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The purpose of this paper is to study the relations between different concepts of dispersive solution for the Vlasov-Poisson system in the gravitational case. Moreover we give necessary conditions for the existence of partially and totally dispersive solutions and a sufficient condition for the occurence of statistical dispersion. These conditions take the form of inequalities involving the energy, the mass and the momentum of the solution. Examples of dispersive and non-dispersive solutions--steady states, periodic solutions and virialized solutions--are also considered.

This paper contains all known errata in the book "Galactic Dynamics".

MOND predicts a number of laws that galactic dynamics should obey. I give here a thorough description of these laws, their validity domains, and details of their derivation. We do not know which of the existing MOND theories, if any, is a step in the right direction towards the inevitable deeper MOND theory. It is thus important to pinpoint predictions that follow from only the basic premises of MOND: departure from Newtonian dynamics at accelerations a

The Galactic Centre (GC) is a unique place to study the extreme dynamical processes occurring near a super-massive black hole (SMBH). Here we investigate the role of supernova (SN) explosions occurring in massive binary systems lying in a disc-like structure within the innermost parsec. We use a regularized algorithm to simulate 30,000 isolated three-body systems composed of a stellar binary orbiting the SMBH. We start the integration when the primary member undergoes a SN explosion, and we analyze the impact of SN kicks on the orbits of stars and compact remnants. We find that SN explosions scatter the lighter stars in the pair on completely different orbits, with higher eccentricity and inclination. In contrast, stellar-mass black holes (BHs) and massive stars retain memory of the orbit of their progenitor star. Our results suggest that SN kicks are not sufficient to eject BHs from the GC. We thus predict that all BHs that form in situ in the central parsec of our Galaxy remain in the GC, building up a cluster of dark remnants. In addition, the change of NS orbits induced by SNe may partially account for the observed dearth of NSs in the GC. About 40 per cent of remnants stay bound to the stellar companion after the kick; we expect up to 70 per cent of them might become X-ray binaries through Roche-lobe filling. Finally, the eccentricity of some light stars becomes > 0.7 as an effect of the SN kick, producing orbits similar to those of the G1 and G2 dusty objects.

We report a new analysis of stellar dynamics in the Galactic centre, based on improved sky and LOS velocities for >100 stars within a few arcsec of SgrA*. Overall the motions do not deviate strongly from isotropy. For 32 stars with all 3 components determined the absolute, LOS and sky velocities agree well, as for a spherical cluster. The projected radial and tangential motions of all 104 pm stars are also consistent with overall isotropy. However, the projected velocities of the young, early type stars have a strong radial dependence. Most of the bright HeI stars 1-10" from SgrA* are on tangential orbits. This anisotropy of the HeI stars and most of the brighter IRS16 complex members is largely caused by a CW and counter-rotating, coherent rotation pattern. The overall rotation of the young star cluster probably is a remnant of the angular momentum in the cloud these stars formed from. The fainter, fast stars within \~1" of SgrA* appear to be largely moving on radial or very elliptical orbits. We have not detected nonlinear motion for any of them. Most of the SgrA* cluster members also are on CW orbits. Spectroscopy shows them to be early type stars. We propose that the SgrA* cluster stars are those members of the early type cluster with small angular momentum which can plunge to the vicinity of SgrA*. Our anisotropy-independent estimate of the Sun-GC distance is 7.8-8.2 kpc (+/- 0.9 kpc). We include velocity anisotropy in estimating the central mass distribution. We confirm previous conclusions that a compact central mass concentration is present and dominates the potential from 0.01-1 pc. The central mass ranges from 2.6-3.3E6 M_sun. (abridged)

The long-term evolution of stellar orbits bound to a massive centre is studied in order to understand the cores of star clusters in central regions of galaxies. Stellar trajectories undergo tiny perturbation, the origin of which is twofold: (i) gravitational field of a thin gaseous disc surrounding the galactic centre, and (ii) cumulative drag due to successive interactions of the stars with material of the disc. Both effects are closely related because they depend on the total mass of the disc, assumed to be a small fraction of the central mass. It is shown that, in contrast to previous works, most of the retrograde (with respect to the disc) orbits are captured by the central object, presumably a massive black hole. Initially prograde orbits are also affected, so that statistical properties of the central star cluster in quasi-equilibrium may differ significantly from those deduced in previous analyses.

The structure, kinematics and dynamics of the Galactic stellar halo are reviewed including evidence of substructure in the spatial distribution and kinematics of halo stars. Implications for galaxy formation theory are subsequently discussed; in particular it is argued that the observed kinematics of stars in the outer Galactic halo can be used as an important constraint on viable galaxy formation scenarios.

