On equilibrium rotation of the central object of an accretion disc

The hydrodynamic interaction of an accretion disc with its central object is reanalysed within the framework of the slim-disc approximation. Arguments are presented against an interpretation of the total angular momentum flux as an eigenvalue of the system. A simple intuitive consideration is provided, which shows that the central object may be in a state of stationary rotation even if the disc imposes the constraint of a finite angular momentum flux into it. It is argued that equilibrium rotation is characterized by vanishing viscous torque rather than by zero total angular momentum flux. As a consequence, the central object can be in a state of stationary rotation below the break-up limit, although its angular momentum increases. Despite accretion, even for positive total angular momentum flux and subcritical rotation, central objects are spun down within a considerable range of their parameters. The results are illustrated by application to FU Orionis systems.     

Differential rotation and meridional circulation in global models of solar convection

In the outer envelope of the Sun and in other stars, differential rotation and meridional circulation are maintained via the redistribution of momentum and energy by convective motions. In order to properly capture such processes in a numerical model, the correct spherical geometry is essential. In this paper I review recent insights into the maintenance of mean flows in the solar interior obtained from high-resolution simulations of solar convection in rotating spherical shells. The Coriolis force induces a Reynolds stress which transports angular momentum equatorward and also yields latitudinal variations in the convective heat flux. Meridional circulations induced by baroclinicity and rotational shear further redistribute angular momentum and alter the mean stratification. This gives rise to a complex nonlinear interplay between turbulent convection, differential rotation, meridional circulation, and the mean specific entropy profile. I will describe how this drama plays out in our simulations as well as in solar and stellar convection zones. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of turbulent convection in a slowly rotating red giant star

The first 3-D non-linear hydrodynamical simulation of the inner convective envelope of a rotating low mass red giant star is presented. This simulation, computed with the ASH code, aims at understanding the redistribution of angular momentum and heat in extended convection zones. The convection patterns achieved in the simulation consist of few broad and warm upflows surrounded by a network of cool downflows. This asymmetry between up and downflows leads to a strong downward kinetic energy flux, that must be compensated by an overluminous enthalpy flux in order to carry outward the total luminosity of the star. The influence of rotation on turbulent convection results in the establishment of largescale mean flows: a strong radial differential rotation and a single cell poleward meridional circulation per hemisphere. A detailed analysis of angular momentum redistribution reveals that the meridional circulation transports angular momentum outward in the radial direction and poleward in the latitudinal direction, with the Reynolds stresses acting in the opposite direction. This simulation indicates that the classical hypothesis of mixing length theory and solid-body rotation in the envelope of red giants assumed in 1-D stellar evolution models are unlikely to be realized and thus should be reconsidered. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Criculation in rotating degenerate objects

It is shown that due to degeneracy rather high Eddington-Vogt circulation velocities occur in cooling white dwarfs. The conclusion is that in fast rotating white dwarfs angular momentum is redistributed within a time scale short compared to the cooling time of the star. This might be important for the theory of very oblate rotating white dwarfs.It is shown that similar mechanisms work in the interior of degenerate, rotating cores of evolved stars, where circulations are driven by contraction energy and by neutrino losses. The circulations redistribute the core's matter within time scales shorter than or comparable with the evolution time scale.     

Co-accretion of the Earth-Moon system after the giant impact: reduction of the total angular momentum by lunar impact ejecta

Though the Moon is considered to have been formed by the so-called giant impact, the mass of the Earth immediately after the impact is still controversial. If the Moon was formed during the Earth's accretion, a subsequent accretion of residual heliocentric planetesimals onto the protoearth and the protomoon must have occurred. In this co-accretion stage, a significant amount of lunar-impact-ejecta would be ejected to circumterrestrial orbits, since the mean impact velocity of the planetesimals with the protomoon is much larger than the escape velocity of the protomoon. Orbital calculations of test particles ejected from the protomoon, whose semimajor axis is smaller than that of the present Moon, reveal that most of the particles escaping from the protomoon also escape from the Hill sphere of the protoearth and reduce the planetocentric angular momentum of the primordial Earth-Moon system. Using the results of the ejecta simulations, we investigate the evolution of the mass ratio and the total angular momentum (Earth's spin angular momentum + Moon's orbital angular momentum) of the Earth-Moon system during the co-accretion. We find that the mass of the protomoon is almost constant or rather decreases and the total angular momentum decreases significantly, if the random velocity of planetesimals is as large as the escape velocity of the protoearth. On the other hand, if the random velocity is the half of the escape velocity of the protoearth, the mass ratio is kept to be almost as large as the present value and the decrease of the total angular momentum is not so significant. Comparing with the results of giant impact simulations, we find that the mass of the protoearth immediately after the Moon-forming impact was 0.7-0.8 times the present value if the impactor-to-target mass ratio was 3:7, whereas the giant impact occurred almost in the end of the Earth's accretion if the impactor-to-target mass ratio was 1:9.     

