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

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

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

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

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

An application of the tensor virial theorem to hole + vortex + bulge systems

The tensor virial theorem for subsystems is formulated for three-component systems and further effort is devoted to a special case where the inner subsystems and the central region of the outer one are homogeneous, the last surrounded by an isothermal homeoid. The virial equations are explicitly written under additional restrictions. An application is made to hole + vortex + bulge systems, in the limit of flattened inner subsystems. Using the Faber-Jackson relation, the standard $M_{\rm H}$-$\sigma_0$ form is deduced from qualitative considerations. The projected bulge velocity dispersion to projected vortex velocity ratio, $\eta$, as a function of the fractional radius, y_{\rm BV}, and the fractional masses, $m_{\rm BH}$, and $m_{\rm VH}$, is plotted for several cases. It is shown that a fixed value of $\eta$ below the maximum corresponds to two different configurations: a compact bulge on the left and an extended bulge on the right. In addition, for fixed $m_{\rm BH}$ or $m_{\rm BV}$, and $y_{\rm BV}$, more massive bulges are related to larger $\eta$ and vice versa. The model is applied to NGC 4374 and NGC 4486, and the bulge mass is inferred and compared with results from different methods. In presence of a massive vortex $(m_{\rm VH}=5)$, the hole mass has to be reduced by a factor 2-3 with respect to the case of a massless vortex, to get the fit.Comment: 29 pages, 2 tables, and 5 figure