Characteristic Velocity Dispersion Research Articles

Gravothermal evolution of dark matter halos with differential elastic scattering

We study gravothermal evolution of dark matter halos in the presence of differential self-scattering that has strong velocity and angular dependencies. We design controlled N-body simulations to model Rutherford and Møller scatterings in the halo, and follow its evolution in both core-expansion and -collapse phases. The simulations show the commonly-used transfer cross section underestimates the effects of dark matter self-interactions, but the viscosity cross section provides an accurate approximation for modeling angular-dependent dark matter scattering. We investigate thermodynamic properties of the halo, and find that the three moments of the Boltzmann equation under the fluid approximation are satisfied. We further propose a constant effective cross section, which integrates over the halo's characteristic velocity dispersion with weighting kernels motivated by kinetic theory of heat conduction. The effective cross section provides a good approximation to differential self-scattering for most of the halo evolution. It indicates that we can map astrophysical constraints on a constant self-interacting cross section to an SIDM model with velocity- and angular-dependent scatterings.

Spurious heating of stellar motions in simulated galactic discs by dark matter halo particles

ABSTRACT We use idealized N-body simulations of equilibrium stellar discs embedded within course-grained dark matter (DM) haloes to study the effects of spurious collisional heating on disc structure and kinematics. Collisional heating artificially increases the vertical and radial velocity dispersions of disc stars, as well as the thickness and size of discs; the effects are felt at all galacto-centric radii. The integrated effects of collisional heating are determined by the mass of DM halo particles (or equivalently, by the number of particles at fixed halo mass), their local density and characteristic velocity dispersion, but are largely insensitive to the stellar particle mass. The effects can therefore be reduced by increasing the mass resolution of DM in cosmological simulations, with limited benefits from increasing the baryonic (or stellar) mass resolution. We provide a simple empirical model that accurately captures the effects of spurious collisional heating on the structure and kinematics of simulated discs, and use it to assess the importance of disc heating for simulations of galaxy formation. We find that the majority of state-of-the-art zoom simulations, and a few of the highest-resolution, smallest-volume cosmological runs, are in principle able to resolve thin stellar discs in Milky Way-mass haloes, but most large-volume cosmological simulations cannot. For example, DM haloes resolved with fewer than ≈106 particles will collisionally heat stars near the stellar half-mass radius such that their vertical velocity dispersion increases by ≳ 10 per cent of the halo’s virial velocity in approximately one Hubble time.

The velocity dispersion function of early-type galaxies and its redshift evolution: the newest results from lens redshift test

ABSTRACT The redshift distribution of galactic-scale lensing systems provides a laboratory to probe the velocity dispersion function (VDF) of early-type galaxies (ETGs) and measure the evolution of ETGs at redshift z ∼ 1. Through the statistical analysis of the currently largest sample of ETG gravitational lenses, we conclude that the VDF inferred solely from strong lensing systems is well consistent with the measurements of SDSS DR5 data in the local Universe. In particular, our results strongly indicate a decline in the number density of lenses by a factor of two and a 20 per cent increase in the characteristic velocity dispersion for the ETG population at z ∼ 1. Such VDF evolution is in perfect agreement with the ΛCDM paradigm (i.e. the hierarchical build-up of mass structures over cosmic time) and different from ‘stellar mass-downsizing’ evolutions obtained by many galaxy surveys. Meanwhile, we also quantitatively discuss the evolution of the VDF shape in a more complex evolution model, which reveals its strong correlation with the number density and velocity dispersion of ETGs. Finally, we evaluate if future missions such as LSST can be sensitive enough to place the most stringent constraints on the redshift evolution of ETGs, based on the redshift distribution of available gravitational lenses.

