Effect Of Dynamical Friction Research Articles

An old galaxy group:ChandraX-ray observations of the nearby fossil group NGC 6482

We present the first detailed X-ray observations, using Chandra, of NGC 6482 - the nearest known fossil group. The group is dominated by an optically luminous giant elliptical galaxy and all other known group members are at least two magnitudes fainter. The global X-ray properties (luminosity, temperature, extent) of NGC 6482 fall within the range of other groups, but the detailed properties show interesting differences. We derive the gas temperature and total mass profiles for the central 30 h -1 70 kpc (∼0.1 r 200 ) using ACIS spatially resolved spectroscopy. The unusually high L X /L opt ratio is found to result from a high central gas density. The temperature profile shows a continuous decrease outward, dropping to 0.63 of its central value at 0.1r 200 . The derived total mass profile is strongly centrally peaked, suggesting an early formation epoch. These results support a picture in which fossil groups are old, giving time for the most massive galaxies to have merged (via the effects of dynamical friction) to produce a central giant elliptical galaxy. Although the cooling time within 0.1r 200 is less than a Hubble time, no decrease in central temperature is detected. The entropy of the system lies toward the low side of the distribution seen in poor groups and drops all the way into the centre of the system, reaching very low values. No isentropic core, such as those predicted in simple pre-heating models, is present. Given the lack of any central temperature drop in the system, it seems unlikely that radiative cooling can be invoked to explain this low central entropy. The lack of any signature of central cooling is especially striking in a system that appears to be old and relaxed, and to have a central cooling time ≤10 8 yr. We find that the centrally peaked temperature profile is consistent with a steady-state cooling-flow solution with an accretion rate of 2 M ○. yr -1 , given the large P dV work arising from the cuspy mass profile. However, solutions involving distributed or non-steady heating cannot be ruled out.

Generic Friction Models for Time-Domain Vibration Analysis of Bladed Disks

New efficient models have been developed to describe dynamic friction effects in order to facilitate analysis of the vibration of bladed disks in the time domain. These friction models describe friction forces occurring at contact interfaces under time-varying normal load variations, including cases of separation. The friction models developed allow one to take into account time-varying friction contact parameters, such as friction coefficient and contact stiffness coefficients. Anisotropy and variation of the friction characteristics over the contact surfaces are included in the proposed models. The capabilities of the new friction models are demonstrated. Analysis of the friction forces is performed for different motion trajectories and different time variations of the normal load, and the effects of anisotropy, variation in time of the friction characteristics and normal load variation are discussed. A numerical analysis of transient vibrations of shrouded blades using the new models is presented.

The effects of photoionization on galaxy formation — III. Environmental dependence in the luminosity function

Using semi-analytic modeling techniques, we calculate the luminosity function of galaxy populations residing in cold dark matter halos of different mass. We pay particular attention to the influence of the reionization of the Universe on the number of faint galaxies and to the effects of dynamical friction and tidal limitation of satellites on the number of bright galaxies. We find substantial differences in the shapes of the galaxy luminosity functions in halos of different mass which reflect generic features of the cold dark matter model of galaxy formation and thus offer the opportunity to test it. We then consider how the individual halo luminosity functions combine together to produce the global luminosity function. Surprisingly, the global function ends up having a shallower faint end slope than those of the constituent halo luminosity functions. We compare our model predictions with the limited datasets compiled by Trentham & Hodgkin. We find good agreement with the luminosity functions measured in the Virgo and Coma clusters but significant disagreement with the luminosity functions measured in the Local Group and Ursa Minor cluster. We speculate on possible inadequacies in our modeling and in the existing observational samples. The luminosity functions of galaxies in groups and clusters identified in the 2dF and SDSS galaxy redshift surveys offer the prospect of testing galaxy formation models in detail.