This paper aims to illustrate the applications of resonant Hamiltonian normal forms to some problems of galactic dynamics. We detail the construction of the 1:1 resonant normal form corresponding to a wide class of potentials with self-similar elliptical equi-potentials and apply it to investigate relevant features of the orbit structure of the system. We show how to compute the bifurcation of the main periodic orbits in the symmetry planes of a triaxial ellipsoid and in the meridional plane of an axi-symmetric spheroid and briefly discuss how to refine these results with higher-order approaches.

We present a study of the dynamics and magnetic activity of M dwarfs using the largest spectroscopic sample of low-mass stars ever assembled. The age at which strong surface magnetic activity (as traced by H-alpha) ceases in M dwarfs has been inferred to have a strong dependence on mass (spectral type, surface temperature) and explains previous results showing a large increase in the fraction of active stars at later spectral types. Using spectral observations of more than 40000 M dwarfs from the Sloan Digital Sky Survey, we show that the fraction of active stars decreases as a function of vertical distance from the Galactic plane (a statistical proxy for age), and that the magnitude of this decrease changes significantly for different M spectral types. Adopting a simple dynamical model for thin disk vertical heating, we assign an age for the activity decline at each spectral type, and thus determine the activity lifetimes for M dwarfs. In addition, we derive a statistical age-activity relation for each spectral type using the dynamical model, the vertical distance from the Plane and the H-alpha emission line luminosity of each star (the latter of which also decreases with vertical height above the Galactic plane).

It has been recently shown (Munyaneza, Tsiklauri and Viollier 1998) that the analysis of the orbits of the fast moving stars close to Sgr A$^{*}$ (Eckart and Genzel 1997) provides a valuable tool to probe the gravitational potential near the Galactic center. As an example, we present here the results on a calculation of possible orbits of the star S0-1 in both, the black hole and degenerate neutrino ball scenarios of the central mass, based on the recent measurements of stellar proper motions at the Galactic center by Ghez et al. 1998. Taking into account the error bars of their analysis, it is shown that within a few years time, the orbit of S0-1 may indeed reveal the nature of the supermassive compact dark object at the Galactic center.

We consider the consequences of applying general relativity to the description of the dynamics of a galaxy, given the observed flattened rotation curves. The galaxy is modeled as a stationary axially symmetric pressure-free fluid. In spite of the weak gravitational field and the non-relativistic source velocities, the mathematical system is still seen to be non-linear. It is shown that the rotation curves for various galaxies as examples are consistent with the mass density distributions of the visible matter within essentially flattened disks. This obviates the need for a massive halo of exotic dark matter. We determine that the mass density for the luminous threshold as tracked in the radial direction is $10^{-21.75}$ kg$\cdot$m$^{-3}$ for these galaxies and conjecture that this will be the case for other galaxies yet to be analyzed. We present a velocity dispersion test to determine the extent, if of any significance, of matter that may lie beyond the visible/HI region. Various comments and criticisms from colleagues are addressed.

We consider the consequences of applying general relativity to the description of the dynamics of a galaxy, given the observed flattened rotation curves. The galaxy is modeled as a stationary axially symmetric pressure-free fluid. In spite of the weak gravitational field and the non-relativistic source velocities, the mathematical system is still seen to be non-linear. It is shown that the rotation curves for various galaxies as examples are consistent with the mass density distributions of the visible matter within essentially flattened disks. This obviates the need for a massive halo of exotic dark matter. We determine that the mass density for the luminous threshold as tracked in the radial direction is $10^{-21.75}$ kg$\cdot$m$^{-3}$ for these galaxies and conjecture that this will be the case for other galaxies yet to be analyzed. We present a velocity dispersion test to determine the extent, if of any significance, of matter that may lie beyond the visible/HI region. Various comments and criticisms from colleagues are addressed.

The kinetic motion of the stars of a galaxy is considered within the framework of a relativistic scalar theory of gravitation. This model, even though unphysical, may represent a good laboratory where to study in a rigorous, mathematical way those problems, like the influence of the gravitational radiation on the dynamics, which are still beyond our present understanding of the physical model represented by the Einstein--Vlasov system. The present paper is devoted to derive the equations of the model and to prove the existence of spherically symmetric equilibria with finite radius.

Certain steady states of the Vlasov-Poisson system can be characterized as minimizers of an energy-Casimir functional, and this fact implies a nonlinear stability property of such steady states. In previous investigations by Y. Guo and the author stability was obtained only with respect to spherically symmetric perturbations. In the present investigation we show how to remove this unphysical restriction.

The interstellar diffusion of galactic civilizations is reexamined by potential theory; both numerical and analytical solutions are derived for the nonlinear partial differential equations which specify a range of relevant models, drawn from blast wave physics, soil science, and, especially, population biology. An essential feature of these models is that, for all civilizations, population growth must be limited by the carrying capacity of the environment. Dispersal is fundamentally a diffusion process; a density-dependent diffusivity describes interstellar emigration. Two models are considered: the first describing zero population growth (ZPG), and the second which also includes local growth and saturation of a planetary population, and for which an asymptotic traveling wave solution is found.

