Hydrodynamic processes of angular momentum transport in the interior of a rotating massive hydrogen-burning star

The evolution of a rotating star with a mass of 16M _⊙ at the hydrogen burning phase is considered together with the hydrodynamic processes of angular momentum transport in its interior. Shear turbulence is shown to limit the amplitude of the latitudinal variations in mean molecular weight on a surface of constant pressure in a layer with variable chemical composition. The resulting nonuniformity in the mean molecular weight distribution and the turbulent energy transport along the surface of constant pressure reduce the absolute value of the meridional circulation velocity. Nevertheless, meridional circulation remains the main mechanism of angular momentum transport in the radial direction in a layer with variable chemical composition. The intensity of the processes of angular momentum transport by meridional circulation and shear turbulence is determined by the angular momentum of the star. At a fairly high angular momentum, more specifically, at J = 3.69 × 10⁵² g cm² s^?1, the star during the second half of the hydrogen-burning phase in its convective core has characteristics typical of classical early Be stars.     

On the angular velocity distribution in a nonhomogeneously rotating star

Some results of the calculations of the angular velocity distribution in the equatorial plane of a nonhomogeneously rotating star, in particular of the Sun, are presented. Hence the hypothesis is advanced of the turbulent viscosity as one of the main factors of the angular momentum transport from a rapidly rotating core through the radiative equilibrium region.     

The angular momentum problem and magnetic braking during star formation: Exact solutions for an aligned and a perpendicular rotator

The problems of fragmentation, angular momentum, and magnetic flux during star formation are reviewed briefly. Then the resolution of the angular momentum problem through magnetic braking is studied rigorously.A disk-like interstellar cloud of uniform density _cl is given an initial angular velocity _o about its axis of symmetry, which isaligned with an initially uniform, frozen-in magnetic field. Torsional Alfvén waves transport angular momentum from the cloud to the external medium, which has a uniform density _ext . The angular velocity of the cloud ( _cl ) is determined analytically as a function of space and time for different ratios _cl / _ext (the only free parameter in the equations), representing different stages of contraction. Despite dissimilar transient response of the cloud (or fragment) structure to different initial conditions, the characteristic time for magnetic braking of the rotation of the cloud (or fragment) as a whole is remarkably insensitive to the initial conditions and independent of the stage of contraction. The latter conclusion is in agreement with an approximate result obtained recently (Mouschovias, 1978; 1979a).A cylindrical cloud (or fragment) of uniform density is also imparted an initial angular velocity about its axis of symmetry with respect to the external medium. The frozen-in magnetic field is now initially radial andperpendicular to the axis of symmetry. In this case magnetic braking becomes more efficient upon contraction. It is more efficient than the aligned rotator case typically by one order of magnitude. The angular momentum problem can be resolved in about 10⁶ yr during the early stages of cloud contraction. Planetary systems, such as the Sun-Jupiter pair, become dynamically possible. A stage exists in which a cloud (or fragment) is in retrograde rotation with respect to its surroundings. This provides the first and only observable prediction of magnetic braking in action. It also constitutes a natural explantation of retrograde rotation in stellar and planetary systems.This work was supported in part by the National Science Foundation under grant NSF AST-77-23568.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.     

On the angular momentum transfer on to compact stars in binary systems

Results of three-dimensional numerical simulations of the gas transfer in close binary systems show that, in addition to the formation of a tidally induced spiral shock wave, it is also possible for accretion streams to be produced, having low specific angular momentum in a region close to the accreting star. These streams are mainly placed above the orbital disc but are also unevenly present in the equatorial plane. The relevance of such flows is related to formation of hot coronae or bulges in regions very close to the accretor centre. The eventual formation of such bulges and shock-heated flows is interesting in the context of advection-dominated solutions and for the explanation of spectral properties of the black hole candidates in binary systems.     

On the variation of specific angular momentum among Main Sequence stars

The specific angular momentum is found to vary with mass for earlier and later-type Main Sequence stars. Of various plausible causes, the difference in the interior density distribution of earlier and later-type stars is not sufficient enough to explain the difference either in angular momentum or in its gradient between earlier and later-type stars. The non-rigid rotation, however, may account for this difference in specific angular momentum as well as its gradient, if faster angular velocity in the interior for later-type and/or slower angular velocity for earlier-type stars than the surface value is allowed. A few other possibilities have also been briefly considered to understand this difference.     

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.     

Bulges versus discs: the evolution of angular momentum in cosmological simulations of galaxy formation

We investigate the evolution of angular momentum in simulations of galaxy formation in a cold dark matter universe. We analyse two model galaxies generated in the N -body/hydrodynamic simulations of Okamoto et al. Starting from identical initial conditions, but using different assumptions for the baryonic physics, one of the simulations produced a bulge-dominated galaxy and the other one a disc-dominated galaxy. The main difference is the treatment of star formation and feedback, both of which were designed to be more efficient in the disc-dominated object. We find that the specific angular momentum of the disc-dominated galaxy tracks the evolution of the angular momentum of the dark matter halo very closely: the angular momentum grows as predicted by linear theory until the epoch of maximum expansion and remains constant thereafter. By contrast, the evolution of the angular momentum of the bulge-dominated galaxy resembles that of the central, most bound halo material: it also grows at first according to linear theory, but 90 per cent of it is rapidly lost as pre-galactic fragments, into which gas had cooled efficiently, merge, transferring their orbital angular momentum to the outer halo by tidal effects. The disc-dominated galaxy avoids this fate because the strong feedback reheats the gas, which accumulates in an extended hot reservoir and only begins to cool once the merging activity has subsided. Our analysis lends strong support to the classical theory of disc formation whereby tidally torqued gas is accreted into the centre of the halo conserving its angular momentum.     