Spatial and Dynamical Biases in Velocity Statistics of Galaxies

We present velocity statistics of galaxies and their biases inferred from the statistics of the underlying dark matter using a cosmological hydrodynamic simulation of galaxy formation in low-density and spatially flat (Ohm(0) = 0.3 and lambda(0) = 0.7) cold dark matter cosmogony. Our simulation is based on a particle-particle-particle-mesh ((PM)-M-3) N-body Poisson solver and smoothed particle hydrodynamics. Galaxies in our simulation are identified as clumps of cold and dense gas particles and classified as young and old galaxies according to their formation epochs. We find that the pairwise velocity dispersion (PVD) of all galaxies is significantly lower than that of the dark matter particles and that the PVD of the young galaxies is lower than that of the old types, and even of all galaxies together, especially at small separations. These results are in reasonable agreement with the recent measurements of PVDs in the Las Campanas redshift survey, the IRAS Point Source Catalogue Redshift Survey, and the Sloan Digital Sky Survey data. We also find that the low PVD of young galaxies is due to the effects of dynamical friction as well as the different spatial distribution, while the difference in the PVD between all galaxies and dark matter can be mostly ascribed to their different spatial distributions. We also consider the mean infall velocity and the POTENT density reconstruction that are often used to measure the cosmological parameters, and investigate the effects of spatial bias and dynamical friction. In our simulation, the mean infall velocity of young galaxies is significantly lower than that of all the galaxies or of the old galaxies, and the dynamical bias becomes important on scales less than 3 h(-1) Mpc. The mass density field reconstructed from the velocity field of young galaxies using the POTENT-style method suffers in accuracy from both the spatial bias and the dynamical friction on the smoothing scale of R-s = 8 h(-1) Mpc. On the other hand, in the case of R-s = 12 h(-1) Mpc, which is typically adopted in the actual POTENT analysis, the density reconstruction based on various tracers of galaxies is reasonably accurate. We also analyze the motions of central galaxies and the velocity dispersion of galaxies within halos and discuss their implications for the motion of cD galaxies and the determination of the mass of galaxy groups.

Dynamical Friction between Lopsided Disks and Spherical Halos

It has long been known that some spiral galaxies have a large-scale lopsided structure (e.g., Baldwin, Lynden-Bell, & Sancisi 1980). The frequency of the lopsidedness in disk galaxies reaches to half of H i disks (e.g., Richter & Sancisi 1994) and one third of stellar disks (e.g., Zaritsky & Rix 1997). The fraction of lopsided disks is large, nevertheless their origin is not understood well. Although some theoretical models are proposed to explain the lopsidedness, dynamical friction between lopsided disks and spherical halos has not been taken into account. Then, in this contribution, we have examined the effect of dynamical friction on lopsided disks. To avoid discreteness noise due to small number of particles on the estimate of dynamical friction, we have used the matrix method.

The Color-Magnitude Relation in Coma: Clues to the Age and Metallicity of Cluster Populations

We have observed three fields of the Coma Cluster of galaxies with a narrowband (modified Stromgren) filter system. Observed galaxies include 31 in the vicinity of NGC 4889, 48 near NGC 4874, and 60 near NGC 4839, complete to M5500 = -18 in all three subclusters. Spectrophotometric classification finds all three subclusters of Coma to be dominated by red, E-type (elliptical/S0) galaxies with a mean blue fraction, fB, of 0.10. The blue fraction increases to fainter luminosities, possible remnants of dwarf starburst population or the effects of dynamical friction removing bright, blue galaxies from the cluster population by mergers. We find the color-magnitude (CM) relation to be well defined and linear over the range of M5500 = -13 to -22. The observational error is lower than the true scatter around the CM relation, indicating that galaxies achieve their final positions in the mass-metallicity plane by stochastic processes. After calibration to multimetallicity models, bright elliptical galaxies are found to have luminosity-weighted mean [Fe/H] values between -0.5 and +0.5, whereas low-luminosity elliptical galaxies have [Fe/H] values ranging from -2 to solar. The lack of CM relation in our continuum color suggests that a systematic age effect cancels the metallicity effects in this bandpass. This is confirmed with our age index Δ(bz-yz), which finds a weak correlation between luminosity and mean stellar age in elliptical galaxies such that the stellar populations of bright elliptical galaxies are 2–3 Gyrs younger than low-luminosity elliptical galaxies. With respect to environmental effects, there is a slight decreasing metallicity gradient with respect to distance to each subcluster center, strongest around NGC 4874. Since NGC 4874 is the dynamic and X-ray center of the Coma Cluster, this implies that environmental effects on low-luminosity elliptical galaxies are strongest at the cluster core compared with outlying subgroups.