General circulation model simulations of superrotation in slowly rotating atmospheres: Implications for Venus

A series of experiments with a three dimensional general circulation model developed to simulate Earth's atmosphere is run with planetary rotation rates varying between 1 and 1/64 times Earth's rotation rate and diurnally averaged thermal forcing. Results are used to evaluate theories of Venus' atmospheric superrotation which invoke upward transport of angular momentum from the solid planet by the zonal mean (i.e., axisymmetric) circulation. The theories predict that superrotation is a common feature of slowly rotating planetary atmospheres, suggesting that superrotation should appear in the idealized slowly rotating cases of the present study. We find, however, that although dynamical mechanisms suggested for axisymmetric forcing of superrotation appear in model spinups from rest, the steady-state circulations include only weak globally averaged superrotation, consistent with previously reported results from lower resolution models. It appears that during spinup the thermally driven equator-to-pole circulation rapidly generates zonal-mean winds near the planetary surface which preclude vertical angular momentum transport and thus suppress further development of the superrotation. If this is the case, then the diurnally varying component of solar heating, such as atmospheric tides or the “moving flame”, must be included to explain Venus' strong atmospheric superrotation.     

Magnetospheric models of pulsars–outstanding questions

The difficulties of the pulsar magnetosphere problem are illustrated by two models for the axisymmetric magnetic rotator: (a) a classical model, in which the return current problem is linked with angular momentum dissipation’ through incoherent gamma radiation beyond the light-cylinder; and (b) a quantum model, in which electron positron pairs are produced near the star, and spin-down is primarily through the transport of angular momentum by an e+-e-wind. The first model has some pedagogic value, but it makes the embarrassing prediction that all the spin-down energy is emitted as gammaradiation. In the second model a predicted small but significant emission in gamma-and X-rays is again linked with the return current problem, but the bulk of the energy emission is through the wind. The presence of both a high-γ primary electron beam and a moderate-γ pair plasma is as required by most models of coherent microwave emission. Problems persist in ensuring that the macroscopic conditions on the electric field are locally consistent with the microphysics. The most promising picture is of a spontaneous local hydromagnetic instability that yields a large effective resistivity. Some remarks are made on future extension of the theory to oblique geometry. For agreement with observations of the Crab nebula, the predicted dominance in the wind of the Poynting flux must be reversed in the far magnetosphere.     

Protostellar angular momentum transport by spiral density waves

The gravitational collapse of molecular clouds or cloud cores is expected to lead to the formation of stars that begin their lives in a state of rapid rotation. It is known that, in at least some specific cases, rapidly rotating, slf-gravitating bodies are subject to instabilities that cause them to assume ellipsoidal shapes. In this paper we investigate the consequences of such instabilities on the angular momentum evolution of a star in the process of formation from a collapsing cloud, and surrounded by a protostellar disk, with a view toward applications to the formation of the Solar System. We use a specific model of star formation to demonstrate the possibility that such a star would become unstable, that the resulting distortion of the star would generate spiral density waves in the circumstellar disk, and that the torque associated with these waves would regulate the angular momentum of the star as it feeds angular momentum to the disk. We conclude that the angular momentum so transported to the disk would not spread the disk to, say, Solar System dimensions, by the action of the spiral density waves alone. However, a viscous disk could effectively extract stellar angular momentum and attain Solar System size. Our results also indicate that viscous disks could feed mass and angular momentum to a growing protostar in such a manner that distortions of the star would occur before gravitational torques could balance the influx of angular momentum. In other situations (in which the viscosity was small), a gap could be cleared between the disk and star.     

Energy, angular momentum and wave action associated with density waves in a rotating magnetized gas disc

Both fast and slow magnetohydrodynamic (MHD) density waves propagating in a thin rotating magnetized gas disc are investigated. In the tight-winding or WKBJ regime, the radial variation of MHD density-wave amplitude during wave propagation is governed by the conservation of wave action surface density which travels at a relevant radial group speed C _g. The wave energy surface density and the wave angular momentum surface density are related to by = and = m respectively, where is the angular frequency in an inertial frame of reference and the integer m , proportional to the azimuthal wavenumber, corresponds to the number of spiral arms. Consequently, both wave energy and angular momentum are conserved for spiral MHD density waves. For both fast and slow MHD density waves, net wave energy and angular momentum are carried outward or inward for trailing or leading spirals, respectively. The wave angular momentum flux contains separate contributions from gravity torque, advective transport and magnetic torque. While the gravity torque plays an important role, the latter two can be of comparable magnitudes to the former. Similar to the role of gravity torque, the part of MHD wave angular momentum flux by magnetic torque (in the case of either fast or slow MHD density waves) propagates outward or inward for trailing or leading spirals, respectively. From the perspective of global energetics in a magnetized gas sheet in rotation, trailing spiral structures of MHD density waves are preferred over leading ones. With proper qualifications, the generation and maintenance as well as transport properties of MHD density waves in magnetized spiral galaxies are discussed.     

