Friction Timescale Research Articles

Evolution of massive binary black holes

ABSTRA C T Since many or most galaxies have central massive black holes (BHs), mergers of galaxies can form massive binary black holes (BBHs). In this paper we study the evolution of massive BBHs in realistic galaxy models, using a generalization of techniques used to study tidal disruption rates around massive BHs. The evolution of BBHs depends on BH mass ratio and host galaxy type. BBHs with very low mass ratios (say, &0.001) are hardly ever formed by mergers of galaxies, because the dynamical friction time-scale is too long for the smaller BH to sink into the galactic centre within a Hubble time. BBHs with moderate mass ratios are most likely to form and survive in spherical or nearly spherical galaxies and in highluminosity or high-dispersion galaxies; they are most likely to have merged in low-dispersion galaxies (line-of-sight velocity dispersion &90 km s 21 ) or in highly flattened or triaxial galaxies. The semimajor axes and orbital periods of surviving BBHs are generally in the range 10 23 ‐ 10 pc and 10 ‐ 10 5 yr; they are also larger in high-dispersion galaxies than in lowdispersion galaxies, larger in nearly spherical galaxies than in highly flattened or triaxial galaxies, and larger for BBHs with equal masses than for BBHs with unequal masses. The orbital velocities of surviving BBHs are generally in the range 10 2 ‐1 0 4 km s 21 . The methods of detecting surviving BBHs are also discussed. If no evidence of BBHs is found in AGNs, this may be either because gas plays a major role in BBH orbital decay or because nuclear activity switches on soon after a galaxy merger, and ends before the smaller BH has had time to spiral to the centre of the galaxy.

Dynamical Friction in dE Globular Cluster Systems

The dynamical friction timescale for globular clusters to sink to the center of a dwarf elliptical galaxy (dE) is significantly less than a Hubble time if the halos have isothermal profiles and the globular clusters formed with the same radial density profile as the underlying stellar population. We examine the summed radial distribution of the entire globular cluster systems and the bright globular cluster candidates in 65 Virgo and Fornax Cluster dEs for evidence of dynamical friction processes. We find that the bright dE nuclei could have been formed from the merger of orbitally decayed massive clusters, but the faint nuclei are several magnitudes fainter than expected. These faint nuclei are found primarily in MV > −14 dEs which have high globular cluster specific frequencies and extended globular cluster systems. In these galaxies, the formation of new star clusters, high central dark matter densities, extended dark matter halos, or tidal interactions may act to prevent dynamical friction from collapsing the entire globular cluster population into a bright nucleus.

Dynamical Friction in dE Globular Cluster Systems

The dynamical friction timescale for globular clusters to sink to the center of a dwarf elliptical galaxy (dE) is significantly less than a Hubble time if the halos have King-model or isothermal profiles and the globular clusters formed with the same radial density profile as the underlying stellar population. We examine the summed radial distribution of the entire globular cluster systems and the bright globular cluster candidates in 51 Virgo and Fornax Cluster dE's for evidence of dynamical friction processes. We find that the summed distribution of the entire globular cluster population closely follows the exponential profile of the underlying stellar population. However, there is a deficit of bright clusters within the central regions of dE's (excluding the nuclei), perhaps due to the orbital decay of these massive clusters into the dE cores. We also predict the nuclear magnitude of each dE assuming that the nuclei form via dynamical friction. The observed trend of decreasing nuclear luminosity with decreasing dE luminosity is much stronger than predicted if the nuclei formed via simple dynamical friction processes. We find that the bright dE nuclei could have been formed from the merger of orbitally decayed massive clusters, but the faint nuclei are several magnitudes fainter than expected. These faint nuclei are found primarily in MV > -14 dE's, which have high globular cluster specific frequencies and extended globular cluster systems. In these galaxies, supernova-driven winds, high central dark matter densities, extended dark matter halos, the formation of new star clusters, or tidal interactions may act to prevent dynamical friction from collapsing the entire globular cluster population into a single bright nucleus.

