The angular momentum content of dwarf galaxies: new challenges for the theory of galaxy formation

We compute the specific angular momentum distributions for a sample of low-mass disc galaxies observed by Swaters. We compare these distributions to those of dark matter haloes obtained by Bullock et al. from high-resolution N -body simulations of structure formation in a ΛCDM universe. We find that although the disc mass fractions are significantly smaller than the universal baryon fraction, the total specific angular momenta of the discs are in good agreement with those of dark matter haloes. This suggests that discs form out of only a small fraction of the available baryons, but yet manage to draw most of the available angular momentum. In addition we find that the angular momentum distributions of discs are clearly distinct from those of the dark matter; discs lack predominantly both low and high specific angular momenta. Understanding these findings in terms of a coherent picture for disc formation is challenging. Cooling, feedback and stripping, which are the main mechanisms to explain the small disc mass fractions found, seem unable to simultaneously explain the angular momentum distributions of the discs. In fact, it seems that the baryons that make up the discs must have been born out of angular momentum distributions that are clearly distinct from those of ΛCDM haloes. However, the dark and baryonic mass components experience the same tidal forces, and it is therefore expected that they should have similar angular momentum distributions. Therefore, understanding the angular momentum content of disc galaxies remains an important challenge for our picture of galaxy formation.     

Formation of trans-Neptunian satellite systems at the stage of condensations

The formation of trans-Neptunian satellite systems at the stage of rarefied preplanetesimals (i.e., condensations of dust and/or objects less than 1 m in diameter) is discussed. It is assumed that trans-Neptunian objects (including those with satellites) could form as a result of compression of parental rarefied preplanetesimals. The formulas for calculating the angular momentum of two colliding condensations with respect to their center of mass, which were applied earlier in (Ipatov, 2010) in the comparison of such momenta with the angular momenta of observed satellite systems, are used to estimate the angular momenta of condensations needed to form satellite systems. It is demonstrated that the angular velocities of condensations used in (Nesvorny et al., 2010) as the initial data in the computer simulation of compression of rarefied preplanetesimals and subsequent formation of trans-Neptunian satellite systems may be obtained in collisions of preplanetesimals with their radii comparable to the corresponding Hill radii. For example, these angular velocities are in the range of possible values of angular velocities of a parental rarefied preplanetesimal formed as a result of a merger of two colliding rarefied preplanetesimals that moved in circular heliocentric orbits before a collision. Some rarefied preplanetesimals formed as a result of collision of preplanetesimals in the region of formation of solid small bodies acquire such angular momenta that are sufficient to form satellite systems of small bodies. It is likely that the ratio of the number of rarefied preplanetesimals with such angular momenta to the total number of rarefied preplanetesimals producing classical trans-Neptunian objects with diameters larger than 100 km was 0.45 (the initial fraction of satellite systems among all classical trans-Neptunian objects).     

The cosmological dependence of galactic specific angular momenta

Hydrodynamical simulations of galaxy formation in spatially flat cold dark matter (CDM) cosmologies with and without a cosmological constant (Λ) are described. A simple star formation algorithm is employed and radiative cooling is allowed only after redshift z =1 so that enough hot gas is available to form large, rapidly rotating stellar discs if angular momentum is approximately conserved during collapse. The specific angular momenta of the final galaxies are found to be sensitive to the assumed background cosmology. This dependence arises from the different angular momenta contained in the haloes at the epoch when the gas begins to collapse and the inhomogeneity of the subsequent halo evolution. In the Λ-dominated cosmology, the ratio of stellar specific angular momentum to that of the dark matter halo (measured at the virial radius) has a median value of ∼0.24 at z =0. The corresponding quantity for the Λ=0 cosmology is over three times lower. It is concluded that the observed frequency and angular momenta of disc galaxies pose significant problems for spatially flat CDM models with Λ=0 but may be consistent with a Λ-dominated CDM universe.     

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.     

A tidal hypothesis about the origin of planetary rotation

We assume that the solar tidal action on accreting protoplanets forced them to corotation. If this is true, and assuming a subsequent conservation of spin angular momentum, we can easily get a rough explanation of: (1) the actual rotation periods of the planets, (2) the trend toward small inclination angles for the rotation axes, (3) the existence of a relation between rotational angular momenta and planetary masses similar to the empirical ones due to McDonald (1964). Hartmann and Larson (1967) and Fish (1967).     

