arXiv subjects

Ewa L. Lokas

Publications and source records attributed to Ewa L. Lokas.

103 records · Page 6Linked to original sources

arXiv2002

Structure formation in the quintessential Universe

I review the main characteristics of structure formation in the quintessential Universe. Assuming equation of state w=p/\varrho=$const I provide a brief description of the background cosmology and discuss the linear growth of density perturbations, the strongly nonlinear evolution, the power spectra and rms fluctuations as well as mass functions focusing on the three values w=-1, -2/3 and -1/3. Finally I describe the presently available and future constraints on w.

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arXiv2002

Dark matter distribution in dwarf spheroidal galaxies

We study the distribution of dark matter in dwarf spheroidal galaxies by modelling the moments of their line-of-sight velocity distributions. We discuss different dark matter density profiles, both cuspy and possessing flat density cores. The predictions are made in the framework of standard dynamical theory of two-component (stars and dark matter) spherical systems with different velocity distributions. We compare the predicted velocity dispersion profiles to observations in the case of Fornax and Draco dwarfs. For isotropic models the dark haloes with cores are found to fit the data better than those with cusps. Anisotropic models are studied by fitting two parameters, dark mass and velocity anisotropy, to the data. In this case all profiles yield good fits but the steeper the cusp of the profile, the more tangential is the velocity distribution required to fit the data. To resolve this well-known degeneracy of density profile versus velocity anisotropy we obtain predictions for the kurtosis of the line-of-sight velocity distribution for models found to provide best fits to the velocity dispersion profiles. It turns out that profiles with cores typically yield higher values of kurtosis which decrease more steeply with distance than the cuspy profiles, which will allow to discriminate between the profiles once the kurtosis measurements become available. We also show that with present quality of the data the alternative explanation of velocity dispersions in terms of Modified Newtonian Dynamics cannot yet be ruled out.

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arXiv2001

Velocity dispersions of dwarf spheroidal galaxies: dark matter versus MOND

We present predictions for the line-of-sight velocity dispersion profiles of dwarf spheroidal galaxies and compare them to observations in the case of the Fornax dwarf. The predictions are made in the framework of standard dynamical theory of spherical systems with different velocity distributions. The stars are assumed to be distributed according to Sersic laws with parameters fitted to observations. We compare predictions obtained assuming the presence of dark matter haloes (with density profiles adopted from N-body simulations) versus those resulting from Modified Newtonian Dynamics (MOND). If the anisotropy of velocity distribution is treated as a free parameter observational data for Fornax are reproduced equally well by models with dark matter and with MOND. If stellar mass-to-light ratio of $1 M_{\sun}/L_{\sun}$ is assumed, the required mass of the dark halo is $1.5 \times 10^9 M_{\sun}$, two orders of magnitude bigger than the mass in stars. The derived MOND acceleration scale is $a_0 = 2.1 \times 10^{-8}$ cm/s$^2$. In both cases a certain amount of tangential anisotropy in the velocity distribution is needed to reproduce the shape of the velocity dispersion profile in Fornax.

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arXiv2000

The spherical collapse model in a universe with cosmological constant

We generalize the spherical collapse model for the formation of dark matter halos to apply in a universe with arbitrary positive cosmological constant. We calculate the critical condition for collapse of an overdense region and give exact values of the characteristic densities and redshifts of its evolution.

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arXiv2000

Properties of spherical galaxies and clusters with an NFW density profile

Using the standard dynamical theory of spherical systems, we calculate the properties of spherical galaxies and clusters whose density profiles obey the universal form first obtained in high resolution cosmological N-body simulations by Navarro, Frenk & White. We adopt three models for the internal kinematics: isotropic velocities, constant anisotropy and increasingly radial Osipkov-Merritt anisotropy. Analytical solutions are found for the radial dependence of the mass, gravitational potential, velocity dispersion, energy and virial ratio and we test their variability with the concentration parameter describing the density profile and amount of velocity anisotropy. We also compute structural parameters, such as half-mass radius, effective radius and various measures of concentration. Finally, we derive projected quantities, the surface mass density and line-of-sight as well as aperture velocity dispersion, all of which can be directly applied in observational tests of current scenarios of structure formation. On the mass scales of galaxies, if constant mass-to-light is assumed, the NFW surface density profile is found to fit well Hubble-Reynolds laws. It is also well fitted by Sersic R^(1/m) laws, for m ~ 3, but in a much narrower range of m and with much larger effective radii than are observed. Assuming in turn reasonable values of the effective radius, the mass density profiles imply a mass-to-light ratio that increases outwards at all radii.

