Internal Angular Velocity Research Articles

The Rotation of the Solar Core Inferred by Genetic Forward Modeling

Genetic forward modeling is a genetic algorithm-based modeling technique that can be used to perform helioseismic inversions of the Sun's internal angular velocity profile. The method can easily accommodate constraints such as positivity and monotonicity and readily lends itself to the use of robust statistical goodness-of-fit estimators. After briefly describing the technique, we ascertain its performance by carrying out a series of inversions for artificial splitting data generated from a set of synthetic internal rotation profiles characterized by various small inward increases in angular velocity in the deep solar core (r/R☉ ≤ 0.5). These experiments indicate that the technique is accurate down to r/R☉ ≃ 0.2, and retains useful sensitivity down to r/R☉ ≃ 0.1.

SEGMENTAL CONTRIBUTIONS TO JAVELIN SPEED 892

The purpose was to quantify the contributions of the thrower's linear translation and segmental rotations to the speed of the javelin. Eight male finalists at the 1995 USA Track and Field Championships were filmed at 100Hz. The two longest throws for each athlete were analyzed and the DLT method was used to obtain three-dimensional coordinates of thrower and javelin landmarks. Data were smoothed using quintic spline functions and the first derivatives of these functions provided instantaneous linear velocity values. Segment angular velocities and instantaneous contributions to javelin speed were computed using methods similar to those reported by Feltner et al. (J. Applied Biomech, 1996, 359-382). The general patterns of component contributions to javelin speed were similar for all analyzed throws. At left foot plant and the start of the double support period prior to release, over 75% of the speed of the javelin (X=7.4 m/s) was due to the linear velocity of the thrower's center of mass (c.m.). During the double support phase, the speed of the javelin rapidly increased and reached its release speed (X=28.1 m/s). During double support and until approximately 0.035 s before release, the horizontal adduction angular velocity of the upper arm was a major contributor to the speed of the javelin. However, the horizontal adduction angular velocity rapidly decreased immediately prior to release. At release, the largest contributors to the speed of the javelin were elbow extension angular velocity(X=34.7±8.1%), upper arm internal rotation angular velocity (X=13.3±9.8%), trunk twist (X=11.9±6.3%), translation of the thrower's c.m. (X=11.8±2.4%) and javelin distortion and recoil(X=9.0±6.7%). All remaining terms independently contributed less than 4% to javelin speed. For each throw, the aforementioned five terms accounted for over 80% of the javelin's release speed. However, the relative magnitudes of each term's percent contribution to javelin speed at release differed for the throws indicating possible technique variations among the athletes.

On the Inference of the Solar Internal Rotation Profile from Frequency-splitting Data

view Abstract Citations (14) References (16) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS On the Inference of the Solar Internal Rotation Profile from Frequency-splitting Data Wilson, P. R. ; Burtonclay, D. ; Li, Y. Abstract From the earliest helioseismology data it was inferred that the internal angular velocity of the Sun is invariant across the convection zone (i.e., it mimics the surface differential rotation). This result caused some concern to theoreticians since many dynamo and dynamical models of the convection zone require that the angular velocity be approximately constant on cylinders concentric about the rotation axis. Stark and others have argued that in order to test models of the angular velocity against frequency- splitting data the uncertainties in these data must be magnified, and it is shown here that within these uncertainties it is indeed difficult to exclude some models in which the angular velocity is independent of radius across a region including the convection zone and some depths below it. Further, Gough and his colleagues have recently claimed that the currently available data are not inconsistent with some models for which the angular velocity is constant on cylinders within the Sun's convection zone. Thus, inferences from frequency-splitting data regarding the internal angular velocity of the Sun would seem to be somewhat uncertain. In this paper, these uncertainties are discussed and an alternative approach is proposed in which a forward method is used to find the simplest model for the angular velocity (i.e., with the least positional variations) consistent with the data, including the quoted uncertainties. While it is not claimed that such a model represents the true angular velocity, its features may be said to "characterize" the essential properties of a particular data set. Publication: The Astrophysical Journal Pub Date: October 1996 DOI: 10.1086/177893 Bibcode: 1996ApJ...470..621W Keywords: CONVECTION; MAGNETOHYDRODYNAMICS: MHD; SUN: INTERIOR; SUN: OSCILLATIONS full text sources ADS |