Exchange of global mean angular momentum between an atmosphere and its underlying planet

This paper investigates the exchange of global mean angular momentum between an atmosphere and its underlying planet by a simple model. The model parameterizes four processes that are responsible for zonal mean momentum budget in the atmospheric boundary layer for a rotating planet: (i) meridional circulation that redistributes the relative angular momentum, (ii) horizontal diffusion that smoothes the prograde and retrograde winds, (iii) frictional drag that exchanges atmospheric angular momentum with the underlying planet, and (iv) internal redistribution of the zonal mean momentum by wave drag. It is shown that under a steady-state or a long-term average condition, the global relative angular momentum in the boundary layer vanishes unless there exists a preferred frictional drag for either the prograde or the retrograde zonal wind. We further show quantitatively that one cannot have either a predominant steady prograde or retrograde wind in the boundary layer of a planetary atmosphere. The parameter dependencies of the global relative angular momentum and the strength of the atmospheric circulation in the boundary layer are derived explicitly and used to explain the observational differences between the atmospheres of Earth and Venus.     

Effects of merging histories on angular momentum distribution of dark matter haloes

The effects of merging histories of proto-objects on the angular momentum distributions of the present-time dark matter haloes are analysed. An analytical approach to the analysis of the angular momentum distributions assumes that the haloes are initially homogeneous ellipsoids and that the growth of the angular momentum of the haloes halts at their maximum expansion time. However, the maximum expansion time cannot be determined uniquely, because in the hierarchical clustering scenario each progenitor, or subunit, of the halo has its own maximum expansion time. Therefore the merging history of the halo may be important in estimating its angular momentum. Using the merger tree model by Rodrigues &38; Thomas, which takes into account the spatial correlations of the density fluctuations, we have investigated the effects of the merging histories on the angular momentum distributions of dark matter haloes. It was found that the merger effects, that is, the effects of the inhomogeneity of the maximum expansion times of the progenitors which finally merge together into a halo, do not strongly affect the final angular momentum distributions, so that the homogeneous ellipsoid approximation happens to be good for the estimation of the angular momentum distribution of dark matter haloes. This is because the effect of the different directions of the angular momenta of the progenitors cancels out the effect of the inhomogeneity of the maximum expansion times of the progenitors.   The contribution of the orbital angular momentum to the total angular momentum when two or more pre-existing haloes merge together was also investigated. It is shown that this contribution is more important than that of the angular momentum of diffuse accreting matter to the total angular momentum, especially when the mergers occur many times.     

Dynamics of rotating triple systems

We investigate the dynamical evolution of 100 000 rotating triple systems with equal-mass components. The system rotation is specified by the parameter ω=?c²E, where c and E are the angular momentum and total energy of the triple system, respectively. We consider ω=0.1,1, 2, 4, 6 and study 20 000 triple systems with randomly specified coordinates and velocities of the bodies for each ω. We consider two methods for specifying initial conditions: with and without a hierarchical structure at the beginning of the evolution. The evolution of each system is traced until the escape of one of the bodies or until the critical time equal to 1000 mean system crossing times. For each set of initial conditions, we computed parameters of the final motions: orbital parameters for the final binary and the escaping body. We analyze variations in the statistical characteristics of the distributions of these parameters with ω. The mean disruption time of triple systems and the fraction of the systems that have not been disrupted in 1000 mean crossing times increase with ω. The final binaries become, on average, wider at larger angular momenta. The distribution of their eccentricities does not depend on ω and generally agrees with the theoretical law f(e)=2e. The velocities of the escaping bodies, on average, decrease with increasing angular momentum of the triple system. The fraction of the angles between the escaping-body velocity vector and the triple-system angular momentum close to 90° increases with ω. Escapes in the directions opposite to rotation and prograde motions dominate at small and large angular momenta, respectively. For slowly rotating systems, the angular momentum during their disruption is, on average, evenly divided between the escaping body and the final binary, whereas in rapidly rotating systems, about 80% of the angular momentum is carried away by the escaping component. We compare our numerical simulations with the statistical theory of triple-system disruption.     

Protostars and the origin of the angular momentum of the solar system

Protostars in a group exert gravitational tidal torques on an aspherical nebula located in the group. The net torque transfers angular momentum from the orbital motions of the stars to rotation of the nebula. A relation can be derived between the parameters describing the protostars and the final angular momentum of the nebula. While the parameters concerned are uncertain, a conservative choice results in a value for the angular momentum equal to about 1/3 of that of the present solar system. This suggests that if the Sun formed in a group, tidal interactions with other protostars may account for a significant part of the angular momentum of the solar system.     

