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NASA NTRS1981

Rotation in solar-type stars. I - Evolutionary models for the spin-down of the sun

Models of rotating, 1 solar mass stars through the pre-main sequence and main sequence stages have been calculated. The calculations begin on the Hayashi track with rapid, rigid-body rotation, with angular momentum removed from the convective envelope to simulate the effect of the solar wind as the models evolve. Interior angular momentum redistribution by circulation flows and rotational instabilities is computed by a diffusion technique. It is found that at the present age of solar evolution, the models employed have internal rotation rates significantly larger than those allowed by measured solar oblateness, suggesting that the effects of circulation currents near the outer boundary of the radiative interior have been underestimated. An important result of this study is the implication that circulation currents produce deep mixing of such minor constituents as He-3 and C-13, perhaps also explaining the observed steady depletion of lithium during the main-sequence stage.

Endal, A. S.↗
NASA NTRS1981

The influence of differential rotation on the equatorial component of the sun's magnetic dipole field

This paper examines the effect that solar differential rotation would have on a hypothetical large-scale equatorial dipole field. The evolving large-scale field pattern is expressed as a series of non-axisymmetric moments. As time increases, power is transferred to progressively higher order moments. In the 27d rotating coordinate system, each moment undergoes a small retrograde drift which remains nearly uniform until that mode begins to fade. The synodic rotation periods of the first few moments are comparable to the observed 28.5d period of the sun's large-scale field near sunspot maximum. Differential rotation may be the source of this 28.5d period, but the eruption of new flux is necessary to keep the pattern going.

Sheeley, N. R., Jr.↗
NASA NTRS1981

Photospheric subrotations, differential rotation and zonal wind bands - A reverse pirouette

It is noted that on the sun the core is assumed to be rotating with a period of about 12 days while the overlying 'mantle' convection zone has a solid body component of about 27 days. It is proposed that this phenomenon could simply be understood as a 'reverse pirouette'. It is noted that while previously proposed models provide solutions of valid equations and computer analyses, they lack a simple physical picture to explain the phenomenon. In the model proposed here, the solar oblateness is conventionally providing added heat input at the poles. The result is the large scale transport of material toward the equator, causing subrotation. The model is thus seen as facilitating an understanding of the formation of a slowly rotating convection zone above the more rapidly rotating core. The latitudinal photospheric differential rotation is interpreted as a 'second order' effect associated with the horizontal transport of momentum.

Schatten, K. H.↗
NASA NTRS1981

Effects of rotation and blade incidence on the properties of turbomachinery rotor wake

An experimental investigation of the effects of the speed of rotation on a turbomachinery rotor blade wake was conducted using a fan rotor in incompressible flow. Measurements were made at two different rotational speeds (1753 and 1010 rpm) but keeping the same blade loading. This was achieved by maintaining the same incidence angle to the rotor blades in both sets of measurements. The blade incidence angle was also varied to discern the effect of blade loading. A tri-axial hot wire probe mounted in a stationary frame of reference was used for the measurements made at several radial and axial stations in the near- and far-wake regions. The three dimensional mean velocity and turbulence profiles, the wake defect, wake decay rate, turbulence intensities and turbulence stresses are appreciably altered when the speed of rotation and the blade loading are changed. The wake defect is substantially reduced and the radial velocity increased when the rotational speed is increased.

Lakshminarayana, B.↗
NASA NTRS1981

Use of Faraday-rotation data from beacon satellites to determine ionospheric corrections for interplanetary spacecraft navigation

