Virialization of matter overdensities within dark energy subsystems: special cases

The virialization of matter overdensities within dark energy subsystems is considered under the restrictive assumptions (i) spherical-symmetric density profiles, (ii) time-independent quintessence equation of state parameter, w, and (iii) nothing but gravitational interaction between dark energy scalar field and matter. In addition, the quintessence subsystem is conceived as made of ``particles'' whose mutual interaction has intensity equal to G(1+3w) and scales as the inverse square of their distance. Then the virial theorem is formulated for subsystems. In the special case of fully clustered quintessence, energy conservation is assumed with regard to either the whole system (global energy conservation), or to the matter subsystem within the tidal potential induced by the quintessence subsystem (partial energy conservation). Further investigation is devoted to a few special values, w=-1/3, -1/2, -2/3, -1. The special case of fully clustered (i.e. collapsing together with the matter) quintessence is studied in detail. The general case of partially clustered quintessence is considered in terms of a degree of quintessence de-clustering, \zeta, ranging from fully clustered (\zeta=0) to completely de-clustered (\zeta=1) quintessence, respectively. The special case of unclustered (i.e. remaining homogeneous) quintessence is also discussed. The trend exhibited by the fractional (virialization to turnaround) radius, \eta, as a function of other parameters, is found to be different from its counterparts reported in earlier attempts. The reasons of the above mentioned discrepancy are discussed.Comment: 44 pages, 8 figure

Evolving statistical systems: application to academic courses

Statistical systems are conceived from the standpoint of statistical mechanics, as made of a (generally large) number of identical units and exhibiting a (generally large) number of different configurations (microstates), among which only equivalence classes (macrostates) are accessible to observations. Further attention is devoted to evolving statistical systems, and a simple case including only a possible event, E, and related opposite event, $\neg$E, is examined in detail. In particular, the expected evolution is determined and compared to the random evolution inferred from a sequence of random numbers, for different sample populations. The special case of radioactive decay is considered and results are expressed in terms of the fractional time, $t/\Delta t$, where the time step, $\Delta t$, is related to the decay probability, $p=p(\Delta t)$. An application is made to data collections from selected academic courses, focusing on the extent to which expected evolutions and model random evolutions fit to empirical random evolutions inferred from data collections. Results could be biased by the assumed number of students who abandoned their course, defined as suitable impostors (SI). Extreme cases related to a lower and an upper limit of the SI number are considered for a time step, $\Delta t=(1/12)$y, where fitting expected evolutions relate to $0.003\le p\le0.200$. In conclusion, evolving statistical systems made of academic courses are similar to poorly populated samples of radioactive nuclides exhibiting equal probabilities, $p$, and time steps, $\Delta t$, where inferred mean lifetimes, $\tau$, and half-life times, $t_{1/2}$, range within $0.37<\tau/{\rm y}<27.73$ and $0.25<t_{1/2}/{\rm y}<19.22$, respectively, and upper limits are related to incomplete data collections.Comment: 31 pages, 3 tables, 10 figure

R fluids

A theory of collisionless fluids is developed in a unified picture, where nonrotating figures with anisotropic random velocity component distributions and rotating figures with isotropic random velocity component distributions, make adjoints configurations to the same system. R fluids are defined and mean and rms angular velocities and mean and rms tangential velocity components are expressed, by weighting on the moment of inertia and the mass, respectively. The definition of figure rotation is extended to R fluids. The generalized tensor virial equations are formulated for R fluids and further attention is devoted to axisymmetric configurations where, for selected coordinate axes, a variation in figure rotation has to be counterbalanced by a variation in anisotropy excess and vice versa. A microscopical analysis of systematic and random motions is performed under a few general hypotheses, by reversing the sign of tangential or axial velocity components of an assigned fraction of particles, leaving the distribution function and other parameters unchanged (Meza 2002). The application of the reversion process to tangential velocity components, implies the conversion of random motion rotation kinetic energy into systematic motion rotation kinetic energy. The application of the reversion process to axial velocity components, implies the conversion of random motion translation kinetic energy into systematic motion translation kinetic energy, and the loss related to a change of reference frame is expressed in terms of systematic (imaginary) motion rotation kinetic energy. A procedure is sketched for deriving the spin parameter distribution (including imaginary rotation) from a sample of observed or simulated large-scale collisionless fluids i.e. galaxies and galaxy clusters.Comment: 29 pages, 2 figure