On the role of magnetic fields in star formation

Magnetic fields are observed in star forming regions. However simulations of the late stages of star formation that do not include magnetic fields provide a good fit to the properties of young stars including the initial mass function (IMF) and the multiplicity. We argue here that the simulations that do include magnetic fields are unable to capture the correct physics, in particular the high value of the magnetic Prandtl number, and the low value of the magnetic diffusivity. The artificially high (numerical and uncontrolled) magnetic diffusivity leads to a large magnetic flux pervading the star forming region. We argue further that in reality the dynamics of high magnetic Prandtl number turbulence may lead to local regions of magnetic energy dissipation through reconnection, meaning that the regions of molecular clouds which are forming stars might be essentially free of magnetic fields. Thus the simulations that ignore magnetic fields on the scales on which the properties of stellar masses, stellar multiplicities and planet-forming discs are determined, may be closer to reality than those which include magnetic fields, but can only do so in an unrealistic parameter regime.     

Amplifying magnetic fields of a newly born neutron star by stochastic angular momentum accretion in core collapse supernovae

I present a novel mechanism to boost magnetic field amplification of newly born neutron stars in core collapse supernovae.In this mechanism,that operates in the jittering jets explosion mechanism and comes on top of the regular magnetic field amplification by turbulence,the accretion of stochastic angular momentum in core collapse supernovae forms a neutron star with strong initial magnetic fields but with a slow rotation.The varying angular momentum of the accreted gas,which is unique to the jittering jets explosion mechanism,exerts a varying azimuthal shear on the magnetic fields of the accreted mass near the surface of the neutron star.This,I argue,can form an amplifying effect which I term the stochastic omega(Sω) effect.In the common αω dynamo the rotation has constant direction and value,and hence supplies a constant azimuthal shear,while the convection has a stochastic behavior.In the Sω dynamo the stochastic angular momentum is different from turbulence in that it operates on a large scale,and it is different from a regular rotational shear in being stochastic.The basic assumption is that because of the varying direction of the angular momentum axis from one accretion episode to the next,the rotational flow of an accretion episode stretches the magnetic fields that were amplified in the previous episode.I estimate the amplification factor of the Sω dynamo alone to be ≈ 10.I speculate that the Sω effect accounts for a recent finding that many neutron stars are born with strong magnetic fields.     

Clarification on the law of angular momentum

In most courses on continuum mechanics the law of angular momentum is studied about a fixed point (usually about the origin of the frame). In this article we clarify this law about any point in three-dimensional Euclidean space and discuss the law, about any point, for an observer in a rotating frame.     

Galaxy formation: Warm dark matter, missing satellites, and the angular momentum problem

We present warm dark matter (WDM) as a possible solution to the missing satellites and angular momentum problem in galaxy formation and introduce improved initial conditions for numerical simulations of WDM models, which avoid the formation of unphysical haloes found in earlier simulations. There is a hint, that because of that the mass function of satellite haloes has been overestimated so far, pointing to higher values for the WDM particle mass. This revised version was published online in August 2006 with corrections to the Cover Date.     

Hysteresis effects and diagnostics of the shock formation in low angular momentum axisymmetric accretion in the Kerr metric

The secular evolution of the purely general relativistic low angular momentum accretion flow around a spinning black hole is shown to exhibit hysteresis effects. This confirms that a stationary shock is an integral part of such an accretion disc in the Kerr metric. The equations describing the space gradient of the dynamical flow velocity of the accreting matter have been shown to be equivalent to a first order autonomous dynamical systems. Fixed point analysis ensures that such flow must be multi-transonic for certain astrophysically relevant initial boundary conditions. Contrary to the existing consensus in the literature, the critical points and the sonic points are proved not to be isomorphic in general, they can form in a completely different length scales. Physically acceptable global transonic solutions must produce odd number of critical points. Homoclinic orbits for the flow possessing multiple critical points select the critical point with the higher entropy accretion rate, confirming that the entropy accretion rate is the degeneracy removing agent in the system. However, heteroclinic orbits are also observed for some special situation, where both the saddle type critical points of the flow configuration possesses identical entropy accretion rate. Topologies with heteroclinic orbits are thus the only allowed non-removable degenerate solutions for accretion flow with multiple critical points, and are shown to be structurally unstable. Depending on suitable initial boundary conditions, a homoclinic trajectory can be combined with a standard non-homoclinic orbit through an energy preserving Rankine-Hugoniot type of stationary shock, and multi-critical accretion flow then becomes truly multi-transonic. An effective Lyapunov index has been proposed to analytically confirm why certain class of transonic flow cannot accommodate shock solutions even if it produces multiple critical points.     

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.     

The angular momentum of eclipsing binaries

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

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.     

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.     

The tidal origin of angular momentum in galaxies

We present the results of numerical simulations of relaxing protogalaxies under the tidal action of other similar systems and also clusters of galaxies. It is found that the bimodal behaviour of the observed angular momentum of galaxies can be explained under the assumption of different initial dynamical conditions induced by the evolving structure of the Universe expected in the adiabatic picture.Observatorio Astronómico, Córdoba, Argentina.CONICET, Buenos Aires, Argentina.