The environment near the massive black hole (MBH) in the Galactic center is very hostile for star formation. Nevertheless, many young stars (both O and B stars) are observed close the MBH. The B-stars seems to have an isotropic, continuous distribution between 0.01 pc and up to a pc. The O (and Wolf-Rayet;WR) stars, in contrast, seem to be distributed in a coherent disk like configuration, extending only between ~0.04 pc to ~0.5 pc. Our current understanding favors an in-situ formation origin for the more massive (O and WR) stars, in gaseous disk and/or streams from an in-falling gas clump. The B-stars seem to have a different origin, more likely through a dynamical capture, following a binary disruption by the MBH. This scenario could also be able to explain the origin of hypervelocity stars in the Galactic halo. These and other possible origins of the young stars in the Galactic center are briefly reviewed and their possible observational signatures and constraints are detailed.

Using strong lensing data Milgrom's MOdified Newtonian Dynamics (MOND) or its covariant TeVeS (Tensor-Vector-Scalar Theory) is being examined here as an alternative to the conventional $\Lambda$CDM paradigm. We examine 10 double-image gravitational lensing systems, in which the lens masses have been estimated by stellar population synthesis models. While mild deviations exist, we do not find out that strong cases for outliers to the TeVeS theory.

We look for observational signatures that could discriminate between Newtonian and modified Newtonian (MOND) dynamics in the Milky Way, in view of the advent of large astrometric and spectroscopic surveys. Indeed, a typical signature of MOND is an apparent disk of "phantom" dark matter, which is uniquely correlated with the visible disk-density distribution. Due to this phantom dark disk, Newtonian models with a spherical halo have different signatures from MOND models close to the Galactic plane. The models can thus be differentiated by measuring dynamically (within Newtonian dynamics) the disk surface density at the solar radius, the radial mass gradient within the disk, or the velocity ellipsoid tilt angle above the Galactic plane. Using the most realistic possible baryonic mass model for the Milky Way, we predict that, if MOND applies, the local surface density measured by a Newtonist will be approximately 78 Msun/pc2 within 1.1 kpc of the Galactic plane, the dynamically measured disk scale-length will be enhanced by a factor of 1.25 with respect to the visible disk scale-length, and the local vertical tilt of the velocity ellipsoid at 1 kpc above the plane will be approximately 6 degrees. None of these tests can be conclusive for the present-day accuracy of Milky Way data, but they will be of prime interest with the advent of large surveys such as GAIA.

Using Dynamic Evolution or Emergent Behavior over billions of years to show the observed Galaxy Disks are natural without Dark Matter needed.

The most characteristic high-energy phenomena in the Galactic center (GC) region is the presence of strong K-shell emission lines from highly ionized Si, S, Ar, Ca, Fe and Ni, which form the Galactic Center X-ray Emission (GCXE). These multiple lines suggest that the GCXE is composed of at least two plasmas with temperatures of ~1 and ~7 keV. The GCXE also exhibits the K-shell lines from neutral Si, S, Ar, Ca, Fe and Ni atoms. A debatable issue is the origin of the GCXE plasma; whether it is a diffuse plasma or integrated emission of many unresolved point sources such as cataclysmic variables and active binaries. Detailed spectroscopy for these lines may provide a reliable picture of the GCXE plasma. The origin of the K-shell lines from neutral atoms is most likely the fluorescence by X-rays from a putative past flare of Sgr A*. Therefore ASTRO-H may provide unprecedented data for the past light curve of Sgr A*. All these lines may provide key information for the dynamics of the GCXE, using possible Doppler shift and/or line broadening. This paper overviews these line features and the previous interpretation of their origin. We propose extended or revised science with the ASTRO-H observations of some select objects in the GC region.

Action-angle coordinates are an essential tool for understanding the properties of the six dimensional phase space involved in orbits of stars in galactic potentials. A new method, which does not require specific knowledge of a generating function, is described, implemented and tested that calculates the actions of an orbit in an arbitrary potential of an integrable Hamiltonian given a set of Cartesian phase space points. The method chooses between the simple harmonic oscillator and isochrone potentials to fit the data using a Levenberg-Marquardt routine. An average is taken over the angle coordinates by calculating volumes in phase space using the metric free FiEstAS algorithm. The perfect ellipsoidal potential, with actions chosen a priori, is used to test the output of the algorithm, giving some results that agree within 1%. Minimisation of a sampling error is discussed along with an identification of a source of noise in the data.

