Angular Momentum Distribution Function Research Articles

Analytical analysis of the origin of core-cusp matter density distributions in galaxies

We propose an analytical method to describe a matter density profile near a galaxy center. The description is based on the study of the distribution function of particles over possible trajectories. We establish a relation between the central slope of density profile and the near-origin behavior of the angular momentum distribution function. We consider both a spherically symmetric (on average) matter distribution as well as deviations from it. If the density profile forms in a background of spherical gravitation potential then a core-type distribution arises. A regular matter may behave in such way if the background potential was formed by the dark matter. In the presence of deviation from spherical symmetry the formation of cusp-type distribution is possible. Moreover, a reduction of spherical symmetry to the axial one leads to a less steep cusp profile. The complete symmetry breaking (which corresponds, in particular, to the common setup of numerical simulations), leads to a steeper cusp profile.

Spinning Dust Radiation: A Review of the Theory

This paper reviews the current status of theoretical modeling of electric dipole radiation from spinning dust grains. The fundamentally simple problem of dust grain rotation appeals to a rich set of concepts of classical and quantum physics, owing to the diversity of processes involved. Rotational excitation and damping rates through various mechanisms are discussed, as well as methods of computing the grain angular momentum distribution function. Assumptions on grain properties are reviewed. The robustness of theoretical predictions now seems mostly limited by the uncertainties regarding the grains themselves, namely, their abundance, dipole moments, and size and shape distribution.

Simple analytic form for the velocity–angular-momentum distribution function of drifting linear ions

A simple analytic form is presented for the full velocity--angular-momentum distribution function for gas-phase linear ions drifting in an atomic bath gas under a constant external electric field. Predictions of temperatures, drift velocities, and alignment parameters from this form are compared in detail against molecular-dynamics calculations for ${\mathrm{NO}}^{+}$ drifting in helium. The form is accurate, compact, and based upon a physically motivated expansion. In essence, simple Maxwellian-like functions are generalized by allowing appropriate temperatures to become functions of velocity and rotational angular momentum. Over a wide range of reduced field strengths, including the equilibrium state, this form is able to account accurately for many properties at a microscopic level with only a few adjustable parameters.

Spin and orbital angular momentum distribution functions of the nucleon

A theoretical prediction is given for the spin and orbital angular momentum distribution functions of the nucleon within the framework of an effective quark model of QCD, i.e., the chiral quark soliton model. An outstanding feature of the model is that it predicts a fairly small quark spin fraction of the nucleon $\ensuremath{\Delta}\ensuremath{\Sigma}\ensuremath{\simeq}0.35,$ which in turn dictates that the remaining 65% of the nucleon spin is carried by the orbital angular momentum of quarks and antiquarks at the model energy scale of ${Q}^{2}\ensuremath{\simeq}0.3$ ${\mathrm{GeV}}^{2}.$ This large orbital angular momentum necessarily affects the scenario of scale dependence of the nucleon spin contents in a drastic way.

Molecular-dynamics study of rotational alignment of NO+ drifting in helium—velocity and angular momentum distribution functions

Collision-induced rotational alignment of NO+ ions drifting in a helium buffer gas is studied with molecular dynamics using the ab initio potential surface of S. K. Pogrebnya et al. [Int. J. Mass Spectrom. Ion Proc. 149/150, 207 (1995)], obtained via a coupled-cluster singles–doubles approximation. We examine average translational and rotational temperatures, velocity and angular momentum distributions, and the dependence of these quantities on the applied electric field. The distributions show that angular momentum is preferentially aligned perpendicular to the electric field vector. We investigate the mechanism of this alignment through a multipolar moment expansion, and propose and demonstrate the accuracy of a bi-Maxwellian analytic form for describing the angular momentum distribution.

Simulation of galaxy mergers in clusters and groups: “Explosive” evolution

Abstract Monte Carlo simulation of galaxy mergers in clusters is carried out. A galactic mass and angular momentum distribution function is found. The “explosive” character of the formation of the mass function is confirmed (an analogue of a phase transition: Cavaliere et al., 1992; Kontorovich et al., 1992). The appearance of a “new phase”, cD-galaxies, is traced. Comparison with the Butcher-Oemler effect and the observed steepening of the luminosity function at the faint end is carried out.