Clausius' Virial vs. Total Potential Energy in the dynamics of a two-component system

In a gravitational virialized bound system built up of two components, one of which is embedded in the other, the Clausius' virial energy of one subcomponent is not, in general, equal to its total potential energy, as occurs in a single system without external forces. This is the main reason for the presence, in the case of two non-coinciding concentric spheroidal subsystems, of a minimum (in absolute value) in the Clausius' virial of the inner component B, when it assumes a special configuration characterized by a value of its semi-major axis we have named "tidal radius". The physical meaning, connected with its appearance, is to introduce a scale length on the gravity field of the inner subsystem, which is induced from the outer one. Its relevance in the galaxy dynamics has been stressed by demonstrating that some of the main features of the Fundamental Plane may follow as consequence of its existence. More physical insight into the dynamics of a two component system may be got by looking at the location of this scale length inside the plots of the potential energies of each subsystem and of the whole system and by also taking into account the trend of the anti-symmetric residual-energy, that is the difference between the tidal and the interaction-energy of each component. Some thermodynamical arguments related to the inner component are also added to prove as special is the "tidal radius configuration". Moreover the role of the divergency at the center of the two subsystems in obtaining this scale length is considered. For the sake of simplicity the analysis has been performed in the case of a frozen external component even if this constraint does not appear to be too relevant in order to preserve the main results.Comment: New Astronomy, accepte

Homeoidally striated density profiles: sequences of virial equilibrium configurations with constant anisotropy parameters

The formulation of the tensor virial equations is generalized to unrelaxed configurations, where virial equilibrium does not coincide with dynamical (or hydrostatic) equilibrium. Further investigation is devoted to special classes of homeoidally striated ellipsoids, defined as homeoidally striated, Jacobi ellipsoids. In particular, virial equilibrium configurations with constant anisotropy parameters are studied with more detail, including both flattened and elongated, triaxial configurations, and the determination of the related bifurcation points. The explicit expression of different rotation parameters is also determined. An application is made to dark matter haloes hosting giant, galaxies, with regard to assigned initial and final configuration, following and generalizing to many respects a procedure conceived by Thuan & Gott (1975). The dependence of the limiting axis ratios, below which no configuration is allowed for the sequence under consideration, on the change in mass, total energy, and angular momentum, during the evolution, is illustrated in some representative situations. The dependence of axis ratios and rotation parameters on an additional parameter, related to the initial conditions of the density perturbation, is analysed in connection with a few special cases. Within the range of Peebles (1969) rotation parameter, inferred from high-resolution numerical simulations, the shape of dark matter haloes is mainly decided by the amount of anisotropy in residual velocity distribution. On the other hand, the contribution of rotation has only a minor effect on the meridional plane, and no effect on the equatorial plane, as bifurcation points occur for larger values of Peebles (1969) rotation parameter. To this respect, dark matter haloes are found to resemble giant elliptical galaxies.Comment: 43 pages, 8 figures, 6 tables; a reduced version has been accepted for publication on A

O and Fe abundance correlations and distributions inferred for the thick and thin disk