The effects of photoionization on galaxy formation - I. Model and results atz=0

We develop a coupled model for the evolution of the global properties of the intergalactic medium (IGM) and the formation of galaxies, in the presence of a photoionizing background due to stars and quasars. We use this model to predict the thermodynamic history of the IGM when photoionized by galaxies forming in a cold dark matter (CDM) universe. The evolution of the galaxies is calculated using a semi-analytical model, including a detailed treatment of the effects of tidal stripping and dynamical friction on satellite galaxies orbiting inside larger dark matter haloes. We include in the model the negative feedback on galaxy formation from the photoionizing background. Photoionization inhibits galaxy formation in low-mass dark matter haloes in two ways: (i) heating of the IGM and inhibition of the collapse of gas into dark haloes by the IGM pressure, and (ii) reduction in the rate of radiative cooling of gas within haloes. The result of our method is a self-consistent model of galaxy formation and the IGM. The IGM is reheated twice (during reionization of H I and He II), and we find that the star formation rate per unit volume is slightly suppressed after each episode of reheating. We find that galaxies brighter than L★ are mostly unaffected by reionization, while the abundance of faint galaxies is significantly reduced, leading to present-day galaxy luminosity functions with shallow faint-end slopes, in good agreement with recent observational data. Reionization also affects other properties of these faint galaxies, in a readily understandable way.

Lifetime of a Lopsided Pattern: Damping of Lopsided Disks by Dynamical Friction

The effect of dynamical friction on the time evolution of lopsided disks is examined by using linear perturbation theory. The friction is caused by the gravitational interaction of a rotating lopsided pattern with a density wake induced in halos. The density wake is determined by solving the linearized collisionless Boltzmann and Poisson equations by means of the Fourier-Laplace transform. Then, it is found that dynamical friction always damps a lopsided pattern in our halo model. In addition, the damping time is much shorter than a Hubble time, typically 1 Gyr, unless the pattern speed is quite slow. Considering such a short damping timescale and the observed large fraction of lopsided disks in spirals, say, 30%, it will be unlikely that all of the lopsided disks are recently excited. Thus, it is suggested that most of the observed lopsided disks are very slowly rotating patterns. The significance of weakly damped modes that have a slow pattern speed is discussed.

The Dynamics of Sinking Satellites around Disk Galaxies: A Poor Man’s Alternative to High‐Resolution Numerical Simulations

We have developed a simple yet surprisingly accurate analytic scheme for tracking the dynamical evolution of substructure within larger dark halos. The scheme incorporates the effects of dynamical friction, tidal mass loss and tidal heating via physically motivated approximations. Using our scheme, we can predict the orbital evolution and mass-loss history of individual subhalos in detail. We are also able to determine the impact and importance of the different physical processes on the dynamical evolution of the subhalos. To test and calibrate this model, we compare it with a set of recent high-resolution numerical simulations of mergers between galaxies and small companions. We find that we can reproduce the orbits and mass-loss rates seen in all of these simulations with considerable accuracy, using a single set of values for the three free parameters in our model. Computationally, our scheme is more than 1000 times faster than the simplest of the high-resolution numerical simulations. This means that we can carry out detailed and statistically meaningful investigations into the characteristics of the subhalo population in different cosmologies, the stripping and disruption of the subhalos, and the interactions of the subhalos with other dynamical structures such as a thin disk. This last point is of particular interest given the ubiquity of minor mergers in hierarchical models. In this regard, our method's simplicity and speed makes it particularly attractive for incorporation into semi-analytic models of galaxy formation.