Initial mass spectrum of black holes in galactic nuclei

Within the framework of the cosmological model with cold dark matter we have calculated the initial mass function of supermassive black holes formed in galactic nuclei. The collapsing region is modeled by a homogeneous ellipsoid. It is assumed that the accumulation of angular momentum by the proto-object takes place under the action of external tidal forces, and that surmounting of the centrifugal barrier with subsequent gravitational collapse occurs as a result of turbulent viscosity. To determine the mass function, we first find the angular momentum distribution function of the nascent objects for an arbitrary spectrum of initial density perturbations. The initial mass function is compared with available observations, and some processes leading to its transformation are indicated.

Resonant tidal disruption in galactic nuclei

It has recently been shown by Rauch 38 Tremaine that the rate of angular momentum relaxation in nearly Keplerian star clusters is greatly increased by a process termed ‘resonant relaxation’; it was also argued, via a series of scaling arguments, that tidal disruption of stars in galactic nuclei containing massive black holes could be noticeably enhanced by this process. We describe here the results of numerical simulations of resonant tidal disruption which quantitatively test the predictions made by Rauch 38 Tremaine. The simulation method is based on an N-body routine incorporating cloning of stars near the loss cone and a semirelativistic symplectic integration scheme. Normalized disruption rates for resonant and non-resonant nuclei are derived at orbital energies both above and below the critical energy, and the corresponding angular momentum distribution functions are found. The black hole mass above which resonant tidal disruption is quenched by relativistic precession is determined. We also briefly describe the discovery of chaos in the Wisdom—Holman symplectic integrator applied to highly eccentric orbits and propose a modified integration scheme that remains robust under these conditions. We find that resonant disruption rates exceed their non-resonant counterparts by an amount consistent with the predictions; in particular, we estimate the net tidal disruption rate for a fully resonant cluster to be about twice that of its non-resonant counterpart. No significant enhancement in rates is observed outside the critical radius. Relativistic quenching of the effect is found to occur for hole masses M> MQ = (8 ± 3) × 107M. The numerical results combined with the observed properties of galactic nuclei indicate that for most galaxies the resonant enhancement to tidal disruption rates will be very small.

Angular-momentum-state occupation-number distribution function of the Laughlin droplet

We have evaluated the angular-momentum distribution functions for finite numbers of electrons in Laughlin states. For very small numbers of electrons the angular-momentum state occupation numbers have been evaluated exactly while for larger numbers of electrons they have been obtained from Monte-Carlo estimates of the one-particle density matrix. An exact relationship, valid for any number of electrons, has been derived for the ratio of the occupation numbers of the two outermost orbitals of the Laughlin droplet and is used to test the accuracy of the MC calculations. We compare the occupation numbers near the outer edges of the droplets with predictions based on the chiral Luttinger liquid picture of Laughlin state edges and discuss the surprisingly large oscillations in occupation numbers which occur for angular momenta far from the edge.

Equilibrium properties of a rotating ion layer in a uniform external magnetic field

The equilibrium properties of a rotating, non-neutral ion layer are examined within the framework of a steady-state Vlasov-Maxwell equations with a monoenergetic, single-canonical angular momentum distribution function. The analysis is carried out assuming that the ion layer is thin and the strength parameter of the ion layer v is much smaller than unity. As the ion layer becomes colder and colder, the influence of the self-fields on the radical thickness of the layer becomes more and more significant and can be large even though v<<1. Effects of the self-fields on the mean radius of the layer are small. The influence of a conducting wall which encloses the ion layer is also shown. Relations between existing theories and the present theory are discussed.

A classical analysis of the ionization threshold vicinity

The classical trajectory method has been used for investigating electron-hydrogen-atom excitation and ionization regions close to the ionization threshold. Final energy and angular momentum distribution functions have been computed with the total angular momentum equal to zero, both below and above the ionization threshold. Combining the analytical result of Vinkalns and Gailitis (1967) with the computed energy distribution function, the threshold behaviour of the high n excitation function has been derived, which is subsequently confirmed by ab initio numerical calculations. The results show that the Wannier theory (1953) is applicable below the threshold, too. The numerical results show that each electron acquires large angular momentum in the threshold vicinity, as predicted by Fano (1974).