Dynamical friction for accelerated motion in a gaseous medium

Dynamical friction arises from the interaction of a perturber and the gravitational wake it excites in the ambient medium. This interaction is usually derived assuming that the perturber has a constant velocity. In realistic situations, motion is accelerated as for instance by dynamical friction itself. Here, we study the effect of acceleration on the dynamical friction force. We characterize the density enhancement associated with a constantly accelerating perturber with rectilinear motion in an infinite homogeneous gaseous medium and show that dynamical friction is not a local force and that its amplitude may depend on the perturber's initial velocity. The force on an accelerating perturber is maximal between Mach 1 and Mach 2, where it is smaller than the corresponding uniform motion friction. In the limit where the perturber's size is much smaller than the distance needed to change the Mach number by unity through acceleration, a subsonic perturber feels a force similar to uniform motion friction only if its past history does not include supersonic episodes. Once an accelerating perturber reaches large supersonic speeds, accelerated motion friction is marginally stronger than uniform motion friction. The force on a decelerating supersonic perturber is weaker than uniform motion friction as the velocity decreases to a few times the sound speed. Dynamical friction on a decelerating subsonic perturber with an initial Mach number larger than 2 is much larger than uniform motion friction and tends to a finite value as the velocity vanishes in contrast to uniform motion friction.     

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.     

Gaseous drag on a gravitational perturber in Modified Newtonian Dynamics and the structure of the wake

We calculate the structure of a wake generated by, and the dynamical friction force on, a gravitational perturber travelling through a gaseous medium of uniform density and constant background acceleration   g _ext  , in the context of Modified Newtonian Dynamics (MOND). The wake is described as a linear superposition of two terms. The dominant part displays the same structure as the wake generated in the Newtonian gravity scaled up by a factor  μ⁻¹( g _ext/ a ₀)  , where a ₀ is the constant MOND acceleration and μ the interpolating function. The structure of the second term depends greatly on the angle between   g _ext  and the velocity of the perturber. We evaluate the dynamical drag force numerically and compare our MOND results with the Newtonian case. We mention the relevance of our calculations to orbit evolution of globular clusters and satellites in a gaseous protogalaxy. Potential differences in the X-ray emission of gravitational galactic wakes in MOND and in Newtonian gravity with a dark halo are highlighted.     

Classes of ring galaxies generated by dynamical friction

Dynamical friction is incorporated in the numerical modeling of colliding ring galaxies. We show that dynamical friction may lead to the capture of an initially unbound companion into a damped oscillatory orbit before ultimately merging with the target disk. In the late stages of its motion the companion may be virtually merged with the main galaxy while rings are still propagating in the disk. This raises the possibility that there exist (at least) two classes of ring galaxies: a class of ring galaxies with separate detached companions in which dynamical friction is too weak to have captured the collider, and a second class with no apparent companion in which the latter has either merged with the target galaxy or has disrupted. These two classes could possibly be identified with O-type and P-type ring galaxies of Few and Madore (1986).     

Dynamical friction force exerted on spherical bodies

We present a rigorous calculation of the dynamical friction force exerted on a spherical massive perturber moving through an infinite homogenous system of field stars. By calculating the shape and mass of the polarization cloud induced by the perturber in the background system, which decelerates the motion of the perturber, we recover Chandrasekhar's drag force law with a modified Coulomb logarithm. As concrete examples, we calculate the drag force exerted on a Plummer sphere or a sphere with the density distribution of a Hernquist profile. It is shown that the shape of the perturber only affects the exact form of the Coulomb logarithm. The latter converges on small scales because encounters of the test and field stars with impact parameters less than the size of the massive perturber become inefficient. We confirm in this way the earlier results based on the impulse approximation of small angle scatterings.     

On acceleration and motion of ions in corona and solar wind

Assuming a stationary, radial, spherically symmetric solar wind and a radial magnetic field direction in the vicinity of the sun, an equation of motion for ions heavier than protons in the solar wind is derived. The general properties of this equation are discussed and the results of numerical integrations are given. These results are based on the assumption of maxwellian velocity distribution functions for electrons, protons and ions, but the effects of first order deviations from such distributions are also presented and discussed. It is shown that dynamical friction, i.e. momentum transfer from protons to heavier ions accounts for the observed fact that heavier ions - if accelerated at all - normally reach the same velocity as the protons in the solar wind. Because of the non-linear relation between dynamical friction and proton-ion velocity difference a minimum proton flux is required to carry a certain ion species in the solar wind. Formulae comparing the minimum fluxes for different ions are given. It is shown that elements up to and beyond iron will be carried along in the solar wind as long as helium is carried along. Substantial isotopic fractionation is possible, in particular in the case of helium. The effects of ion motion and escape on abundances in the corona and in the outer convective zone of the sun are discussed.     

Energy exchange during collision of a pair of disc-sphere galaxies

We have considered the collision of a pair of disc-sphere galaxies under the impulsive approximation to study the variation of the energy change of the disc due to the passage of a spherical galaxy. Various collision parameters like the impact parameter the orientation of the disc galaxy and the relative velocity of the perturber were considered. It is shown that for small impact parameters and high relative velocities, a slightly inclined position of the disc galaxy produces maximum energy exchange. The energy exchange is observed to be asymmetric with respect to the direction of motion of the perturber.     

