The angular momentum transport in rotating turbulent convection

The angular momentum transport in rotating turbulent convection is simulated with the NIRVANA code for Taylor numbers up to 10⁶. The box consists of an unstable layer embedded in two stable overshoot layers. We find the expected anisotropies in the rotating anisotropic turbulence field: 〈u^′2_r〉 exceeds 〈u^′2_ϕ〉, and 〈u^′2_ϕ〉 exceeds 〈u^′2_θ〉. The resulting radial angular momentum transport is directed inwards and peaks in the middle of the convective layer. The resulting latitudinal angular momentum transport is equatorwards, peaks at the surface and is highly concentrated to the equatorial region. Apart from a factor of 2–3 the total amplitudes of the cross‐correlations are of the same order of magnitude. In the lower overshoot region (‘tachocline’) the cross‐correlations are negative. It is argued that the concentration of the latitudinal angular momentum transport towards the surface and towards the equator does not too strongly reduce its potential to produce rotation laws with accelerated equators. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Tracing spiral density waves in M81

We use Spitzer IRAC 3.6 and 4.5 μm near-infrared data from the Spitzer Infrared Nearby Galaxies Survey (SINGS), optical B, V and I and Two-Micron All-Sky Survey K _s-band data to produce mass surface density maps of M81. The IRAC 3.6- and 4.5-μm data, whilst dominated by emission from old stellar populations, are corrected for small-scale contamination by young stars and polycyclic aromatic hydrocarbon emission. The I -band data are used to produce a mass surface density map by a   B − V   colour correction, following the method of Bell and de Jong. We fit a bulge and exponential disc to each mass map, and subtract these components to reveal the non-axisymmetric mass surface density. From the residual mass maps, we are able to extract the amplitude and phase of the density wave, using azimuthal profiles. The response of the gas is observed via dust emission in the 8-μm IRAC band, allowing a comparison between the phase of the stellar density wave and gas shock. The relationship between this angular offset and radius suggests that the spiral structure is reasonably long-lived and allows the position of corotation to be determined.     

Radial heating of a galactic disc by multiple spiral density waves

We consider a differentially rotating, 2D stellar disc perturbed by two steady-state spiral density waves moving at different pattern speeds. Our investigation is based on direct numerical integration of initially circular test-particle orbits. We examine a range of spiral strengths and spiral speeds and show that stars in this time-dependent gravitational field can be heated (their random motions increased). This is particularly noticeable in the simultaneous propagation of a two-armed spiral density wave near the corotation resonance (CR), and a weak four-armed one near the inner and outer 4:1 Lindblad resonances. In simulations with two spiral waves moving at different pattern speeds, we find: (i) the variance of the radial velocity,  σ² _R   , exceeds the sum of the variances measured from simulations with each individual pattern; (ii)  σ² _R   can grow with time throughout the entire simulation; (iii)  σ² _R   is increased over a wider range of radii compared to that seen with one spiral pattern; and (iv) particles diffuse radially in real space, whereas they do not when only one spiral density wave is present. Near the CR with the stronger, two-armed pattern, test-particles are observed to migrate radially. These effects take place at or near resonances of both spirals, so we interpret them as the result of stochastic motions. This provides a possible new mechanism for increasing the stellar velocity dispersion in galactic discs. If multiple spiral patterns are present in the Galaxy, we predict that there should be large variations in the stellar velocity dispersion as a function of radius.     

Turbulence‐driven angular momentum transport in modulated Kepler flows

The velocity fluctuations in a spherical shell arising from sinusoidal perturbations of a Keplerian shear flow with a free amplitude parameter ε are studied numerically by means of fully 3D nonlinear simulations. The investigations are performed at high Reynolds numbers, i.e. 3000 < Re < 5000. We find Taylor‐Proudman columns of large eddies parallel to the rotation axis for sufficiently strong perturbations. An instability sets in at critical amplitudes with ε_crit ∝ Re^—1. The whole flow turns out to be almost axisymmetric and nonturbulent exhibiting, however, a very rich radial and latitudinal structure. The Reynolds stress 〈u′_ru′_ϕ〉 is positive in the entire computational domain, from its Gaussian radial profile a positive viscosity‐alpha of about 10^—4 is derived. The kinetic energy of the turbulent state is dominated by the azimuthal component 〈u^′2_ϕ whereas the other components are smaller by two orders of magnitude. Our simulations reveal, however, that these structures disappear as soon as the perturbations are switched off. We did not find an “effective” perturbation whose amplitude is such that the disturbance is sustained for large times (cf. Dauchot & Daviaud 1995) which is due to the effective violation of the Rayleigh stability criterion. The fluctuations rapidly smooth the original profile towards to pure Kepler flow which, therefore, proves to be stable in that sense.     

Outward transport of angular momentum by gas convection and the equatorial acceleration of the Sun

A new mechanism for sustaining enhanced rotational velocity of the outer layers of the solar convective envelope is considered.The gas density inside turbulent eddies decreases because of centrifugal scattering of matter. The decrease of density in eddies rotating in the same sense as the Sun on the whole is larger than that in eddies rotating in the opposite sense. As a result, the former ascend while the latter sink down, thus producing a continuous outward flux of angular momentum.A distribution of angular velocity in the radius of the solar convective envelope in the equatorial plane was obtained in the approximation of the mixing length theory of thermal convection. The results agree rather well with observations.     

