A Novel Geometric Model of Natural Spirals Based on Right Triangle Polygonal Modular Formations (original) (raw)
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Spirals of Creation (Module Handbook)
Spirals of Creation, 2010
"The story of creation begins with Source. This is what makes sense of everything. It is the great story of how Source in its infinite freedom, aliveness and creativity creates structure within itself and experiences this structure as a means of exploring its own nature. We are an integral part of this process – it is our story too. We are creation in action. Spirals are a significant structure in the whole dynamic of creation. They provide a fascinating cross section across many levels of creation and help illustrate the beauty, scale and profundity of the vast cosmic structure we are part of. We will explore a little math (geometry and number) and science along the way. This helps us appreciate the sheer depth, coherence, integrity and power of this vast and wonderful body of knowledge. It is an exciting journey that explores the larger reality we live in and ultimately helps us explore our own nature as it connects all the way back to Source." *this handbook was compiled by Noel Tobin on behalf of the Kathara Team.
Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences
We describe the structure and composition of six major stellar streams in a population of 20 574 local stars in the New Hipparcos Reduction with known radial velocities. We find that, once fast moving stars are excluded, almost all stars belong to one of these streams. The results of our investigation have lead us to re-examine the hydrogen maps of the Milky Way, from which we identify the possibility of a symmetric two-armed spiral with half the conventionally accepted pitch angle. We describe a model of spiral arm motions which matches the observed velocities and composition of the six major streams, as well as the observed velocities of the Hyades and Praesepe clusters at the extreme of the Hyades stream. We model stellar orbits as perturbed ellipses aligned at a focus in coordinates rotating at the rate of precession of apocentre. Stars join a spiral arm just before apocentre, follow the arm for more than half an orbit, and leave the arm soon after pericentre. Spiral pattern spe...
The Onset of Spiral Structure in the Universe
The Astrophysical Journal, 2014
The onset of spiral structure in galaxies appears to occur between redshifts 1.4 and 1.8 when disks have developed a cool stellar component, rotation dominates over turbulent motions in the gas, and massive clumps become less frequent. During the transition from clumpy to spiral disks, two unusual types of spirals are found in the Hubble Ultra Deep Field that are massive, clumpy and irregular like their predecessor clumpy disks, yet spiral-like or sheared like their descendants. One type is "woolly" with massive clumpy arms all over the disk and is brighter than other disk galaxies at the same redshift, while another type has irregular multiple arms with high pitch angles, star formation knots and no inner symmetry like today's multiple-arm galaxies. The common types of spirals seen locally are also present in a redshift range around z ∼ 1, namely grand design with two symmetric arms, multiple arm with symmetry in the inner parts and several long, thin arms in the outer parts, and flocculent, with short, irregular and patchy arms that are mostly from star formation. Normal multiple arm galaxies are found only closer than z ∼ 0.6 in the UDF. Grand design galaxies extend furthest to z ∼ 1.8, presumably because interactions can drive a two-arm spiral in a disk that would otherwise have a more irregular structure. The difference between these types is understandable in terms of the usual stability parameters for gas and stars, and the ratio of the velocity dispersion to rotation speed.
Spiral structure and the dynamics of galaxies
Physics Reports, 1976
Conten ts: 1. General characteristics of spiral galaxies 317 5. Stabilization of density waves by the gas 364 1.1. A brief review of two centuries of observations 317 5.1. Introduction 364 1.2. Theories of spiral structure 321 5.2. Stabilization mechanism 1.3. Outline of the present study 324 5.3. Discussion 2. Mathematical tools 326 6. Quasi-linear theory 3. Dynamical properties of flat stellar systems 328 6.1. Introduction 3.1. Introduction 328 6.2. Derivation of the diffusion equation 3.2. Stellar orbits 328 6.3. Diffusion coefficients 3.3. Distribution functions 341 6.4. The persistence of spiral structure 4. Stability of slightly perturbed disks 346 7. Conclusions and summary 4.1. Introduction 346 Acknowledgements 4.2. Mathematical formulation 347 Appendix 4.3. Instabilities 354 References 4.3.1. The rate of change of angular momentum 354 4.3.2. Growing waves 356 4.3.3. Damped waves 358 4.3.4. Physical significance of the growth rate y 359 4.3.5. Astronomical implications 361
Celestial Mechanics and Dynamical Astronomy, 2012
We study the role of asymptotic curves in supporting the spiral structure of a N-body model simulating a barred spiral galaxy. Chaotic orbits with initial conditions on the unstable asymptotic curves of the main unstable periodic orbits follow the shape of the periodic orbits for an initial interval of time and then they are diffused outwards supporting the spiral structure of the galaxy. Chaotic orbits having small deviations from the unstable periodic orbits, stay close and along the corresponding unstable asymptotic manifolds, supporting the spiral structure for more than 10 rotations of the bar. Chaotic orbits of different Jacobi constants support different parts of the spiral structure. We also study the diffusion rate of chaotic orbits outwards and find that chaotic orbits that support the outer parts of the galaxy are diffused outwards more slowly than the orbits supporting the inner parts of the spiral structure.