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arXiv2000

Formation of cuspy density profiles - a generic feature of collisionless gravitational collapse

Using the formalism of the spherical infall model the structure of collapsed and virialized dark halos is calculated for a variety of scale-free initial conditions. In spite of the scale-free cosmological nature of the problem, the collapse of individual objects is not self-similar. Unlike most of previous calculations the dynamics used here relies only on adiabatic invariants and not on self-similarity. The paper focuses on the structure of the innermost part of the collapsed halos and addresses the problem of central density cusps. The slopes of density profiles at 1% of virial radius are calculated for a variety of cosmological models and are found to vary with the mass of the halos and power spectrum of the initial conditions. The inner slopes range between r^-2.3 and r^-2 with the limiting case of r^-2 reached for the largest masses. The steep cusps found here correspond to the limiting case where all particles move on radial orbits. The introduction of angular momentum will make the density profile shallower. We expect this to resolve the discrepancy found between the calculated profiles and the ones found in high resolution N-body simulations, where the exponent ranges from -0.5 to -1.5. The robust prediction here is that collisionless gravitational collapse in an expanding universe is expected to form density cups and not halos with a core structure.

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arXiv1999

Evolution of density profiles of dark matter halos

I apply the modified spherical infall model to test the dependence of the shape of density profiles of dark matter halos on redshift. The model predicts that the density profile of a halo of a given mass steepens with time and its concentration parameter changes like c~1/(1+z_0)^2.

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arXiv1999

Density profiles of galactic dark halos

I propose a modification of the spherical infall model for the evolution of density fluctuations with initially Gaussian probability distribution and scale-free power spectra. I introduce a generalized form of the initial density distribution around an overdense region and cut it off at half the inter-peak separation accounting in this way for the presence of neighbouring fluctuations. Contrary to the original predictions of the model, resulting density profiles within virial radii no longer have power-law dependence on the distance, but are well fitted by the universal formula of changing slope obtained as a result of N-body simulations. The profiles of halos of a given mass are in general flatter than the corresponding ones from the simulations, but the trend of steeper profiles for smaller masses is reproduced. The profiles of galaxy size objects are in general in better agreement with N-body simulations than those of larger ones.

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arXiv1999

Universal profile of dark matter halos and the spherical infall model

I propose a modification of the spherical infall model for the evolution of density fluctuations with initially Gaussian probability distribution and scale-free power spectra in Einstein-de Sitter universe as developed by Hoffman & Shaham. I introduce a generalized form of the initial density distribution around an overdense region and cut it off at half the inter-peak separation accounting in this way for the presence of the neighbouring fluctuations. Contrary to the original predictions of Hoffman & Shaham the resulting density profiles within virial radii no longer have power-law shape but their steepness increases with distance. The profiles of halos of galactic mass are well fitted by the universal profile formula of changing slope obtained as a result of N-body simulations by Navarro, Frenk & White. The trend of steeper profiles for smaller masses and higher spectral indices is also reproduced. The agreement between the model and simulations is better for smaller masses and lower spectral indices which suggests that galaxies form mainly by accretion while formation of clusters involves merging.

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arXiv1997

Halo profiles from weakly nonlinear initial conditions

Using weakly nonlinear conditional PDF for the density field around an overdense region we find that the expected density contrast around a peak is always smaller while its rms fluctuation larger than in the linear case. We apply these results to the spherical model of collapse as developed by Hoffman & Shaham (1985) and find that in the case of open Universe the effect of weakly nonlinear interactions is to decrease the scale from which a peak gathers mass and the mass itself as well as to steepen the final profile of the virialized protoobject.

