arXiv subjects

Scott Tremaine

Publications and source records attributed to Scott Tremaine.

At least 73 records · Page 4Linked to original sources

arXiv2013

Dynamics of warped accretion discs

Accretion discs are present around both stellar-mass black holes in X-ray binaries and supermassive black holes in active galactic nuclei. A wide variety of circumstantial evidence implies that many of these discs are warped. The standard Bardeen--Petterson model attributes the shape of the warp to the competition between Lense--Thirring torque from the central black hole and viscous angular-momentum transport within the disc. We show that this description is incomplete, and that torques from the companion star (for X-ray binaries) or the self-gravity of the disc (for active galactic nuclei) can play a major role in determining the properties of the warped disc. Including these effects leads to a rich set of new phenomena. For example, (i) when a companion star is present and the warp arises from a misalignment between the companion's orbital axis and the black hole's spin axis, there is no steady-state solution of the Pringle--Ogilvie equations for a thin warped disc when the viscosity falls below a critical value; (ii) in AGN accretion discs, the warp can excite short-wavelength bending waves that propagate inward with growing amplitude until they are damped by the disc viscosity. We show that both phenomena can occur for plausible values of the black hole and disc parameters, and briefly discuss their observational implications.

astro-ph.HE↗

arXiv2012

Planets Near Mean-Motion Resonances

The multiple-planet systems discovered by the Kepler mission exhibit the following feature: planet pairs near first-order mean-motion resonances prefer orbits just outside the nominal resonance, while avoiding those just inside the resonance. We explore an extremely simple dynamical model for planet formation, in which planets grow in mass at a prescribed rate without orbital migration or dissipation. We develop an analytic version of this model for two-planet systems in two limiting cases: the planet mass grows quickly or slowly relative to the characteristic resonant libration time. In both cases the distribution of systems in period ratio develops a characteristic asymmetric peak-trough structure around the resonance, qualitatively similar to that observed in the Kepler sample. We verify this result with numerical integrations of the restricted three-body problem. We show that for the 3:2 resonance, where the observed peak-trough structure is strongest, our simple model is consistent with the observations for a range of mean planet masses 20-100M_{\oplus}. This mass range is higher than expected, by at least a factor of three, from the few Kepler planets with measured masses, but part of this discrepancy could be due to oversimplifications in the dynamical model or uncertainties in the planetary mass-radius relation.

astro-ph.EP↗

arXiv2012

On the local dark matter density

An analysis of the kinematics of 412 stars at 1-4 kpc from the Galactic mid-plane by Moni Bidin et al. (2012) has claimed to derive a local density of dark matter that is an order of magnitude below standard expectations. We show that this result is incorrect and that it arises from the assumption that the mean azimuthal velocity of the stellar tracers is independent of Galactocentric radius at all heights. We substitute the assumption, supported by data, that the circular speed is independent of radius in the mid-plane. We demonstrate that the assumption of constant mean azimuthal velocity is implausible by showing that it requires the circular velocity to drop more steeply than allowed by any plausible mass model, with or without dark matter, at large heights above the mid-plane. Using the approximation that the circular velocity curve is flat in the mid-plane, we find that the data imply a local dark-matter density of 0.008 +/- 0.003 Msun/pc^3 = 0.3 +/- 0.1 GeV/cm3, fully consistent with standard estimates of this quantity. This is the most robust direct measurement of the local dark-matter density to date.

astro-ph.GA↗

arXiv2012

Gravitational Collapse in One Dimension

We simulate the evolution of one-dimensional gravitating collisionless systems from non- equilibrium initial conditions, similar to the conditions that lead to the formation of dark- matter halos in three dimensions. As in the case of 3D halo formation we find that initially cold, nearly homogeneous particle distributions collapse to approach a final equilibrium state with a universal density profile. At small radii, this attractor exhibits a power-law behavior in density, ρ(x) \propto |x|^(-γ_crit), γ_crit \simeq 0.47, slightly but significantly shallower than the value γ = 1/2 suggested previously. This state develops from the initial conditions through a process of phase mixing and violent relaxation. This process preserves the energy ranks of particles. By warming the initial conditions, we illustrate a cross-over from this power-law final state to a final state containing a homogeneous core. We further show that inhomogeneous but cold power-law initial conditions, with initial exponent γ_i > γ_crit, do not evolve toward the attractor but reach a final state that retains their original power-law behavior in the interior of the profile, indicating a bifurcation in the final state as a function of the initial exponent. Our results rely on a high-fidelity event-driven simulation technique.