A linear [Fe/H]-[O/H] relation is found for different stellar populations in the Galaxy (halo, thick disk, thin disk) from a data sample obtained in a recent investigation (Ram{\'\i}rez et al. 2013). These correlations support previous results inferred from poorer samples: stars display a "main sequence" expressed as [Fe/H] = $a$[O/H$]+b\mp\Delta b$ where a unit slope, $a=1$, implies a constant [O/Fe] abundance ratio. Oxygen and iron empirical abundance distributions are then determined for different subsamples, which are well explained by the theoretical predictions of multistage closed-(box+reservoir) (MCBR) chemical evolution models by taking into account the found correlations. The interpretation of these distributions in the framework of MCBR models gives us clues about inflow/outflow rates in these different Galactic regions and their corresponding evolution. Outflow rate for the thick and the thin disks are lower than the halo outflow rate. Moreover if the thin disk built up from the thick disk, both systems result of comparable masses. Besides that, the iron-to-oxygen yield ratio and the primary to not primary contribution ratio for the iron production are obtained from the data, resulting consistent with SNII progenitor nucleosynthesis and with the iron production from SNIa supernova events.Comment: 44 pages, 12 tables and 8 figures. A reduced version of the current paper has been accepted for publication on SA

Simple MCBR models of chemical evolution: an application to the thin and the thick disk

Simple MCBR models of chemical evolution are extended to the limit of dominant gas inflow or outflow with respect to gas locked up into long-lived stars and remnants. For an assigned empirical differential oxygen abundance distribution, which can be linearly fitted, a family of theoretical curves is built up with assigned prescriptions. For curves with increasing cut parameter, the gas mass fraction locked up into long-lived stars and remnants is found to attain a maximum and then decrease towards zero as the flow tends to infinity, while the remaining parameters show a monotonic trend. The theoretical integral oxygen abundance distribution is also expressed. An application is performed to the empirical distribution deduced from two different samples of disk stars, for both the thin and the thick disk. The constraints on formation and evolution are discussed in the light of the model. The evolution is tentatively subdivided into four stages, A, F, C, E. The empirical distribution related to any stage is fitted by all curves for a wide range of the cut parameter. The F stage may safely be described by a steady inflow regime, implying a flat theoretical distribution, in agreement with the results of hydrodynamical simulations. Finally, (1) the change of fractional mass due to the extension of the linear fit to the empirical distribution, towards both the (undetected) low-metallicity and high-metallicity tail, is evaluated and (2) the idea of a thick disk-thin disk collapse is discussed, in the light of the model.Comment: 31 pages, 9 tables and 4 figures; accepted for publication on Serbian Astronomical Journa

A numerical fit of analytical to simulated density profiles in dark matter haloes

Analytical and geometrical properties of generalized power-law (GPL) density profiles are investigated in detail. In particular, a one-to-one correspondence is found between mathematical parameters and geometrical parameters. Then GPL density profiles are compared with simulated dark haloes (SDH) density profiles, and nonlinear least-absolute values and least-squares fits involving the above mentioned five parameters (RFSM5 method) are prescribed. More specifically, the sum of absolute values or squares of absolute logarithmic residuals is evaluated on a large number of points making a 5-dimension hypergrid, through a few iterations. The size is progressively reduced around a fiducial minimum, and superpositions on nodes of earlier hypergrids are avoided. An application is made to a sample of 17 SDHs on the scale of cluster of galaxies, within a flat $\Lambda$CDM cosmological model (Rasia et al. 2004). In dealing with the mean SDH density profile, a virial radius, averaged over the whole sample, is assigned, which allows the calculation of the remaining parameters. Using a RFSM5 method provides a better fit with respect to other methods. No evident correlation is found between SDH dynamical state (relaxed or merging) and asymptotic inner slope of the logarithmic density profile or (for SDH comparable virial masses) scaled radius. Mean values and standard deviations of some parameters are calculated, and a comparison with previous results is made with regard to the scaled radius. A certain degree of degeneracy is found in fitting GPL to SDH density profiles. If it is intrinsic to the RFSM5 method or it could be reduced by the next generation of high-resolution simulations, still remains an open question.Comment: 44 pages, 6 figures, updated version with recent results from high-resolution simulations (Diemand et al. 2004; Reed et al. 2005) included in the discussion; accepted for publication on SAJ (Serbian Astronomical Journal