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Register a new userHydrodynamics, Vortices and Angular Momenta of Celestial Objects
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The current observational evidences suggest there are about hundred billion galaxies in the observable universe and within each, on an average, about hundred billion stars. But no cosmological model indicates as to why there are these many galaxies and stars. In this paper we invoke the property of non-irrotational hydrodynamic flow in order to explain how a primordial rotation (as considered in a recent paper) of the universe broken up into vortex line structures, can indeed lead to formation of a large number of galactic structures and these in turn can lead to equally large number of stars within each galaxy.
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The origin of rotation or spin of objects, from stars to galaxies, is still an unanswered question. Even though there are models which try to explain this, none of them can account for the initial impulse that gave rise to this spin. In this paper we present that a cosmological model that contains a term involving the primordial spin of the universe can explain how these objects acquired the property of spin. This model also gives a natural explanation for the quadratic scaling of angular momentum with mass. Again, from this model, the background torsion due to a universal spin density not only give rise to angular momenta for all structures but also provide a background centrifugal term acting as a repulsive gravity accelerating the universe, with spin density acting as effective cosmological constant.
We report a complete calculation of the quark and glue momenta and angular momenta in the proton. These include the quark contributions from both the connected and disconnected insertions. The calculation is carried out on a $16^3 times 24$ quenched lattice at $beta = 6.0$ and for Wilson fermions with $kappa = 0.154, 0.155,$ and 0.1555 which correspond to pion masses at 650, 538, and 478 MeV. The quark loops are calculated with $Z_4$ noise and signal-to-noise is improved further with unbiased subtractions. The glue operator is comprised of gauge-field tensors constructed from the overlap operator. The $u$ and $d$ quark momentum/angular momentum fraction is 0.66(5)/0.72(5), the strange momentum/angular momentum fraction is 0.024(6)/0.023(7), and that of the glue is 0.31(6)/0.25(8). The orbital angular momenta of the quarks are obtained from subtracting the angular momentum component from its corresponding spin. As a result, the quark orbital angular momentum constitutes 0.50(2) of the proton spin, with almost all it coming from the disconnected insertion. The quark spin carries a fraction 0.25(12) and glue carries a fraction 0.25(8) of the total proton spin.
This paper analyzes the algebraic and physical properties of the spin and orbital angular momenta of light in the quantum mechanical framework. The consequences of the fact that these are not angular momenta in the quantum mechanical sense are worked out in mathematical detail. It turns out that the spin part of the angular momentum has continuous eigenvalues. Particular attention is given to the paraxial limit, and to the definition of Laguerre--Gaussian modes for photons as well as classical light fields taking full account of the polarization degree of freedom.
Eigenvalues and eigenfunctions of the volume operator, associated with the symmetric coupling of three SU(2) angular momentum operators, can be analyzed on the basis of a discrete Schroedinger-like equation which provides a semiclassical Hamiltonian picture of the evolution of a `quantum of space, as shown by the authors in a recent paper. Emphasis is given here to the formalization in terms of a quadratic symmetry algebra and its automorphism group. This view is related to the Askey scheme, the hierarchical structure which includes all hypergeometric polynomials of one (discrete or continuous) variable. Key tool for this comparative analysis is the duality operation defined on the generators of the quadratic algebra and suitably extended to the various families of overlap functions (generalized recoupling coefficients). These families, recognized as lying at the top level of the Askey scheme, are classified and a few limiting cases are addressed.
Building on our previous hydrodynamic study of the angular momenta of cloud cores formed during gravitational collapse of star-forming molecular gas in our previous work, we now examine core properties assuming ideal magnetohydrodynamics (MHD). Using the same sink-patch implementation for the emph{Athena} MHD code, we characterize the statistical properties of cores, including the mass accretion rates, specific angular momenta, and alignments between the magnetic field and the spin axis of the core on the $0.1 mathrm{pc}$ scale. Our simulations, which reproduce the observed relation between magnetic field strength and gas density, show that magnetic fields can help collimate low density flows and help seed the locations of filamentary structures. Consistent with our previous purely hydrodynamic simulations, stars (sinks) form within the heterogeneous environments of filaments, such that accretion onto cores is highly episodic leading to short-term variability but no long-term monotonic growth of the specific angular momenta. With statistical characterization of protostellar cores properties and behaviors, we aim to provide a starting point for building more realistic and self-consistent disk formation models, helping to address whether magnetic fields can prevent the development of (large) circumstellar disks in the ideal MHD limit.
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