Triplets of Galaxies: Some Dynamical Aspects

In celestial mechanics the 3-body problem has a long and rich history, yet the particular problem of 3-galaxy systems has been rather less studied (see review by Valtonen & Mikkola 1991). Most of the up-to-date works have addressed the 3-galaxy problem using a point-like approach, although some explicit-physics simulations have been performed to simulate dynamical friction effects and merging processes (Zheng et al. 1993). These studies have provided important understanding on the general behaviour of observed galaxy triplets (Karachentsev 2000), and some accordance with observations has been obtained.However galaxies are not point-like particles, but rather consist of a large number of stars which can be approximated as point-like particles. Qualitative and quantitative differences result in the dynamics when the 3-galaxy problem is addressed self-consistently; i. e. when galaxies are able to redistribute energy and angular momentum among their stars. Since not using self-consistent galaxies necessarily casts some doubts on earlier results, we address here the 3-galaxy problem self-consistently and compare some results with observations. A full report on this work is in preparation.

Tracking control of mechanical systems in the presence of nonlinear dynamic friction effects

In this paper, we design an observer-based exact model knowledge position tracking controller for a second-order mechanical system with nonlinear load dynamics and a nonlinear dynamic friction model. Since the controller requires an estimate of the unmeasurable friction state, we demonstrate how the friction dynamics can be exploited to design three different observers which foster different transient response characteristics for the composite closed-loop system. We then present two adaptive controllers which utilize nonlinear observer/filter structures to provide for asymptotic position tracking while compensating for selected parametric uncertainty. Dynamic simulation and experimental results are utilized to illustrate control performance.

The Interplay Between the Nuclear Bars, Central Starburst, and Remarkable Outflow in NGC 2782

We show that the nearby peculiar interacting galaxy NGC 2782 (Arp 215) harbors a clumpy molecular CO bar. The gas bar has a radius of ~7.5″ (1.3 kpc), a mass of ~ 2.4 × 109M⊙, and leads a nuclear stellar bar of similar extent (Jogee et al. 1997b). We estimate the gravitational torque exerted by the nuclear stellar bar and find large gas inflow rates (≫ 1 M⊙ yr−1) into the central 200 pc where the starburst activity peaks. We suggest that the nuclear gas bar will disappear on timescales ranging from few × 108 years to a Gyr, under the effect of star formation, dynamical friction, and gravitational torque. We also show that NGC 2782 harbors a starburst-driven outflow with a remarkable bubble morphology that has not been observed to date in any other starburst galaxy of comparable luminosity (Jogee et al. 1997a). The outflow is driving hot, warm, and possibly cold phases of the ISM out of the central kpc. The estimated outflow rate is less than the inflow rate, and this suggests the dynamical mass in the inner 100 pc might increase by several folds within a Gyr. These results might be relevant to theory (Shlosman et al. 1989) and simulations (Friedli & Martinet 1993) which propose nuclear bars and ‘bars within bars’ as efficient mechanisms for fueling central starbursts/AGNs.

