Central cusp due to a super-massive black hole in axisymmetric models of elliptical galaxies

We use numerical simulations to investigate the cusp at the centre of elliptical galaxies, due to the slow growth of a super-massive black hole. We study this problem for axisymmetric models of galaxies, with or without rotation. The numerical simulations are based on the `Perturbation Particles' method, and use GRAPEs to compute the force due to the cusp. We study how the density cusp is affected by the initial flattening of the model, as well as the role played by initial rotation. The logarithmic slope of the density cusp is found to be very much insensitive to flattening; as a consequence, we deduce that tangential velocity anisotropy -which supports the flattening- is also of little influence on the final cusp. We investigate via two different kinds of rotating models the efficiency with which a rotation velocity component builds within the cusp. A cusp in rotation develops only for models where a net rotation component is initially present at high energy levels. The eventual observation of a central rotational velocity peak in E galaxies has therefore some implications for the galaxy dynamical history.Comment: 16 pages Latex, 19 figures, accepted for publication in MNRA

The Effect of the Outer Lindblad Resonance of the Galactic Bar on the Local Stellar Velocity Distribution

Hydro-dynamical modeling of the inner Galaxy suggest that the radius of the outer Lindblad resonance (OLR) of the Galactic bar lies in the vicinity of the Sun. How does this resonance affect the distribution function in the outer parts of a barred disk, and can we identify any effect of the resonance in the velocity distribution f(v) actually observed in the solar neighborhood? To answer these questions, detailed simulations of f(v) in the outer parts of an exponential stellar disks with nearly flat rotation curves and a rotating central bar have been performed. For a model resembling the old stellar disk, the OLR causes a distinct feature in f(v) over a significant fraction of the outer disk. For positions <2kpc outside the OLR radius and at bar angles of \~10-70 degrees, f(v) inhibits a bi-modality between the low-velocity stars moving like the local standard of rest (LSR) and a secondary mode of stars predominantly moving outward and rotating more slowly than the LSR. Such a bi-modality is indeed present in f(v) inferred from the Hipparcos data for late-type stars in the solar neighborhood. If one interpretes this observed bi-modality as induced by the OLR -- and there are hardly any viable alternatives -- then one is forced to deduce that the OLR radius is slightly smaller than Ro. Moreover, by a quantitative comparison of the observed with the simulated distributions one finds that the pattern speed of the bar is 1.85+/-0.15 times the local circular frequency, where the error is dominated by the uncertainty in bar angle and local circular speed. Also other, less prominent but still significant, features in the observed f(v) resemble properties of the simulated velocity distributions, in particular a ripple caused by orbits trapped in the outer 1:1 resonance.Comment: 14 pages, 10 figures (Fig.2 in full resolution available upon request), accepted for publication in A

Formation of a galaxy with a central black hole in the Lemaitre-Tolman model

We construct two models of the formation a galaxy with a central black hole, starting from a small initial fluctuation at recombination. This is an application of previously developed methods to find a Lemaitre-Tolman model that evolves from a given initial density or velocity profile to a given final density profile. We show that the black hole itself could be either a collapsed object, or a non-vacuum generalisation of a full Schwarzschild-Kruskal-Szekeres wormhole. Particular attention is paid to the black hole's apparent and event horizons.Comment: REVTeX, 22 pages including 11 figures (25 figure files). Replacement has minor changes in response to the referee, and editorial corrections. To appear in PR

Dynamical friction on cold fractal gas clouds,applications to disc formation

It is likely that cold molecular clouds form at high redshift, before galaxies. Considering these cold clouds instead of hot homogeneous gas as the main baryonic component of proto-galactic halos may affect several issues during galaxy formation. In particular, the baryonic matter loses angular momentum through dynamical friction on the dark matter halo. In numerical simulations using hot gas for baryonic matter, this gives rise to the so-called angular momentum problem. In this work, we study the dynamical friction exerted on cold fractal gas by a collisionless background (dark matter) through high-resolution numerical simulations. First, we find that, for values of the parameters relevant during galaxy formation, the friction does not alter the morphology of the fractal, which is mainly driven by internal dynamics. Then, we show that the presence of substructures and inhomogeneities in a body has little effect on the global value of the friction. Parameters such as branching ratio and fractal dimension also have little effect. In fact, we find out that the main effect comes from the deformations and fluctuations of the fractal structure in cold gas clumps. If the deformation time is of the same order of magnitude or shorter than the typical build-up time of the friction, the friction is weakened. We argue that this effect is relevant for galaxy formation, and that the angular momentum problem should not be worsened by including the small scale inhomogeneities of the cold gas which occur at a resolution out of reach of present simulations.Comment: 19 pages, 8 figures, Accepted for publication in A&

