Lattice Stellar Dynamics

We describe a technique for solving the combined collisionless Boltzmann and Poisson equations in a discretised, or lattice, phase space. The time and the positions and velocities of `particles' take on integer values, and the forces are rounded to the nearest integer. The equations of motion are symplectic. In the limit of high resolution, the lattice equations become the usual integro-differential equations of stellar dynamics. The technique complements other tools for solving those equations approximately, such as $N$-body simulation, or techniques based on phase-space grids. Equilibria are found in a variety of shapes and sizes. They are true equilibria in the sense that they do not evolve with time, even slowly, unlike existing $N$-body approximations to stellar systems, which are subject to two-body relaxation. They can also be `tailor-made' in the sense that the mass distribution is constrained to be close to some pre-specified function. Their principal limitation is the amount of memory required to store the lattice, which in practice restricts the technique to modeling systems with a high degree of symmetry. We also develop a method for analysing the linear stability of collisionless systems, based on lattice equilibria as an unperturbed model.Comment: Accepted for publication in Monthly Notices. 18 pages, compressed PostScript, also available from http://www.cita.utoronto.ca/~syer/papers

Made-to-measure N-body systems

We describe an algorithm for constructing N-body realisations of equilibrium stellar systems. The algorithm complements existing orbit-based modelling techniques using linear programming or other optimization algorithms. The equilibria are constructed by integrating an N-body system while slowly adjusting the masses of the particles until the time-averaged density field and other observables converge to a prescribed value. The procedure can be arranged to maximise a linear combination of the entropy of the system and the $\chi^2$ statistic for the observables. The equilibria so produced may be useful as initial conditions for N-body simulations or for modelling observations of individual galaxies.Comment: 8 pages, tex, figures included, accepted by MNRAS, also available at http://www.mpa-garching.mpg.de/~syer/papers

Dark Matter from Early Decays

Two leading dark matter candidates from supersymmetry and other theories of physics beyond the standard model are WIMPs and weak scale gravitinos. If the lightest stable particle is a gravitino, then a WIMP will decay into it with a natural lifetime of order a month ~ M_{pl}^2/M_{weak}^3. We show that if the bulk of dark matter today came from decays of neutral particles with lifetimes of order a year or smaller, then it could lead to a reduction in the amount of small scale substructure, less concentrated halos and constant density cores in the smallest mass halos. Such beneficial effects may therefore be realized naturally, as discussed by Cembranos, Feng, Rajaraman, and Takayama, in the case of supersymmetry.Comment: Matches version accepted for publication in PRD. Added a paragraph to Sec V. 9 pages, 3 figure

Dynamical Origin of Extrasolar Planet Eccentricity Distribution

We explore the possibility that the observed eccentricity distribution of extrasolar planets arose through planet-planet interactions, after the initial stage of planet formation was complete. Our results are based on ~3250 numerical integrations of ensembles of randomly constructed planetary systems, each lasting 100 Myr. We find that for a remarkably wide range of initial conditions the eccentricity distributions of dynamically active planetary systems relax towards a common final equilibrium distribution, well described by the fitting formula dn ~ e exp[-1/2 (e/0.3)^2] de. This distribution agrees well with the observed eccentricity distribution for e > 0.2, but predicts too few planets at lower eccentricities, even when we exclude planets subject to tidal circularization. These findings suggest that a period of large-scale dynamical instability has occurred in a significant fraction of newly formed planetary systems, lasting 1--2 orders of magnitude longer than the ~1 Myr interval in which gas-giant planets are assembled. This mechanism predicts no (or weak) correlations between semimajor axis, eccentricity, inclination, and mass in dynamically relaxed planetary systems. An additional observational consequence of dynamical relaxation is a significant population of planets (>10%) that are highly inclined (>25deg) with respect to the initial symmetry plane of the protoplanetary disk; this population may be detectable in transiting planets through the Rossiter-McLaughlin effect.Comment: Accepted to ApJ, conclusions updated to reflect the current observational constraint

Apsidal Alignment in Upsilon Andromedae

One of the parameters fitted by Doppler radial velocity measurements of extrasolar planetary systems is omega, the argument of pericenter of a given planet's orbit referenced to the plane of the sky. Curiously, the omega's of the outer two planets orbiting Upsilon Andromedae are presently nearly identical: Delta-omega = omega_D - omega_C = 4.8 deg +/- 4.8 deg (1 sigma). This observation is least surprising if planets C and D occupy orbits that are seen close to edge-on (sin i_C, sin i_D > 0.5) and whose mutual inclination Theta does not exceed 20 deg. In this case, planets C and D inhabit a secular resonance in which Delta-omega librates about 0 deg with an amplitude of 30 deg and a period of 4000 yr. The resonant configuration spends about one-third of its time with |Delta-omega| 40 deg, either Delta-omega circulates or the system is unstable. This instability is driven by the Kozai mechanism which couples the eccentricity of planet C to Theta to drive the former quantity to values approaching unity. Our expectation that Theta < 20 deg suggests that planets C and D formed in a flattened, circumstellar disk, and may be tested by upcoming astrometric measurements with the FAME satellite.Comment: Refereed version, accepted by AJ, to appear in September 2001 issu