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arXiv1997

Evolution of peaks in weakly nonlinear density field and dark halo profiles

Using the two-point Edgeworth series up to second order we construct the weakly nonlinear conditional probability distribution function for the density field around an overdense region. This requires calculating the two-point analogues of the skewness parameter $S_{3}$. We test the dependence of the two-point skewness on distance from the peak for scale-free power spectra and Gaussian smoothing. The statistical features of such conditional distribution are given as the values obtained within linear theory corrected by the terms that arise due to weakly nonlinear evolution. The expected density around the peak is found to be always below the linear prediction while its rms fluctuation is always larger than in the linear case. We apply these results to the spherical model of collapse as developed by Hoffman & Shaham (1985) and find that in general the effect of weakly nonlinear interactions is to decrease the scale from which a peak gathers mass and therefore also the mass itself. In the case of open universe this results in steepening of the final profile of the virialized protoobject.

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arXiv1997

Weakly Nonlinear Density-Velocity Relation

We rigorously derive weakly nonlinear relation between cosmic density and velocity fields up to third order in perturbation theory. The density field is described by the mass density contrast, $\de$. The velocity field is described by the variable $\te$ proportional to the velocity divergence, $\te = - f(Ω)^{-1} H_0^{-1} \nabla\cdot\bfv$, where $f(Ω) \simeq Ω^{0.6}$, $Ω$ is the cosmological density parameter and $H_0$ is the Hubble constant. Our calculations show that mean $\de$ given $\te$ is a third order polynomial in $\te$, $\lan \de \ran|_{\te} = a_1 \te + a_2 (\te^2 - \s_\te^2) + a_3 \te^3$. This result constitutes an extension of the formula $\lan \de \ran|_{\te} = \te + a_2 (\te^2 - \s_\te^2)$, found by Bernardeau~(1992) which involved second order perturbative solutions. Third order perturbative corrections introduce the cubic term. They also, however, cause the coefficient $a_1$ to depart from unity, in contrast with the linear theory prediction. We compute the values of the coefficients $a_p$ for scale-free power spectra, as well as for standard CDM, for Gaussian smoothing. The coefficients obey a hierarchy $a_3 \ll a_2 \ll a_1$, meaning that the perturbative series converges very fast. Their dependence on $Ω$ is expected to be very weak. The values of the coefficients for CDM spectrum are in qualitative agreement with the results of N-body simulations by Ganon et al. (1996). The results provide a method for breaking the $Ω$-bias degeneracy in comparisons of cosmic density and velocity fields such as IRAS-POTENT.

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arXiv1996

Previrialization: Perturbative and N-Body Results

We present a series of N-body experiments which confirm the reality of the previrialization effect. We also use weakly nonlinear perturbative approach to study the phenomenon. These two approaches agree when the rms density contrast, $σ$, is small; more surprisingly, they remain in agreement when $σ\approx 1$. When the slope of the initial power spectrum is $n>-1$, nonlinear tidal interactions slow down the growth of density fluctuations and the magnitude of the suppression increases when $n$ (i.e. the relative amount of small scale power) is increased. For $n<-1$ we see an opposite effect: the fluctuations grow more rapidly than in linear theory. The transition occurs at $n=-1$ when the weakly nonlinear correction to $σ$ is close to zero and the growth rate is close to linear. Our results resolve recent controversy between two N-body studies of previrialization. Peebles (1990) assumed $n=0$ and found strong evidence in support of previrialization, while Evrard \& Crone (1992), who assumed $n=-1$, reached opposite conclusions. As we show here, the initial conditions with $n=-1$ are rather special because the nonlinear effects nearly cancel out for that particular spectrum. In addition to our calculations for scale-free initial spectra, we show results for a more realistic spectrum of Peacock \& Dodds (1994). Its slope near the scale usually adopted for normalization is close to $-1$, so $σ$ is close to linear. Our results retroactively justify linear normalization at 8$h^{-1}$ Mpc, while also demonstrating the danger and limitations of this practice.

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