Showing papers by "Scott Tremaine published in 2010"

The evolution of wide binary stars

Abstract: We study the orbital evolution of wide binary stars in the solar neighbourhood due to gravitational perturbations from passing stars. We include the effects of the Galactic tidal field and continue to follow the stars after they become unbound. For a wide variety of initial semimajor axes and formation times, we find that the number density (stars per unit logarithmic interval in projected separation) exhibits a minimum at a few times the Jacobi radius r J , which equals 1.7 pc for a binary of solar-mass stars. The density peak interior to this minimum arises from the primordial distribution of bound binaries, and the exterior density, which peaks at a separation of ∼100-300 pc, arises from formerly bound binaries that are slowly drifting apart. The exterior peak gives rise to a significant long-range correlation in the positions and velocities of disc stars that should be detectable in large astrometric surveys such as Gaia that can measure accurate three-dimensional distances and velocities.

A correlation between central supermassive black holes and the globular cluster systems of early-type galaxies

Abstract: Elliptical, lenticular, and early-type spiral galaxies show a remarkably tight power-law correlation between the mass M • of their central supermassive black hole (SMBH) and the number N GC of globular clusters (GCs): M • = m •/ × N 1.08±0.04 GC with m •/ = 1.7 × 105 M ☉. Thus, to a good approximation the SMBH mass is the same as the total mass of the GCs. Based on a limited sample of 13 galaxies, this relation appears to be a better predictor of SMBH mass (rms scatter 0.2 dex) than the M •-σ relation between SMBH mass and velocity dispersion σ. The small scatter reflects the fact that galaxies with high GC specific frequency SN tend to harbor SMBHs that are more massive than expected from the M •-σ relation.

Comparison of approximately isothermal gravitational potentials of elliptical galaxies based on X-ray and optical data

Abstract: We analyze six X-ray bright elliptical galaxies, observed with Chandra and XMM-Newton, and approximate their gravitational potentials by isothermal spheres ϕ =v 2c logr over a range of radii from ∼0.5 to ∼ 25 kpc. We then compare the circularspeed v c derived from X-ray data with the estimators available from optical data. Inparticular we discuss two simple and robust procedures for evaluating the circularspeed of the galaxy using the observed optical surface brightness and the line-of-sight velocity dispersion profiles. The best fitting relation between the circular speedsderived from optical observations of stars and X-ray observations of hot gas is v c,opt ≃η v c,X , where η = 1.10 − 1.15 (depending on the method), suggesting, albeit withlarge statistical and systematic uncertainties, that non-thermal pressure on averagecontributes ∼20-30% of the gas thermal pressure.Key words: Galaxies: Kinematics and Dynamics, X-Rays: Galaxies: Clusters 1 INTRODUCTIONIn spiral galaxies, disk rotation curves offer an accurateand robust way of measuring total gravitational potentialsto distances as large as 10–30 kpc. To a first approxi-mation the rotation curves are flat over a broad rangeof radii, suggesting an isothermal (logarithmic) potentialcharacterized by ϕ(r) = v

Long-lived planetesimal discs

Abstract: We investigate the survival of planetesimal discs over Gyr time-scales, using a unified approach that is applicable to all Keplerian discs of solid bodies – dust grains, asteroids, planets, etc. Planetesimal discs can be characterized locally by four parameters: surface density, semimajor axis, planetesimal size and planetesimal radial velocity dispersion. Any planetesimal disc must have survived all dynamical processes, including gravitational instability, dynamical chaos, gravitational scattering, physical collisions, and radiation forces, that would lead to significant evolution over its lifetime. These processes lead to a rich set of constraints that strongly restrict the possible properties of long-lived discs. Within this framework, we also discuss the detection of planetesimal discs using radial velocity measurements, transits, microlensing and the infrared emission from the planetesimals themselves or from dust generated by planetesimal collisions.