Implications of the lens redshift distribution of strong lensing systems: cosmological parameters and the global properties of early-type galaxies

In this paper, we assemble a well-defined sample of early-type gravitational lenses extracted from a large collection of 158 systems, and use the redshift distribution of galactic-scale lenses to test the standard cosmological model (varLambda CDM) and the modified gravity theory (DGP). Two additional sub-samples are also included to account for possible selection effect introduced by the detectability of lens galaxies. Our results show that independent measurement of the matter density parameter (varOmega _m) could be expected from such strong lensing statistics. Based on future measurements of strong lensing systems from the forthcoming LSST survey, one can expect varOmega _m to be estimated at the precision of varDelta varOmega _msim 0.006, which provides a better constraint on varOmega _m than Planck 2015 results. Moreover, use the lens redshift test is also used to constrain the characteristic velocity dispersion of the lensing galaxies, which is well consistent with that derived from the optical spectroscopic observations. A parameter f_E is adopted to quantify the relation between the lensing-based velocity dispersion and the corresponding stellar value. Finally, the accumulation of detectable galactic lenses from future LSST survey would lead to more stringent fits of varDelta f_Esim 10^{-3}, which encourages us to test the global properties of early-type galaxies at much higher accuracy.

Interaction of multiple courses of wave‐induced fluid flow in layered porous media

ABSTRACTDifferent theoretical and laboratory studies on the propagation of elastic waves in layered hydrocarbon reservoir have shown characteristic velocity dispersion and attenuation of seismic waves. The wave‐induced fluid flow between mesoscopic‐scale heterogeneities (larger than the pore size but smaller than the predominant wavelengths) is the most important cause of attenuation for frequencies below 1 kHz. Most studies on mesoscopic wave‐induced fluid flow in the seismic frequency band are based on the representative elementary volume, which does not consider interaction of fluid flow due to the symmetrical structure of representative elementary volume. However, in strongly heterogeneous media with unsymmetrical structures, different courses of wave‐induced fluid flow may lead to the interaction of the fluid flux in the seismic band; this has not yet been explored. This paper analyses the interaction of different courses of wave‐induced fluid flow in layered porous media. We apply a one‐dimensional finite‐element numerical creep test based on Biot's theory of consolidation to obtain the fluid flux in the frequency domain. The characteristic frequency of the fluid flux and the strain rate tensor are introduced to characterise the interaction of different courses of fluid flux. We also compare the behaviours of characteristic frequencies and the strain rate tensor on two scales: the local scale and the global scale. It is shown that, at the local scale, the interaction between different courses of fluid flux is a dynamic process, and the weak fluid flux and corresponding characteristic frequencies contain detailed information about the interaction of the fluid flux. At the global scale, the averaged strain rate tensor can facilitate the identification of the interaction degree of the fluid flux for the porous medium with a random distribution of mesoscopic heterogeneities, and the characteristic frequency of the fluid flux is potentially related to that of the peak attenuation. The results are helpful for the prediction of the distribution of oil–gas patches based on the statistical properties of phase velocities and attenuation in layered porous media with random disorder.