Faraday-rotation data from the linearly polarized 137-MHz beacons of the ATS-1, SIRIO, and Kiku-2 geosynchronous satellites are used to determine the ionospheric corrections to the range and Doppler data for interplanetary spacecraft navigation. The JPL operates the Deep Space Network of tracking stations for NASA; these stations monitor Faraday rotation with dual orthogonal, linearly polarized antennas, Teledyne polarization tracking receivers, analog-to-digital converter/scanners, and other support equipment. Computer software examines the Faraday data, resolves the pi ambiguities, constructs a continuous Faraday-rotation profile and converts the profile to columnar zenith total electron content at the ionospheric reference point; a second program computes the line-of-sight ionospheric correction for each pass of the spacecraft over each tracking complex. Line-of-sight ionospheric electron content using mapped Faraday-rotation data is compared with that using dispersive Doppler data from the Voyager spacecraft; a difference of about 0.4 meters, or 5 x 10 to the 16th electrons/sq m is obtained. The technique of determining the electron content of interplanetary plasma by subtraction of the ionospheric contribution is demonstrated on the plasma torus surrounding the orbit of Io.

Royden, H. N.↗
NASA NTRS1980

Rotational history of the sun: Spin-down of the interior by circulation currents and fluid instabilities

A number of astronomical observations show that solar-type stars begin the main-sequence stage with surface rotation rates which are much greater than that of the sun. The subsequent decrease in the surface rotation rate is due to the braking torque exerted by magnetically-coupled mass loss (the solar wind). The direct braking action of the solar wind should be confined to the convective envelope so the rotation of the radiative interior remains an open question. After reviewing the relevant astronomical data, we describe how angular momentum could be transported out of the radiative interior by fluid instabilities and estimate the time scales for such transport. This picture is used to construct an evolutionary model of the sun, which predicts the present rotation of the radiative interior. The results of such a model are interpreted in terms of the measured oblateness of the solar surface.

Endal, A. S.↗
NASA NTRS1981

Rotation of dwarf star chromospheres in the ultraviolet

Periodic variations in the ultraviolet fluxes of chromospheric emission line multiplets are investigated for F, G and K stars as evidence of rotational modulation. Vacuum ultraviolet spectra were obtained with the IUE spacecraft for six stars as many as 11 times over the period April 23 to December 3, 1980. Variations in the emission fluxes of the hydrogen Lyman-alpha, Si II and Mg II lines are observed with periods up to 47 days. The periodicity, which is identified with rotational modulation, is found to persist over many rotational cycles, although the periods and time dependences of the fluxes from the different ionic species are not identical, probably due to differential rotation and global distributions. The spread of the UV periods is observed to be within 10%, with one or two peaks per cycle and a ratio of modulated to umodulated flux ranging from 1.1 to 3.0, analogous to solar behavior.

Hallam, K. L.↗
NASA NTRS1953

Preliminary Results of Heat Transfer from a Stationary and Rotating Ellipsoidal Spinner

Convective heat-transfer coefficients in dry air were obtained for an ellipsoidal spinner of 30-inch maximum diameter for both stationary and rotating operation over a range of conditions including airspeeds up to 275 miles per hour, rotational speeds up to 1200 rpm, and angles of attack of zero and 40 The results are presented in terms of Nusselt numbers, Reynolds numbers, and convective heat-transfer coefficients. The studies included both uniform heating densities over the spinner and uniform surface temperatures.. In general, the results showed that rotation will increase the convective heat transfer from a spinner, especially in the turbulent-flow regions. Rotation of the spinner at 1200 rpm and at a free-stream velocity of 275 miles per hour increased the Nusselt number parameter in the turbulent-flow region by 32 percent over that obtained with a stationary spinner; whereas in the nose region, where the flow was laminar, an increase of only 18 percent was observed. Transition from laminar to turbulent flow occurred over a large range of Reynolds numbers primarily because of surface roughness of the spinner. Operation at an angle of attack of 40 had only small effects on the local convective heat transfer for the model studied.

vonGlahn, U.↗
NASA NTRS1981

Faraday rotation measurement method and apparatus

A method and device for measuring Faraday rotation of a received RF signal is described. A simultaneous orthogonal polarization receiver compensates for a 3 db loss due to splitting of a received signal into left circular and right circular polarization channels. The compensation is achieved by RF and modulation arraying utilizing a specific receiver array which also detects and measures Faraday rotation in the presence or absence of spin stabilization effects on a linear polarization vector. Either up-link or down-link measurement of Faraday rotation is possible. Specifically, the Faraday measurement apparatus utilized in conjunction with the specific receiver array provides a means for comparing the phase of a reference signal in the receiver array to the phase of a tracking loop signal related to the incoming signal, and comparing the phase of the reference signal to the phase of the tracking signal shifted in phase by 90 degrees. The averaged and unaveraged signals, are compared, the phase changes between the two signals being related to Faraday rotation.