Dynamical evolutuion of planetesimals driven by a massive planet: First simulations

N-body simulations of the dynamical evolution of proto-planets embedded in a swarm of planetesimals and perturbed by a massive Jupiter-like planet were performed with the GRAPE-4 system recently installed in Marseille observatory. Initially both the protoplanets and the planetesimals are on circular and coplanar orbits distributed in a ring located within the orbital radius of the perturber. The first simulations show that, for a perturber significantly more massive than Jupiter, the system of the proto-planets becomes strongly unstable with the possibility of orbit crossing.     

Effects of stellar wind,dynamical friction,and star mergers on the dynamical evolution of multiple stars

The dynamical evolution of small stellar groups composed of N=6 components was numerically simulated within the framework of a gravitational N-body problem. The effects of stellar mass loss in the form of stellar wind, dynamical friction against the interstellar medium, and star mergers on the dynamical evolution of the groups were investigated. A comparison with a purely gravitational N-body problem was made. The state distributions at the time of 300 initial system crossing times were analyzed. The parameters of the forming binary and stable triple systems as well as the escaping single and binary stars were studied. The star-merger and dynamical-friction effects are more pronounced in close systems, while the stellar wind effects are more pronounced in wide systems. Star-mergers and stellar wind slow down the dynamical evolution. These factors cause the mean and median semimajor axes of the final binaries as well as the semimajor axes of the internal and external binaries in stable triple systems to increase. Star mergers and dynamical friction in close systems decrease the fraction of binary systems with highly eccentric orbits and the mean component mass ratios for the final binaries and the internal and external binaries in stable triple systems. Star mergers and dynamical friction in close systems increase the fraction of stable triple systems with prograde motions. Dynamical friction in close systems can both increase and decrease the mean velocities of the escaping single stars, depending on the density of the interstellar medium and the mean velocity of the stars in the system.     

Supersonic motions of galaxies in clusters

We study motions of galaxies in galaxy clusters formed in the concordance Λ cold dark matter cosmology. We use high-resolution cosmological simulations that follow the dynamics of dark matter and gas and include various physical processes critical for galaxy formation: gas cooling, heating and star formation. Analysing the motions of galaxies and the properties of intracluster gas in a sample of eight simulated clusters at z = 0, we study the velocity dispersion profiles of the dark matter, gas and galaxies. We measure the mean velocity of galaxy motions and gas sound speed as a function of radius and calculate the average Mach number of galaxy motions. The simulations show that galaxies, on average, move supersonically with the average Mach number of ≈1.4, approximately independent of the cluster-centric radius. The supersonic motions of galaxies may potentially provide an important source of heating for the intracluster gas by driving weak shocks and via dynamical friction, although these heating processes appear to be inefficient in our simulations. We also find that galaxies move slightly faster than the dark matter particles. The magnitude of the velocity bias,   b _v ≈ 1.1  , is, however, smaller than the bias estimated for subhaloes in dissipationless simulations. Interestingly, we find velocity bias in the tangential component of the velocity dispersion, but not in the radial component. Finally, we find significant random bulk motions of gas. The typical gas velocities are of order ≈20–30 per cent of the gas sound speed. These random motions provide about 10 per cent of the total pressure support in our simulated clusters. The non-thermal pressure support, if neglected, will bias measurements of the total mass in the hydrostatic analyses of the X-ray cluster observations.     

Relativistic dynamical friction in a collisional fluid

The dynamical friction force experienced by a body moving at relativistic speed in a gaseous medium is examined. This force, which arises due to the gravitational interaction of the body with its own gravitationally-induced wake, is calculated for straight-line motion and circular motion, generalizing previous results by several authors. Possible applications to the study of extreme mass-ratio inspirals around strongly accreting supermassive black holes are suggested.     

Orbital motion of a massive object in a dense stellar system

In this paper we show the positional oscillation of a massive object in a dense stellar system by numerical N -body simulations. We found that the central massive object, which at first is placed at rest at the centre of the surrounding spherical stellar system, promptly departs from the centre and rotates in accordance with the rotation of the stellar system, if the stellar system has an appreciable rotation. This oscillatory motion continues for a long time because of the absence of dynamical friction. Such a long-lasting oscillation may explain the asymmetric structure observed in the centres of M31 and NGC 4486B, may cause the secular flow of gaseous elements distributed in the central regions of galaxies on to the massive object, and may ignite activity in the centres of galaxies.     