Is the Fast Evolution Scenario for Virialized Compact Groups Really Compelling? The Role of a Dark Massive Group Halo

We report on results of N-body simulations aimed at testing the hypothesis that galaxies in X-ray-emitting (i.e., virialized) compact groups are not tidally stripped when they are embedded in a common, massive, quiescent dark matter halo. To disentangle the effects of interactions from spurious effects due to an incorrect choice of the initial galaxy model configurations, these have been chosen to be tidally limited King spheres, representing systems in quasi-equilibrium within the tidal field of the halo. The potential of the halo has been assumed to be frozen and the braking due to dynamical friction neglected. Our results confirm the hypothesis of low rates of tidal stripping and suggest a scenario for virialized compact group evolution in their quiescent phases where only very moderate tidally induced galaxy evolution can generally be expected. This implies the group is stable, provided that the dynamical friction timescales in these systems are not much shorter than the Hubble time. We discuss briefly this possibility, in particular taking account of the similarity between the velocity dispersions of a typical virialized compact group and the internal velocity dispersion of typical member galaxies.

Dynamical friction of bodies orbiting in a gaseous sphere

The dynamical friction experienced by a body moving in a gaseous medium is different from the friction in the case of a collisionless stellar system. Here we consider the orbital evolution of a gravitational perturber inside a gaseous sphere using three-dimensional simulations, ignoring however self-gravity. The results are analysed in terms of a ‘local’ formula with the associated Coulomb logarithm taken as a free parameter. For forced circular orbits, the asymptotic value of the component of the drag force in the direction of the velocity is a slowly varying function of the Mach number in the range 1.0–1.6. The dynamical friction time-scale for free decay orbits is typically only half as long as in the case of a collisionless background, which is in agreement with E. C. Ostriker's recent analytic result. The orbital decay rate is rather insensitive to the past history of the perturber. It is shown that, similarly to the case of stellar systems, orbits are not subject to any significant circularization. However, the dynamical friction time-scales are found to increase with increasing orbital eccentricity for the Plummer model, whilst no strong dependence on the initial eccentricity is found for the isothermal sphere.

Frozen Condition for the Charged Particles in Molecular Clouds

How the ambipolar diffusion prior to star formation proceeds in molecular clouds is often discussed. At that time, it is fundamental to determine its timescale, which depends on the abundance of various charged particles. Interestingly, when the grains become dominant negatively charged particles instead of electrons, the diffusion timescale lengthens if they attach to the magnetic field. This attachment occurs even when the charged grains are not frozen into the field directly since they are attracted by the frozen ions via the electrostatic force. In other words, even when ωτ/Cg 1, the charged grains can be frozen into the field. Here ω and τ are the gyrofrequency and the friction timescale caused by the neutral of negatively charged grains, and Cg is a correction factor caused by the charge state exchange of grains. This paper investigates the diffusion processes of various charged particles, including charged grains. We present the mobility parameters of charged grains, Θ, and ions, Θi, relative to electrons, which are frozen into the magnetic fields very tightly at the density range considered here. Thus, when Θ > 1, the charged grains are frozen into the magnetic field. Moreover, even when ωiτin 1, it is possible that Θi becomes smaller than unity, and ions are never frozen into the field as far as Θi 1 for ions and ωτ > 1 for negatively charged grains becomes the good approximation. It seems that when the electrostatic interaction between ions and negatively charged grains is not so effective, the naive criterion for the frozen conditions is always reasonable.

