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Chapter 8 Relationship Between Rotational Speed and Magnetic
Chapter 8 Relationship Between Rotational Speed and Magnetic Fields 8.1 Introduction It is well-known that sunspots and other solar magnetic features rotate faster than the surface plasma (Howard & Harvey, 1970). The sidereal rotation speeds of weak magnetic features and plages (Howard, Gilman, & Gilman, 1984; Komm, Howard, & Harvey, 1993), individual sunspots (Howard, Gilman, & Gilman, 1984; Sivaraman, Gupta, & Howard, 1993) and sunspot groups (Howard, 1992) have been studied for many years by different research groups by use of different observatory data (see reviews of Howard 1996 and Beck 2000). Such studies are deemed as diagnostics of subsurface conditions based on the assumption that the faster rotation of magnetic features was caused by the faster-rotating plasma in the interior where the magnetic features were anchored (Gilman & Foukal, 1979). By matching the sunspot surface speed with the solar interior rotational speed robustly derived by helioseismology (e.g., Thompson et al., 1996; Kosovichev et al., 1997; Howe et al., 2000a), several studies estimated the depth of sunspot roots for sunspots of different sizes and life spans (e.g., Hiremath, 2002; Sivaraman et al., 2003). Such studies are valuable for understanding the solar dynamo and origin of solar active regions. However, D’Silva & Howard (1994) proposed a different explanation, namely that effects of buoyancy 111 112 CHAPTER 8. ROTATIONAL SPEED AND MAGNETIC FIELDS and drag coupled with the Coriolis force during the emergence of active regions might lead to the faster rotational speed. Although many studies were done to infer the rotational speed of various solar magnetic features, the relationship between the rotational speed of the magnetic fea- tures and their magnetic strength has not yet been studied. -
(Dark) Matter! Luminous Matter Is Concentrated at the Center
Cosmology Two Mysteries and then How we got here Dark Matter Orbital velocity law Derivable from Kepler's 3rd law and Newton's Law of gravity r v2 M = r G M : mass lying within stellar orbit r r: radius from the Galactic center v: orbital velocity From Sun's r and v: there are about 100 billion solar masses inside the Sun's orbit! 4 Rotation curve of the Milky Way: Speed of stars and clouds of gas (from Doppler shift) vs distance from center Galaxy: rotation curve flattens out with distance Indicates much more mass in the Galaxy than observed as stars and gas! Mass not concentrated at center5 From the rotation curve, inferred distribution of dark matter: The Milky Way is surrounded by an enormous halo of non-luminous (dark) matter! Luminous matter is concentrated at the center 6 We can make measurements for other galaxies Weighing spiral galaxies C Compare shifts of spectral lines (in atomic H gas clouds) as a function of distance from the center 7 Rotation curves for various spiral galaxies First measured in 1960's by Vera Rubin They all flatten out with increasing radius, implying that all spiral galaxies have vast haloes of dark matter – luminous matter 1/6th of mass 8 This mass is the DARK MATTER: It's some substance that interacts gravitationally (equivalent to saying that it has mass)... It neither emits nor absorbs light in any form (equivalent to saying that it does not interact electromagnetically) Dark matter might conceivably have 'weak' (radioactive force) interactions 9 Gaggles of Galaxies • Galaxy groups > The Local group -
Rotating Objects Tend to Keep Rotating While Non- Rotating Objects Tend to Remain Non-Rotating