THE VERTICAL MOTIONS OF MONO-ABUNDANCE SUB-POPULATIONS IN THE MILKY WAY DISK

We present the vertical kinematics of stars in the Milky Way's stellar disk inferred from SDSS/SEGUE G-dwarf data, deriving the vertical velocity dispersion, \sigma_z, as a function of vertical height |z| and Galactocentric radius R for a set of 'mono-abundance' sub-populations of stars with very similar elemental abundances [\alpha/Fe] and [Fe/H]. We find that all components exhibit nearly isothermal kinematics in |z|, and a slow outward decrease of the vertical velocity dispersion: \sigma_z (z,R|[\alpha/Fe],[Fe/H]) ~ \sigma_z ([\alpha/Fe],[Fe/H]) x \exp (-(R-R_0)/7 kpc}). The characteristic velocity dispersions of these components vary from ~ 15 km/s for chemically young, metal-rich stars, to >~ 50 km/s for metal poor stars. The mean \sigma_z gradient away from the mid plane is only 0.3 +/- 0.2 km/s/kpc. We find a continuum of vertical kinetic temperatures (~\sigma^2_z) as function of ([\alpha/Fe],[Fe/H]), which contribute to the stellar surface mass density as \Sigma_{R_0}(\sigma^2_z) ~ \exp(-\sigma^2_z). The existence of isothermal mono-abundance populations with intermediate dispersions reject the notion of a thin-thick disk dichotomy. This continuum of disks argues against models where the thicker disk portions arise from massive satellite infall or heating; scenarios where either the oldest disk portion was born hot, or where internal evolution plays a major role, seem the most viable. The wide range of \sigma_z ([\alpha/Fe],[Fe/H]) combined with a constant \sigma_z(z) for each abundance bin provides an independent check on the precision of the SEGUE abundances: \delta_[\alpha/Fe] ~ 0.07 dex and \delta_[Fe/H] ~ 0.15 dex. The radial decline of the vertical dispersion presumably reflects the decrease in disk surface-mass density. This measurement constitutes a first step toward a purely dynamical estimate of the mass profile the disk in our Galaxy. [abridged]

Anisotropic dispersion and attenuation due to wave‐induced fluid flow: Quasi‐static finite element modeling in poroelastic solids

Heterogeneous porous media such as hydrocarbon reservoir rocks are effectively described as anisotropic viscoelastic solids. They show characteristic velocity dispersion and attenuation of seismic waves within a broad frequency band, and an explanation for this observation is the mechanism of wave‐induced pore fluid flow. Various theoretical models quantify dispersion and attenuation of normal incident compressional waves in finely layered porous media. Similar models of shear wave attenuation are not known, nor do general theories exist to predict wave‐induced fluid flow effects in media with a more complex distribution of medium heterogeneities. By using finite element simulations of poroelastic relaxation, the total frequency‐dependent complex stiffness tensor can be computed for a porous medium with arbitrary internal heterogeneity. From the stiffness tensor, velocity dispersion and frequency‐dependent attenuation are derived for compressional and shear waves as a function of the angle of incidence. We apply our approach to the case of layered media and to that of an ellipsoidal poroelastic inclusion. In the case of the ellipsoidal inclusion, compressional and shear wave modes show significant attenuation, and the characteristic frequency dependence of the effect is governed by the spatiotemporal scale of the pore fluid pressure relaxation. In our anisotropic examples, the angle dependence of the attenuation is stronger than that of the velocity dispersion. It becomes clear that the spatial attenuation patterns show specific characteristics of wave‐induced fluid flow, implying that anisotropic attenuation measurements may contribute to the inversion of fluid transport properties in heterogeneous porous media.

Testing Modified Gravity with Globular Cluster Velocity Dispersions

Globular clusters (GCs) in the Milky Way have characteristic velocity dispersions that are consistent with the predictions of Newtonian gravity, and may be at odds with Modified Newtonian Dynamics (MOND). We discuss a modified gravity (MOG) theory that successfully predicts galaxy rotation curves, galaxy cluster masses and velocity dispersions, lensing, and cosmological observations, yet produces predictions consistent with Newtonian theory for smaller systems, such as GCs. MOG produces velocity dispersion predictions for GCs that are independent of the distance from the Galactic center, which may not be the case for MOND. New observations of distant GCs may produce strong criteria that can be used to distinguish between competing gravitational theories.

