The distribution of two-dimensional eccentricity of Sunyaev-Zeldovich Effect and X-ray surface brightness profiles

With the triaxial density profile of dark matter halos and the corresponding equilibrium gas distribution, we derive two-dimensional Sunyaev-Zeldovich (SZ) effect and X-ray surface brightness profiles for clusters of galaxies. It is found that the contour map of these observables can be well approximated by a series of concentric ellipses with scale-dependent eccentricities. The statistical distribution of their eccentricities (or equivalently axial ratios) is analyzed by taking into account the orientation of clusters with respect to the line of sight and the distribution of the axial ratios and the concentration parameters of dark matter halos. For clusters of mass $10^{13}h^{-1}{M}_{\odot}$ at redshift $z=0$, the axial ratio is peaked at $\eta \sim 0.9$ for both SZ and X-ray profiles. For larger clusters, the deviation from circular distributions is more apparent, with $\eta$ peaked at $\eta \sim 0.85$ for $M=10^{15}h^{-1}{M}_{\odot}$. To be more close to observations, we further study the axial-ratio distribution for mass-limited cluster samples with the number distribution of clusters at different redshifts described by a modified Press-Schechter model. For a mass limit of value $M_{lim}=10^{14}h^{-1}{M}_{\odot}$, the average axial ratio is $\sim 0.84$ with a tail extended to $\eta \sim 0.6$. With fast advance of high quality imaging observations of both SZ effect and X-ray emissions, our analyses provide a useful way to probe cluster halo profiles and therefore to test theoretical halo-formation models.Comment: 28 pages, 6 figures. Accepted for publication in the Astrophysical Journa

The Pattern Speed of the Galactic Bar

Most late-type stars in the solar neighborhood have velocities similar to the local standard of rest (LSR), but there is a clearly separated secondary component corresponding to a slower rotation and a mean outward motion. Detailed simulations of the response of a stellar disk to a central bar show that such a bi-modality is expected from outer-Lindblad resonant scattering. When constraining the run of the rotation curve by the proper motion of Sgr A* and the terminal gas velocities, the value observed for the rotation velocity separating the two components results in a value of (53+/-3)km/s/kpc for the pattern speed of the bar, only weakly dependent on the precise values for Ro and bar angle phi.Comment: 5 pages LaTeX, 2 Figs, accepted for publication in ApJ Letter

Galactic rotation curves in modified gravity with non-minimal coupling between matter and geometry

We investigate the possibility that the behavior of the rotational velocities of test particles gravitating around galaxies can be explained in the framework of modified gravity models with non-minimal matter-geometry coupling. Generally, the dynamics of test particles around galaxies, as well as the corresponding mass deficit, is explained by postulating the existence of dark matter. The extra-terms in the gravitational field equations with geometry-matter coupling modify the equations of motion of test particles, and induce a supplementary gravitational interaction. Starting from the variational principle describing the particle motion in the presence of the non-minimal coupling, the expression of the tangential velocity of a test particle, moving in the vacuum on a stable circular orbit in a spherically symmetric geometry, is derived. The tangential velocity depends on the metric tensor components, as well as of the coupling function between matter and geometry. The Doppler velocity shifts are also obtained in terms of the coupling function. If the tangential velocity profile is known, the coupling term between matter and geometry can be obtained explicitly in an analytical form. The functional form of this function is obtained in two cases, for a constant tangential velocity, and for an empirical velocity profile obtained from astronomical observations, respectively. Therefore, these results open the possibility of directly testing the modified gravity models with non-minimal coupling between matter and geometry by using direct astronomical and astrophysical observations at the galactic or extra-galactic scale.Comment: 8 pages, accepted for publication in PR

Does the Second Caustic Ring of Dark Matter Cause the Monoceros Ring of Stars ?

Caustic rings of dark matter were predicted to exist in the plane of the Galaxy at radii $a_n \simeq 40 {\rm kpc}/n$ for $n = 1,2,3 ..$. The recently discovered Monoceros Ring of stars is located near the $n=2$ caustic, prompting us to consider a possible connection between these two objects. We identify two processes through which the Monoceros Ring of stars may have formed. One process is the migration of gas to an angular velocity minimum at the caustic leading to enhanced star formation there. The other is the adiabatic deformation of star orbits as the caustic slowly grows in mass and radius. The second process predicts an order 100% enhancement of the density of disk stars at the location of the caustic ring.Comment: 21 pages, 3 figure

The Effect of the Outer Lindblad Resonance of the Galactic Bar on the Local Stellar Velocity Distribution

Hydro-dynamical modeling of the inner Galaxy suggest that the radius of the outer Lindblad resonance (OLR) of the Galactic bar lies in the vicinity of the Sun. How does this resonance affect the distribution function in the outer parts of a barred disk, and can we identify any effect of the resonance in the velocity distribution f(v) actually observed in the solar neighborhood? To answer these questions, detailed simulations of f(v) in the outer parts of an exponential stellar disks with nearly flat rotation curves and a rotating central bar have been performed. For a model resembling the old stellar disk, the OLR causes a distinct feature in f(v) over a significant fraction of the outer disk. For positions <2kpc outside the OLR radius and at bar angles of \~10-70 degrees, f(v) inhibits a bi-modality between the low-velocity stars moving like the local standard of rest (LSR) and a secondary mode of stars predominantly moving outward and rotating more slowly than the LSR. Such a bi-modality is indeed present in f(v) inferred from the Hipparcos data for late-type stars in the solar neighborhood. If one interpretes this observed bi-modality as induced by the OLR -- and there are hardly any viable alternatives -- then one is forced to deduce that the OLR radius is slightly smaller than Ro. Moreover, by a quantitative comparison of the observed with the simulated distributions one finds that the pattern speed of the bar is 1.85+/-0.15 times the local circular frequency, where the error is dominated by the uncertainty in bar angle and local circular speed. Also other, less prominent but still significant, features in the observed f(v) resemble properties of the simulated velocity distributions, in particular a ripple caused by orbits trapped in the outer 1:1 resonance.Comment: 14 pages, 10 figures (Fig.2 in full resolution available upon request), accepted for publication in A

Why do starless cores appear more flattened than protostellar cores?