We present 0.2" resolution near-infrared integral field spectroscopy of H-alpha emission from six star forming galaxies at z~1.6 (look-back time of ~9.6 Gyr). These observations were obtained with OSIRIS using the Keck Laser Guide Star Adaptive Optics system. All sources have a compact spatial extent of ~1", with an average half light radius of r=2.9 kpc and average dereddened star formation rate of 22 Msolar per year. Based on H-alpha kinematics we find that these six galaxies are dynamically distinguishable, and we classify them as either merger or disk candidate systems. We find three merger systems (HDF-BX1287, HDF-BX1315, and Q1623-BX491) with varying geometries and dynamical properties. Three galaxies (HDF-BMZ1299, Q2343-BX344, and Q2343-BM145) are well-fit by an inclined-disk model with low velocity residuals (20 to 46 km/sec). An average plateau velocity of v_p=185 km/sec is achieved within 1.0 kpc. The majority of observed velocity dispersions (~88 km/sec) can be explained by the residual seeing halo, and are not intrinsic to our sources. However, one merger and one disk candidate have high velocity dispersions (> 200 km/sec) that cannot be solely explained by beam smearing. For two disk candidates, we detect [NII] emission and are able to map the [NII]/H-alpha ratio on kiloparsec scales. In both cases, [NII] emission is more concentrated than H-alpha emission ( < 0.2"), and peak ratios are best explained by the presence of an AGN. These are among the weakest known AGN at high redshift, however their emission is strong enough to impact high redshift metallicity studies that use nebular ratios. All disk candidates have likely completed only a few orbital periods, and if left unperturbed are excellent candidates to become present-day spiral galaxies.

Gaskell et al. (2007) introduced polarization reverberation mapping as a new technique to explore the structure of active galactic nuclei. We present modeling results for the time-dependent polarization signal expected from scattering inside a centrally illuminated spheroid. Such a model setup describes a larger corona surrounding the compact source of an active nucleus. Time-delays between the polarized and the total flux are computed and related to the geometry of the cloud and the viewing angle. When including the in-flow dynamics of the cloud, it is possible to constrain its optical depth and velocity, which enables estimations of the mass inflow rate.

In the framework of the study of the Galactic metallicity gradient and its time evolution, we present new high-resolution spectroscopic observations obtained with FLAMES and the fiber link to UVES at VLT of three open clusters (OCs) located within $\sim$7~kpc from the Galactic Center (GC): NGC~6192, NGC~6404, NGC~6583. We also present new orbit determination for all OCs with Galactocentric distances (R$_{\rm{GC}}) \leq$8~kpc and metallicity from high-resolution spectroscopy. We aim to investigate the slope of the inner disk metallicity gradient as traced by OCs and at discussing its implication on the chemical evolution of our Galaxy. We have derived memberships of a group of evolved stars for each clusters, obtaining a sample of 4, 4, and 2 member stars in NGC~6192, NGC~6404, and NGC~6583, respectively. Using standard LTE analysis we derived stellar parameters and abundance ratios for the iron-peak elements Fe, Ni, Cr, and for the $\alpha$-elements Al, Mg, Si, Ti, Ca. We calculated the orbits of the OCs currently located within 8~kpc from the GC, and discuss their implication on the present-time radial location. {The average metallicities of the three clusters are all oversolar: [Fe/H]= $+0.12\pm0.04$ (NGC~6192), $+0.11\pm0.04$ (NGC 6404), $+0.37\pm0.03$ (NGC 6583). They are in qualitative agreement with their Galactocentric distances, being all internal OCs, and thus expected to be metal richer than the solar neighborhood. The abundance ratios of the other elements over iron [X/Fe] are consistent with solar values. The clusters we have analysed, together with other OC and Cepheid data, confirm a steep gradient in the inner disk, a signature of an evolutionary rate different than in the outer disk.

We follow the sinking of two massive black holes in a spherical stellar system where the black holes become bound under the influence of dynamical friction. Once bound, the binary hardens by three-body encounters with surrounding stars. We find that the binary wanders inside the core, providing an enhanced supply of reaction partners for the hardening. The binary evolves into a highly eccentric orbit leading to coalescence well beyond a Hubble time. These are the first results from a hybrid ``self consistent field'' (SCF) and direct Aarseth N-body integrator (NBODY6), which combines the advantages of the direct force calculation with the efficiency of the field method. The code is designed for use on parallel architectures and is therefore applicable to collisional N-body integrations with extraordinarily large particle numbers (> 10^5). This creates the possibility of simulating the dynamics of both globular clusters with realistic collisional relaxation and stellar systems surrounding supermassive black holes in galactic nuclei.

The study of off-equatorial orbits in razor-thin disks is still in its beginnings. Contrary to what was presented in the literature in recent publications, the vertical stability criterion for equatorial circular orbits cannot be based on the vertical epicyclic frequency, because of the discontinuity in the gravitational field on the equatorial plane. We present a rigorous criterion for the vertical stability of circular orbits in systems composed by a razor-thin disk surrounded by a smooth axially symmetric distribution of matter, the latter representing additional structures such as thick disk, bulge and (dark matter) halo. This criterion is satisfied once the mass surface density of the thin disk is positive. Qualitative and quantitative analyses of nearly equatorial orbits are presented. In particular, the analysis of nearly equatorial orbits allows us to construct an approximate analytical third integral of motion in this region of phase-space, which describes the shape of these orbits in the meridional plane.