Brockman, M. H.↗
NASA NTRS1981

Development of rotation sample designs for the estimation of crop acreages

The idea behind the use of rotation sample designs is that the variation of the crop acreage of a particular sample unit from year to year is usually less than the variation of crop acreage between units within a particular year. The estimation theory is based on an additive mixed analysis of variance model with years as fixed effects, (a sub t), and sample units as a variable factor. The rotation patterns are decided upon according to: (1) the number of sample units in the design each year; (2) the number of units retained in the following years; and (3) the number of years to complete the rotation pattern. Different analytic formulae for the variance of (a sub t) and the variance comparisons in using a complete survey of the rotation patterns.

Lycthuan-Lee, T. G.↗
NASA NTRS1982

Acoustically induced oscillation and rotation of a large drop in space

A 2.5 cm diameter water drop was successfully deployed and manipulated in a triaxial acoustic resonance chamber during a 240 sec low-gravity SPAR rocket flight. Oscillation and rotation were induced by modulating and phase shifting the signals to the speakers. Portions of the film record were digitized and analyzed. Spectral analysis brought out the n = 2, 3, 4 free oscillation modes of the drop, its very low-frequency center-of-mass motion in the acoustic potential well, and the forced oscillation frequency. The drop boundaries were least-square fitted to general ellipses, providing eccentricities of the distorted drop. The normalized equatorial area of the rotating drop was plotted vs a rotational parameter, and was in excellent agreement with values derived from the theory of equilibrium shapes of rotating liquid drops.

Jacobi, N.↗
NASA NTRS1982

The numerical analysis of the rotational theory for the formation of lunar globules

The morphology of lunar globules is studied through the application of a numerical analysis of their rotation in space during cooling. It is assumed that molten rock is shot from the surface of the moon, solidifies in space above the moon and then falls back to the surface. The rotational theory studied makes the following assumptions: the volume of the molten rock does not change during cooling; the angular momentum is conserved; there are no internal motions because of the high viscosity of the molten rock, i.e., in equilibrium the globule is rotating as a rigid body; finally, the kinetic reaction of the globule to the forces is fast relative to the rate of cooling, i.e., the globule reaches equilibrium at constant energy. These assumptions are subjected to numerical analysis yielding good agreement between the actual globule shapes and the numerical results, but leaving some doubt as to the validity of the rotational theory due to the failure to establish the existence of true local minima and an incomplete understanding of the thermokentics.

Ross, J.↗
NASA NTRS1982

The chromospheric rotation activity relation in late type close binary systems

The IUE data on 36 late type close binary stars are presented. It is shown that the chromospheric and TR line fluxes increase with decreasing stellar rotation period, though not as rapidly as does the X-ray flux. There is an increasing dependence upon rotation with increasing line temperature. The data are consistent with the hypothesis that there exists a critical rotation rate, which depends on temperature, below which the emission flux is independent of rotation and above which it increases linearly with increasing angular velocity omega.

Walter, F. M.↗
NASA NTRS1981

Earth rotation from lunar laser ranging

Since the time when the first laser retroreflector was placed on the lunar surface by the Apollo 11 astronauts, lunar laser ranging (LLR) has led to advances in a wide range of disciplines, including the study of variations in the rotation of the earth. The conventional techniques used to monitor earth rotation suffer from lack of precision on time scales of a few months and less. LLR, by contrast, makes it possible to monitor small changes in earth rotation with a temporal resolution of the order of 1 day. Studies of earth rotation by LLR are discussed, taking into account data sensitivity, aspects of data analysis, the variation of latitude, and UTO, the mean solar time at the site as affected by polar motion.