Propagation of spiral density waves in a magneto-active disk

The propagation of spiral density waves in a differentially rotating, self-gravitating, magnetoactive and highly flattened disk is investigated by using the asymptotic theory for tightly wound spirals developed by Lin and his collaborators. We adopt the continuum fluid model as the primary basis, and our treatment will be largely analytical. The disk plasma is studied in the frozen field approximation and inhomogenceous magnetic fields in the plane of the disk are considered in detail.In a differentially rotating disk with strong magnetic fields, the field lines will be considerably distorted and the mutual influence of magnetic fields and differential rotation is by no means obvious.In this paper we present a new asymptotic dispersion relation for tightly wound spiral density waves with magnetic fields along the spiral armsB (r). The effects of the magnetic fields lead to such terms likek ²(a ² +V _A ² ), wherek is the wave number,a represents the speed of sound,V _A = (B ²/4)^1/2 is the Alfvén speed,B denotes the field strength, and is the plasma density. These terms depict the well-known magnetoacoustic waves and could have been anticipated without a detailed computation. However the interaction of magnetic fields and differential rotation may give rise to other significant terms which are not so easy to foresee.We also present a more exact local dispersion relation by using the WKB approximation and study the effects of magnetic fields on the growth rate through the parametersQ andJ defined in the literature.Although the effects of the magnetic fields are rather insignificant for applications to Galactic dynamics, the effects of the magnetic fields are important for applications to star formation and problems related to the solar nebula.     

Transfer of solar angular momentum by inertial induction

Transfer of angular momentum from the Sun to the planetary system has been found to be inevitable in all evolutionary models for the origin of the solar system. In cold theories it has been proposed to be achieved through friction whereas electromagnetic forces are considered to be the agent for this transfer in hot theories. In the present paper it has been shown that the required order of magnitude of angular momentum can be transferred by another mechanism based on the principle of inertial induction. In the previous theories most of the transfer had been assumed to have taken place during the pre-Main-Sequence period whereas in this proposed theory most of the transfer takes place during the Main-Sequence period of the Sun. The paper does not intend to go into the details of planet formation and the evolutionary process but confines itself only to the problem of angular momentum transfer.     

Constraints on angular momentum transport in the Sun from simulations of the tachocline

I present a new numerical tool for studying the interaction of meridional flows and magnetic fields, and study their role in establishing angular-momentum balance in the solar radiative zone. Quantitative comparisons with helioseismic observations provide stringent constraints on existing models of the dynamics of the solar interior. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The angular momentum of the asteroids

Consideration of the basic physics involved in the structure of the object are used to obtain relationships for the radius, period, angular momentum, etc. of a typical asteroid. The mass-angular momentum relation for asteroids would tend to favour the fragmentation hypothesis.     

The angular momentum of eclipsing binaries

The angular momentum-mass relationship for 1048 eclipsing binaries is presented.     

How galaxies lose their angular momentum

The processes are investigated by which gas loses its angular momentum during the protogalactic collapse phase, leading to disc galaxies that are too compact with respect to the observations. High-resolution N -body/SPH simulations in a cosmological context are presented including cold gas and dark matter (DM). A halo with quiet merging activity since redshift   z ∼ 3.8  and with a high-spin parameter is analysed that should be an ideal candidate for the formation of an extended galactic disc. We show that the gas and the DM have similar specific angular momenta until a merger event occurs at   z ∼ 2  with a mass ratio of 5:1. All the gas involved in the merger loses a substantial fraction of its specific angular momentum due to tidal torques and dynamical friction processes falls quickly into the centre. In contrast, gas infall through small subclumps or accretion does not lead to catastrophic angular momentum loss. In fact, a new extended disc begins to form from gas that was not involved in the 5:1 merger event and that falls in subsequently. We argue that the angular momentum problem of disc galaxy formation is a merger problem: in cold dark matter cosmology substantial mergers with mass ratios of 1:1 to 6:1 are expected to occur in almost all galaxies. We suggest that energetic feedback processes could in principle solve this problem, however only if the heating occurs at the time or shortly before the last substantial merger event. Good candidates for such a coordinated feedback would be a merger-triggered starburst or central black hole heating. If a large fraction of the low angular momentum gas would be ejected, late-type galaxies could form with a dominant extended disc component, resulting from late infall, a small bulge-to-disc ratio and a low baryon fraction, in agreement with observations.     

Oceanic and solid Earth angular momentum

We reconsider two hypotheses used in calculating the transfer of angular momentum between the oceans and the solid Earth: (1) The locked-cean-ypothesis was already given up some time ago; here we provide a simple manner of understanding the relative importance of the motion and matter term. (2) The isolation hypothesis implied the isolation of the whole Earth in short timescales with regard to angular momentum exchange, and consequently, the neglection of the exchange with the tide-enerating body. It is shown that for present accuracy requirements this exchange has to be taken into account.