12 Rotational Motion Rotating objects tend to keep rotating while non- rotating objects tend to remain non-rotating. 12 Rotational Motion In the absence of an external force, the momentum of an object remains unchanged— conservation of momentum. In this chapter we extend the law of momentum conservation to rotation. 12 Rotational Motion 12.1 Rotational Inertia The greater the rotational inertia, the more difficult it is to change the rotational speed of an object. 1 12 Rotational Motion 12.1 Rotational Inertia Newton’s first law, the law of inertia, applies to rotating objects. • An object rotating about an internal axis tends to keep rotating about that axis. • Rotating objects tend to keep rotating, while non- rotating objects tend to remain non-rotating. • The resistance of an object to changes in its rotational motion is called rotational inertia (sometimes moment of inertia). 12 Rotational Motion 12.1 Rotational Inertia Just as it takes a force to change the linear state of motion of an object, a torque is required to change the rotational state of motion of an object. In the absence of a net torque, a rotating object keeps rotating, while a non-rotating object stays non-rotating. 12 Rotational Motion 12.1 Rotational Inertia Rotational Inertia and Mass Like inertia in the linear sense, rotational inertia depends on mass, but unlike inertia, rotational inertia depends on the distribution of the mass. The greater the distance between an object’s mass concentration and the axis of rotation, the greater the rotational inertia. 2 12 Rotational Motion 12.1 Rotational Inertia Rotational inertia depends on the distance of mass from the axis of rotation. -
Galaxy Disks Annual Reviews Content Online, Including: 1 2 • Other Articles in This Volume P.C
AA49CH09-vanderKruit ARI 5 August 2011 9:18 ANNUAL REVIEWS Further Click here for quick links to Galaxy Disks Annual Reviews content online, including: 1 2 • Other articles in this volume P.C. van der Kruit and K.C. Freeman • Top cited articles 1 • Top downloaded articles Kapteyn Astronomical Institute, University of Groningen, 9700 AV Groningen, • Our comprehensive search The Netherlands; email: [email protected] 2Research School of Astronomy and Astrophysics, Australian National University, Mount Stromlo Observatory, ACT 2611, Australia; email: [email protected] Annu. Rev. Astron. Astrophys. 2011. 49:301–71 Keywords The Annual Review of Astronomy and Astrophysics is disks in galaxies: abundance gradients, chemical evolution, disk stability, online at astro.annualreviews.org formation, luminosity distributions, mass distributions, S0 galaxies, scaling This article’s doi: laws, thick disks, surveys, warps and truncations 10.1146/annurev-astro-083109-153241 Copyright c 2011 by Annual Reviews. Abstract ! All rights reserved The disks of disk galaxies contain a substantial fraction of their baryonic mat- 0066-4146/11/0922-0301$20.00 ter and angular momentum, and much of the evolutionary activity in these galaxies, such as the formation of stars, spiral arms, bars and rings, and the various forms of secular evolution, takes place in their disks. The formation and evolution of galactic disks are therefore particularly important for under- standing how galaxies form and evolve and the cause of the variety in which they appear to us. Ongoing large surveys, made possible by new instrumen- tation at wavelengths from the UV (Galaxy Evolution Explorer), via optical (Hubble Space Telescope and large groundbased telescopes) and IR (Spitzer Space Telescope), to the radio are providing much new information about disk galaxies over a wide range of redshift. -
Pt Symmetry, Quantum Gravity, and the Metrication of the Fundamental Forces Philip D. Mannheim Department of Physics University
PT SYMMETRY, QUANTUM GRAVITY, AND THE METRICATION OF THE FUNDAMENTAL FORCES PHILIP D. MANNHEIM DEPARTMENT OF PHYSICS UNIVERSITY OF CONNECTICUT PRESENTATION AT DISCRETE 2014 KING'S COLLEGE LONDON, DECEMBER 2014 1 TOPICS TO BE DISCUSSED 1. PT SYMMETRY AS A DYNAMICS 2. HIDDEN SECRET OF PT SYMMETRY{UNITARITY/NO GHOSTS 3. PT SYMMETRY AND THE LORENTZ GROUP 4. PT SYMMETRY AND THE CONFORMAL GROUP 5. PT SYMMETRY AND GRAVITY 6. PT SYMMETRY AND GEOMETRY 7. PT SYMMETRY AND THE DIRAC ACTION i 8. PT SYMMETRY AND THE METRICATION OF Aµ AND Aµ 9. THE UNEXPECTED PT SURPRISE 10. ASTROPHYSICAL EVIDENCE FOR THE PT REALIZATION OF CONFORMAL GRAVITY 2 GHOST PROBLEMS, UNITARITY OF FOURTH-ORDER THEORIES AND PT QUANTUM MECHANICS 1. P. D. Mannheim and A. Davidson, Fourth order theories without ghosts, January 2000 (arXiv:0001115 [hep-th]). 2. P. D. Mannheim and A. Davidson, Dirac quantization of the Pais-Uhlenbeck fourth order oscillator, Phys. Rev. A 71, 042110 (2005). (0408104 [hep-th]). 3. P. D. Mannheim, Solution to the ghost problem in fourth order derivative theories, Found. Phys. 37, 532 (2007). (arXiv:0608154 [hep-th]). 4. C. M. Bender and P. D. Mannheim, No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model, Phys. Rev. Lett. 100, 110402 (2008). (arXiv:0706.0207 [hep-th]). 5. C. M. Bender and P. D. Mannheim, Giving up the ghost, Jour. Phys. A 41, 304018 (2008). (arXiv:0807.2607 [hep-th]) 6. C. M. Bender and P. D. Mannheim, Exactly solvable PT-symmetric Hamiltonian having no Hermitian counterpart, Phys. Rev. D 78, 025022 (2008). -