Alongshore currents over variable beach topography

The nonlinear dynamics of unstable alongshore currents in the nearshore surf zone over variable barred beach topography are studied using numerical experiments. These experiments extend the recent studies of Allen et al. [1996] and Slinn et al. [1998], which utilized alongshore uniform beach topographies by including sinusoidal alongshore variation to shore parallel sandbars. The model involves finite difference solutions to the nonlinear shallow water equations for forced, dissipative, initial value problems and employs periodic boundary conditions in the alongshore direction. Effects of dissipation are modeled by linear bottom friction. Forcing for the alongshore currents is provided by gradients in the radiation stress, which are specified using linear theory and the dissipation function for breaking waves formulated by Thornton and Guza [1983]. Distinct flows develop depending on the amplitude ∈ and wavelength λ of the topographic variability and the dimensionless parameter Q, the ratio of an advective to a frictional timescale. For Q greater than a critical value QC the flows are linearly stable. For ΔQ = QC ‐ Q>0 the flow can be unstable. For small values of ΔQ the effect of increasing ∈; is to stabilize or regularize the flows and to cause the mean flow to approximately follow contours of constant depth. Equilibrated shear waves develop that propagate along the mean current path at phase speeds and wavelengths that are close to predictions for the most unstable mode from linear theory applied to alongshore‐averaged conditions. At intermediate values of ΔQ, unsteady vortices form and exhibit nonlinear interactions as they propagate along the mean current path, occasionally merging, pairing, or being shed seaward of the sandbar. Eddies preferentially form in the mean current when approaching alongshore troughs of the sandbar and break free from the mean current when approaching alongshore crests of the sandbar. At the largest values of ΔQ examined the resulting flow fields resemble a turbulent shear flow and are less strongly influenced by the alongshore variability in topography. As the amplitude of the alongshore topographic variability increases, alongshore wavenumber‐frequency spectra of the across‐shore velocity show a corresponding increase in energy at both higher alongshore wavenumbers and over a broader frequency range with significant energy at wavenumbers of topographic variability and harmonics. Across‐shore fluxes of mass and momentum generally increase with increasing topographic amplitude and increasing ΔQ. Time‐ and space‐lagged correlations of the across‐shore velocity show that correlation length scales decrease as topographic perturbation amplitudes increase. Terms from the vorticity equation show that the alongshore variation of the radiation stresses and the value of ΔQ are of importance to the flow behavior. Hybrid experiments separating effects of spatially variable forcing and the dynamic influence of topography on time‐averaged currents show that the effects are generally comparable with the relative importance of each effect a function of ΔQ. The results show that topographic variability has a significant influence on nearshore circulation.

Dynamical Friction and the Evolution of Satellites in Virialized Halos: The Theory of Linear Response

The evolution of a small satellite inside a more massive truncated isothermal spherical halo is studied using both the Theory of Linear Response for dynamical friction and N-Body simulations. The analytical approach includes the effects of the gravitational wake, of the tidal deformation and the shift of the barycenter of the primary, so unifying the local versus global interpretation of dynamical friction. Sizes, masses, orbital energies and eccentricities are chosen as expected in hierarchical clustering models. We find that in general the drag force in self-gravitating backgrounds is weaker than in uniform media and that the orbital decay is not accompanied by a significant circularization. We also show that the dynamical friction time scale is weakly dependent on the initial circularity. We provide a fitting formula for the decay time that includes the effect of mass and angular momentum loss. Live satellites with dense cores can survive disruption up to an Hubble time within the primary, notwithstanding the initial choice of orbital parameters. Dwarf spheroidal satellites of the Milky Way, like Sagittarius A and Fornax, have already suffered mass stripping and, with their present masses, the sinking times exceed 10 Gyr even if they are on very eccentric orbits.

Gas-Rich Companions of Isolated Galaxies

We have used the VLA to search for gaseous remnants of the galaxy formation process around six extremely isolated galaxies. We found two distinct H I clouds around each of two galaxies in our sample (UGC 9762 and UGC 11124). These clouds are rotating and appear to have optical counterparts, strongly implying that they are typical dwarf galaxies. The companions are currently weakly interacting with the primary galaxy but look to be in stable orbits as they have dynamical friction timescales of 5–100 Gyr. In one case, (UGC 11124N), we see ongoing accretion of the companion onto the primary galaxy. The small mass ratio involved in this interaction means that the resulting merger will be a minor one. The companion does, however, contain enough gas that the merger will represent a significant infusion of fuel to drive future star formation in UGC 11124 while building up the mass of the disk.