Understanding the spiral structure of the Milky Way using the local kinematic groups
Monthly Notices of The Royal Astronomical Society, 2011
We study the spiral arm influence on the solar neighbourhood stellar kinematics. As the nature of the Milky Way (MW) spiral arms is not completely determined, we study two models: the Tight-Winding Approximation (TWA) model, which represents a local approximation, and a model with self-consistent material arms named sPiral arms potEntial foRmed by obLAte Spheroids (PERLAS). This is a mass distribution with more abrupt gravitational forces. We perform test particle simulations after tuning the two models to the observational range for the MW spiral arm properties. We find that some of the currently observed MW spiral arm properties are not in obvious agreement with the TWA model. We explore the effects of the arm properties and find that a significant region of the allowed parameter space favours the appearance of kinematic groups. The velocity distribution is mostly sensitive to the relative spiral arm phase and pattern speed. In all cases the arms induce strong kinematic imprints for pattern speeds around 17 km s-1 kpc-1 (close to the 4:1 inner resonance) but no substructure is induced close to corotation. The groups change significantly if one moves only ˜0.6 kpc in galactocentric radius, but ˜2 kpc in azimuth. The appearance time of each group is different, ranging from 0 to more than 1 Gyr. Recent spiral arms can produce strong kinematic structures. The stellar response to the two potential models is significantly different near the Sun, both in density and in kinematics. The PERLAS model triggers more substructure for a larger range of pattern speed values. The kinematic groups can be used to reduce the current uncertainty about the MW spiral structure and to test whether this follows the TWA. However, groups such as the observed ones in the solar vicinity can be reproduced by different parameter combinations. Data from velocity distributions at larger distances are needed for a definitive constraint.
No evidence for small disk-like bulges in a sample of late-type spirals
Astronomy & Astrophysics
Context. About 20% of low-redshift galaxies are late-type spirals with a small or no bulge component. Although they are the simplest disk galaxies in terms of structure and dynamics, the role of the different physical processes driving their formation and evolution is not yet fully understood. Aims. We investigated whether small bulges of late-type spirals follow the same scaling relations traced by ellipticals and large bulges and if small bulges are disk-like or classical bulges. Methods. We derived the photometric and kinematic properties of nine nearby late-type spirals. To this aim, we analyzed the surfacebrightness distribution from the i-band images of the Sloan Digital Sky Survey and obtained the structural parameters of the galaxies from a two-dimensional photometric decomposition. We found a bulge component in seven galaxies of the sample, while the remaining two resulted in pure disk galaxies. We measured the line-of-sight stellar velocity distribution within the bulge effective radius from the long-slit spectra taken with high spectral resolution at the Telescopio Nazionale Galileo. We used the photometric and kinematic properties of the sample bulges to study their location in the fundamental plane, Kormendy, and Faber-Jackson relations defined for ellipticals and large bulges. Results. We found that our bulges satisfy some of the photometric and kinematic prescriptions for being considered disk-like bulges, such as small sizes and masses with nearly exponential light profiles, small bulge-to-total luminosity ratios, low stellar velocity dispersions, and ongoing star formation. However, each of these bulges follows the same scaling relations of ellipticals, massive bulges, and compact early-type galaxies so they cannot be classified as disk-like systems. Conclusions. We find a single population of galaxy spheroids that follow the same scaling relations, where the mass seems to lead to a smooth transition in the photometric and kinematic properties from less massive bulges to more massive bulges and ellipticals.
A Fundamental Plane of Spiral Structure in Disk Galaxies
Spiral structure is the most distinctive feature of disk galaxies and yet debate persists about which theory of spiral structure is correct. Many versions of the density wave theory demand that the pitch angle be uniquely determined by the distribution of mass in the bulge and disk of the galaxy. We present evidence that the tangent of the pitch angle of logarithmic spiral arms in disk galaxies correlates strongly with the density of neutral atomic hydrogen in the disk and with the central stellar bulge mass of the galaxy. These three quantities, when plotted against each other, form a planar relationship that we argue should be fundamental to our understanding of spiral structure in disk galaxies. We further argue that any successful theory of spiral structure must be able to explain this relationship.
Self-regulated model of galactic spiral structure formation
Physical Review E - PHYS REV E, 2002
The presence of spiral structure in isolated galaxies is a problem that has only been partially explained by theoretical models. Because the rate and pattern of star formation in the disk must depend only on mechanisms internal to the disk, we may think of the spiral galaxy as a self-regulated system far from equilibrium. This paper uses this idea to look at a reaction-diffusion model for the formation of spiral structures in certain types of galaxies. In numerical runs of the model, spiral structure forms and persists over several revolutions of the disk, but eventually dies out.
Monthly Notices of the Royal Astronomical Society, 2013
We investigate the dynamics of a barred-spiral model, rotating with a single pattern speed, which is characterized by a corotation-to-bar-radius ratio (R c /R b) about 2.9. The response morphology of the model consists of an inner barred-spiral structure, surrounded by an ovalshaped disc and a fainter set of arms at larger radii. The oval-shaped disc and the barred-spiral structure included in it are located inside corotation, while the outer spiral arms extend beyond it. The system harbours two main different dynamical mechanisms, which shape its morphology. The bar and the spiral arms inside corotation are structured to a large extent by regular orbits, while the spiral arms beyond corotation are built by chaotic orbits. Chaotic orbits play a role inside corotation also, specifically in building weak extensions of the inner spirals as well as in the central part of the bar. The oval-shaped disc is also shaped by chaotic orbits. For the outer spirals, we find that the vast majority of the chaotic orbits, which reinforce the spirals at least for a time interval of eight pattern rotations, includes in its morphology the imprints of '4:1-resonance-like' orbits, in agreement with previous studies, as well as of 'long-period-banana-like' orbits. Both of them belong to orbits of the 'hot orbital population' that visit both areas, inside and outside corotation. This orbital population plays the key role for supporting structures out of chaos. In the case we study, order and chaos cooperate in building a galactic morphology that is encountered among grand design spiral galaxies (NGC 1566 and NGC 5248). The fact that in the model are implicated on one hand the 'precessing ellipses flow' supporting the spiral arms of normal spirals and on the other hand the 'chaotic spirals' found in barred-spiral systems, indicates that it is a model bridging two different orbital stellar dynamics.