The work presented here examines populations of double compact binary systems and tidally enhanced collapsars. We make use of BINPOP and BINKIN, two components of a recently developed population synthesis package. Results focus on correlations of both binary and spatial evolutionary population characteristics. Pulsar and long duration gamma-ray burst observations are used in concert with our models to draw the conclusions that: double neutron star binaries can merge rapidly on timescales of a few million years (much less than that found for the observed double neutron star population), common envelope evolution within these models is a very important phase in double neutron star formation, and observations of long gamma-ray burst projected distances are more centrally concentrated than our simulated coalescing double neutron star and collapsar Galactic populations. Better agreement is found with dwarf galaxy models although the outcome is strongly linked to the assumed birth radial distribution. The birth rate of the double neutron star population in our models range from 4-160 Myr^-1 and the merger rate ranges from 3-150 Myr^-1. The upper and lower limits of the rates results from including electron capture supernova kicks to neutron stars and decreasing the common envelope efficiency respectively. Our double black hole merger rates suggest that black holes should receive an asymmetric kick at birth.

There is an effect in the modified dynamics (MOND) that is conducive to formation of warps. Because of the nonlinearity of the theory the internal dynamics of a galaxy is affected by a perturber over and above possible tidal effects. For example, a relatively distant and light companion or the mean influence of a parent cluster, with negligible tidal effects, could still produce a significant warp in the outer part of a galactic disk. We present results of numerical calculations for simplified models that show, for instance, that a satellite with the (baryonic) mass and distance of the Magellanic clouds can distort the axisymmetric field of the Milky Way enough to produce a warp of the magnitude (and position) observed. Details of the warp geometry remain to be explained: we use a static configuration that can produce only warps with a straight line of nodes. In more realistic simulations one must reckon with the motion of the perturbing body, which sometimes occurs on time scales not much longer than the response time of the disk.

The Galactic center hosts several hundred early-type stars, about 20% of which lie in the so-called clockwise disk, while the remaining 80% do not belong to any disks. The circumnuclear ring (CNR), a ring of molecular gas that orbits the supermassive black hole (SMBH) with a radius of 1.5 pc, has been claimed to induce precession and Kozai-Lidov oscillations onto the orbits of stars in the innermost parsec. We investigate the perturbations exerted by a gas ring on a nearly-Keplerian stellar disk orbiting a SMBH by means of combined direct N-body and smoothed particle hydrodynamics simulations. We simulate the formation of gas rings through the infall and disruption of a molecular gas cloud, adopting different inclinations between the infalling gas cloud and the stellar disk. We find that a CNR-like ring is not efficient in affecting the stellar disk on a timescale of 3 Myr. In contrast, a gas ring in the innermost 0.5 pc induces precession of the longitude of the ascending node Omega, significantly affecting the stellar disk inclination. Furthermore, the combined effect of two-body relaxation and Omega-precession drives the stellar disk dismembering, displacing the stars from the disk. The impact of precession on the star orbits is stronger when the stellar disk and the inner gas ring are nearly coplanar. We speculate that the warm gas in the inner cavity might have played a major role in the evolution of the clockwise disk.

We discuss experiments achievable via monitoring of stellar dynamics near the massive black hole at the Galactic center with a next generation, extremely large telescope (ELT). Given the likely observational capabilities of an ELT and current knowledge of the stellar environment at the Galactic center, we synthesize plausible samples of stellar orbits around the black hole. We use the Markov Chain Monte Carlo method to evaluate the constraints that orbital monitoring places on the matter content near the black hole. Results are expressed as functions of the number N of stars with detectable orbital motions and the astrometric precision dtheta and spectroscopic precision dv at which stellar proper motions and radial velocities are monitored. For N = 100, dtheta = 0.5 mas, and dv = 10 km/s -- a conservative estimate of the capabilities of a 30 meter telescope -- the extended matter distribution enclosed by the orbits will produce measurable deviations from Keplerian motion if >1000 Msun is enclosed within 0.01 pc. The black hole mass and distance to the Galactic center will be measured to better than ~0.1%. Lowest-order relativistic effects, such as the prograde precession, will be detectable if dtheta < 0.5 mas. Higher-order effects, including frame dragging due to black hole spin, requires dtheta < 0.05 mas, or the favorable discovery of a compact, highly eccentric orbit. Finally, we calculate the rate at which monitored stars undergo detectable nearby encounters with background stars. Such encounters probe the mass function of stellar remnants that accumulate near the black hole. We find that ~30 encounters will be detected over a 10 yr baseline for dtheta = 0.5 mas.

Orbital and self-consistent dynamics of non-integrable galaxy models are reviewed. Topics covered include torus construction; resonances; triaxial systems with central singularities; mixing and collisionless relaxation; and chaos in collisional systems.