Molecular Gas in Hickson Compact Groups

Compact groups are ideal sites to study the influence of strong dynamical evolution due to environment on molecular cloud formation and star formation efficiency. We have observed 70 galaxies belonging to 45 Hickson compact groups (HCGs) in the 12CO(1→0) and 12CO(2→1) lines, in order to determine their molecular content. We compare the gas content relative to blue and LFIR luminosities of galaxies in compact groups with respect to other samples in the literature, including various environments and morphological types. We find that there is some hint, of enhanced MH2/LB and Mdust/LB ratios in the galaxies from compact group with respect to our control sample, especially for the most compact groups, suggesting that tidal interactions can drive the gas component inwards, by removing its angular momentum, and concentrating it in the dense central regions, where it is easily detected. The threshold at 20–30 kpc in mean galaxy separation for the enhancement of H2 suggests that it must correspond to an acceleration of the merging process and a significant inward gas flow. The molecular gas content in compact group galaxies is similar to that in pairs and starburst samples. However, the total LFIR luminosity of HCGs is quite similar to that of the control sample, and therefore the star formation efficiency appears lower than in the control galaxies. However this assumes that the FIR spatial distributions are similar in both samples which is not the case at radio frequencies. Higher spatial resolution FIR data are needed to make a valid comparison. Given their short dynamical friction time-scale, it is possible that some of these systems are in the final stage before merging, leading to ultraluminous starburst phases. We also find for all galaxy samples that the H2 content (normalized to blue luminosity) is strongly correlated with LFIR, while the total gas content (H2+HI) is not.

Substructure in Dark Halos: Orbital Eccentricities and Dynamical Friction

The virialized regions of galaxies and clusters contain significant amounts of substructure; clusters have hundreds to thousands of galaxies, and satellite systems and globular clusters orbit the halos of individual galaxies. These orbits can decay owing to dynamical friction. Depending on their orbits and their masses, the substructures either merge, are disrupted, or survive to the present day. We examine the distributions of eccentricities of orbits within mass distributions similar to those we see for galaxies and clusters. A comprehensive understanding of these orbital properties is essential to calculate the rates of physical processes relevant to the formation and evolution of galaxies and clusters. We derive the orbital eccentricity distributions for a number of spherical potentials. These distributions depend strongly on the velocity anisotropy, but only slightly on the shape of the potential. The eccentricity distributions in the case of an isotropic distribution function are strongly skewed toward high eccentricities, with a median value of typically ~0.6, corresponding to an apocenter-to-pericenter ratio of 4.0. We also present high-resolution N-body simulations of the orbital decay of satellite systems on eccentric orbits in an isothermal halo. The dynamical friction timescales are found to decrease with increasing orbital eccentricity because of the dominating deceleration at the orbit's pericenter. The orbital eccentricity stays remarkably constant throughout the decay; although the eccentricity decreases near pericenter, it increases again near apocenter, such that there is no net circularization. We briefly discuss several applications for our derived distributions of orbital eccentricities and the resulting decay rates from dynamical friction. We compare the theoretical eccentricity distributions to those of globular clusters and galactic satellites for which all six phase-space coordinates (and therewith their orbits) have been determined. We find that the globular clusters are consistent with a close-to-isotropic velocity distribution, and they show large orbital eccentricities because of this (not in spite of this, as has been previously asserted). In addition, we find that the limited data on the Galactic system of satellites appears to be different and warrants further investigation as a clue to the formation and evolution of our Milky Way and its halo substructure.

Nonlinear shear instabilities of alongshore currents over barred beaches

The nonlinear dynamics of finite amplitude shear instabilities of alongshore currents in the nearshore surf zone over barred beach topography are studied using numerical experiments. These experiments extend the recent study of Allen et al. [1996], which utilized plane beach (constant slope) topography by including shore‐parallel sandbars. The model involves finite‐difference solutions to the nonlinear shallow water equations for forced, dissipative, initial‐value problems and employs periodic boundary conditions in the alongshore direction. Effects of dissipation are modeled by linear bottom friction. Forcing for the alongshore currents is specified using a model formulated by Thornton and Guza [1986] (T‐G). Distinct classes of flows develop depending on the dimensionless parameter Q, the ratio of an advective to a frictional timescale. For Q greater than a critical value Qc the flows are linearly stable. For ΔQ=Qc–Q >0 the flow is unstable. For small values of ΔQ, equilibrated shear waves develop that propagate alongshore at phase speeds and wavelengths that are in agreement with predictions from linear theory for the most unstable mode. At intermediate values of ΔQ, unsteady vortices form and exhibit nonlinear interactions as they propagate alongshore, occasionally merging, pairing, or being shed seaward of the sandbar. At the largest values of ΔQ examined, the resulting flow field resembles a turbulent shear flow. A net effect of the instabilities at large AQ is to distribute the time‐averaged alongshore momentum from local maxima of the T‐G forcing, located over the sandbar and near the shore, into the region of the trough. The across‐shore structure of the time‐averaged alongshore current is in substantially better qualitative agreement with observations than that given by a steady frictional balance with T‐G forcing. The results point to the possible existence in the nearshore surf zone of an energetic eddy field associated with instabilities of the alongshore current.