Mass loss from the inner regions of accretion discs due to centrifugally driven magnetic wind flows

Wind flows and collimated jets are believed to be a feature of a range of disc accreting systems. These include active galactic nuclei, T Tauri stars, X-ray binaries and cataclysmic variables. The observed collimation implies large-scale magnetic fields and it is known that dipole-symmetry fields of sufficient strength can channel wind flows emanating from the surfaces of a disc. The disc inflow leads to the bending of the poloidal magnetic field lines, and centrifugally driven magnetic winds can be launched when the bending exceeds a critical value. Such winds can result in angular momentum transport at least as effective as turbulent viscosity, and hence they can play a major part in driving the disc inflow.
It is shown here that if the standard boundary condition of vanishing viscous stress close to the stellar surface is applied, together with the standard connection between viscosity and magnetic diffusivity, then poloidal magnetic field bending increases as the star is approached with a corresponding increase in the wind mass loss rate. A significant amount of material can be lost from the system via the enhanced wind from a narrow region close to the stellar surface. This occurs for a Keplerian angular velocity distribution and for a modified form of angular velocity, which allows for matching of the disc and stellar rotation rates through a boundary layer above the stellar surface. The enhanced mass loss is significantly affected by the behaviour of the disc angular velocity as the stellar surface is approached, and hence by the stellar rotation rate. Such a mechanism may be related to the production of jets from the inner regions of disc accreting systems.     

Observed mid-to-high latitude interchange of atmospheric angular momentum and some implications

The global distribution of atmospheric angular momentum (M) during 1977–1978 and 1982–1983 is examined to identify evidence of prominent short term interchanges of relative atmospheric momentum between mid and high latitude zones, in both hemispheres. Thirty day detrended angular momentum time series, prepared from the NMC gridded zonal wind data are examined in latitude bands. These data exhibit obvious quasi-coherent oscillations with periods near 30 days plus variations with shorter periods. An examination of latitude/altitude cross sections of zonal winds reveals that the oscillations are present almost simultaneously at all altitude levels between 1000 and 50 mb. Cross latitude teleconnections, evident as strong anticorrelated signatures between adjacent latitude bands are observed in the midlatitudes of both hemispheres. Comparison of these signatures with the time integrated flux of angular momentum across the nodal interface confirms that direct eddy transport of momentum is occurring. Transport of momentum from the mid latitude bands results in an increase in the momentum of the higher latitude bands and vice versa. Transport of planetary angular momentum by a Hadley/Ferrel type meridional circulation is specifically ruled out although that process may contribute to seasonal and longer term modulations. The short term oscillations in M can reach magnitudes which dominate the global variation in momentum, as noted in the recent 1982–83 El Niño episode in which the January 1983 momentum peaked at a decadal high. Similar El-Niño like changes in the trans-latitude momentum redistribution are observed in the Southern Hemisphere winters, following the Northern Hemisphere episode. Overall, our results confirm and describe in more detail the long recognized fact that momentum can be selectively redistributed between tropical, temperate, and high latitudes, in patterns indicative of the development and dissipation of interacting regions, described variously in studies of the index cycle, seesaws and teleconnections. In emphasizing the large scale coordination of these interchanges, and moreover their occasional very short time scales, these results will hopefully stimulate studies relating atmospheric behavior in distant regions thereby contributing to improvements in forecasting the circulation process.     

Stratospheric superrotation in the TitanWRF model

TitanWRF general circulation model simulations performed without sub-grid-scale horizontal diffusion of momentum produce roughly the observed amount of superrotation in Titan’s stratosphere. We compare these results to Cassini-Huygens measurements of Titan’s winds and temperatures, and predict temperature and winds at future seasons. We use angular momentum and transformed Eulerian mean diagnostics to show that equatorial superrotation is generated during episodic angular momentum ‘transfer events’ during model spin-up, and maintained by similar (yet shorter) events once the model has reached steady state. We then use wave and barotropic instability analysis to suggest that these transfer events are produced by barotropic waves, generated at low latitudes then propagating poleward through a critical layer, thus accelerating low latitudes while decelerating the mid-to-high latitude jet in the late fall through early spring hemisphere. Finally, we identify the dominant waves responsible for the transfers of angular momentum close to northern winter solstice during spin-up and at steady state. Problems with our simulations include peak latitudinal temperature gradients and zonal winds occurring ∼60 km lower than observed by Cassini CIRS, and no reduction in zonal wind speed around 80 km, as was observed by Huygens. While the latter may have been due to transient effects (e.g. gravity waves), the former suggests that our low (∼420 km) model top is adversely affecting the circulation near the jet peak, and/or that we require active haze transport in order to correctly model heating rates and thus the circulation. Future work will include running the model with a higher top, and including advection of a haze particle size distribution.     

