Papers by antonino del popolo
Int J Mod Phys D, 2005
In a planetary or satellite system, idealized as n small bodies in an initially coplanar with con... more In a planetary or satellite system, idealized as n small bodies in an initially coplanar with concentric orbits around a large central body obeying the Newtonian point-particle mechanics, resonant perturbations will cause a dynamical evolution of the orbital radii except for cases with highly specific mutual relationships. In particular, the most stable situation can be achieved only when each planetary orbit is roughly twice as far from the Sun as the preceding one. This has been empirically observed by Titius (1766) and Bode (1778). By reformulating the problem as a hierarchical sequence of (unrestricted) 3-body problems and considering only the gravitational interactions among the central body and the body of interest and the adjacent outer body in the orbits, it is proved that the resonant perturbations from the outer body will destabilize the inner body (and vice versa) unless its mean orbital radius is a unique and specific multiple of β, the distal multiplier, of the inner body. In this way a sequence of concentric orbits can each stabilize the adjacent inner orbit, and since the outermost orbit is already tied to the collection of the inner orbits by conservation of total angular momentum, the entire configuration is stabilized.
I study the role of shear fields on the evolution of density perturbations by using an analytical... more I study the role of shear fields on the evolution of density perturbations by using an analytical approximate solution for the equations of motion of homogeneous ellipsoids embedded in a homogeneous background. The equations of motion of a homogeneous ellipsoid (Icke 1973; White & Silk 1979, hereafter WS) are modified in order to take account of the tidal field, as done in Watanabe (1993) and then are integrated analytically, similar to what was done in WS. The comparison of the analytical solution with numerical simulations shows that it is a good approximation of the numerical one. This solution is used to study the evolution of the configuration of the ellipsoids, to calculate the evolution of the density contrast and that of the axial peculiar velocity of the ellipsoids for several values of the amplitude of the external tidal field, and is compared again with numerical simulations. In order to calculate the evolution of the density contrast at turnaround and collapse velocity at the epoch of collapse, as a function of the ratio of the initial value of the semi-axes, I use the previously-obtained approximate solution to modify the analytical model proposed by Barrow & Silk (1981) for the ellipsoid evolution in the non-linear regime. The density contrast at turnaround and the collapse velocity are found to be reduced with respect to that found by means of the spherical model. The reduction increases with increasing strength of the external tidal field and with increasing initial asymmetry of the ellipsoids. These last calculations are also compared with numerical solutions and they are again in good agreement with the numerical ones.
We study the effect of the dynamical friction induced by the presence of substructure on the stat... more We study the effect of the dynamical friction induced by the presence of substructure on the statistics of the collapse of density peaks. Applying the results of a recent paper by Antonuccio-Delogu & Colafrancesco (1994), we show that within high-density environments, such as rich clusters of galaxies, the collapse of the low-v peaks is strongly delayed until very late epochs. A bias of dynamical nature thus naturally arises because high-density peaks preferentially collapse to form halos within which visible objects eventually will condense. We then derive a selection function for these collapsing structures. Using this physical selection mechanism, we can calculate the values of the bias coefficient on cluster scales for any hierarchical clustering scenario. For a standard cold dark matter model, we show here that the dynamical bias that we derive can account for a substantial part of the total bias required by observations on cluster scales.
In this paper I study the probability distribution of the gravitational force in gravitational sy... more In this paper I study the probability distribution of the gravitational force in gravitational systems through numerical experiments. I show that Kandrup's (1980) and Antonuccio-Delogu & Atrio-Barandela's (1992) theories describe correctly the stochastic force probability distribution respectively in inhomogeneous and clustered systems. I find equations for the probability distribution of stochastic forces in finite systems, both homogeneous and clustered, which I use to compare the theoretical predictions with Montecarlo simulations of spherically symmetric systems. The agreement between theoretical predictions and simulations proves to be quite satisfactory.