Comments on Alfven Waves and Plasma Drift in a Slightly Ionized Gas

It is well known that there exist two critical wavelengths for Alfven waves in a slightly ionized medium. One of the two is λ1 ≡ πVAτni, where VA is the Alfven speed in the medium and τni is the friction timescale for neutral particles due to ions. The other is λ2 ≡ 4πV τ, where V is the Alfven speed in the ions and τin is the friction timescale for the ions, respectively. In typical molecular clouds, λ2 is much smaller than λ1. We let λ* denote the intermediate range: λ2 < λ* < λ1, where the so-called ion-neutral damping of the Alfven waves occurs. In this paper, we show that magnetic forces affect the neutral fluid even at λ*. This is possible when λ2 is much larger than the mean free path Λ of the neutral particles for neutral-neutral collision. When τin is much longer than the collision timescale among the neutral particles, τnn, the communication timescale of the magnetic fields and the neutral fluid is τin. If τin τnn, the neutral fluid can adjust itself to the magnetic forces during τin. For typical molecular clouds, it is estimated that Λ λ2 and τnn τin(τni). It may suggest that magnetically subcritical cloud cores contract quasi-statically with magnetic flux loss, even if the size is λ*. On the other hand, if a disturbance scale of the magnetic field is smaller than λ2, the magnetic stress can escape as Alfven waves that couple almost exclusively with the ions. In addition, we point out that it is difficult for the Jeans length to become smaller than λ2 in isolated molecular clouds or cores. Observational implications are also presented.

Nonlinear shear instabilities of alongshore currents on plane beaches

Evidence for the existence in the nearshore surf zone of energetic alongshore propagating waves with periods O(100 s) and wavelengths O(100 m) was found from observations by Oltman-Shay et al. (1989). These oscillations have wavelengths that are much too short to be surface gravity waves at the observed frequencies. The existence and properties of the wave-like motions were found to be related to the presence, strength and direction of an alongshore current in the surf zone. Based on a linear stability analysis of a mean alongshore current with offshore scale O(100 m), Bowen &amp; Holman (1989) described these fluctuations as unstable waves associated with a shear instability. Good agreement of wavelengths and wave speeds from observations and from predictions based on the most unstable linear mode was obtained by Dodd et al. (1992). The nonlinear dynamics of finite-amplitude shear instabilities of alongshore currents in the surf zone are studied here utilizing numerical experiments involving finite-difference solutions to the shallow water equations for idealized forced dissipative initial-value problems. Plane beach (i.e. constant slope) geometry is used with periodic boundary conditions in the alongshore direction. Forcing effects from obliquely incident breaking surface waves are approximated by an across-shore-varying steady force in the alongshore momentum equation. Dissipative effects are modelled by linear bottom friction. The solutions depend on the dimen-sionless parameter Q, which is the ratio of an advective to a frictional time scale. The steady frictionally balanced, forced, alongshore current is linearly unstable for Q less than a critical value Qc. The response of the fluid is studied for different values of ΔQ = Qc - Q. In a set of experiments with the alongshore scale of the domain equal to the wavelength 2π/k0 of the most unstable linear mode, disturbances that propagate alongshore in the direction of the forced current with propagation velocities similar to the linear instability values are found for positive ΔQ. The disturbances equilibrate with constant amplitude for small ΔQ and with time-varying amplitudes for larger ΔQ. For increasing values of ΔQ the behaviour of this fluid system, as represented in a phase plane with area-averaged perturbation kinetic energy and area-averaged energy conversion as coordinates, is similar to that found in low-dimensional nonlinear dynamical systems including the existence of non-trivial steady solutions, bifurcation to a limit cycle, period-doubling bifurcations, and irregular chaotic oscillations. In experiments with the alongshore scale of the domain substantially larger than the wavelength of the most unstable linear mode, different behaviour is found. For small positive ΔQ, propagating disturbances grow at wavelength 2π/k0. If ΔQ is small enough, these waves equilibrate with constant or spatially varying amplitudes. For larger ΔQ, unstable waves of length 2π/k0 grow initially, but subsequently evolve into longer-wavelength nonlinear propagating steady or unsteady wave-like disturbances with behaviour dependent on ΔQ. The eventual development of large-scale nonlinear propagating disturbances appears to be a robust feature of the flow response over plane beach geometry for moderate, positive values of ΔQ and indicates the possible existence in the nearshore surf zone of propagating finite-amplitude shear waves with properties not directly related to results of linear theory.

