Surface term effects on mass estimators

Context. We propose a way of estimating the mass contained in the volume occupied by a sample of galaxies in a virialized system. Aims. We analyze the influence of surface effects and the contribution of the cosmological constant terms on our mass estimations of galaxy systems. Methods. We propose two equations that contain surface terms to estimate galaxy sample masses. When the surface terms are neglected, these equations provide the so-called virial and projected masses. Both equations lead to a single equation that allows sample masses to be estimated without the need for calculating surface terms. Sample masses for some nearest galaxy groups are estimated and compared with virialized masses determined from turn-around radii and results of a spherical infall model. Results. Surface effects have a considerable effect on the mass estimations of the studied galaxy groups. According to our results, they lead sample masses of some groups to being less than half the virial mass estimations and even less than 10% of projected mass estimations. However, the contributions of cosmological constant terms to mass estimations are smaller than 2% for the majority of the virialized groups studied. Our estimations are in agreement with virialized masses calculated from turn-around radii. Virialized masses for complexes were found to be: (8.9 +/- 2.8) x 10(11) M-circle dot for the Milky Way - M31; (12.5 +/- 2.5) x 10(11) M-circle dot for M81 - NGC 2403; (21.5 +/- 7.7) x 10(11) M-circle dot. for Cantaurs A - M83; and (7.9 +/- 2.6) x 10(11) M-circle dot. for IC 324 - Maffei. Conclusions. The nearest galaxy groups located inside a sphere of 5 Mpc have been addressed to explore the performance of our mass estimator. We have seen that surface effects make mass estimations of galaxy groups rather smaller than both virial and projected masses. In mass calculations, cosmological constant terms can be neglected; nevertheless, the collapse of cold dark matter leading to virialized structures is strongly affected by the cosmological constant. We have also seen that, if mass density were proportional to luminosity density on different scales in the Universe, the 5 Mpc sphere would have a mean density close to that of the sphere region containing galaxies and systems of galaxies; thus, the rest of the sphere could contain regions of low-mass dark halos with similar mass density. This mass density would be about 4.5 times greater than that of the matter background of the Universe at present

Effects of the cosmological constant on cold dark matter clusters

Context. Cold dark matter inhomogeneities are considered in a homogeneous background of matter, radiation, and the cosmological constant in a flat universe. Aims. We investigate the influence of the cosmological constant on the non-linear collapse of cold dark matter clusters. Methods. For simplicity, a spherical infall model has been used to describe the collapse of non-relativistic mass shells; besides, an average distribution of density around a cluster of galaxies has been taken. Boundary conditions are imposed by the solution of the linearized equation for the growth of matter perturbations and by the cold dark matter power spectrum. Results. For an average cluster, the radii of shells and masses enclosed by them have been obtained at their zero proper accelera- tion (ZA) redshifts, at their turn-around (TA) redshifts and at their virialization (VIR) redshifts. According to our results at present, the shell that reaches its turn-around point shows [rTA]0 = 6.85 Mpc and [MTA]0 = 6.76 × 1014 M¿. The virializing shell fulfills [rTA]0 = 4.57[rVIR]0 and [MTA]0 = 1.95[MVIR]0. These results differ appreciably from those derived from a model with cosmolog- ical constant equal to zero in a flat universe: [rTA(¿ = 0)]0 = 6.62[rVIR(¿ = 0)]0 and [MTA(¿ = 0)]0 = 5.26[MVIR(¿ = 0)]0; this discrepancy could be considered as a new independent proof of the existence of dark energy. The shell with zero proper acceleration presents [rZA ]0 = 1.59 [rTA ]0 and [MZA ]0 = 1.63 [MTA ]0 . We have found that there is a limit to the mass of the average cluster, which is able to virialize; its value is {MVIR}MAX = 8.1 × 1014 M¿. As expected, we found that shells present null proper acceleration at redshift values that are smaller than 0.755. Conclusions. We have noticed that the cosmological constant imposes an upper limit for the mass enclosed by shells, which are able to reach zero proper velocity. Hence, this mass is the maximum mass of the virialized core, {MVIR}MAX. For the average cluster addressed in this work, the value is 2.34 times the mass of the virialized core at present. Shells enclosing masses M > {MVIR}MAX achieve zero proper acceleration and speed up, moving away from the virialized core, and never reach a turn-around point. Shells with M » {MVIR}MAX show zero proper aceleration at redshifts close to that at which the universe background acceleration is null. Finally, we have found that the relation between shell proper velocities and their radii can be adjusted by a straight line at z = 0 and from approximately 20 up to 40 Mpc; however, this line does not intercept the origin as velocities due to the Hubble flux do

About the stability of the dodecatoplet

A new investigation is done of the possibility of binding the "dodecatoplet", a system of six top quarks and six top antiquarks, using the Yukawa potential mediated by Higgs exchange. A simple variational method gives a upper bound close to that recently estimated in a mean-field calculation. It is supplemented by a lower bound provided by identities among the Hamiltonians describing the system and its subsystems.Comment: 5 pages, two figures merged, refs. added, typos correcte