Orbital and self-consistent dynamics of non-integrable galaxy models are reviewed. Topics covered include torus construction; resonances; triaxial systems with central singularities; mixing and collisionless relaxation; and chaos in collisional systems.

We present the results of time-dependent hydrodynamic calculations of line- driven winds from accretion disks in AGN. To calculate the radiation force, we take into account radiation from the disk and the central engine. The gas temperature and ionization state in the wind are calculated self-consistently. We find that a disk accreting onto a 10^8 MSUN black hole at the rate of 1.8 MSUN/YR can launch a wind at about 10^16 cm from the central engine. The X-rays from the central object are attenuated by the disk atmosphere so they cannot prevent the local disk radiation from pushing matter away from the disk. For a reasonable X-ray opacity, the disk wind can be accelerated by the central UV radiation to velocities of up to 15000 km/s at a distance of about 10^17 cm from the central engine. The covering factor of the disk wind is $\sim 0.2$. The wind is unsteady and consists of an opaque, slow vertical flow near the disk that is bounded on the polar side by a high-velocity stream. A typical column density through the fast stream is a few 10^23 cm^-2. The fast stream contributes nearly 100% to the total wind mass loss rate of 0.5 MSUN/YR.

We propose a new dynamical mechanism to account for the bar off-centering observed in many barred galaxies. It is based on the presence of a m=1 density wave, non-linearly excited by the strong m=2 component due to the linearly unstable bar and by a m=3 mode. N-body simulations suggest that this mechanism is at work in the centers of galaxies, and provide a natural explanation by spontaneously producing bar off-centering which amounts to several tens of parsecs.

We present Sauron 2D spectrography of the central 1.5 kpc of the nearby Sey2 galaxy NGC1068, encompassing the well-known NIR inner bar. We have successively disentangled the respective contributions of the ionized gas and stars, thus deriving their 2D distribution and kinematics. The [OIII] and Hbeta emission lines exhibit very different spatial distribution and kinematics, the latter following inner spiral arms with clumps associated with star formation. Strong inwards streaming motions are observed in both the Hbeta and [OIII] kinematics. The stellar kinematics also exhibit clear signatures of a non-axisymmetric tumbling potential, with a twist in both the velocity and h3 fields. We re-examined the long-slit data of Shapiro et al (2003) using pPXF: a strong decoupling of h3 is revealed, and the central decrease in h4 hinted in the Sauron data is confirmed. These data also suggest that NGC1068 is a good candidate for a so-called sigma-drop. We confirm the possible presence of two pattern speeds. We also examine the stellar kinematics of bars formed in N-body+SPH simulations built from axisymmetric initial conditions. These successfully reproduce a number of properties observed in the 2D kinematics of NGC1068, and the long-slit data, showing that the kinematic signature of the NIR bar is imprinted in the stellar kinematics. The remaining differences between the models and the observed properties are mostly due to the exclusion of star formation and the lack of the primary large-scale oval/bar in the simulations. These models suggest that the inner bar could drive a significant amount of gas down to a scale of ~300 pc. This is consistent with the interpretation of the sigma-drop in NGC1068 being the result of central gas accretion followed by an episode of star formation.

We present Sauron 2D spectrography of the central 1.5 kpc of the nearby Sey2 galaxy NGC1068, encompassing the well-known NIR inner bar. We have successively disentangled the respective contributions of the ionized gas and stars, thus deriving their 2D distribution and kinematics. The [OIII] and Hbeta emission lines exhibit very different spatial distribution and kinematics, the latter following inner spiral arms with clumps associated with star formation. Strong inwards streaming motions are observed in both the Hbeta and [OIII] kinematics. The stellar kinematics also exhibit clear signatures of a non-axisymmetric tumbling potential, with a twist in both the velocity and h3 fields. We re-examined the long-slit data of Shapiro et al (2003) using pPXF: a strong decoupling of h3 is revealed, and the central decrease in h4 hinted in the Sauron data is confirmed. These data also suggest that NGC1068 is a good candidate for a so-called sigma-drop. We confirm the possible presence of two pattern speeds. We also examine the stellar kinematics of bars formed in N-body+SPH simulations built from axisymmetric initial conditions. These successfully reproduce a number of properties observed in the 2D kinematics of NGC1068, and the long-slit data, showing that the kinematic signature of the NIR bar is imprinted in the stellar kinematics. The remaining differences between the models and the observed properties are mostly due to the exclusion of star formation and the lack of the primary large-scale oval/bar in the simulations. These models suggest that the inner bar could drive a significant amount of gas down to a scale of ~300 pc. This is consistent with the interpretation of the sigma-drop in NGC1068 being the result of central gas accretion followed by an episode of star formation.

