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.Comment: 28 pages, 11 figure

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, {\rho}(x) \propto |x|^(-{\gamma}_crit), {\gamma}_crit \simeq 0.47, slightly but significantly shallower than the value {\gamma} = 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 {\gamma}_i > {\gamma}_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.Comment: 14 Pages, 13 Figures. Submitted to MNRA

A class of symplectic integrators with adaptive timestep for separable Hamiltonian systems

Symplectic integration algorithms are well-suited for long-term integrations of Hamiltonian systems because they preserve the geometric structure of the Hamiltonian flow. However, this desirable property is generally lost when adaptive timestep control is added to a symplectic integrator. We describe an adaptive-timestep symplectic integrator that can be used if the Hamiltonian is the sum of kinetic and potential energy components and the required timestep depends only on the potential energy (e.g. test-particle integrations in fixed potentials). In particular, we describe an explicit, reversible, symplectic, leapfrog integrator for a test particle in a near-Keplerian potential; this integrator has timestep proportional to distance from the attracting mass and has the remarkable property of integrating orbits in an inverse-square force field with only "along-track" errors; i.e. the phase-space shape of a Keplerian orbit is reproduced exactly, but the orbital period is in error by O(1/N^2), where N is the number of steps per period.Comment: 24 pages, 3 figures, submitted to Astronomical Journal; minor errors in equations and one figure correcte

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

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

On the Proof of Dark Matter, the Law of Gravity and the Mass of Neutrinos

We develop a new method to predict the density associated with weak lensing maps of (un)relaxed clusters in a range of theories interpolating between GR and MOND (General Relativity and Modified Newtonian Dynamics). We apply it to fit the lensing map of the bullet merging cluster 1E0657-56, in order to constrain more robustly the nature and amount of collisionless matter in clusters {\it beyond} the usual assumption of spherical equilibrium (Pointecouteau & Silk 2005) and the validity of GR on cluster scales (Clowe et al. 2006). Strengthening the proposal of previous authors we show that the bullet cluster is dominated by a collisionless -- most probably non-baryonic -- component in GR as well as in MOND, a result consistent with the dynamics of many X-ray clusters. Our findings add to the number of known pathologies for a purely baryonic MOND, including its inability to fit the latest data from the Wilkinson Microwave Anisotropy Probe. A plausible resolution of all these issues and standard issues of Cold Dark Matter with galaxy rotation curves is the "marriage" of MOND with ordinary hot neutrinos of 2eV. This prediction is just within the GR-independent maximum of neutrino mass from current $\beta$-decay experiments, and is falsifiable by the Karlsruhe Tritium Neutrino (KATRIN) experiment by 2009. Issues of consistency with strong lensing arcs and the large relative velocity of the two clusters comprising the bullet cluster are also addressed.Comment: 4 pages, 1 figure, accepted for publication in ApJL. Added a simple model of the bullet cluster's high velocity in TeVeS, and discussions of sterile neutrinos and of non-uniqueness of the lensing deprojectio

Radio Galaxy NGC 1265 unveils the Accretion Shock onto the Perseus Galaxy Cluster

We present a consistent 3D model for the head-tail radio galaxy NGC 1265 that explains the complex radio morphology and spectrum by a past passage of the galaxy and radio bubble through a shock wave. Using analytical solutions to the full Riemann problem and hydrodynamical simulations, we study how this passage transformed the plasma bubble into a toroidal vortex ring. Adiabatic compression of the aged electron population causes it to be energized and to emit low-surface brightness and steep-spectrum radio emission. The large infall velocity of NGC 1265 and the low Faraday rotation measure values and variance of the jet strongly argue that this transformation was due to the accretion shock onto Perseus situated roughly at R_200. Estimating the volume change of the radio bubble enables inferring a shock Mach number of M = 4.2_{-1.2}^{+0.8}, a density jump of 3.4_{-0.4}^{+0.2}, a temperature jump of 6.3_{-2.7}^{+2.5}, and a pressure jump of 21.5 +/- 10.5 while allowing for uncertainties in the equation of state of the radio plasma and volume of the torus. Extrapolating X-ray profiles, we obtain upper limits on the gas temperature and density in the infalling warm-hot intergalactic medium of kT < 0.4 keV and n < 5e-5 / cm^3. The orientation of the ellipsoidally shaped radio torus in combination with the direction of the galaxy's head and tail in the plane of the sky is impossible to reconcile with projection effects. Instead, this argues for post-shock shear flows that have been caused by curvature in the shock surface with a characteristic radius of 850 kpc. The energy density of the shear flow corresponds to a turbulent-to-thermal energy density of 14%. The shock-injected vorticity might be important in generating and amplifying magnetic fields in galaxy clusters. Future LOFAR observations of head-tail galaxies can be complementary probes of accretion shocks onto galaxy clusters.Comment: 14 pages, 4 figures, ApJ, in print; v3: typos corrected to match the published version; v2: improved presentation, added 2D numerical simulations and exact solution to the 1D Riemann problem of a shock overrunning a spherical bubble that gets transformed into a vortex rin

Resolving the timing problem of the globular clusters orbiting the Fornax dwarf galaxy

We re-investigate the old problem of the survival of the five globular clusters orbiting the Fornax dwarf galaxy in both standard and modified Newtonian dynamics. For the first time in the history of the topic, we use accurate mass models for the Fornax dwarf, obtained through Jeans modelling of the recently published line of sight velocity dispersion data, and we are also not resigned to circular orbits for the globular clusters. Previously conceived problems stem from fixing the starting distances of the globulars to be less than half the tidal radius. We relax this constraint since there is absolutely no evidence for it and show that the dark matter paradigm, with either cusped or cored dark matter profiles, has no trouble sustaining the orbits of the two least massive globular clusters for a Hubble time almost regardless of their initial distance from Fornax. The three most massive globulars can remain in orbit as long as their starting distances are marginally outside the tidal radius. The outlook for modified Newtonian dynamics is also not nearly as bleak as previously reported. Although dynamical friction inside the tidal radius is far stronger in MOND, outside dynamical friction is negligible due to the absence of stars. This allows highly radial orbits to survive, but more importantly circular orbits at distances more than 85% of Fornax's tidal radius to survive indefinitely. The probability of the globular clusters being on circular orbits at this distance compared with their current projected distances is discussed and shown to be plausible. Finally, if we ignore the presence of the most massive globular (giving it a large line of sight distance) we demonstrate that the remaining four globulars can survive within the tidal radius for the Hubble time with perfectly sensible orbits.Comment: 8 pages, 10 figures, 1 table, MNRAS in pres