Langley, R. B.↗
NASA NTRS1982

Radiative lifetimes and quenching rate coefficients for directly excited rotational levels of OH/A 2Sigma +, v-prime = 0/

A narrow-bandwidth pulsed dye laser was used to excite OH X 2Pi i radicals to the A 2Sigma(+) state by pumping in the (0, 0) vibrational band around 308 nm. The radiative lifetimes of specific (K-prime, J-prime) rotational levels in v-prime = 0 were measured at low pressures (not greater than 1 mtorr), which yielded a mean lifetime of 0.71 + or - 0.009 microsec (2 sigma). Electronic quenching rate constants for N2, O2, H2O, and H2 were measured for a range of initially excited rotational levels. A strong dependence of this rate constant on the initially excited rotational level was found for N2, and less markedly for O2, with the rate constant tending to increase for the lowest rotational levels K-prime not greater than 3. The implications of these results for the laser-induced fluorescence detection of atmospheric OH are discussed.

Mcdermid, I. S.↗
NASA NTRS1982

The rotation of Uranus

The determination of the rotation rate of Uranus based on available observational evidence is discussed. Previous determinations of the rotation rate since the work of Lowell and Slipher (1912), which tended to converge on a period of 10.8 days until the mid 1970s, most likely due to mutual reinforcement between unreliable results, are reviewed. Recent independent determinations based on (1) the use of theoretical interior models together with observations of oblateness and the gravitational moment J2; (2) periodic brightness fluctuations; and (3) spectrographic measurements of Doppler shifts are then presented which yield a weighted mean value of 16.31 + or - 0.27 h for the rotational period of Uranus. It is noted that the detection of the motion of surface features across the disk by future high-resolution imaging and Voyager 2 observations may allow a direct determination of the rotational period of Uranus.

Goody, R. M.↗
NASA NTRS1982

The rotational spectra of HOCO/plus/, HOCN, HN3, and HNCO from quantum mechanical calculations

Ab initio molecular orbital theory has been used to determine the equilibrium geometries, rotational constants, and rotational spectra of four isoelectronic molecules. Two of these, HOCO(plus) and HOCN, are candidate interstellar molecules. The other two, HNCO and HN3, have known rotational constants. Theoretical rotational constants and spectra for the two unknown species were corrected with the mean experimental to theoretical ratios from the two known species. This procedure resulted in predicted frequencies of 83.75 plus or minus 0.2 GHz for the 4(04) to 3(03) transition in HOCN and 85.08 plus or minus 0.2 GHz for the same transition in HOCO(plus). These are the central lines of triplets whose other members are the 4(14) to 3(13) and 4(13) to 3(12) transitions. The triplet splittings were predicted to be 0.36 plus or minus 0.01 GHz for HOCN and 0.33 plus or minus 0.01 GHz for HOCO(plus). These results indicate that HOCO(plus) is a better candidate for the source of a series of lines reported by Thaddeus, Guelin, and Linke than is HOCN.

Defrees, D. J.↗
NASA NTRS1982

Axisymmetric collapse of rotating, isothermal clouds

The results of over 50 new models of the axisymmetric collapse of rotating, isothermal clouds are presented, with the following objectives: (1) to fully explore the initial conditions necessary for collapse from uniform density and uniform rotation, subject to constant volume and constant pressure boundary conditions; (2) to catalog the possible end states for cloud collapse from these initial conditions; and (3) to determine if there is a critical value of rotational energy/gravitational energy associated with ring formation, as appears to be the case for adiabatic clouds. Three end states are obtained: Bonnor-Ebert spheroids, rings and collapsing disks. The rings are formed with values of the ratio of rotational energy to the absolute value of the gravitational energy typically less than the Maclaurin spheroid value for dynamic instability to ring formation.

Boss, A. P.↗