Gravitational Shear, Flexion, and Strong Lensing in Abell 1689

We present a gravitational lensing analysis of the galaxy cluster Abell 1689, incorporating measurements of the weak shear, flexion, and strong lensing induced in background galaxies. This is the first time that a shapelet technique has been used to reconstruct the distribution of mass in this cluster, and the first time that a flexion signal has been measured using cluster members as lenses. From weak shear measurements alone, we generate a non-parametric mass reconstruction, which shows significant substructure corresponding to groups of galaxies within the cluster. Additionally, our galaxy-galaxy flexion signal demonstrates that the cluster galaxies can be well-fit by a singular isothermal sphere model with a characteristic velocity dispersion of $\sigma_v = 295\pm 40 km/s $. We identify a major, distinct dark matter clump, offset by 40$h^{-1}$kpc from the central cluster members, which was not apparent from shear measurements alone. This secondary clump is present in a parametric mass reconstruction using flexion data alone, and its existence is suggested in a non-parametric reconstruction of the cluster using a combination of strong and weak lensing. As found in previous studies, the mass profile obtained by combining weak and strong lensing data shows a much steeper profile than that obtained from only weak lensing data.

Kinematics of the Open Cluster System in the Galaxy

Absolute proper motions and radial velocities of 202 open clusters in the solar neighborhood, which can be used as tracers of the Galactic disk, are used to investigate the kinematics of the Galaxy in the solar vicinity, including the mean heliocentric velocity components (u(1), u(2), u(3)) of the open cluster system, the characteristic velocity dispersions (sigma(1), sigma(2), sigma(3)), Oort constants (A, B) and the large-scale radial motion parameters (C, D) of the Galaxy. The results derived from the observational data of proper motions and radial velocities of a subgroup of 117 thin disk young open clusters by means of a maximum I likelihood algorithm, are: (u(1), u(2), u(3)) = (-16.1 +/- 1.0, -7.9 +/- 1.4, -10.4 +/- 1.5) km s(-1), (sigma(1), sigma(2), sigma(3)) = (17.0 +/- 0.7,12.2 +/- 0.9, 8.0 +/- 1.3) km s(-1), (A, B) = (14.8 +/- 1.0, -13.0 +/- 2.7) km s(-1) kpc(-1), and (C, D) = (1.5 +/- 0.7, -1.2 +/- 1.5) km s(-1) kpc(-1). A discussion on the results and comparisons with what was obtained by other authors is given.

Constraints on the Velocity Dispersion Function of Early‐Type Galaxies from the Statistics of Strong Gravitational Lensing

We use the distribution of gravitationally lensed image separations observed in the Cosmic Lens All-Sky Survey (CLASS) and the PMN-NVSS Extragalactic Lens Survey (PANELS), which are (nearly) complete for the image separation range 03 ≤ Δθ ≤ 6'', to constrain a model velocity dispersion function (VF) of early-type galaxies. Assuming a current concordance cosmological model and adopting a singular isothermal ellipsoid (SIE) model for galactic potentials, we consider constraining both a characteristic velocity dispersion (parameter σ*) and the shape of the function (parameters α and β; from Sheth et al.) for 0.3 z 1. If all three parameters are allowed to vary, then none of the parameters can be tightly constrained by the lensing data because of the small size of the sample. If we fix the shape of the function by either the SDSS local stellar VF or an inferred local stellar VF based on the SSRS2 galaxy sample, then the constrained values of σ* are nearly equal to the corresponding stellar values; we have fSIE/center(≡ σ*,SIE/σ*,center) = 0.90 ± 0.18 (SDSS) or 1.04 ± 0.19 (SSRS2), assuming nonevolution of the function between the present epoch and z ~ 0.6. Finally, using only the CLASS statistical sample (from Browne et al.), and thus including an absolute multiple-imaging probability, we find that the SDSS stellar VF may have significantly underestimated the abundance of morphologically early-type galaxies.