Slow modes in stellar systems with nearly harmonic potentials: II. Gravitational loss-cone instability

Using a consistent perturbation theory for collisionless disk-like and spherical star clusters, we construct a theory of slow modes for systems having an extended central region with a nearly harmonic potential due to the presence of a fairly homogeneous (on the scales of the stellar system) heavy, dynamically passive halo. In such systems, the stellar orbits are slowly precessing, centrally symmetric ellipses (2: 1 orbits). We consider star clusters with monoenergetic distribution functions that monotonically increase with angular momentum in the entire range of angular momenta (from purely radial orbits to circular ones) or have a growing region only at low angular momenta. In these cases, there are orbits with a retrograde precession, i.e., in a direction opposite to the orbital rotation of the star. The presence of a gravitational loss-cone instability, which is also observed in systems of 1: 1 orbits in near-Keplerian potentials, is associated with such orbits. In contrast to 1: 1 systems, the loss-cone instability takes place even for distribution functions monotonically increasing with angular momentum, including those for systems with circular orbits. The regions of phase space with retrograde orbits do not disappear when the distribution function is smeared in energy. We investigate the influence of a weak inhomogeneity of a heavy halo with a density that decreases with distance from the center.     

Structure and evolution of low-mass W Ursae Majoris type systems – III. The effects of the spins of the stars

In a previous paper, using Eggleton's stellar evolution code, we have discussed the structure and evolution of low-mass W Ursae Majoris (W UMa) type contact binaries with angular momentum loss owing to gravitational radiation or magnetic braking. We find that gravitational radiation is almost insignificant for cyclic evolution of low-mass W UMa type systems, and it is possible for angular momentum to be lost from W UMa systems in a magnetic stellar wind. The weaker magnetic activity shown by observations in W UMa systems is likely caused by the lower mass of the convective envelopes in these systems than in similar but non-contact binaries. The spin angular momentum cannot be neglected at any time for W UMa type systems, especially for those with extreme mass ratios. The spin angular momenta of both components are included in this paper and they are found to have a significant influence on the cyclic evolution of W UMa systems. We investigate the influence of the energy transfer on the common convective envelopes of both components in detail. We find that the mass of the convective envelope of the primary in contact evolution is slightly more than that in poor thermal contact evolution, and that the mass of the convective envelope of the secondary in contact evolution is much less than that in poor thermal contact evolution. Meanwhile, the rate of angular momentum loss of W UMa type systems is much lower than that of poor thermal contact systems. This is indeed caused by the lower masses of the convective envelopes of the components in W UMa type systems. Although the models with angular momentum loss for W UMa systems exhibit cyclic evolution, they seem to show that a W UMa system cannot continue this type of cyclic evolution indefinitely, and it might coalesce into a fast-rotating star after about 1200 cycles of evolution (about  7.0 × 10⁹ yr  ).     

Tides and angular momentum redistribution inside low-mass stars hosting planets: a first dynamical model

We introduce a general mathematical framework to model the internal transport of angular momentum in a star hosting a close-in planetary/stellar companion. By assuming that the tidal and rotational distortions are small and that the deposit/extraction of angular momentum induced by stellar winds and tidal torques are redistributed solely by an effective eddy-viscosity that depends on the radial coordinate, we can formulate the model in a completely analytic way. It allows us to compute simultaneously the evolution of the orbit of the companion and of the spin and the radial differential rotation of the star. An illustrative application to the case of an F-type main-sequence star hosting a hot Jupiter is presented. The general relevance of our model to test more sophisticated numerical dynamical models and to study the internal rotation profile of exoplanet hosts, submitted to the combined effects of tides and stellar winds, by means of asteroseismology are discussed.     

Quaternions and the rotation of a rigid body

The orientation of an arbitrary rigid body is specified in terms of a quaternion based upon a set of four Euler parameters. A corresponding set of four generalized angular momentum variables is derived (another quaternion) and then used to replace the usual three-component angular velocity vector to specify the rate by which the orientation of the body with respect to an inertial frame changes. The use of these two quaternions, coordinates and conjugate moments, naturally leads to a formulation of rigid-body rotational dynamics in terms of a system of eight coupled first-order differential equations involving the four Euler parameters and the four conjugate momenta. The equations are formally simple, easy to handle and free of singularities. Furthermore, integration is fast, since only arithmetic operations are involved.     