Internal dynamics and magnetism of the Sun

The present internal dynamics and magnetism of the Sun have been determined by the initial conditions in the pre-main sequence age, by the angular momentum loss and its redistribution in the interior, and the interaction of motion with magnetic field.The history of the Sun rotation is traced back by observing the present rotation of stars with the same mass as the Sun at earlier evolutionary stages. The present angular momentum of the Sun, as deduced from its internal rotational behavior derived from helioseismological data, appears to be a small percentage of the original one contained in similar mass stars (T Tauri and α Persei). It is not easy to reconcile the sharp decrease in the surface angular velocity, which follows the α Persei phase, with the subsequent soft decrease, taking place after Pleiades phase, unless some very effective mechanism transfers angular momentum from inner to outer regions, where is lost in the solar wind. Such a mechanism is probably magnetic in origin, since purely hydrodynamic instabilities fail to transfer angular momentum at a rate sufficient to determine the presently observed flat radial gradient of the internal angular velocity.

Rotation and magnetic fields during the evolution of massive stars through B(e) and Wolf-Rayet phases

view Abstract Citations (16) References (38) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Rotation and Magnetic Fields during the Evolution of Massive Stars through B[e] and Wolf-Rayet Phases Maheswaran, Murugesapillai ; Cassinelli, Joseph Abstract The wind phenomena of a variety of early-type stars, including the evolved B(e) and Wolf-Rayet (W-R) stars, have been explained using the presence of rotation and magnetic fields. However, if a star had a significant wind throughout its previous evolutionary lifetime, spin-down would have occurred. This paper is a first step in an exploration of possible evolutionary scenarios of rotation in massive stars with continuous winds, from zero-age main sequence (ZAMS) through terminal W-R stage. Magnetic fields with varying strengths are considered. A kinematic approach is developed to derive equations for the evolution of angular momentum. The equations are applied to heuristic models that represent single stars with a ZAMS mass of 60 solar mass. Computations are performed for models with different internal angular velocity distributions. Omnidirectional and two-component winds are considered, and, in some models, allowance is made for possible bipolar mass ejection at the Humphreys-Davidson (HD) limit. The effects of the important factors that govern the evolution of the equatorial rotation are discussed. Publication: The Astrophysical Journal Pub Date: February 1994 DOI: 10.1086/173684 Bibcode: 1994ApJ...421..718M Keywords: B Stars; Main Sequence Stars; Massive Stars; Stellar Evolution; Stellar Magnetic Fields; Stellar Models; Stellar Rotation; Wolf-Rayet Stars; Angular Momentum; Field Strength; Kinematics; Mathematical Models; Stellar Winds; Astrophysics; STARS: EMISSION-LINE; BE; STARS: EVOLUTION; STARS: MAGNETIC FIELDS; STARS: ROTATION; STARS: WOLF-RAYET full text sources ADS |

Seismic Evidence of Modulation of the Structure and Angular Velocity of the Sun Associated with the Solar Cycle

Solar p-mode multiplet oscillation frequencies and expansion coefficients for degeneracy splitting have been measured in the summers of 1986 and 1988–1990. Temporal variations not unlike the differences between 1988 and 1986 reported by Libbrecht & Woodard (1990) continue into 1990. These differences are possibly associated with the solar cycle. We report here on our first findings about the variation of the internal angular velocity and asphericity deduced from these frequency differences.

Observations of intermediate- and high-degree p-mode oscillations during sunspot cycles 21 and 22

Extensive time series of resolved solar images have been available for helioseismological studies since the late 1970s. We will first review the temporal coverage that has been built up over the past 11 years at several different observatories. Next, we will present examples of the frequencies, power levels, modal energies, and widths of solar intermediate-(5< ℓ <120) and high-degree (120< ℓ <600) p-modes which were obtained at the Mount Wilson Observatory's 60-Foot Solar Tower Telescope during the rising phase of the current sunspot cycle. We will demonstrate that the inclusion of frequency splittings from the high-degree p-modes has allowed us to demonstrate that the sun's internal equatorial angular velocity is not constant with radius but rather varies systematically with radius throughout the solar convection zone and below. Lastly, we will show that, by intercomparing many of the available p-mode frequency datasets, we have been able to confirm the recent suggestion by Libbrecht and Woodard /1/ that the frequencies of the intermediate-degree p-modes do vary systematically with varying levels of solar activity. In particular, we will demonstrate that such frequency shifts have been occurring in every year that observations have been obtained since 1980 and that such variations are also consistent with similar variations that have been recently noted in low-degree p-mode frequencies.