The Cosmic Lens All-Sky Survey: statistical strong lensing, cosmological parameters, and global properties of galaxy populations

Extensive analyses of statistical strong gravitational lensing are performed based on the final Cosmic Lens All-Sky Survey (CLASS) well-defined statistical sample of flat-spectrum radio sources and current estimates of galaxy luminosity functions per morphological type. The analyses are carried out under the assumption that galactic lenses are well-approximated by singular isothermal ellipsoids and early-type galaxies evolved passively since redshift z ∼ 1. Two goals of the analyses are: (i) to constrain cosmological parameters independently of other techniques (e.g. Type Ia supernovae magnitude-redshift relation, cosmic microwave background anisotropies, galaxy matter power spectra); and (ii) to constrain the characteristic line-of-sight velocity dispersion and the mean projected mass ellipticity for the early-type galaxy population. Depending on how the late-type galaxy population is treated (i.e. whether its characteristic velocity dispersion is constrained or not), we find for a flat universe with a classical cosmological constant that the matter fraction of the present critical density Ω m = 0.31 + 0 . 2 7 -0.14 (68 per cent) for the unconstrained case or 0.40 + 0 . 2 8 -0.16 (68 per cent) for the constrained case, with an additional systematic uncertainty of 0.11 arising from the present uncertainty in the distribution of CLASS sources in redshift and flux density. For a flat universe with a constant equation of state for dark energy w = p x (pressure)/ρ x (energy density) and the prior constraint ω ≥ -1, we find that -1 ≤ ω < -0.55 + 0 . 1 8 -0.11 (68 per cent) for the unconstrained case or -1 ≤ w < -0.41 + 0 . 2 8 -0.16 (68 per cent) for the constrained case, where w = -1 corresponds to a classical cosmological constant. The determined value of the early-type characteristic velocity dispersion [σ ( e ) *] depends on the faint-end slope of the early-type luminosity function [α ( 3 ) ] and the intrinsic shape distribution of galaxies; for equal frequencies of oblates and prolates, we find that σ ( e ) *(0.3 ≤ z ≤ 1) = 198 + 2 2 -18 km s - 1 (68 per cent) for a 'steep' α ( 3 ) = -1 or σ ( e ) *(0.3 ≤ z ≤ 1) = 181 + 1 8 -15 km s - 1 (68 per cent) for a 'shallow' α ( e ) = -0.54. Finally, from the relative frequencies of doubly imaged sources and quadruply imaged sources, we find that a mean projected mass ellipticity of early-type galaxies ∈ m a s s = 0.42 with a 68 per cent lower limit of 0.28 assuming equal frequencies of oblates and prolates.

Studies of Coma cluster of galaxies 5. Dynamical problems

We use the radial velocity data for 414 galaxies in the Coma cluster region provided by Kent and Gunn and the results of applying a membership criterion to carry out a discussion on the dynamical aspects of the Coma cluster. Our analysis shows that the Coma cluster has no bulk rotation that is clearly a dynamical effect. Fitting with the King-Mitchie model we find a core radius of 5.2′ or 210 kpc at H 0 = 50(km/s)/Mpc and a characteristic velocity dispersion of 935 km/s. Viewed dynamically, there is clear morphological segregation, and there is evidence that substructure exists in the central region.

Ultrasonic Absorption in Water Containing Plankton in Suspension

A study is made to determine the frequency and concentration dependence of the ultrasonic absorption in aqueous suspensions of (1) scenedesmus and diatoms, two forms of algae, and (2) artemia (brine shrimp) eggs. The measurements were made over a frequency range of 125 kc/sec to 55 Mc/sec. The excess absorption caused by scenedesmus is found to be linearly dependent on concentration and has a value of α/f2=7×10 16 m−1 sec2 for the highest concentration measured, 0.72 g/liter of water. The excess absorption caused by diatoms is also linearly dependent on concentration and has a value of 25×10−15 m−1 sec2 for 290 g/liter of water, the highest concentration measured. For both scenedesmus and diatoms, it is concluded that the normal concentration of these forms of algae found in large bodies of water causes negligible absorption compared to the absorption of the water itself. The major portion of the excess attenuation due to the shrimp eggs in the kilocycle region is attributed to a scattering mechanism. Application of a theory for elastic scattering in this wavelength region (ka&amp;lt;1) gave good agreement with experimental results. A phase-velocity investigation of a resonance phenomenon at 7 Mc/sec revealed a characteristic velocity dispersion.