A 2D study of the effects of the size of a solid core on the equatorial flow in giant planets

Zonal winds simulated in two-dimensional computer models of turbulent convection in the equatorial plane of giant planets have greater surface amplitudes for cases with smaller solid cores, and therefore larger buoyancy driving, all other properties being equal. This differential rotation in radius is maintained by the convergence of angular momentum flux, which occurs because of the convective flow that develops due to the effects of planetary rotation and density stratification. The superposition of the convective flow and the stronger zonal flow produces wave-like, instead of cellular convection.     

Wave excitation in three-dimensional discs by external potential

We study the excitation of density and bending waves and the associated angular momentum transfer in gaseous discs with finite thickness by a rotating external potential. The disc is assumed to be isothermal in the vertical direction and has no self-gravity. The disc perturbations are decomposed into different modes, each characterized by the azimuthal index m and the vertical index n , which specifies the nodal number of the density perturbation along the disc normal direction. The   n = 0  modes correspond to the two-dimensional density waves previously studied by Goldreich & Tremaine and others. In a three-dimensional disc, waves can be excited at both Lindblad resonances (LRs; for modes with   n = 0, 1, 2, …  ) and vertical resonances (VRs; for the   n ≥ 1  modes only). The torque on the disc is positive for waves excited at outer Lindblad/vertical resonances and negative at inner Lindblad/vertical resonances. While the   n = 0  modes are evanescent around corotation, the   n ≥ 1  modes can propagate into the corotation region where they are damped and deposit their angular momenta. We have derived analytical expressions for the amplitudes of different wave modes excited at LRs and/or VRs and the resulting torques on the disc. It is found that for   n ≥ 1  , angular momentum transfer through VRs is much more efficient than LRs. This implies that in some situations (e.g. a circumstellar disc perturbed by a planet in an inclined orbit), VRs may be an important channel of angular momentum transfer between the disc and the external potential. We have also derived new formulae for the angular momentum deposition at corotation and studied wave excitations at disc boundaries.     

Decadal variations in a Venus general circulation model

The Community Atmosphere Model (CAM), a 3-dimensional Earth-based climate model, has been modified to simulate the dynamics of the Venus atmosphere. The most current finite volume version of CAM is used with Earth-related processes removed, parameters appropriate for Venus introduced, and some basic physics approximations adopted. A simplified Newtonian cooling approximation has been used for the radiation scheme. We use a high resolution (1° by 1° in latitude and longitude) to take account of small-scale dynamical processes that might be important on Venus. A Rayleigh friction approach is used at the lower boundary to represent surface drag, and a similar approach is implemented in the uppermost few model levels providing a ‘sponge layer’ to prevent wave reflection from the upper boundary. The simulations generate superrotation with wind velocities comparable to those measured in the Venus atmosphere by probes and around 50-60% of those measured by cloud tracking. At cloud heights and above the atmosphere is always superrotating with mid-latitude zonal jets that wax and wane on an approximate 10 year cycle. However, below the clouds, the zonal winds vary periodically on a decadal timescale between superrotation and subrotation. Both subrotating and superrotating mid-latitude jets are found in the approximate 40-60 km altitude range. The growth and decay of the sub-cloud level jets also occur on the decadal timescale. Though subrotating zonal winds are found below the clouds, the total angular momentum of the atmosphere is always in the sense of superrotation. The global relative angular momentum of the atmosphere oscillates with an amplitude of about 5% on the approximate 10 year timescale. Symmetric instability in the near surface equatorial atmosphere might be the source of the decadal oscillation in the atmospheric state. Analyses of angular momentum transport show that all the jets are built up by poleward transport by a meridional circulation while angular momentum is redistributed to lower latitudes primarily by transient eddies. Possible changes in the structure of Venus’ cloud level mid-latitude jets measured by Mariner 10, Pioneer Venus, and Venus Express suggest that a cyclic variation similar to that found in the model might occur in the real Venus atmosphere, although no subrotating winds below the cloud level have been observed to date. Venus’ atmosphere must be observed over multi-year timescales and below the clouds if we are to understand its dynamics.     

The angular momentum loss of low-mass close binary systems

The detailed evolution of low-mass main-sequence stars (M < 1M ) with a compact companion is studied. For angular momentum loss associated with magnetic braking it is found that about 10^–11–10^–12 M yr^–1 in stellar wind loss would be required. This wind is 10²–10³ times stronger than the solar wind, so we believe here magnetic stellar wind is insufficient. It is well known that there is mass outflow in low-mass close binary systems. We believe here that these outflows are centrifugal driven winds from the outer parts of the accretion disks. The winds extract angular momentum from these systems and therefore drive secular evolution. Disk winds are preferred to winds from the secondary, because of the lower disk surface gravity.