We show how the results given by several authors relatively to the mass of a density peak are cha... more We show how the results given by several authors relatively to the mass of a density peak are changed when small scale substructure induced by dynamical friction are taken into account. The peak mass obtained is compared to the result of Peacock & Heavens (1990) and to the peak mass when dynamical friction is absent to show how these effects conspire to reduce the mass accreted by the peak.
In this paper I extend the results of Ahmad & Cohen (1973), regarding the study of the probabilit... more In this paper I extend the results of Ahmad & Cohen (1973), regarding the study of the probability distribution of the stochastic force in homogeneous gravitational systems, to inhomogeneous gravitational ones. To this aim, I study the stochastic force distribution using N-body realizations of Plummer's spherically symmetric models. I find that the stochastic force distribution obtained for the evolved system is in good agreement with Kandrup's (1980) theory of stochastic force in inhomogeneous systems. Correlation effects that arise during the evolution of the system of particles are well described by Antonuccio-Delogu & Atrio-Barandela's (1992) theory
We solve numerically the equations of motion for the collapse of a shell of baryonic matter, made... more We solve numerically the equations of motion for the collapse of a shell of baryonic matter, made of galaxies and substructure of 10 6 M −10 9 M , falling into the central regions of a cluster of galaxies taking account of dynamical friction. We calculate the evolution of the expansion parameter, a(t), of the perturbation using a coefficient of dynamical friction, η 0 , calculated for a perturbation in which clustering is absent and a coefficient η cl obtained from a clustered one. The effect of the dynamical friction is to slow down the collapse (V. Antonuccio-Delogu & S. Colafrancesco 1994, hereafter AC) producing an observable variation of the parameter of expansion of the shell. The effect increases with increasing η and with the increasing of clustering. Finally, we show how the collapse time depends on η 0 and η cl .
We study the effect of tidal torques on the collapse of density peaks through the equations of mo... more We study the effect of tidal torques on the collapse of density peaks through the equations of motion of a shell of barionic matter falling into the central regions of a cluster of galaxies. We calculate the time of collapse of the perturbation taking into account the gravitational interaction of the quadrupole moment of the system with the tidal field of the matter of the neighbouring proto-clusters. We show that within high-density environments, such as rich clusters of galaxies, tidal torques slow down the collapse of low-ν peaks producing an observable variation in the time of collapse of the shell and, as a consequence, a reduction in the mass bound to the collapsed perturbation. Moreover, the delay of the collapse produces a tendency for less dense regions to accrete less mass, with respect to a classical spherical model, inducing a biasing of over-dense regions toward higher mass. Finally we calculate the bias coefficient using a selection function properly defined showing that for a Standard Cold Dark Matter (SCDM) model this bias can account for a substantial part of the total bias required by observations on cluster scales.
In this paper we fix our attention, on hadron structure, and show that also the strong interactio... more In this paper we fix our attention, on hadron structure, and show that also the strong interaction strength α S , ordinarily called the " (perturba-tive) coupling–constant square " , can be evaluated within our theory, and found to decrease (increase) as the " distance " r decreases (increases). This yields both the confinement of the hadron constituents, and their asymptotic freedom: in qualitative agreement with the experimental evidence. In other terms, our approach leads us, on a purely theoretical ground, to a dependence of α S on r which had been previously found only on phenomenological and heuristic grounds. We expect the above agreement to be also quantitative, on the basis of a few checks performed in this work.
In this paper we extend Chandrasekhar and von Neumann's analysis of the statistics of the gravita... more In this paper we extend Chandrasekhar and von Neumann's analysis of the statistics of the gravitational field to systems in which particles (e.g. stars, galaxies) are not homogeneously distributed. We derive a distribution function W (F,dF/dt) giving the joint probability that a test particle is subject to a force F and an associated rate of change of F given by dF/dt. We calculate the first moment of dF/dt to study the effects of inhomogenity on dynamical friction.