We simultaneously integrate in a numerical way the equations of motion of both the Magellanic Clouds (MCs) in MOND, MOG and CDM for -1

Electromagnetic observations over the last 15 years have yielded a growing appreciation for the importance of supermassive black holes (SMBH) to the evolution of galaxies, and for the intricacies of dynamical interactions in our own Galactic center. Here we show that future low-frequency gravitational wave observations, alone or in combination with electromagnetic data, will open up unique windows to these processes. In particular, gravitational wave detections in the 10^{-5}-10^{-1} Hz range will yield SMBH masses and spins to unprecedented precision and will provide clues to the properties of the otherwise undetectable stellar remnants expected to populate the centers of galaxies. Such observations are therefore keys to understanding the interplay between SMBHs and their environments.

We present a spectroscopic study and dynamical analysis of ~2600 M7 dwarfs. We confirm our previous finding that the fraction of magnetically active stars decreases with vertical distance from the Galactic plane. We also show that the mean luminosity of the H-alpha emission has a small but statistically significant decrease with distance. Using space motions for ~1300 stars and a simple one-dimensional dynamical simulation, we demonstrate that the drop in the activity fraction of M7 dwarfs can be explained by thin disk dynamical heating and a rapid decrease of magnetic activity at a mean stellar age of ~6-7 Gyr.

We present a spectroscopic study and dynamical analysis of ~2600 M7 dwarfs. We confirm our previous finding that the fraction of magnetically active stars decreases with vertical distance from the Galactic plane. We also show that the mean luminosity of the H-alpha emission has a small but statistically significant decrease with distance. Using space motions for ~1300 stars and a simple one-dimensional dynamical simulation, we demonstrate that the drop in the activity fraction of M7 dwarfs can be explained by thin disk dynamical heating and a rapid decrease of magnetic activity at a mean stellar age of ~6-7 Gyr.

It is well known that steady states of the Vlasov-Poisson system, a widely used model in non-relativistic galactic dynamics, have negative energy. In this paper we derive the analogous property for two relativistic generalizations of the Vlasov-Poisson system: The Nordstr\"om-Vlasov system and the Einstein-Vlasov system. In the first case we show that the energy of steady states is bounded by their total rest mass; in the second case, where we also assume spherical symmetry, we prove an inequality which involves not only the energy and the rest mass, but also the central redshift. In both cases the proof makes use of integral inequalities satisfied by time depedent solutions and which are derived using the vector fields multipliers method.

Massive gravity provides a natural solution for the dark energy problem of cosmology and is also a candidate for resolving the dark matter problem. I demonstrate that, assuming reasonable scaling relations, massive gravity can provide for Milgrom's law of gravity (or "modified Newtonian dynamics") which is known to remove the need for particle dark matter from galactic dynamics. Milgrom's law comes with a characteristic acceleration, Milgrom's constant, which is observationally constrained to $a_0\approx1.1\times10^{-10}$ m/s$^2$. In the derivation presented here, this constant arises naturally from the cosmologically required mass of gravitons like $a_0\propto c\sqrt{\Lambda}\propto c H_0\sqrt{3\Omega_{\Lambda}}$, with $\Lambda$, $H_0$, and $\Omega_{\Lambda}$ being the cosmological constant, the Hubble constant, and the third cosmological parameter, respectively. My derivation suggests that massive gravity could be the mechanism behind both, dark matter and dark energy.

Allowing the energy of a gravitational field to serve partially as its own source allows gravitating bodies to exhibit stronger fields, as if they were more massive. Depending on degree of compaction of the body, the field could be one to five times larger than the newtonian field. This is a comfortable range of increase in field strength and may prove to be of convenience in the study of velocity curves of spirals, of velocity dispersions in clusters of galaxies and in interpreting the Tully-Fisher or Faber-Jackson relations in galaxies or systems of galaxies. The revised gravitation admits of superposition principle but only approximately in systems whose components are widely separated. The revised dynamics admits of the equivalence principle in that, the effective force acting on a test particle is derived from a potential, and could be eliminated in a freely falling frame of reference

In recent work we proposed a novel theory of dark matter (DM) superfluidity that matches the successes of the LambdaCDM model on cosmological scales while simultaneously reproducing MOdified Newtonian Dynamics (MOND) phenomenology on galactic scales. The agents responsible for mediating the MONDian force law are superfluid phonons that couple to ordinary (baryonic) matter. In this paper we propose an alternative way for the MOND phenomenon to emerge from DM superfluidity. The central idea is to use higher-gradient corrections in the superfluid effective theory. These next-to-leading order terms involve gradients of the gravitational potential, and therefore effectively modify the gravitational force law. In the process we discover a novel mechanism for generating the non-relativistic MOND action, starting from a theory that is fully analytic in all field variables. The idea, inspired by the symmetron mechanism, uses the spontaneous breaking of a discrete symmetry. For large acceleration, the symmetry is unbroken and the action reduces to Einstein gravity. For small acceleration, the symmetry is spontaneously broken and the action reduces to MONDian gravity. Cosmologically, however, the universe is always in the Einstein-gravity, symmetry-restoring phase. The expansion history and linear growth of density perturbations are therefore indistinguishable from LambdaCDM cosmology.