astro-ph.CO↗

arXiv2012

Density waves in debris discs and galactic nuclei

We study the linear perturbations of collisionless near-Keplerian discs. Such systems are models for debris discs around stars and the stellar discs surrounding supermassive black holes at the centres of galaxies. Using a finite-element method, we solve the linearized collisionless Boltzmann equation and Poisson's equation for a wide range of disc masses and rms orbital eccentricities to obtain the eigenfrequencies and shapes of normal modes. We find that these discs can support large-scale `slow' modes, in which the frequency is proportional to the disc mass. Slow modes are present for arbitrarily small disc mass so long as the self-gravity of the disc is the dominant source of apsidal precession. We find that slow modes are of two general types: parent modes and hybrid child modes, the latter arising from resonant interactions between parent modes and singular van Kampen modes. The most prominent slow modes have azimuthal wavenumbers $m=1$ and $m=2$. We illustrate how slow modes in debris discs are excited during a fly-by of a neighbouring star. Many of the non-axisymmetric features seen in debris discs (clumps, eccentricity, spiral waves) that are commonly attributed to planets could instead arise from slow modes; the two hypotheses can be distinguished by long-term measurements of the pattern speed of the features.

astro-ph.EP↗

arXiv2011

Super-Eccentric Migrating Jupiters

An important class of formation theories for hot Jupiters involves the excitation of extreme orbital eccentricity (e=0.99 or even larger) followed by tidal dissipation at periastron passage that eventually circularizes the planetary orbit at a period less than 10 days. In a steady state, this mechanism requires the existence of a significant population of super-eccentric (e>0.9) migrating Jupiters with long orbital periods and periastron distances of only a few stellar radii. For these super-eccentric planets, the periastron is fixed due to conservation of orbital angular momentum and the energy dissipated per orbit is constant, implying that the rate of change in semi-major axis a is \dot a \propto a^0.5 and consequently the number distribution satisfies dN/dlog a\propto a^0.5. If this formation process produces most hot Jupiters, Kepler should detect several super-eccentric migrating progenitors of hot Jupiters, allowing for a test of high-eccentricity migration scenarios.

astro-ph.EP↗

arXiv2011

The statistics of multi-planet systems

We describe statistical methods for measuring the exoplanet multiplicity function - the fraction of host stars containing a given number of planets - from transit and radial-velocity surveys. The analysis is based on the approximation of separability - that the distribution of planetary parameters in an n-planet system is the product of identical 1-planet distributions. We review the evidence that separability is a valid approximation for exoplanets. We show how to relate the observable multiplicity function in surveys with similar host-star populations but different sensitivities. We also show how to correct for geometrical selection effects to derive the multiplicity function from transit surveys if the distribution of relative inclinations is known. Applying these tools to the Kepler transit survey and radial-velocity surveys, we find that (i) the Kepler data alone do not constrain the mean inclination of multi-planet systems; even spherical distributions are allowed by the data but only if a small fraction of host stars contain large planet populations (> 30); (ii) comparing the Kepler and radial-velocity surveys shows that the mean inclination of multi-planet systems lies in the range 0-5 degrees; (iii) the multiplicity function of the Kepler planets is not well-determined by the present data.

astro-ph.EP↗

arXiv2011

Observational selection effects and the M-sigma relation

We examine the possibility that the observed relation between black-hole mass and host-galaxy stellar velocity dispersion (the M-sigma relation) is biased by an observational selection effect, the difficulty of detecting a black hole whose sphere of influence is smaller than the telescope resolution. In particular, we critically investigate recent claims that the M-sigma relation only represents the upper limit to a broad distribution of black-hole masses in galaxies of a given velocity dispersion. We find that this hypothesis can be rejected at a high confidence level, at least for the early-type galaxies with relatively high velocity dispersions (median 268 km/s) that comprise most of our sample. We also describe a general procedure for incorporating observational selection effects in estimates of the properties of the M-sigma relation. Applying this procedure we find results that are consistent with earlier estimates that did not account for selection effects, although with larger error bars. In particular, (i) the width of the M-sigma relation is not significantly increased; (ii) the slope and normalization of the M-sigma relation are not significantly changed; (iii) most or all luminous early-type galaxies contain central black holes at zero redshift. Our results may not apply to late-type or small galaxies, which are not well-represented in our sample.