Tidal Torques Dynamical Friction and the Structure of Clusters of Galaxies

We study the joint effect of tidal torques and dynamical friction on the collapse of density peaks solving numerically the equations of motion of a shell of barionic matter falling into the central regions of a cluster of galaxies. We calculate the evolution of the expansion parameter, a(t), of the perturbation using a coefficient of dynamical friction ηcl obtained from a clustered system and taking into account the gravitational interaction of the quadrupole moment of the system with the tidal field of the matter of the neighboring proto-galaxies. We find that the tidal torques and the dynamical friction slow down the collapse of low-v (v < 3) peaks producing an observable variation of a(t) (Del Popolo & Gambera 1996,1997). As consequence we have a reduction of the mass bound to collapsed perturbations and a raising of the critical threshold, δc. Besides, we have a bias of dynamical nature arises because high-density peaks preferentially collapse to form halos within which visible objects. We calculate the selection function and using it and the prescriptions given by Bardeen et al. 1986 we find a value of the coefficient of bias, b = 2.25 on clusters scales for Rf = 4h–1Mpc comparable both with that obtained from the mean mass-to-light ratio of clusters, APM survey, or from N-body simulations combined with hydrodynamical models and with the values of b given by Kauffmann et al. 1996. This means that non-radial motions and dynamical friction play a significant role in determining the bias level.

Evolution of the mass function of the Galactic globular cluster system

In this work we investigate the evolution of the mass function of the Galactic globular cluster system (GCMF) taking into account the effects of stellar evolution, two‐body relaxation, disc shocking and dynamical friction on the evolution of individual globular clusters. We have adopted a lognormal initial GCMF and considered a wide range of initial values for the dispersion, σ, and the mean value, 〈log M〉. We have studied in detail the dependence on the initial conditions of the final values of σ, 〈log M〉, the fraction of the initial number of clusters surviving after one Hubble time and the difference between the properties of the GCMF of clusters closer to the Galactic Centre and those of clusters located in the outer regions of the Galaxy. In most of the cases considered, evolutionary processes alter significantly the initial population of globular clusters and the disruption of a significant number of globular clusters leads to a flattening in the spatial distribution of clusters in the central regions of the Galaxy. The initial lognormal shape of the GCMF is preserved in most cases and if a power‐law in M is adopted for the initial GCMF, evolutionary processes tend to modify it into a lognormal GCMF. The difference between initial and final values of σ and 〈log M〉 as well as the difference between the final values of these parameters for inner and outer clusters can be positive or negative depending on initial conditions. A significant effect of evolutionary processes does not necessarily give rise to a strong trend of 〈log M〉 with the galactocentric distance. The existence of a particular initial GCMF able to keep its initial shape and parameters unaltered during the entire evolution through a subtle balance between disruption of clusters and evolution of the masses of those which survive, suggested by Vesperini, is confirmed.

Evolution of the globular cluster system of a triaxial galaxy

Dynamical friction and tidal disruption are effective mechanisms of evolution of globular cluster systems, especially in non-axysimmetric galaxies with a central compact nucleus. With a semi-analytical approach based on the knowledge of the dependence of the dynamical friction and tidal disruption effects on the relevant parameters, we are able to follow the time evolution of the globular cluster system in a model of a triaxial galaxy and give its observable properties to compare with observational data. An important result is that the flatter distribution of the globular cluster system relatively to that of the stellar bulge, as observed in many galaxies, can be explained by the evolution of the globular cluster system, starting from the same density profile.

Theoretical study of the trans-stilbene isomerization reaction in ethane

A theoretical investigation of the experimental measurements of the isomerization rate of trans-stilbene in liquids is presented. Monte Carlo and molecular dynamics simulations of the reaction indicate that the predominant solvent effect is in raising the isomerization barrier in the potential of mean force as the solvent density is increased. Dynamic friction effects are small. Good agreement is obtained between the numerical and experimental rates.

Evolution of the Galactic Globular Cluster System

Recent surveys of the observational properties of galactic globular clusters have shown the existence of interesting correlations and trends between structural parameters and between structural parameters and location inside the Galaxy (Chernoff & Djorgovski 1989, Djorgovski & Meylan 1994). The origin of most of these correlations is not clear yet and it is not clear to what extent they reflect the primordial conditions or the result of evolution. We have carried out a set of simulations following the evolution of the properties of a globular cluster system (mass function, spatial distribution, correlations between structural parameters) starting from given initial conditions. The evolution of each individual cluster has been followed by the same method applied by Chernoff et al. (1986) and Chernoff & Shapiro (1987). The effects of internal relaxation, disk shocking and dynamical friction have been considered. The main goal of the analysis is that of establishing the role of initial conditions and evolutionary processes in determining the present observational properties.