The network of cosmic ray observatories reaching across the heliosphere has given new insight into the process of solar modulation, establishing that the decreases occur principally in the outer heliosphere and are produced by interplanetary flow systems; that the hysteresis effects appear to be produced by changes in the rigidity dependence of the diffusion coefficient and that the predicted effects on the cosmic ray gradients associated with the reversal of the solar magnetic field polarity are not observed.

We address the question of the dynamics in the inner 50 pc of the Galactic Centre. In a first step we investigate the cloud-cloud collision rate in the Circumnuclear Disk (CND) with the help of a three dimensional N-body code using gas particles that can have inelastic collisions. The CND might be a longer lived structure than previously assumed. The whole disk-like structure of the CND can thus survive for several million years. A realistic simulation of the CND shows the observed disk height structure. In a second step the environment of the CND is taken into account. Retrograde and prograde encounters of a cloud of several 10^4 M_solar falling onto an already existing nuclear disk using different energy loss rates per collision are simulated. The influence of the energy loss rate per collision on the evolution of the mass accretion and cloud collision rates is strongest for a prograde encounter. A composite data cube of two different snapshots of a prograde encounter together with the CND shows striking similarity with the observed Sgr A cloud complex. The current appearance of the Galactic Centre environment can thus be explained by at least two dynamically distinct features together with the CND. The current mass accretion rate within the CND ranges between 10^-3 and 10^-4 M_solar yr^-1. It can rise up to several 10^-2 M_solar yr^-1 during massive accretion events.

Our understanding of the mechanisms governing the structure and secular evolution galaxies assume nearly integrable Hamiltonians with regular orbits; our perturbation theories are founded on the averaging theorem for isolated resonances. On the other hand, it is well-known that dynamical systems with many degrees of freedom are irregular in all but special cases. The best developed framework for studying the breakdown of regularity and the onset is the Kolmogorov-Arnold-Moser (KAM) theory. Here, we use a numerical version of the KAM procedure to construct regular orbits (tori) and locate irregular orbits (broken tori). Irregular orbits are most often classified in astronomical dynamics by their exponential divergence using Lyapunov exponents. Although their computation is numerically challenging, the procedure is straightforward and they are often used to estimate the measure of regularity. The numerical KAM approach has several advantages: 1) it provides the morphology of perturbed orbits; 2) its constructive nature allows the tori to be used as basis for studying secular evolution; 3) for broken tori, clues to the cause of the irregularity may be found by studying the largest, diverging Fourier terms; and 4) it is more likely to detect weak chaos and orbits close to bifurcation. Conversely, it is not a general technique and works most cleanly for small perturbations. We develop a perturbation theory that includes chaos by retaining an arbitrary number of interacting terms rather than eliminating all but one using the averaging theorem. The companion papers show that models with significant stochasticity seem to be the rule, not the exception.

We consider the dynamical evolution of a disk of stars orbiting a central black hole. In particular, we focus on the effect of the stellar mass function on the evolution of the disk, using both analytic arguments and numerical simulations. We apply our model to the ring of massive stars at ~0.1pc from the Galactic Center, assuming that the stars formed in a cold, circular disk, and find that our model requires the presence of a significant population of massive (>100Msun) stars in order to explain the the observed eccentricities of 0.2-0.3. Moreover, in order to limit the damping of the heavier stars' eccentricities, we also require fewer low-mass stars than expected from a Salpeter mass function, giving strong evidence for a significantly ``top-heavy'' mass function in the rings of stars seen near to the Galactic Center. We also note that the maximum possible eccentricities attainable from circular initial conditions at ages of

The present lecture notes are an introduction to selected topics of {\it Galactic Dynamics}. The focus is on topics that we consider more relevant to the main theme of this workshop, {\it Celestial Mechanics}. This is not intended to be a review article. In fact, any of the topics below could be the subject of a separate review. Only the main ideas and notions are introduced, as well as some important currently open problems in each topic. Some relevant results from our own research are also presented. We discuss topics related mostly to the so-called {\it ellipsoidal components} of galaxies. These are \textbf{a)} the dark halos of both elliptical and disk galaxies, \textbf{b)} the luminous matter in elliptical galaxies, and \textbf{c)} the bulges of disk galaxies. We shall only occasionally refer to the dynamics of disks, bars or spiral structure.

Self-consistent hybrid N-body and SPH simulations are used to give a new and coherent interpretation of the main features standing out from the HI and CO longitude-velocity observations within the Galactic bar. In particular, the traces of the gas associated to the Milky Way's dustlanes can be reliably identified and the 3-kpc arm appears as a gaseous stream rather than a density wave. The bar and the gaseous nuclear ring in the simulations undergo synchronised and long lived oscillations around the centre of mass, and the gas flow always remains non-stationary, suggesting a transient nature of the observed gas kinematics.