Comparison of an approximately isothermal gravitational potentials of elliptical galaxies based on X-ray and optical data

Abstract: We analyze six X-ray bright elliptical galaxies, observed with Chandra and XMM-Newton, and approximate their gravitational potentials by isothermal spheres phi(r)=v_c^2 ln(r) over a range of radii from ~0.5 to ~25 kpc. We then compare the circular speed v_c derived from X-ray data with the estimators available from optical data. In particular we discuss two simple and robust procedures for evaluating the circular speed of the galaxy using the observed optical surface brightness and the line-of-sight velocity dispersion profiles. The best fitting relation between the circular speeds derived from optical observations of stars and X-ray observations of hot gas is v_{c,opt}~ \eta * v_{c,X}, where \eta=1.10-1.15 (depending on the method), suggesting, albeit with large statistical and systematic uncertainties, that non-thermal pressure on average contributes ~20-30% of the gas thermal pressure.

Resonant relaxation and the warp of the stellar disc in the Galactic centre

Abstract: Observations of the spatial distribution and kinematics of young stars in the Galactic centre can be interpreted as showing that the stars occupy one, or possibly two, discs of radii ~0.05-0.5 pc. The most prominent (`clockwise') disc exhibits a strong warp: the normals to the mean orbital planes in the inner and outer third of the disc differ by ~60 deg. Using an analytical model based on Laplace-Lagrange theory, we show that such warps arise naturally and inevitably through vector resonant relaxation between the disc and the surrounding old stellar cluster.

Generalized Schwarzschild’s method

Abstract: We describe a new finite element method (FEM) to construct continuous equilibrium distribution functions (DFs) of stellar systems. The method is a generalization of Schwarzschild’s orbit superposition method from the space of discrete functions to continuous ones. In contrast to Schwarzschild’s method, FEM produces a continuous DF and satisfies the intra-element continuity and Jeans equations. The method employs two finite element meshes, one in configuration space and one in action space. The DF is represented by its values at the nodes of the action-space mesh and by interpolating functions inside the elements. The Galerkin projection of all equations that involve the DF leads to a linear system of equations, which can be solved for the nodal values of the DF using linear or quadratic programming, or other optimization methods. We illustrate the superior performance of FEM by constructing ergodic and anisotropic equilibrium DFs for spherical stellar systems (Hernquist models). We also show that explicitly constraining the DF by the Jeans equations leads to smoother and/or more accurate solutions with both Schwarzschild’s method and FEM.

A correlation between central supermassive black holes and the globular cluster systems of early-type galaxies

Abstract: Elliptical, lenticular, and early-type spiral galaxies show a remarkably tight power-law correlation between the mass M_BH of their central supermassive black hole (SMBH) and the number N_GC of globular clusters: M_BH=m*N_GC^(1.08+/-0.04) with m=1.7*10^5 solar masses. Thus, to a good approximation the SMBH mass is the same as the total mass of the globular clusters. Based on a limited sample of 13 galaxies, this relation appears to be a better predictor of SMBH mass (rms scatter 0.2 dex) than the M_BH-sigma relation between SMBH mass and velocity dispersion sigma. The small scatter reflects the fact that galaxies with high globular cluster specific frequency S_N tend to harbor SMBHs that are more massive than expected from the M_BH-sigma relation.

Generalized Schwarzschild's method

Abstract: We describe a new finite element method (FEM) to construct continuous equilibrium distribution functions of stellar systems. The method is a generalization of Schwarzschild's orbit superposition method from the space of discrete functions to continuous ones. In contrast to Schwarzschild's method, FEM produces a continuous distribution function (DF) and satisfies the intra element continuity and Jeans equations. The method employs two finite-element meshes, one in configuration space and one in action space. The DF is represented by its values at the nodes of the action-space mesh and by interpolating functions inside the elements. The Galerkin projection of all equations that involve the DF leads to a linear system of equations, which can be solved for the nodal values of the DF using linear or quadratic programming, or other optimization methods. We illustrate the superior performance of FEM by constructing ergodic and anisotropic equilibrium DFs for spherical stellar systems (Hernquist models). We also show that explicitly constraining the DF by the Jeans equations leads to smoother and/or more accurate solutions with both Schwarzschild's method and FEM.