OBSERVATIONAL EVIDENCE for the NON-DIAGONALIZABLE HAMILTONIAN of CONFORMAL GRAVITY Philip D. Mannheim University of Connecticut
OBSERVATIONAL EVIDENCE FOR THE NON-DIAGONALIZABLE HAMILTONIAN OF CONFORMAL GRAVITY Philip D. Mannheim University of Connecticut Seminar in Dresden June 2011 1 On January 19, 2000 a paper by P. D. Mannheim and A. Davidson,“Fourth order theories without ghosts” appeared on the arXiv as hep-th/0001115. The paper was later published as P. D. Mannheim and A. Davidson, “Dirac quantization of the Pais-Uhlenbeck fourth order oscillator”, Physical Review A 71, 042110 (2005). (hep-th/0408104). The abstract of the 2000 paper read: Using the Dirac constraint method we show that the pure fourth-order Pais-Uhlenbeck oscillator model is free of observable negative norm states. Even though such ghosts do appear when the fourth order theory is coupled to a second order one, the limit in which the second order action is switched off is found to be a highly singular one in which these states move off shell. Given this result, construction of a fully unitary, renormalizable, gravitational theory based on a purely fourth order action in 4 dimensions now appears feasible. Then in the 2000 paper it read: “We see that the complete spectrum of eigenstates of H(ǫ = 0) =8γω4(2b†b + a†b + b†a)+ ω is the set of all states (b†)n|Ωi, a spectrum whose dimensionality is that of a one rather than a two-dimensional harmonic oscillator, even while the complete Fock space has the dimensionality of the two-dimensional oscillator.” With a pure fourth-order equation of motion being of the form 2 2 2 (∂t −∇ ) φ(x)=0, (1) the solutions are of the form ¯ ¯ φ(x)= eik·x¯−iωt, φ(x)= t eik·x¯−iωt. -
Exploring Robotics Joel Kammet Supplemental Notes on Gear Ratios
CORC 3303 – Exploring Robotics Joel Kammet Supplemental notes on gear ratios, torque and speed Vocabulary SI (Système International d'Unités) – the metric system force torque axis moment arm acceleration gear ratio newton – Si unit of force meter – SI unit of distance newton-meter – SI unit of torque Torque Torque is a measure of the tendency of a force to rotate an object about some axis. A torque is meaningful only in relation to a particular axis, so we speak of the torque about the motor shaft, the torque about the axle, and so on. In order to produce torque, the force must act at some distance from the axis or pivot point. For example, a force applied at the end of a wrench handle to turn a nut around a screw located in the jaw at the other end of the wrench produces a torque about the screw. Similarly, a force applied at the circumference of a gear attached to an axle produces a torque about the axle. The perpendicular distance d from the line of force to the axis is called the moment arm. In the following diagram, the circle represents a gear of radius d. The dot in the center represents the axle (A). A force F is applied at the edge of the gear, tangentially. F d A Diagram 1 In this example, the radius of the gear is the moment arm. The force is acting along a tangent to the gear, so it is perpendicular to the radius. The amount of torque at A about the gear axle is defined as = F×d 1 We use the Greek letter Tau ( ) to represent torque. -
Pt Symmetry, Quantum Gravity, and the Metrication of the Fundamental Forces Philip D. Mannheim Department of Physics University