Galaxies in clusters: the observational characteristics of bow shocks, wakes and tails

The dynamical signatures of the interaction between galaxies in clusters and the intracluster medium (ICM) can potentially yield significant information about the structure and dynamical history of clusters. To develop our understanding of this phenomenon we present results from numerical modelling of the galaxy–ICM interaction, as the galaxy moves through the cluster. The simulations have been performed for a broad range of ICM temperatures ( kT _cl=1, 4 and 8 keV), representative of poor clusters or groups through to rich clusters.
There are several dynamical features that can be identified in these simulations. For supersonic galaxy motion, a leading bow shock is present, and also a weak gravitationally focused wake or tail behind the galaxy (analogous to Bondi–Hoyle accretion). For galaxies with higher mass replenishment rates and a denser interstellar medium (ISM), the dominant feature is a dense ram-pressure stripped tail. In line with other simulations, we find that the ICM/galaxy–ISM interaction can result in complex time-dependent dynamics, with ram-pressure stripping occurring in an episodic manner.
In order to facilitate this comparison between the observational consequences of dynamical studies and X-ray observations we have calculated synthetic X-ray flux and hardness maps from these simulations. These calculations predict that the ram-pressure stripped tail will usually be the most visible feature, though in nearby galaxies the bow shock preceding the galaxy should also be apparent in deeper X-ray observations. We briefly discuss these results and compare them with X-ray observations of galaxies where there is evidence of such interactions.     

Enhanced Cloud Disruption by Magnetic Field Interaction

We present results from the first three-dimensional numerical simulations of moderately supersonic cloud motion through a tenuous, magnetized medium. We show that the interaction of the cloud with a magnetic field perpendicular to its motion has a great dynamical impact on the development of instabilities at the cloud surface. Even for initially spherical clouds, magnetic field lines become trapped in surface deformations and undergo stretching. The consequent field amplification that occurs there and, in particular, its variation across the cloud face then dramatically enhance the growth rate of Rayleigh-Taylor unstable modes, hastening the cloud disruption.     

Magnetogravitational instability of a finitely-conducting medium with variable streaming motion

A discussion of gravitational instability of a finitely conducting medium with streams of variable velocity distribution is made in the presence of a uniform magnetic field. It is found that the variable streaming motion shows a destabilizing effect and affects the instability criterion only in the case of general wave propagation. For purely parallel propagation to the direction of the magnetic field and the streaming motion, the criterion is independent of the variation in the streaming motion and further the Jeans's criterion is found to remain unaffected in this case. For purely transverse propagation, the criterion is independent of any streaming motion and the Jeans's criterion remains unaffected. The criterion is further independent of the magnetic field and the finite conductivity except in the case of transverse propagation where the magnetic field exhibits a stabilizing influence in case of an infinitely conducting medium.     

The Parabolic Three-Body Problem

In this communication we present an analytical model for the restricted three-body problem, in the case where the perturber is in a parabolic orbit with respect to the central mass. The equations of motion are derived explicitly using the so-called Global Expansion of the disturbing function, and are valid for any eccentricity of the massless body, as well as in the case where both secondary masses have crossing orbits. Integrating the equations of motion over the complete passage of the perturber through the system, we are then able to construct a first-order algebraic mapping for the change in semimajor axis, eccentricity and inclination of the perturbed body.Comparisons with numerical solutions of the exact equations show that the map yields precise results, as long as the minimum distance between both bodies is not too small. Finally, we discuss several possible applications of this model, including the evolution of asteroidal satellites due to background bodies, and simulations of passing stars on extra-solar planets.     

Arnold diffusion: an overview through dynamical astronomy

The aim of this work is to review the fundamental ideas behind the stability problem, emphasizing the differences between two well-known mechanisms that could lead to chaos, namely overlap of resonances and Arnold diffusion. Here we restrict the discussion to multidimensional autonomous Hamiltonian systems which are of major relevance in Dynamical Astronomy. Arnold diffusion is reviewed in a standard mathematical language, by means of different tools such as heuristic reasoning, graphic and geometrical considerations and numerical experiments. In this direction the pioneer work due to Chirikov [PhR 52 (1979) 263] is followed, but including additional notes, further examples and useful discussions that may well illuminate the understanding of Arnold diffusion. We also summarize the main difficulties when coping with this instability, from both the analytical and numerical sides of the problem. The discussion whether Arnold diffusion could play any role in the dynamical evolution of, for instance elliptical galaxies, is also included.     

Dynamical friction in an isentropic gas

When a gravitating object moves across a given mass distribution, it creates an overdense wake behind it. Here, we performed an analytical study of the structure of the flow far from object when the flow is isentropic and the object moves subsonically within it. We show that the dynamical friction force is the main drag force on the object and by using a perturbation theory, we obtain the density, velocity and pressure of the perturbed flow far from the mass. We derive the expression of the dynamical friction force in an isentropic flow and show its dependence on the Mach number of the flow and on the adiabatic index. We find that the dynamical friction force becomes lower as the adiabatic index increases. We show analytically that the wakes are less dense in our isentropic case in comparison to the isothermal ones.     

Propagation of solitary waves in non uniform dusty plasmas

Interaction of dust acoustic solitary waves in plasmas consisting of medium disorders is investigated. Disorders and inhomogeneities of the medium are added to the equation of motion as perturbative terms through the medium parameters. The effects of these perturbations on the behaviour of solitary waves are studied with numerical simulations and the results are compared with theoretical predictions in a uniform media.