Reaction-coordinate-dependent friction in classical activated barrier crossing dynamics: When it matters and when it doesn’t

The impact of the symmetry of the reaction-coordinate dependence of the solvent friction on the thermally activated barrier crossing rate is examined. Possible symmetry forms are defined for the reaction-coordinate dependence of the solvent friction. The implications in the effective Grote–Hynes theory of Voth [J. Chem. Phys. 97, 5908 (1992)] and the theory recently presented by Haynes, Voth, and Pollak [J. Chem. Phys. 101, 7811 (1994)] of a spatially antisymmetric solvent friction are illustrated. Surprisingly, no correction to the Kramers–Grote–Hynes theory for the transmission coefficient is predicted, although an antisymmetric spatial dependence of the solvent friction is a strong departure from the usual spatially independent friction-based generalized Langevin equation. The results from the analytical theories are compared to numerically exact generalized Langevin equation simulation results for a simple model system and found to agree well for a wide range of damping strengths and friction time scales, confirming the interesting predictions of these theories.

Simulations of Compact Groups of Galaxies: The Effect of the Dark Matter Distribution

view Abstract Citations (59) References (23) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Simulations of Compact Groups of Galaxies: The Effect of the Dark Matter Distribution Bode, Paul W. ; Cohn, Haldan N. ; Lugger, Phyllis M. Abstract The dynamical evolution of compact groups, beginning from virial equilibrium, is explored by using self-consistent N-body simulations employing Hernquist's implementation of the Barnes-Hut tree algorithm. A total N = 5000 particles is used to represent both galaxies and a smoothly distributed intracluster background (ICB). The ICB mass fraction, β, is varied from 0 to 0.9, with all the models beginning in a virialized state. The first merger occurs near the center of the cluster; the product of this merger is quickly involved in further merging. This process is found to take longer as less of the cluster mass is put into the galaxy halos. For β = 0 the second merger can occur within one dynamical time (∼0.4 Gyr), while for β = 0.75 it occurs after two dynamical times. Increasing β from 0.75 to 0.90 delays the onset of merging by a greater amount; merging begins only after 3-5 dynamical times in the latter case. This delay in merging is consistent with the lengthening of the dynamical friction time scale as galaxy masses are reduced. Stripping of mass from galaxies has less effect than merging does on the evolution. When the projected median separations and line-of-sight velocity dispersions of the models are scaled to be similar to those of Hickson's groups, the crossing times are longer than is observed. The range of values taken on by these parameters shows little dependence on β. The merging histories of models with 10 galaxies behave in a similar fashion to those of the five-galaxy groups. Publication: The Astrophysical Journal Pub Date: October 1993 DOI: 10.1086/173211 Bibcode: 1993ApJ...416...17B Keywords: GALAXIES: CLUSTERING; METHODS: NUMERICAL full text sources ADS |

Stirring and dynamical friction rates of planetesimals in the solar gravitational field

The random velocity (eccentricity and inclination) change of planetesimals due to mutual gravitational scattering is investigated, taking into account the solar gravitational field. Viscous stirring and dynamical friction rates are presented with three-body formalism (using eccentricity and inclination), and calculated through a large number ∼10 7−8) of three-body orbital integrations. The results are summarized as follows: (1) The role of distant encounters is not important. (2) In the low energy cases where Keplerian shear dominates, eccentricity grows much more rapidly than inclination, and dynamical friction is not effective. The viscous stirring time scale for eccentricity is much greater than the two-body relaxation time. (3) In the high energy cases where random motion dominates, a 2:1 ratio of eccentricity to inclination is spontaneously attained. Both stirring and dynamical friction time scales are almost given by the two-body relaxation time, and dynamical friction is effective for the larger planetesimals, which should lead to “runaway growth” of protoplanets.