Inferring the sun's internal angular velocity from observed p-mode frequency splittings

view Abstract Citations (337) References (41) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Inferring the Sun's Internal Angular Velocity from Observed p-Mode Frequency Splittings Brown, Timothy M. ; Christensen-Dalsgaard, Jorgen ; Dziembowski, Wojciech A. ; Goode, Philip ; Gough, Douglas O. ; Morrow, Cherilynn A. Abstract The sun's internal solar velocity Omega is studied as a function of latitude and radius using the solar oscillation data of Brown and Morrow (1987). An attempt is made to separate robust inferences about the sun from artifacts of the analysis. It is found that a latitudinal variation of Omega similar to that observed at the solar surface exists throughout the sun's convection zone and that the variation of Omega with latitude persists to some extent even beneath the convection zone. Publication: The Astrophysical Journal Pub Date: August 1989 DOI: 10.1086/167727 Bibcode: 1989ApJ...343..526B Keywords: Angular Velocity; Solar Interior; Solar Oscillations; Solar Rotation; Error Analysis; Forward Scattering; Integral Equations; Inverse Scattering; Kernel Functions; Tachometers; Solar Physics; SUN: INTERIOR; SUN: OSCILLATIONS; SUN: ROTATION full text sources ADS |

B. R. DURNEY and S. %HA (Eds.): The Internal Solar Angular Velocity. Theory, Observations and Relationships to Solar Magnetic Fields. Proceedings of the 8th National Solar Observatory Summer Sympo‐sium, held in Sunspot, New Mexico, August 11‐14, 1986. Astro‐physics and Space Science Library Vol. 137

Astronomische NachrichtenVolume 310, Issue 3 p. 251-252 Buchbesprechungen B. R. DURNEY and S. %HA (Eds.): The Internal Solar Angular Velocity. Theory, Observations and Relationships to Solar Magnetic Fields. Proceedings of the 8th National Solar Observatory Summer Sympo-sium, held in Sunspot, New Mexico, August 11-14, 1986. Astro-physics and Space Science Library Vol. 137 Jiirgen Siaude, Jiirgen Siaude PotsdamSearch for more papers by this author Jiirgen Siaude, Jiirgen Siaude PotsdamSearch for more papers by this author First published: 1989 https://doi.org/10.1002/asna.2113100331AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume310, Issue31989Pages 251-252 RelatedInformation

Rotational splitting of global solar oscillations and its relevance to tests of general relativity

The estimation of the sun's internal angular velocity using rotational splitting of low-order, low-degree global oscillations in the limb-darkening function is reviewed. Observed spatial properties of the eigenfunctions confirm the multiplet classifications previously identified by the existence of Zeeman-like frequency patterns characteristic of rotational splitting. From the observed rotational splitting, a sidereal rotational frequency of ≥3.0 μ Hz is derived for the deep interior; this value is more than six times greater than the equatorial rotational frequency of the photosphere. Upper limits have also been estimated for the internal magnetic field by analyzing the splitting for departures from uniform spacing. The inferred angular velocity distribution, together with the estimated upper limit on the internal magnetic field, yield a gravitational quadrupole moment,J2 of (5.5±1.3)×10−6. When this result is combined with different published results from planetary radar observations, values of 0.987±0.006 and 0.991±0.006 are obtained for (2+2γ−β)/3, a combination of Eddington-Robertson PPN parameters which in general relativity takes the value of 1.