Retrograde precession of stellar orbits and gravitational loss-cone instability in galactic centers

We consider disk and spherical subsystems of stars with nearly radial orbits under conditions when the well-known radial orbit instability is not possible. This requires that the precession of stellar orbits be retrograde, i.e., in the direction opposite to the orbital rotation of stars. We show that an instability that is an analogue of the loss-cone instability known in plasma physics can then develop in the presence of a “loss cone” in the angular momentum distribution of stars, which ensures a deficit or even absence of stars with low angular momenta. Examples of systems with a loss cone are the centers of galaxies or star clusters with massive black holes. The instability can produce a flux of stars onto the galactic center, i.e., it can serve as a mechanism of fueling the nuclear activity of galaxies. Mathematically, the problem is reduced to analyzing simple characteristic equations that describe small perturbations in a disk and a sphere of radially highly elongated stellar orbits. In turn, these characteristics equations are derived through a number of successive simplifications of the general linearized Vlasov equations (i.e., the system that includes the collisionless Boltzmann kinetic equation and the Poisson equation) in action—angle variables.     

Relativistic Jets from Accretion Disks

The jets observed to emanate from many compact accreting objects may arise from the twisting of a magnetic field threading a differentially rotating accretion disk which acts to magnetically extract angular momentum and energy from the disk. Two main regimes have been discussed, hydromagnetic jets, which have a significant mass flux and have energy and angular momentum carried by both matter and electromagnetic field and, Poynting jets, where the mass flux is small and energy and angular momentum are carried predominantly by the electromagnetic field. Here, we describe recent theoretical work on the formation of relativistic Poynting jets from magnetized accretion disks. Further, we describe new relativistic, fully electromagnetic, particle-in-cell (PIC) simulations of the formation of jets from accretion disks. Analog Z-pinch experiments may help to understand the origin of astrophysical jets.     

Rotational fission of contact binary asteroids

The energetics and dynamics of contact binary asteroids as they approach and pass the rotational fission limit is studied. We presume that the asteroids are subject to an external torque, such as from the YORP effect, that increases their angular momentum. Furthermore, we assume the asteroids can be described by a fairly minimal model comprised of a sphere and ellipsoid resting on each other. The minimum energy configurations for contact binary asteroids at different levels of angular momentum are computed and discussed. We find distinct transitions between different configurations as the angular momentum of the system is increased. These indicate that rapidly rotating contact binary asteroids may seek out clearly different relative configurations than slowly rotating systems. We find a single end state of the systems prior to rotational fission, and distinct dynamical outcomes as a function of mass distribution and shape when the rotational fission limit is exceeded. Our theoretical results agree qualitatively with observed properties of near-Earth asteroids, and can be used to help explain the spin-rate barrier, contact binaries, and the observed morphology of most NEO binaries.     

Bounded motion for a modified three-body problem

The energy and the angular momentum integral of motion for the planar three point problem cannot assure bounded motion. In this paper it is shown that if one of the points is replaced by a homogeneous sphere then bounded motion can be found. The zero velocity surfaces for this modified problem are found and their evolution is described.     

On the maintenance of thermal wind balance and equatorial superrotation in Titan's stratosphere

Titan's atmospheric winds, like those on Venus, exhibit superrotation at high altitudes. Titan general circulation models have yielded conflicting results on whether prograde winds in excess of 100 m s⁻¹ at the 1 mbar level are possible based on known physical processes that drive wind systems. A comprehensive two-dimensional (2D) model for Titan's stratosphere was constructed to systematically explore the physical mechanisms that produce and maintain stratospheric wind systems. To ensure conservation of angular momentum in the limit of no net exchange of atmospheric angular momentum with the solid satellite and no external sources and sinks, the zonal momentum equation was solved in flux form for total angular momentum. The relationships among thermal wind balance, meridional circulation, and zonal wind were examined with numerical experiments over a range of values for fundamental input parameters, including planetary rotation rate, radius, internal friction due to wave stresses, and net radiative drive. The magnitude of mid-latitude jets is most sensitive to a single parameter, the planetary rotation rate and results from the conversion of planetary angular momentum to relative angular momentum by the meridional circulation, whereas the strength of meridional circulation is mainly determined by the magnitude of the radiative drive. For Titan's slowly rotating atmosphere, the meridional temperature gradient is vanishingly small, even when the radiative drive is enhanced beyond reasonable magnitudes, and can be inferred from zonal winds in gradient/thermal wind balance. In our 2D model large equatorial superrotation in Titan's stratosphere can be only produced through internal drag forcing by eddy momentum fluxes, which redistribute angular momentum within the atmosphere, while still conserving the total angular momentum of the atmosphere with time. We cannot identify any waves, such as gravitational or thermal tides, that are sufficiently capable of generating the required eddy forcing of >50 m s⁻¹ Titan-day⁻¹ to maintain peak prograde winds in excess of 100 m s⁻¹ at the 1 mbar level.     