We show how non-radial motions, originating in the outskirts of clusters of galaxies, may reduce ... more We show how non-radial motions, originating in the outskirts of clusters of galaxies, may reduce the discrepancy between the Cold Dark Matter (CDM) predicted X-ray temperature distribution function of clusters of galaxies and the observed one and also the discrepancy between the CDM predicted two-point correlation function of clusters of galaxies and that observed. We compare Edge et al. (1990) and Henry & Arnaud (1991) data with the distribution function of X-ray temperature, calculated using Press & Schechter's (1974-hereafter PS) theory and Evrard's (1990) prescriptions for the mass-temperature relation and taking account of the non-radial motions originating from the gravitational interaction of the quadrupole moment of the protocluster with the tidal field of the matter of the neighboring protostructures. We find that the model produces a reasonable clusters temperature distribution. We compare the two-point cluster correlation function which takes account of the non-radial motions both with that obtained by Sutherland & Efstathiou (1991), from the analysis by Huchra et al. (1990) deep redshift survey, and with the data points for the Automatic Plate Measuring (APM) clusters, computed by Efstathiou et al. (1992a), showing that non-radial motions reduce the discrepancy between the theoretical and the obsservational correlation function.
We study the effect of non-radial motions, originating from the gravitational interaction of the ... more We study the effect of non-radial motions, originating from the gravitational interaction of the quadrupole moment of a protogalaxy with the tidal field of the matter of the neighboring protostructures, on the angular correlation function of galaxies. We calculate the angular correlation function using a Standard Cold Dark Matter (hereafter SCDM) model (Ω=1 , h=0.5, n =1) and we compare it with the angular correlation function of the APM galaxy survey (Maddox et al. 1990; Maddox et al. 1996). We find that taking account of non-radial motions in the calculation of the angular correlation function gives a better agreement of the theoretical prediction of the SCDM model to the observed estimates of large-scale power in the galaxy distribution.
In this paper we study the role of dynamical friction on the evolution of a population of large o... more In this paper we study the role of dynamical friction on the evolution of a population of large objects (m>10 22 g) at heliocentric distances > 70 AU in the Kuiper Belt. We show that the already flat distribution of these objects must flatten further due to non-spherically symmetric distribution of matter in the Kuiper Belt. Moreover the dynamical drag, produced by dynamical friction, causes objects of masses ≥ 10 24 g to lose angular momentum and to fall through more central regions in a timescale ≈ 10 9 yr. This mechanism is able to transport inwards objects of the size of Pluto, supposing it was created beyond 50AU, according to a Stern & Colwell's (1997b) suggestion.
We study the effect of non-radial motions on the mass function, the velocity dispersion function ... more We study the effect of non-radial motions on the mass function, the velocity dispersion function (hereafter VDF) and on the shape of clusters of galaxies using the model introduced in Del Popolo & Gambera (1998a,b, 1999). The mass function of clusters, obtained using the quoted model, is compared with the statistical data by Bahcall & Cen (1992, 1993) and Girardi et al. (1998), while the VDF is compared with the Center for Astrophysics (hereafter CfA) data by Zabludoff et al. (1993) for local clusters and those of Mazure et al. (1996) and Fadda et al. (1996). In both cases the model predictions are in good agreement with the observational data showing once more how non-radial motions can reduce many of the discrepancies between Cold Dark Matter (hereafter CDM) model predictions and observational data. Finally we study the effect of non-radial motions on the intrinsic shape of clusters of galaxies showing that non-radial motions produce clusters less elongated with respect to CDM model in agreement with de Theije et al. (1995, 1997) results.
We study the effect of non-radial motions on the mass function, the velocity dispersion function ... more We study the effect of non-radial motions on the mass function, the velocity dispersion function (hereafter VDF) and on the shape of clusters of galaxies using the model introduced in Del Popolo & Gambera (1998a,b, 1999). The mass function of clusters, obtained using the quoted model, is compared with the statistical data by Bahcall & Cen (1992, 1993) and Girardi et al. (1998), while the VDF is compared with the Center for Astrophysics (hereafter CfA) data by Zabludoff et al. (1993) for local clusters and those of Mazure et al. (1996) and Fadda et al. (1996). In both cases the model predictions are in good agreement with the observational data showing once more how non-radial motions can reduce many of the discrepancies between Cold Dark Matter (hereafter CDM) model predictions and observational data. Finally we study the effect of non-radial motions on the intrinsic shape of clusters of galaxies showing that non-radial motions produce clusters less elongated with respect to CDM model in agreement with de Theije et al. (1995, 1997) results.
