp k-space filtering apparently allows to reproduce the larger multi-stream regions. The mass function theory does not reproduce well the clumps found with the standard friends-of-friends algorithm; however, the performance of this algorithm has not been thoroughly tested in the 1D cosmology. Our preliminary analyses of the 3D case confirms that the techniques developed in this paper are precious in understanding the cosmological mass function problem in 3D.Comment: 25 pages, revtex, postscript figures included, in press on Physical Review

Interpreting the possible break in the Black Hole - Bulge mass relation

Recent inspections of local available data suggest that the almost linear relation between the stellar mass of spheroids ($M_{\rm sph}$) and the mass of the super massive Black Holes (BHs) residing at their centres, shows a break below $M_{\rm sph} \sim 10^{10}\ {\rm M}_\odot$, with a steeper, about quadratic relation at smaller masses. We investigate the physical mechanisms responsible for the change in slope of this relation, by comparing data with the results of the semi-analytic model of galaxy formation MORGANA, which already predicted such a break in its original formulation. We find that the change of slope is mostly induced by effective stellar feedback in star-forming bulges. The shape of the relation is instead quite insensitive to other physical mechanisms connected to BH accretion such as disc instabilities, galaxy mergers, Active Galactic Nucleus (AGN) feedback, or even the exact modelling of accretion onto the BH, direct or through a reservoir of low angular momentum gas. Our results support a scenario where most stars form in the disc component of galaxies and are carried to bulges through mergers and disc instabilities, while accretion onto BHs is connected to star formation in the spheroidal component. Therefore, a model of stellar feedback that produces stronger outflows in star-forming bulges than in discs will naturally produce a break in the scaling relation. Our results point to a form of co-evolution especially at lower masses, below the putative break, mainly driven by stellar feedback rather than AGN feedback.Comment: MNRAS accepted, 10 pages, 6 figures, 1 tabl

LA FUNZIONE DI MASSA COSMOLOGICA

1995/1996VIII Ciclo1969Versione digitalizzata della tesi di dottorato cartacea

The Formation of Supermassive Black Holes from Population III.1 Seeds. I. Cosmic Formation Histories and Clustering Properties

We calculate cosmic distributions in space and time of the formation sites of the first, "Pop III.1" stars, exploring a model in which these are the progenitors of all supermassive black holes (SMBHs), seen in the centers of most large galaxies. Pop III.1 stars are defined to form from primordial composition gas in dark matter minihalos with $\sim10^6\:M_\odot$ that are isolated from neighboring astrophysical sources by a given isolation distance, $d_{\rm{iso}}$. We assume Pop III.1 sources are seeds of SMBHs, based on protostellar support by dark matter annihilation heating that allows them to accrete a large fraction of their minihalo gas, i.e., $\sim10^5\:M_\odot$. Exploring $d_{\rm{iso}}$ from $10 - 100\:\rm{kpc}$ (proper distances), we predict the redshift evolution of Pop III.1 source and SMBH remnant number densities. The local, $z=0$ density of SMBHs constrains $d_{\rm{iso}}\lesssim 100\:\rm{kpc}$ (i.e., $3\:\rm{Mpc}$ comoving distance at $z\simeq30$). In our simulated ($\sim60\:\rm{Mpc}$)$^3$ comoving volume, Pop III.1 stars start forming just after $z=40$. Their formation is largely complete by $z\simeq25$ to $20$ for $d_{\rm{iso}}=100$ to $50\:\rm{kpc}$. We follow source evolution to $z=10$, by which point most SMBHs reside in halos with $\gtrsim10^8\:M_\odot$. Over this period, there is relatively limited merging of SMBHs for these values of $d_{\rm{iso}}$. We also predict SMBH clustering properties at $z=10$: feedback suppression of neighboring sources leads to relatively flat angular correlation functions.Comment: 18 pages, 10 figures, MNRAS accepte

Environmental Effects on Local Active Galactic Nuclei

Using an extensive sample of nearby galaxies (the Nearby Galaxies Catalog, by Tully), we investigate the environment of the galaxies hosting low-luminosity AGNs (Seyferts and LINERs). We define the local galaxy density, adopting a new correction for the incompleteness of the galaxy sample at large distances. We consider both a complete sample of bright and nearby AGNs, identified from the nuclear spectra obtained in available wide optical spectroscopic surveys, and a complete sample of nearby Seyferts. Basically, we compare the local galaxy density distributions of the AGNs with those of non-AGN samples, chosen in order to match the magnitude and morphological type distributions of the AGN samples. We find, only for the early-type spirals more luminous than $\sim M^*$, that both LINERs and Seyferts tend to reside in denser environments on all the scales tested, from tenths of Mpc to a few Mpc; moreover Seyferts show an enhanced small-scale density segregation with respect to LINERs. This gives support to the idea that AGNs can be stimulated by interactions. On larger scales, tens of Mpc, we find that the AGNs hosted in luminous early-type spirals show a tendency to stay near the center of the Local Supercluster. Finally we discuss the interpretations of our findings and their consequences for some possible scenarios of AGN formation and evolution and for the problem of how AGNs trace the large-scale structures.Comment: 16 pages+3 figures, uuencoded postscript file, preprint SISSA 76/94/A , ApJ November 20, 199

Mass function of dormant black holes and the evolution of the Active Galactic Nuclei

We derive the mass function of the relic black holes and compared with that of the Massive Dark Objects in galaxies. Under the assumption that accretion onto massive BH's powers the Active Galactic Nuclei, the mass function of the BH responsibile for the past activity of QSO/AGN is computed. Our results support the scenario in which the QSO phase has exclusively occurred in every proto-elliptical.Comment: 10 pages, 8 Figures. Version improved with referee comments. J. Accepted on MNRA