PT SYMMETRY, QUANTUM GRAVITY, AND THE METRICATION OF THE FUNDAMENTAL FORCES PHILIP D. MANNHEIM DEPARTMENT OF PHYSICS UNIVERSITY OF CONNECTICUT PRESENTATION AT MIAMI 2014 FORT LAUDERDALE FLORIDA, DECEMBER 2014 1 UBIQUITY OF PT SYMMETRY 1. PT SYMMETRY AS A DYNAMICS 2. HIDDEN SECRET OF PT SYMMETRY{UNITARITY/NO GHOSTS 3. PT SYMMETRY AND THE LORENTZ GROUP 4. PT SYMMETRY AND THE CONFORMAL GROUP 5. PT SYMMETRY AND GRAVITY 6. PT SYMMETRY AND GEOMETRY 7. PT SYMMETRY AND THE DIRAC ACTION i 8. PT SYMMETRY AND THE METRICATION OF Aµ AND Aµ 9. THE UNEXPECTED PT SURPRISE 10. ASTROPHYSICAL EVIDENCE FOR THE PT REALIZATION OF CONFORMAL GRAVITY 2 GHOST PROBLEMS, UNITARITY OF FOURTH-ORDER THEORIES AND PT QUANTUM MECHANICS 1. P. D. Mannheim and A. Davidson, Fourth order theories without ghosts, January 2000 (arXiv:0001115 [hep-th]). 2. P. D. Mannheim and A. Davidson, Dirac quantization of the Pais-Uhlenbeck fourth order oscillator, Phys. Rev. A 71, 042110 (2005). (0408104 [hep-th]). 3. P. D. Mannheim, Solution to the ghost problem in fourth order derivative theories, Found. Phys. 37, 532 (2007). (arXiv:0608154 [hep-th]). 4. C. M. Bender and P. D. Mannheim, No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model, Phys. Rev. Lett. 100, 110402 (2008). (arXiv:0706.0207 [hep-th]). 5. C. M. Bender and P. D. Mannheim, Giving up the ghost, Jour. Phys. A 41, 304018 (2008). (arXiv:0807.2607 [hep-th]) 6. C. M. Bender and P. D. Mannheim, Exactly solvable PT-symmetric Hamiltonian having no Hermitian counterpart, Phys. Rev. D 78, 025022 (2008). -
Analysis of Repulsive Central Universal Force Field on Solar and Galactic
Open Phys. 2019; 17:364–372 Research Article Kamal Barghout* Analysis of repulsive central universal force field on solar and galactic dynamics https://doi.org/10.1515/phys-2019-0041 otic matter-energy to the matter side of Einstein field equa- Received Jun 30, 2018; accepted Apr 02, 2019 tions, dubbed “dark matter” and “dark energy”; see [5] and references therein. Abstract: Recent astrophysical observations hint toward The existence of dark matter is mostly inferred from the need for an extended theory of gravity to explain puz- gravitational effects on visible matter and is thought toac- zles presented by the standard cosmological model such count for approximately 85% of the matter in the universe as the need for dark matter and dark energy to understand while dark energy is inferred from the accelerated expan- the dynamics of the cosmos. This paper investigates the ef- sion of the universe and along with dark matter constitutes fect of a repulsive central universal force field on the be- about 95% of the total mass-energy content in the universe. havior of celestial objects. Negative tidal effect on the solar The origin of dark matter is a mystery and a wide range and galactic orbits, like that experienced by Pioneer space- of theories speculate its type, its particle’s mass, its self- crafts, was derived from the central force and was shown to interaction and its interaction with normal matter. Also, manifest itself as dark matter and dark energy. Vertical os- experiments to directly detect dark matter particles in the cillation of the sun about the galactic plane was modeled lab have failed to produce positive results which presents a as simple harmonic motion driven by the repulsive force. -
A Case for Alternate Theories of Gravity C Sivaram Indian Institute Of
Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 19 June 2020 doi:10.20944/preprints202006.0239.v1 Non-detection of Dark Matter particles: A case for alternate theories of gravity C Sivaram Indian Institute of Astrophysics, Bangalore, 560 034, India e-mail: [email protected] Kenath Arun Christ Junior College, Bangalore, 560 029, India e-mail: [email protected] A Prasad Center for Space Plasma & Aeronomic Research, The University of Alabama in Huntsville, Huntsville, Alabama 35899 email: [email protected] Louise Rebecca Christ Junior College, Bangalore - 560 029, India e-mail: [email protected] Abstract: While there is overwhelming evidence for dark matter (DM) in galaxies and galaxy clusters, all searches for DM particles have so far proved negative. It is not even clear whether only one particle is involved or a combination or particles, their masses not precisely predicted. This non-detectability raises the possible relevance of modified gravity theories – MOND, MONG, etc. Here we consider a specific modification of Newtonian gravity (MONG) which involves gravitational self-energy, leading to modified equations whose solutions imply flat rotation curves and limitations of sizes of clusters. The results are consistent with current observations including that involving large spirals. This modification could also explain the current Hubble tension. We also consider effects of dark energy (DE) in terms of a cosmological constant. 