Comparison of N-Body Simulations to Statistical Observations of Galaxy Pairs

N-body simulations were conducted of pairs of galaxies with a 3:1 mass ratio on parabolic orbits, in order to quantify the effect of dynamical friction. The effects of varying the ratio of the dark matter halo size to the distance of closest approach were explored. Once the dark matter halos are fully overlapping, the more massive simulated galaxies achieve a larger maximum separation after the first encounter despite the increased dynamical friction caused by the more extended halos. Projected separation and radial velocity histograms were generated by "observing" the simulation results at various times and from various orientations. These histograms were compared with observations of galaxy pairs (Charlton & Salpeter 1991; Chengalur, Salpeter, & Terzian 1993) with the result that large halo radii (~200 - 600 kpc) and wide distances of closest approach are generally favored. It is difficult to reconcile the small radial velocity differences that have been observed (median of ~ 30 km/s, Chengalur et al. 1993) with the simulations when we sample all parts of the orbits equally. Including an additional population of wide pairs that have just recently reached "turnabout" from the Hubble flow would lower the median velocity differences. Models suggest that additional data for pairs at intermediate separations should have a somewhat larger median velocity difference than the wide pairs. Very narrow pairs include galaxies which are interacting, and whose gaseous components respond to forces other than gravity. If consistently small $\Delta v$ are measured from neutral hydrogen velocities in a larger sample of narrow pairs, pressure forces and dissipation effects on the gaseous components could be responsible.

Dynamics of Binary Galaxies. III. Details of the Close Pairs

In a previous paper [Chengalur et al. ApJ, 107, 1984(1994)] H I synthesis data and CCD images were presented for an objectively chosen sample of six close spiral-spiral galaxy pairs. In this paper we present a detailed analysis of the data. Although the presence of tidal features was not an explicit selection criterion, five of our six pairs show tidal tails and bridges. The remaining pair also shows signs of interaction: both galaxies in the pair have disturbed velocity fields and one of the two galaxies has a central concentration of molecular gas and is undergoing a starburst. The morphology of three of the six pairs implies that the galaxies are on high eccentricity, low total energy orbits, and for one of these pairs there is some evidence that the impact parameter is as small as ~1 disk radius. For the remaining three pairs the tidal features are not as pronounced, and the observations do not yield as much information on the orbit. However, even for these pairs, the observed morphology is consistent with the galaxies being on slow, small impact parameter orbits, provided the galaxies are at a relatively early phase of the orbit, i.e., prior to the first close encounter. We also find weak evidence for preferential alignment in the pairs (with the lack of preferential alignment being ruled out at the 97% level), in the sense that the major axis of a galaxy tends to point toward the companion galaxy. This sample of close pairs is complemented by a larger sample of wide pairs (Chengalur et al. 1993). The median velocity difference {DELTA}V of the sample of close pairs in low-density regions is not much different from that for the wide pairs sample, in particular, there is no evidence for positive energy impacts. The effect of dynamical friction on infall velocities is controversial and will be discussed in the following paper [Chengalur et al., in preparation (1995)] which combines the data on close and wide pairs.

Triple black holes in the cores of galaxies

We investigate the evolution of black hole (BH) triples in the cores of galaxies. A triple BH system can be formed when a merger remnant of ellipticals having central BHs merges again with another galaxy. The spiral-in of massive BHs, which are proposed as a candidates for constituents of the dark halo of our Galaxy, can also make a triple BH system in the core of the Galaxy. It has been argued that such a triple system will inevitably result in the ejection of at least one of the BHs by the gravitational slingshot. We will show that such a slingshot is unlikely to occur and that two of the three BHs are likely to merge by gravitational radiation. The final state is the binary of this merged BH and the third BH, which may or may not merge by the combined effect of dynamical friction from the stars in the core and gravitational radiation.