astro-ph.CO↗

arXiv2011

Symplectic integrators in the shearing sheet

The shearing sheet is a model dynamical system that is used to study the small-scale dynamics of astrophysical disks. Numerical simulations of particle trajectories in the shearing sheet usually employ the leapfrog integrator, but this integrator performs poorly because of velocity-dependent (Coriolis) forces. We describe two new integrators for this purpose; both are symplectic, time-reversible and second-order accurate, and can easily be generalized to higher orders. Moreover, both integrators are exact when there are no small-scale forces such as mutual gravitational forces between disk particles. In numerical experiments these integrators have errors that are often several orders of magnitude smaller than competing methods. The first of our new integrators (SEI) is well-suited for disks in which the typical inter-particle separation is large compared to the particles' Hill radii (e.g., planetary rings), and the second (SEKI) is designed for disks in which the particles are on bound orbits or the separation is smaller than the Hill radius (e.g., irregular satellites of the giant planets).

astro-ph.EP↗

arXiv2011

The Black-Hole Mass in M87 from Gemini/NIFS Adaptive Optics Observations

We present the stellar kinematics in the central 2" of the luminous elliptical galaxy M87 (NGC 4486), using laser adaptive optics to feed the Gemini telescope integral-field spectrograph, NIFS. The velocity dispersion rises to 480 km/s at 0.2". We combine these data with extensive stellar kinematics out to large radii to derive a black-hole mass equal to (6.6+-0.4)x10^9 Msun, using orbit-based axisymmetric models and including only the NIFS data in the central region. Including previously-reported ground-based data in the central region drops the uncertainty to 0.25x10^9 Msun with no change in the best-fit mass; however, we rely on the values derived from the NIFS-only data in the central region in order to limit systematic differences. The best-fit model shows a significant increase in the tangential velocity anisotropy of stars orbiting in the central region with decreasing radius; similar to that seen in the centers of other core galaxies. The black-hole mass is insensitive to the inclusion of a dark halo in the models --- the high angular-resolution provided by the adaptive optics breaks the degeneracy between black-hole mass and stellar mass-to-light ratio. The present black-hole mass is in excellent agreement with the Gebhardt & Thomas value, implying that the dark halo must be included when the kinematic influence of the black hole is poorly resolved. This degeneracy implies that the black-hole masses of luminous core galaxies, where this effect is important, may need to be re-evaluated. The present value exceeds the prediction of the black hole-dispersion and black hole-luminosity relations, both of which predict about 1x10^9 Msun for M87, by close to twice the intrinsic scatter in the relations. The high-end of the black hole correlations may be poorly determined at present.

astro-ph.CO↗

arXiv2010

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

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.

astro-ph.GA↗

arXiv2010

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

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.

astro-ph.CO↗

arXiv2010

Generalized Schwarzschild's method

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.

astro-ph.IM↗

arXiv2010

Long-lived planetesimal discs

We investigate the survival of planetesimal discs over Gyr timescales, 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, semi-major 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.

astro-ph.EP↗

arXiv2009

The Evolution of Wide Binary Stars

We study the orbital evolution of wide binary stars in the solar neighborhood 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 semi-major 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 \sim 100--300 pc separation, 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 disk stars that should be detectable in large astrometric surveys such as GAIA that can measure accurate three-dimensional distances and velocities.

astro-ph.GA↗

arXiv2009

The M-sigma and M-L Relations in Galactic Bulges and Determinations of their Intrinsic Scatter

