Search

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. Aim. 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 × 10-22 $3.5_{-1.0}^{+1.3}\times 10^{-22}$ 3.5 − 1.0 + 1.3 × 10 − 22 eV for the particle mass and a lower limit of 5.1-2.8+2.2 × 106M⊙ $5.1^{+2.2}_{-2.8}\times 10^6\,{M_{\odot}}$ 3.5 − 1.0 + 1.3 × 10 − 22 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 ×107M⊙. With these values, they would not be affected by the cosmological constant (ξ < 10−8). However, dark halo masses smaller than 107M⊙ (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 ×103L⊙. 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. [ABSTRACT FROM AUTHOR]

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 acceleration (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 [MVIR]0 = 1.95 [MVIR]0. These results differ appreciably from those derived from a model with cosmological constant equal to zero in a flat universe: [rTA(Λ = 0)]0 = 6.62 [rVIR(Λ = 0)]0 and [MTA(Λ = 0)]0 = 5.26 [MVIR(Λ = 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 [MZA0 = 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]