Preliminary Determination of the Sun's Gravitational Quadrupole Moment from Rotational Splitting of Global Oscillations and its Relevance to Tests of General Relativity

The sun's internal angular velocity is estimated from observations of rotational splitting of low-order, low-degree global oscillations detected as fluctuations in the limb-darkening function. The inferred rapid rotation implies a unitless gravitational quadrupole moment, J/sub 2/, of (5.5 +- 1.3) x 10/sup -6/. When this result is combined with two published planetary radar results values of 0.987 +- 0.006 and 0.991 +- 0.006 are obtained for (1/3)(2+2..gamma..-..beta..), a quantity equal to one in the general theory of relativity. .ID LRK206 .PG 1798 1798

Internal rotation and gravitational quadrupole moment of the Sun

The internal angular velocity of the Sun is estimated from observations of apparent rotational splitting of low-order low-degree global oscillations detected in fluctuations in the limb-darkening function. A sidereal rotation of 3 µHz is inferred for the deep interior; this is more than six times greater than the equatorial rotation frequency of the photosphere. The inferred angular velocity distribution does not vary strongly with latitude, and yields a gravitational quadrupole moment J2≃3.6×10−6. When combined with the results of planetary radar observations to determine (2−β+2γ)/3, a combination of Eddington–Robertson post-newtonian parameters which in general relativity is unity, a value of about 0.994 (±0.012) is thus obtained.

A new method for determining the internal rotational angular velocity of the stars

Some physical aspects of the effect of rotation on the nonradial oscillations are discussed by the perturbation method. A new method to estimate the inner rotational angular velocity in stars with use of the rotational frequency splitting of the nonradial oscillations is proposed, and the “effective depth” for a specified mode is defined for practical procedure. The necessary quantities (frequencies, “effective depths” andCk, l values) to derive the inner rotational angular velocity through the observations by this method are calculated for models of several early type stars with masses ranging from 1.5M⊙ to 20M⊙.

Time variations of the angular momentum of the sun

view Abstract Citations (3) References (12) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Time variation of the angular momentum of the Sun. Schatten, K. H. Abstract Time variations of density models of the sun are investigated. This is an attempt to estimate the changing moment of inertia of the sun in order to calculate the internal solar angular velocity based upon Newton's equation of motion. Previous estimates of dI/dt disagree with those based upon central densities in a homologously contracting model. It is shown that the homologously contracting model leads to large errors in dI/dt. Based upon an integration of Sears's (1964) solar model, dI/dt is determined as -5.5 by 10 to the 34th power gm-sq cm/sec. This suggests a core angular velocity of about 0.00015 per sec, corresponding to a period of 0.5 + or - 0.1 day, assuming a constant angular velocity with time. Publication: The Astrophysical Journal Pub Date: September 1977 DOI: 10.1086/155505 Bibcode: 1977ApJ...216..650S Keywords: Angular Momentum; Astronomical Models; Solar Rotation; Time Dependence; Angular Velocity; Density Distribution; Solar Oblateness; Stellar Models; Solar Physics full text sources ADS |

Relativistic particle with internal rotational structure

General kinematical and dynamical aspects of any covariant theory of particles possessing internal angular velocity together with internal angular momentum are analysed. Theory is classified according to the form of subsidiary conditions required. A precise theory is constructed by the aid of a spinor ζ as the kinematical representation of such structure, postulating the equation of motion, $$2iQ\frac{{d\zeta }}{{d\tau }}{\mathbf{ }}---{\mathbf{ }}ip_\mu \gamma _\mu \zeta {\mathbf{ }}---{\mathbf{ }}\left( {m'^2 /m} \right)\left\{ {\left( {\bar \zeta \zeta } \right){\mathbf{ }}\zeta {\mathbf{ }}---{\mathbf{ }}\left( {\bar \zeta \gamma _5 \zeta } \right)\gamma _5 \zeta } \right\}{\mathbf{ }} = {\mathbf{ }}0$$ where ζ is defined along a world line,Q andm represent the structure constants of the original particle, whilem′ means observable rest mass which can take a certain constant value between zero andm. The equation contains a self-interaction term of the third order, and thus the theory may be considered to represent the particle analogue to the non-linear field of Heisenberg. Still it can be solved exactly, the result showing that the particle performs, besides its mean rectilinear motion represented by the constant momentum vectorpµ, an orbital zitterbewegung around it, and the synchronized precession of the internal third axis around the constant helicity pseudovector. The theory of Weyssenhoff is included in the present theory as a degenerate case in which the internal angular velocity becomes physically arbitrary. It is expected that a unified model of elementary particles may be reached by quantization starting from this generalized classical model.