Dynamics for galactic archaeology

Our Galaxy is a complex machine in which several processes operate simultaneously: metal-poor gas is accreted, is chemically enriched by dying stars, and then drifts inwards, surrendering its angular momentum to stars; new stars are formed on nearly circular orbits in the equatorial plane and then diffuse through orbit space to eccentric and inclined orbits; the central stellar bar surrenders angular momentum to the surrounding disc and dark halo while acquiring angular momentum from inspiralling gas; the outer parts of the disc are constantly disturbed by satellite objects, both luminous and dark, as they sweep through pericentre. We review the conceptual tools required to bring these complex happenings into focus. Our first concern must be the construction of equilibrium models of the Galaxy, for upon these hang our hopes of determining the Galaxy’s mean gravitational field, which is required for every subsequent step. Ideally our equilibrium model should be formulated so that the secular evolution of the system can be modelled with perturbation theory. Such theory can be used to understand how stars diffuse through orbit space from either the thin gas disc in which we presume disc stars formed, or the debris of an accreted object, the presumed origin of many halo stars. Coupling this understanding to the still very uncertain predictions of the theory of stellar evolution and nucleosynthesis, we can finally extract a complete model of the chemodynamic evolution of our reasonably generic Galaxy. We discuss the relation of such a model to cosmological simulations of galaxy formation, which provide general guidance but cannot be relied on for quantitative detail.     

Accretion of gas on to nearby spiral galaxies

We present evidence for cosmological gas accretion on to spiral galaxies in the local universe. The accretion is seen through its effects on the dynamics of the extraplanar neutral gas. The accretion rates that we estimate for two nearby spiral galaxies are of the order of their star formation rates. Our model shows that most of the extraplanar gas is produced by supernova feedback (galactic fountain) and only 10–20 per cent comes from accretion. The accreting material must have low specific angular momentum about the disc's spin axis, although the magnitude of the specific angular momentum vector can be higher. We also explore the effects of a hot corona on the dynamics of the extraplanar gas and find that it is unlikely to be responsible for the observed kinematical pattern and the source of accreted gas. However, the interaction with the fountain flow should profoundly affect the hydrodynamics of the corona.     

The role of tidal interactions in star formation

Nearly all of the initial angular momentum of the matter that goes into each forming star must somehow be removed or redistributed during the formation process. The possible transport mechanisms and the possible fates of the excess angular momentum are discussed, and it is argued that transport processes in discs are probably not sufficient by themselves to solve the angular momentum problem, while tidal interactions with other stars in forming binary or multiple systems are likely to be of very general importance in redistributing angular momentum during the star formation process. Most, if not all, stars probably form in binary or multiple systems, and tidal torques in these systems can transfer much of the angular momentum from the gas around each forming star to the orbital motions of the companion stars. Tidally generated waves in circumstellar discs may contribute to the overall redistribution of angular momentum. Stars may gain much of their mass by tidally triggered bursts of rapid accretion, and these bursts could account for some of the most energetic phenomena of the earliest stages of stellar evolution, such as jet-like outflows. If tidal interactions are indeed of general importance, planet-forming discs may often have a more chaotic and violent early evolution than in standard models, and shock heating events may be common. Interactions in a hierarchy of subgroups may play a role in building up massive stars in clusters and in determining the form of the upper initial mass function (IMF) . Many of the processes discussed here have analogues on galactic scales, and there may be similarities between the formation of massive stars by interaction-driven accretion processes in clusters and the buildup of massive black holes in galactic nuclei.     

Convection in planetary interiors-the effects of rotation

The conservation equations of mass, energy and momentum are applied to the problem of thermal and non thermal convective motions inside a homogeneous, compressible fluid sphere of uniform viscosity which is rotating with a constant angular velocity about thez-axis. The resulting equations are manipulated into a form which should be suitable for solution.