1 © 2020 by the author(s). Distributed under a Creative Commons CC BY license. Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 19 June 2020 doi:10.20944/preprints202006.0239.v1 Over the past few decades there have been a plethora of sophisticated experiments involving massive sensitive detectors trying to catch faint traces of the elusive Dark Matter (DM) particles. -
A Molecular Stopwatch
PHYSICAL REVIEW X 1, 011002 (2011) Ensemble of Linear Molecules in Nondispersing Rotational Quantum States: A Molecular Stopwatch James P. Cryan,1,2,* James M. Glownia,1,3 Douglas W. Broege,1,3 Yue Ma,1,3 and Philip H. Bucksbaum1,2,3 1PULSE Institute, SLAC National Accelerator Laboratory 2575 Sand Hill Road, Menlo Park, California 94025, USA 2Department of Physics, Stanford University Stanford, California 94305, USA 3Department of Applied Physics, Stanford University Stanford, California 94305, USA (Received 16 May 2011; published 8 August 2011) We present a method to create nondispersing rotational quantum states in an ensemble of linear molecules with a well-defined rotational speed in the laboratory frame. Using a sequence of transform- limited laser pulses, we show that these states can be established through a process of rapid adiabatic passage. Coupling between the rotational and pendular motion of the molecules in the laser field can be used to control the detailed angular shape of the rotating ensemble. We describe applications of these rotational states in molecular dissociation and ultrafast metrology. DOI: 10.1103/PhysRevX.1.011002 Subject Areas: Atomic and Molecular Physics, Chemical Physics, Optics I. INTRODUCTION of the molecule, where circularly polarized photons of one rotational handedness are absorbed and the other handed- We present a method to create a rotating ensemble of ness are stimulated to emit. nondispersing quantum rotors based on ideas of strong- The use of strong-field laser pulses to create rotating J Þ 0 field rapid adiabatic passage. The ensemble has h zi molecular distributions was first considered in a series of and a definite alignment phase angle , which increases papers on the optical centrifuge [2–4]. -
New Type of Black Hole Detected in Massive Collision That Sent Gravitational Waves with a 'Bang'
New type of black hole detected in massive collision that sent gravitational waves with a 'bang' By Ashley Strickland, CNN Updated 1200 GMT (2000 HKT) September 2, 2020 <img alt="Galaxy NGC 4485 collided with its larger galactic neighbor NGC 4490 millions of years ago, leading to the creation of new stars seen in the right side of the image." class="media__image" src="//cdn.cnn.com/cnnnext/dam/assets/190516104725-ngc-4485-nasa-super-169.jpg"> Photos: Wonders of the universe Galaxy NGC 4485 collided with its larger galactic neighbor NGC 4490 millions of years ago, leading to the creation of new stars seen in the right side of the image. Hide Caption 98 of 195 <img alt="Astronomers developed a mosaic of the distant universe, called the Hubble Legacy Field, that documents 16 years of observations from the Hubble Space Telescope. The image contains 200,000 galaxies that stretch back through 13.3 billion years of time to just 500 million years after the Big Bang. " class="media__image" src="//cdn.cnn.com/cnnnext/dam/assets/190502151952-0502-wonders-of-the-universe-super-169.jpg"> Photos: Wonders of the universe Astronomers developed a mosaic of the distant universe, called the Hubble Legacy Field, that documents 16 years of observations from the Hubble Space Telescope. The image contains 200,000 galaxies that stretch back through 13.3 billion years of time to just 500 million years after the Big Bang. Hide Caption 99 of 195 <img alt="A ground-based telescope&amp;#39;s view of the Large Magellanic Cloud, a neighboring galaxy of our Milky Way.