We study the nonlinear evolution of a dust ellipsoid embedded in a Ñat Friedmann background unive... more We study the nonlinear evolution of a dust ellipsoid embedded in a Ñat Friedmann background universe , in order to determine the evolution of the density of the ellipsoid as the perturbation associated with it detaches from the general expansion and begins to collapse. We show that while the growth rate of the density contrast of a mass element is enhanced by shear, in agreement with Ho †manÏs 1986 result, the angular momentum acquired by the ellipsoid has the right magnitude to counterbalance the e †ect of the shear. This result conÐrms the previrialization conjecture by showing that initial asphericities and tidal interactions begin to slow the collapse after the system has broken away from the general expansion.
I study the evolution of halo density profiles as a function of time in the SCDM and LCDM cosmolo... more I study the evolution of halo density profiles as a function of time in the SCDM and LCDM cosmologies. Following Del Popolo, I calculate the concentration parameter c ¼ r v /a and study its time evolution. For a given halo mass, I find that cðzÞ/1=ð1 1 zÞ in both the LCDM and SCDM cosmology, in agreement with the analytic model of Bullock et al. and N-body simulations. In both models, a(z) is roughly constant. The present model predicts a stronger evolution of c(z) with respect to the Navarro, Frenk & White model. Finally I show some consequences of the results on galaxy modelling.
Planets orbiting a planetesimal circumstellar disc can migrate inward from their initial position... more Planets orbiting a planetesimal circumstellar disc can migrate inward from their initial positions because of dynamical friction between planets and planetesimals. The migration rate depends on the disc mass and on its time evolution. Planets that are embedded in long-lived planetesimal discs, having total mass of 10 24 –0:01 M (, can migrate inward a large distance and can survive only if the inner disc is truncated or as a result of tidal interaction with the star. In this case the semimajor axis, a, of the planetary orbit is less than 0.1 au. Orbits with larger a are obtained for smaller values of the disc mass or for a rapid evolution (depletion) of the disc. This model may explain not only several of the orbital features of the giant planets that have been discovered in recent years orbiting nearby stars, but also the metallicity enhancement found in several stars associated with short-period planets.
I discuss the effect of non-radial motions on the small-scale peculiar pairwise velocity dispersi... more I discuss the effect of non-radial motions on the small-scale peculiar pairwise velocity dispersions (PVD) of galaxies in a cold dark matter (CDM) model and calculate the PVD for the SCDM model by means of the refined cosmic virial theorem (CVT), taking account of non-radial motions by means of the Del Popolo & Gambera model. I compare the results of the present model with the data from Davis & Peebles, the IRAS value at 1 h 21 Mpc of Fisher et al. and Marzke et al. I show that while the SCDM model disagrees with the observed values, as pointed out by several authors, taking account of non-radial motions produces smaller values for the PVD. At r # 1 h 21 Mpc the result is in agreement with Bartlett & Blanchard. In the light of this last paper, the result may be also read as a strong dependence of the CVT prediction on the model chosen to describe the mass distribution around galaxies, suggesting that the CVT cannot be taken as a direct evidence for a low-density Universe. Similarly to what is shown by Del Popolo & Gambera and Del Popolo et al., the agreement of our model to the observational data is because of a scale-dependent bias induced by the presence of non-radial motions. As the assumptions on which CVT is based have been questioned by several authors, I also calculated the PVD using the redshift distortion in the redshift-space correlation function, j z (r p , p), and compared it with the PVD measured from the Las Campanas Redshift Survey by Jing et al. The result confirms that non-radial motions influence the PVD making them agree better with the observed data.
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Papers by antonino del popolo