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.Comment: 13 pages, 9 figures, 3 tables, accepted for publication in MNRAS. Significantly revised, conclusions weakened, predictions for the kurtosis of the line-of-sight velocity distribution adde

The orbital structure of a tidally induced bar

Orbits are the key building blocks of any density distribution and their study helps us understand the kinematical structure and the evolution of galaxies. Here we investigate orbits in a tidally induced bar of a dwarf galaxy, using an $N$-body simulation of an initially disky dwarf galaxy orbiting a Milky Way-like host. After the first pericenter passage, a tidally induced bar forms in the stellar component of the dwarf. The bar evolution is different than in isolated galaxies and our analysis focuses on the period before it buckles. We study the orbits in terms of their dominant frequencies, which we calculate in a Cartesian coordinate frame rotating with the bar. Apart from the well-known x$_1$ orbits we find many other types, mostly with boxy shapes of various degree of elongation. Some of them are also near-periodic, admitting frequency ratios of 4/3, 3/2 and 5/3. The box orbits have various degrees of vertical thickness but only a relatively small fraction of those have banana (i.e. smile/frown) or infinity-symbol shapes in the edge-on view. In the very center we also find orbits known from the potential of triaxial ellipsoids. The elongation of the orbits grows with distance from the center of the bar in agreement with the variation of the shape of the density distribution. Our classification of orbits leads to the conclusion that more than $80 \%$ of them have boxy shapes, while only $8 \%$ have shapes of classical x$_1$ orbits.Comment: 15 pages, 15 figures, accepted for publication in Ap

Tidally induced bars in dwarf galaxies on different orbits around a Milky Way-like host

Bars in galaxies may develop through a global instability or due to an interaction with another system. We study bar formation in disky dwarf galaxies orbiting a Milky Way-like galaxy. We employ $N$-body simulations to study the impact of initial orbital parameters: the size of the dwarf galaxy orbit and the inclination of its disc with respect to the orbital plane. In all cases a bar develops in the center of the dwarf during the first pericenter on its orbit around the host. Between subsequent pericenter passages the bars are stable, but at the pericenters they are usually weakened and shortened. The initial properties and details of the further evolution of the bars depend heavily on the orbital configuration. We find that for the exactly prograde orientation, the strongest bar is formed for the intermediate-size orbit. On the tighter orbit, the disc is too disturbed and stripped to form a strong bar. On the wider orbit, the tidal interaction is too weak. The dependence on the disc inclination is such that weaker bars form in more inclined discs. The bars experience either a very weak buckling or none at all. We do not observe any secular evolution, possibly because the dwarfs are perturbed at each pericenter passage. The rotation speed of the bars can be classified as slow ($R_\mathrm{CR}/l_\mathrm{bar}\sim2-3$). We attribute this to the loss of a significant fraction of the disc's rotation during the encounter with the host galaxy.Comment: 17 pages, 14 figures, accepted to Ap

Previrialization

We propose a method to solve the "previrialization" problem of whether the non-linear interactions between perturbations at different scales increase or decrease the rate of growth of structure. As a measure of this effect we calculate the weakly non-linear corrections to the variance of the probability distribution function of the density field. We assume Gaussian initial conditions and use perturbative expansions to calculate these corrections for scale-free initial power spectra. As a realistic example, we also compute the corrections for the spectrum proposed by Peacock \& Dodds (1994). The calculations are performed for both a Gaussian and a top-hat smoothing of the evolved fields. We show that the effect of weakly non-linear interactions depends strongly on the spectral index; they increase the variance for the spectral index n=-2, but decrease it for n \ge -1. Finally, we compare our perturbative calculations to N-body simulations and a formula of a type proposed by Hamilton et al. (1991)

Nonlinear Velocity-Density Coupling: Analysis by Second-Order Perturbation Theory

Cosmological linear perturbation theory predicts that the peculiar velocity $V(x)$ and the matter overdensity $\delta(x)$ at a same point $x$ are statistically independent quantities, as log as the initial density fluctuations are random Gaussian distributed. However nonlinear gravitational effects might change the situation. Using framework of second-order perturbation theory and the Edgeworth expansion method, we study local density dependence of bulk velocity dispersion that is coarse-grained at a weakly nonlinear scale. For a typical CDM model, the first nonlinear correction of this constrained bulk velocity dispersion amounts to $\sim 0.3\delta$ (Gaussian smoothing) at a weakly nonlinear scale with a very weak dependence on cosmological parameters. We also compare our analytical prediction with published numerical results given at nonlinear regimes.Comment: 16 pages including 2 figures, ApJ 537 in press (July 1

Adventures of a tidally induced bar

Using N-body simulations, we study the properties of a bar induced in a discy dwarf galaxy as a result of tidal interaction with the Milky Way. The bar forms at the first pericentre passage and survives until the end of the evolution at 10 Gyr. Fourier decomposition of the bar reveals that only even modes are significant and preserve a hierarchy so that the bar mode is always the strongest. They show a characteristic profile with a maximum, similar to simulated bars forming in isolated galaxies and observed bars in real galaxies. We adopt the maximum of the bar mode as a measure of the bar strength and we estimate the bar length by comparing the density profiles along the bar and perpendicular to it. The bar strength and the bar length decrease with time, mainly at pericentres, as a result of tidal torques acting at those times and not to secular evolution. The pattern speed of the bar varies significantly on a time-scale of 1 Gyr and is controlled by the orientation of the tidal torque from the Milky Way. The bar is never tidally locked, but we discover a hint of a 5/2 orbital resonance between the third and fourth pericentre passage. The speed of the bar decreases in the long run so that the bar changes from initially rather fast to slow in the later stages. The boxy/peanut shape is present for some time and its occurrence is preceded by a short period of buckling instability