We derive improved versions of the relations between supermassive black hole mass (M_BH) and host-galaxy bulge velocity dispersion (sigma) and luminosity (L) (the M-sigma and M-L relations), based on 49 M_BH measurements and 19 upper limits. Particular attention is paid to recovery of the intrinsic scatter (epsilon_0) in both relations. We find log(M_BH / M_sun) = alpha + beta * log(sigma / 200 km/s) with (alpha, beta, epsilon_0) = (8.12 +/- 0.08, 4.24 +/- 0.41, 0.44 +/- 0.06) for all galaxies and (alpha, beta, epsilon_0) = (8.23 +/- 0.08, 3.96 +/- 0.42, 0.31 +/- 0.06) for ellipticals. The results for ellipticals are consistent with previous studies, but the intrinsic scatter recovered for spirals is significantly larger. The scatter inferred reinforces the need for its consideration when calculating local black hole mass function based on the M-sigma relation, and further implies that there may be substantial selection bias in studies of the evolution of the M-sigma relation. We estimate the M-L relationship as log(M_BH / M_sun) = alpha + beta * log(L_V / 10^11 L_sun,V) of (alpha, beta, epsilon_0) = (8.95 +/- 0.11, 1.11 +/- 0.18, 0.38 +/- 0.09); using only early-type galaxies. These results appear to be insensitive to a wide range of assumptions about the measurement errors and the distribution of intrinsic scatter. We show that culling the sample according to the resolution of the black hole's sphere of influence biases the relations to larger mean masses, larger slopes, and incorrect intrinsic residuals.

astro-ph.GA↗

arXiv2008

Dynamics of WIMPs in the solar system and implications for direct and indirect detection

Semi-analytic treatments of the evolution of orbits of weakly interacting massive particles (WIMPs) in the solar system suggest that the WIMPs bound to the solar system may enhance the direct detection rate relative to that of the unbound population by up to a factor of order unity, and boost the flux of neutrinos from WIMP annihilation in the Earth by up to two orders of magnitude. To test these important but uncertain results, we perform a suite of numerical orbit integrations to explore the properties of the bound WIMP population as a function of the WIMP mass and the scattering cross section with baryonic matter. For regions of WIMP parameter space presently allowed by experiments, we find that (i) the bound WIMP population enhances the direct detection rate by at most ~1% relative to the rate from unbound halo WIMPs; (ii) it is unlikely that planned km^3-scale neutrino telescopes will detect neutrinos from WIMP annihilation in the Earth; (iii) the event rate from neutrinos produced by WIMP annihilation in the Sun may be much smaller than implied by the usual calculations, which assume that WIMPs scattered onto bound orbits are rapidly thermalized in the Sun.

astro-ph↗

arXiv2008

Stability of Distant Satellites of Giant Planets in the Solar System

We conduct a systematic survey of the regions in which distant satellites can orbit stably around the four giant planets in the solar system, using orbital integrations of up to $10^9$ yr. In contrast to previous investigations, we use a grid of initial conditions on a surface of section to explore phase space uniformly inside and outside the planet's Hill sphere (radius $r_{\rm H}$; satellites outside the Hill sphere sometimes are also known as quasi-satellites). Our confirmations and extensions of old results and new findings include the following: (i) many prograde and retrograde satellites can survive out to radii $\sim 0.5r_{\rm H}$ and $\sim 0.7r_{\rm H}$, respectively, while some coplanar retrograde satellites of Jupiter and Neptune can survive out to $\sim r_{\rm H}$; (ii) stable orbits do not exist within the Hill sphere at high ecliptic inclinations when the semi-major axis is large enough that the solar tide is the dominant non-Keplerian perturbation; (iii) there is a gap between $\sim r_{\rm H}$ and $2r_{\rm H}$ in which no stable orbits exist; (iv) at distances $\gtrsim 2r_{\rm H}$ stable satellite orbits exist around Jupiter, Uranus and Neptune (but not Saturn). For Uranus and Neptune, in particular, stable orbits are found at distances as large as $\sim 10r_{\rm H}$; (v) the differences in the stable zones beyond the Hill sphere arise mainly from differences in the planet/Sun mass ratio and perturbations from other planets; in particular, the absence of stable satellites around Saturn is mainly due to perturbations from Jupiter. It is therefore likely that satellites at distances $\gtrsim 2r_{\rm H}$ could survive for the lifetime of the solar system around Uranus, Neptune, and perhaps Jupiter.

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