We evaluate the intrinsic three dimensional shapes of molecular cores, by analysing their projected shapes. We use the recent catalogue of molecular line observations of Jijina et al. and model the data by the method originally devised for elliptical galaxies. Our analysis broadly supports the conclusion of Jones et al. that molecular cores are better represented by triaxial intrinsic shapes (ellipsoids) than biaxial intrinsic shapes (spheroids). However, we find that the best fit to all of the data is obtained with more extreme axial ratios ($1:0.8:0.4$) than those derived by Jones et al. More surprisingly, we find that starless cores have more extreme axial ratios than protostellar cores -- starless cores appear more `flattened'. This is the opposite of what would be expected from modeling the freefall collapse of triaxial ellipsoids. The collapse of starless cores would be expected to proceed most swiftly along the shortest axis - as has been predicted by every modeller since Zel'dovich - which should produce more flattened cores around protostars, the opposite of what is seen.Comment: 7 pages, 3 figure

Thermodynamics of the self-gravitating ring model

We present the phase diagram, in both the microcanonical and the canonical ensemble, of the Self-Gravitating-Ring (SGR) model, which describes the motion of equal point masses constrained on a ring and subject to 3D gravitational attraction. If the interaction is regularized at short distances by the introduction of a softening parameter, a global entropy maximum always exists, and thermodynamics is well defined in the mean-field limit. However, ensembles are not equivalent and a phase of negative specific heat in the microcanonical ensemble appears in a wide intermediate energy region, if the softening parameter is small enough. The phase transition changes from second to first order at a tricritical point, whose location is not the same in the two ensembles. All these features make of the SGR model the best prototype of a self-gravitating system in one dimension. In order to obtain the stable stationary mass distribution, we apply a new iterative method, inspired by a previous one used in 2D turbulence, which ensures entropy increase and, hence, convergence towards an equilibrium state

Microscopic approach to orientational order of domain walls

We develop a fully microscopic, statistical mechanics approach to study phase transitions in Ising systems with competing interactions at different scales. Our aim is to consider orientational and positional order parameters in a unified framework. In this work we consider two dimensional stripe forming systems, where nematic, smectic and crystal phases are possible. We introduce a nematic order parameter in a lattice, which measures orientational order of interfaces. We develop a mean field approach which leads to a free energy which is a function of both the magnetization (density) and the orientational (nematic) order parameters. Self-consistent equations for the order parameters are obtained and the solutions are described for a particular system, the Dipolar Frustrated Ising Ferromagnet. We show that this system has an Ising-nematic phase at low temperatures in the square lattice, where positional order (staggered magnetization) is zero. At lower temperatures a crystal-stripe phase may appear. In the continuum limit the present approach connects to a Ginsburg-Landau theory, which has an isotropic-nematic phase transition with breaking of a continuous symmetry.Comment: 9 pages, 7 figures, revised and expanded, published versio

Astrophysical limitations to the identification of dark matter: indirect neutrino signals vis-a-vis direct detection recoil rates

A convincing identification of dark matter (DM) particles can probably be achieved only through a combined analysis of different detections strategies, which provides an effective way of removing degeneracies in the parameter space of DM models. In practice, however, this program is made complicated by the fact that different strategies depend on different physical quantities, or on the same quantities but in a different way, making the treatment of systematic errors rather tricky. We discuss here the uncertainties on the recoil rate in direct detection experiments and on the muon rate induced by neutrinos from dark matter annihilations in the Sun, and we show that, contrarily to the local DM density or overall cross section scale, irreducible astrophysical uncertainties affect the two rates in a different fashion, therefore limiting our ability to reconstruct the parameters of the dark matter particle. By varying within their respective errors astrophysical parameters such as the escape velocity and the velocity dispersion of dark matter particles, we show that the uncertainty on the relative strength of the neutrino and direct-detection signal is as large as a factor of two for typical values of the parameters, but can be even larger in some circumstances.Comment: 12 pages, 3 figures. Improved presentation and Fig.3; clarifications, references and an appendix added; conclusions unchanged. Matches version published in PR

Formation of trapped surfaces for the spherically symmetric Einstein-Vlasov system

We consider the spherically symmetric, asymptotically flat, non-vacuum Einstein equations, using as matter model a collisionless gas as described by the Vlasov equation. We find explicit conditions on the initial data which guarantee the formation of a trapped surface in the evolution which in particular implies that weak cosmic censorship holds for these data. We also analyze the evolution of solutions after a trapped surface has formed and we show that the event horizon is future complete. Furthermore we find that the apparent horizon and the event horizon do not coincide. This behavior is analogous to what is found in certain Vaidya spacetimes. The analysis is carried out in Eddington-Finkelstein coordinates.Comment: 2