The Rotation Period of the Planet-Hosting Star HD 189733

We present synoptic optical photometry of HD 189733, the chromospherically active parent star of one of the most intensively studied exoplanets. We have significantly extended the timespan of our previously reported observations and refined the estimate of the stellar rotation period by more than an order of magnitude: $P = 11.953\pm 0.009$ days. We derive a lower limit on the inclination of the stellar rotation axis of 56\arcdeg (with 95% confidence), corroborating earlier evidence that the stellar spin axis and planetary orbital axis are well aligned.Comment: To appear in A

Unstable Disk Galaxies. I. Modal Properties

I utilize the Petrov-Galerkin formulation and develop a new method for solving the unsteady collisionless Boltzmann equation in both the linear and nonlinear regimes. In the first order approximation, the method reduces to a linear eigenvalue problem which is solved using standard numerical methods. I apply the method to the dynamics of a model stellar disk which is embedded in the field of a soft-centered logarithmic potential. The outcome is the full spectrum of eigenfrequencies and their conjugate normal modes for prescribed azimuthal wavenumbers. The results show that the fundamental bar mode is isolated in the frequency space while spiral modes belong to discrete families that bifurcate from the continuous family of van Kampen modes. The population of spiral modes in the bifurcating family increases by cooling the disk and declines by increasing the fraction of dark to luminous matter. It is shown that the variety of unstable modes is controlled by the shape of the dark matter density profile.Comment: Accepted for publication in The Astrophysical Journa

The Dark Matter at the End of the Galaxy

Dark matter density profiles based upon Lambda-CDM cosmology motivate an ansatz velocity distribution function with fewer high velocity particles than the Maxwell-Boltzmann distribution or proposed variants. The high velocity tail of the distribution is determined by the outer slope of the dark matter halo, the large radius behavior of the Galactic dark matter density. N-body simulations of Galactic halos reproduce the high velocity behavior of this ansatz. Predictions for direct detection rates are dramatically affected for models where the threshold scattering velocity is within 30% of the escape velocity.Comment: 10 pages, 5 figure

Thermodynamics of MHD flows with axial symmetry

We present strategies based upon extremization principles, in the case of the axisymmetric equations of magnetohydrodynamics (MHD). We study the equilibrium shape by using a minimum energy principle under the constraints of the MHD axisymmetric equations. We also propose a numerical algorithm based on a maximum energy dissipation principle to compute in a consistent way the equilibrium states. Then, we develop the statistical mechanics of such flows and recover the same equilibrium states giving a justification of the minimum energy principle. We find that fluctuations obey a Gaussian shape and we make the link between the conservation of the Casimirs on the coarse-grained scale and the process of energy dissipation

Evidence for Quasar Activity Triggered by Galaxy Mergers in HST Observations of Dust-reddened Quasars

We present Hubble ACS images of thirteen dust reddened Type-1 quasars selected from the FIRST/2MASS Red Quasar Survey. These quasars have high intrinsic luminosities after correction for dust obscuration (-23.5 > M_B > -26.2 from K-magnitude). The images show strong evidence of recent or ongoing interaction in eleven of the thirteen cases, even before the quasar nucleus is subtracted. None of the host galaxies are well fit by a simple elliptical profile. The fraction of quasars showing interaction is significantly higher than the 30% seen in samples of host galaxies of normal, unobscured quasars. There is a weak correlation between the amount of dust reddening and the magnitude of interaction in the host galaxy, measured using the Gini coefficient and the Concentration index. Although few host galaxy studies of normal quasars are matched to ours in intrinsic quasar luminosity, no evidence has been found for a strong dependence of merger activity on host luminosity in samples of the host galaxies of normal quasars. We thus believe that the high merger fraction in our sample is related to their obscured nature, with a significant amount of reddening occurring in the host galaxy. The red quasar phenomenon seems to have an evolutionary explanation, with the young quasar spending the early part of its lifetime enshrouded in an interacting galaxy. This might be further indication of a link between AGN and starburst galaxies.Comment: 18 pages, 6 low resolution figures, accepted for publication in Ap