Phase transitions in self-gravitating systems. Self-gravitating fermions and hard spheres models

We discuss the nature of phase transitions in self-gravitating systems both in the microcanonical and in the canonical ensemble. We avoid the divergence of the gravitational potential at short distances by considering the case of self-gravitating fermions and hard spheres models. Three kinds of phase transitions (of zeroth, first and second order) are evidenced. They separate a ``gaseous'' phase with a smoothly varying distribution of matter from a ``condensed'' phase with a core-halo structure. We propose a simple analytical model to describe these phase transitions. We determine the value of energy (in the microcanonical ensemble) and temperature (in the canonical ensemble) at the transition point and we study their dependance with the degeneracy parameter (for fermions) or with the size of the particles (for a hard spheres gas). Scaling laws are obtained analytically in the asymptotic limit of a small short distance cut-off. Our analytical model captures the essential physics of the problem and compares remarkably well with the full numerical solutions.Comment: Submitted to Phys. Rev. E. New material adde

A study of the remarkable galaxy system AM 546-324 (the core of Abell S0546)

We report first results of an investigation of the tidally disturbed galaxy system AM\,546-324, whose two principal galaxies 2MFGC 04711 and AM\,0546-324 (NED02) were previously classified as interacting doubles. This system was selected to study the interaction of ellipticals in a moderately dense environment. We provide spectral characteristics of the system and present an observational study of the interaction effects on the morphology, kinematics, and stellar population of these galaxies. The study is based on long-slit spectrophotometric data in the range of $\sim$ 4500-8000 $\AA$ obtained with the Gemini Multi-Object Spetrograph at Gemini South (GMOS-S). We have used the stellar population synthesis code STARLIGHT to investigate the star formation history of these galaxies. The Gemini/GMOS-S direct r-G0303 broad band pointing image was used to enhance and study fine morphological structures. The main absorption lines in the spectra were used to determine the radial velocity. Along the whole long-slit signal, the spectra of the Shadowy galaxy (discovered by us), 2MFGC 04711, and AM\,0546-324 (NED02) resemble that of an early-type galaxy. We estimated redshifts of z= 0.0696, z= 0.0693 and z= 0.0718, corresponding to heliocentric velocities of 20\,141 km s$^{-1}$, 20\,057 km s$^{-1}$, and 20\,754 km s$^{-1}$ for the Shadowy galaxy, 2MFGC 04711 and AM\,0546-324 (NED02), respectively. ..

Statistical mechanics of violent relaxation in stellar systems

We discuss the statistical mechanics of violent relaxation in stellar systems following the pioneering work of Lynden-Bell (1967). The solutions of the gravitational Vlasov-Poisson system develop finer and finer filaments so that a statistical description is appropriate to smooth out the small-scales and describe the ``coarse-grained'' dynamics. In a coarse-grained sense, the system is expected to reach an equilibrium state of a Fermi-Dirac type within a few dynamical times. We describe in detail the equilibrium phase diagram and the nature of phase transitions which occur in self-gravitating systems. Then, we introduce a small-scale parametrization of the Vlasov equation and propose a set of relaxation equations for the coarse-grained dynamics. These relaxation equations, of a generalized Fokker-Planck type, are derived from a Maximum Entropy Production Principle (MEPP). We make a link with the quasilinear theory of the Vlasov-Poisson system and derive a truncated model appropriate to collisionless systems subject to tidal forces. With the aid of this kinetic theory, we qualitatively discuss the concept of ``incomplete relaxation'' and the limitations of Lynden-Bell's theory