Mass limits for dark clusters of degenerate fermions

We calculate the range of possible masses for dark spheres of bound fully degenerate fermions as a function of the fermion mass. The cosmological constant is included in our calculations. We deduce that the minimum fermion mass that is able to give rise to degenerate fermion clusters is ~0.02   g−1/4   eV, where g is the spin degeneracy parameter. We show that degenerate fermions of mc2 ≈ (15−30)   g−1/4   eV can build bound degenerate dark haloes that could reproduce the values of the rotation velocities of galaxies. The masses and radii derived for these degenerate dark haloes of typical galaxies, without considering any cosmological information, agree with the Jeans masses and radii of a cosmological background of ~(20−30)   g−1/4   eV degenerate fermions at redshift z ≈ 50. However, degenerate fermion objects of 1015   M⊙ composed of these particles are too small to constitute the dark halo of galaxy clusters. We also derive degeneracy conditions for hot and cold dark matter fermions

Bose–Einstein condensate haloes embedded in dark energy

Context. We have studied clusters of self-gravitating collisionless Newtonian bosons in their ground state and in the presence of the cosmological constant to model dark haloes of dwarf spheroidal (dSph) galaxies. Aims. We aim to analyse the influence of the cosmological constant on the structure of these systems. Observational data of Milky Way dSph galaxies allow us to estimate the boson mass. Methods. We obtained the energy of the ground state of the cluster in the Hartree approximation by solving a variational problem in the particle density. We have also developed and applied the virial theorem. Dark halo models were tested in a sample of 19 galaxies. Galaxy radii, 3D deprojected half-light radii, mass enclosed within them, and luminosity-weighted averages of the square of line-of-sight velocity dispersions are used to estimate the particle mass. Results. Cosmological constant repulsive effects are embedded in one parameter ξ. They are appreciable for ξ > 10−5. Bound structures appear for ξ ≤ ξc = 1.65 × 10−4, what imposes a lower bound for cluster masses as a function of the particle mass. In principle, these systems present tunnelling through a potential barrier; however, after estimating their mean lifes, we realize that their existence is not affected by the age of the Universe. When Milky Way dSph galaxies are used to test the model, we obtain 3.5_{-1.0}^{+1.3}\times 10^{-22} eV for the particle mass and a lower limit of 5.1^{+2.2}_{-2.8}\times 10^6\,{M_{\odot}} for bound haloes. Conclusions. Our estimation for the boson mass is in agreement with other recent results which use different methods. From our particle mass estimation, the treated dSph galaxies would present dark halo masses ~5–11 ×107 M⊙. With these values, they would not be affected by the cosmological constant (ξ 10−5) would already feel their effects. Our model that includes dark energy allows us to deal with these dark haloes. Assuming quantities averaged in the sample of galaxies, 10−5 < ξ ≤ ξc dark haloes would contain stars up to ~8–15 kpc with luminosities ~9–4 ×103 L⊙. Then, their observation would be complicated. The comparison of our lower bound for dark halo masses with other bounds based on different arguments, leads us to think that the cosmological constant is actually the responsible of limiting the halo mass

Dark energy and limit of existence of self-gravitating dark matter clusters: Fermions and bosons

The stability of any self-gravitating cluster of matter is affected by the repulsive effect of the so-called dark energy. Using a simple method we estimate the limit of existence of Newtonian clusters formed by pure fermion or boson populations in their ground state. These clusters simulate lumps of dark matter. As the length scale of the clusters is limited by the effect of dark energy, this implies a lower bound for their mass. From these bounds for the clusters one can infer constraints for the mass of the underlying constituent dark matter particle. The computations are carried out comparing two characteristic length scales which provide an order of magnitude for this problem. The repulsive effect of dark energy is implemented by using an up-to-date value of the cosmological constant. For both fermions and bosons, the condition of existence is expressed in a similar way and a significant common mass scale is identified

Dark energy versus

We explore the possibility of discriminating dark energy models from the study of the growth of matter perturbations. For the sake of simplicity, instead of dealing with a great number of models, we have chosen a simple model of dark energy ($p_x=\omega_0\rho_{x}^{\gamma}$, with $\omega_00$; px, and $\rho_x$ being pressure and energy density), which is able to reproduce a great number of different behaviours. A combination of WMAP data with other results have been used to estimate model parameters. The study has been made for collapsing shells in spherical clusters virialized at redshifts $z=1$, 0.1 and 0.025 with line-of-sight velocity dispersion $\sigma_{\rm los}= 750$ and $1000~\rm km\, s^{-1}$. According to shell velocities, our dark energy models are clearly differentiated from the $\Omega_{\rm m0}=1$ model (the greater the $\sigma_{\rm los}$ is, the more differentiated the models are). However, the differences among dark energy models are not so large. From our results, the nearest clusters with large $\sigma_{\rm los}$ are the idoneous ones to discriminate models. In fact, we think that from observations of caustics in nearby spherical clusters, it would be possible to make an estimation of $\Omega_{\rm m0}$.

Présentation des Actes de la table-ronde de mai 1987

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