Bound populations around cD galaxies

view Abstract Citations (33) References (26) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Bound Populations around cD Galaxies Bothun, Gregory D. ; Schombert, James M. Abstract Velocity measurements of a complete sample of galaxies within a projected separation of 200 kpc and L > 0.5 L_*_ are presented for the cD clusters A2271, A2589, and A2634. For A2271 and A2634, the distribution of velocities are consistent with Gaussian distributions with dispersions of 460 and 842 km s^-1^, respectively. In contrast, A2589 contains a conspicuous excess of low-velocity galaxies (|{DELTA}v| < 200 km s^-1^) in the cluster core. We present evidence that this low-velocity component represents a bound population of satellite galaxies to the central cD galaxy. For this bound population, the dynamical friction time scale is significantly less than the Hubble time and therefore these galaxies should eventually merge with the cD. However, our remaining two clusters do not exhibit such dramatic evidence for a bound population, and the data of Tonry also indicate that mostly high-velocity companions are found in the vicinity of brightest cluster members. In addition, a recent velocity study around the cD galaxy in A2029 by Bower, Ellis, and Efstathiou has failed to discover a low-velocity component. Thus, if cD galaxies are the result of mergers, this dynamical evolution occurred early in the lifetime of rich clusters. In this context, A2589 is postulated to be unique since the merger process is still continuing. Moreover, a comparison between the observed tidal radii of the companions in A2589 with the dynamical friction time scale demands that the orbits be highly noncircular, else this population would have long since been destroyed. Publication: The Astrophysical Journal Pub Date: December 1988 DOI: 10.1086/166953 Bibcode: 1988ApJ...335..617B Keywords: Galactic Clusters; Galactic Evolution; Galactic Nuclei; Red Shift; Velocity Distribution; Hubble Constant; Normal Density Functions; Stellar Evolution; Astrophysics; GALAXIES: CLUSTERING; GALAXIES: REDSHIFTS full text sources ADS | data products SIMBAD (43) NED (43)

Numerical simulation of a two-dimensional turbulence experiment in magnetohydrodynamics

Numerical simulations of a two-dimensional turbulence experiment within a confined domain are presented. The setup consists of a layer of mercury enclosed in a square box and driven by the injection of electric currents in a uniform magnetic field. The numerical finite difference model simulates the Navier–Stokes equation in two dimensions with steady forcing and linear bottom friction. Subgrid scales are modeled by an artificial constant viscosity or a higher order (biharmonic) lateral friction. The model provides an accurate representation of the (inverse) transfers of energy from the forcing scale toward the size of the domain. These transfers lead to the spontaneous appearance of a mean rotating flow, when dissipation is sufficiently weak. Thin vorticity sheets are shown to have an important role for the dynamics of the large scales. Therefore a critical spatial resolution, increasing with the bottom friction time scale, is required to get an accurate calculation. The requirement of a high resolution could not be avoided by means of the subgrid scale dissipation. Furthermore, for some low values of the dissipation, a second flow regime, without laboratory counterpart, is obtained.

Spin‐down of baroclinic eddies under sea ice

A linear model is used to examine the spin‐down of a baroclinic eddy under the sea ice. For anti‐cyclonic eddies the ice stress, besides directly spinning down the azimuthal flow within the mixed layer, generates an Ekman divergence that raises the pycnocline near the eddy axis. For eddies of the size of the baroclinic radius of deformation (based on the unperturbed mixed layer depth H and the density jump across the pycnocline), the doming reaches a quasi‐stationary state on the frictional time scale T (defined as H/α, where α is the resistence coefficient at the ice‐water interface), which generally is of the order of days. Upward entrainment of the fluid across the pycnocline causes a flow convergence below the mixed layer that continues to spin down the deeper flow and flatten the dome. The erosion of the dome, however, occurs over a much longer time scale of (γN)−1T, where γ and N are dimensionless parameters characterizing the entrainment rate and the deep stratification. Using realistic parameter values for the polar eddies, this time scale is of the order of a year or longer. The pycnocline dome observed over the Antarctic warm cells is thus likely to survive into the following freezing season and provide a preconditioning for the deep convection in the Weddell Sea.