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NASA NTRS1992

A new determination of the solar rotation rate

We use 'stackplot' displays to compare observations of the photospheric magnetic field during sunspot cycle 21 with simulations based on the flux-transport model. Adopting nominal rates of diffusion, differential rotation, and meridional flow, we obtain slanted patterns similar to those of the observed field, even when the sources of flux are assigned random longitudes in the model. At low latitudes, the slopes of the nearly vertical patterns of simulated field are sensitive to the rotation rate used in the calculation, and insensitive to the rates of diffusion and flow during much of the sunspot cycle. Good agreement between the observed and simulated patterns requires a synodic equatorial rotation period of 26.75 +/- 0.05 days.

Sheeley, N. R., Jr.↗

NASA NTRS1976

Solar rotation during the Maunder Minimum

Solar surface rotation has been measured from sunspot drawings made in A.D. 1642-1644, probable differences from present-day rates are found. The 17th-century sunspots rotated faster near the equator by 3 or 4%, and the differential rotation between zero and + or - 20 deg latitude was enhanced by about a factor 3. These differences are consistent features in both spots and groups of spots and in both hemispheres. It is assumed that this apparent change in surface rotation was related to the ensuing dearth of solar activity (the Maunder Minimum) which persisted until about 1715.

Eddy, J. A.↗

NASA NTRS1986

Density waves in the solar nebula - Differential Lindblad torque

The differential torque exerted by Lindblad resonances on a perturbing object embedded in a two-dimensional nonself-gravitating disk with density, pressure and sound speed gradients is quantified. First-order corrections are made to account for Keplerian rotation and the presence of the gradients. The total torque is calculated by summing over all resonances in the absence of local wave damping. When applied to the primordial solar nebula disk, the calculations show that disks that cool with increasing heliocentric distance will cause decay of the orbit of the perturbing object. Conditions in which the perturber will escape orbit delay are also described. The characteristic drift time will be no greater than the stochastic accretion time scales. Implications of the calculations for planetary formation are discussed.

Ward, W. R.↗

NASA NTRS1978

Magnetic field in the primitive solar nebula

Carbonaceous chondrites have apparently been magnetized in their early history in magnetic fields with intensities of 0.1 to 10 G, but the origin of the magnetizing field has remained obscured. It is suggested that the magnetic field recorded in the remanence of carbonaceous chondrites may have been produced by a self-excited hydromagnetic dynamo in the gaseous preplanetary nebula from which the solar system is thought to have formed. Recently computed models for the evolution of the preplanetary nebula, consisting of turbulent and differentially rotating gaseous disks with characteristic radial scales of several AU, are used to demonstrate the feasibility of this hypothesis. The maximum field intensity that might be realized by the dynamo production process is estimated to be as high as 1 to 10 G, taking into account two dynamical mechanisms that limit the strength of the field (the Coriolis force and ambipolar diffusion).

Levy, E. H.↗

NASA NTRS1984

Numerical Simulations of Convectively Excited Gravity Waves

Magneto-convection and gravity waves are numerically simulated with a nonlinear, three-dimensional, time-dependent model of a stratified, rotating, spherical fluid shell heated from below. A Solar-like reference state is specified while global velocity, magnetic field, and thermodynamic perturbations are computed from the anelastic magnetohydrodynamic equations. Convective overshooting from the upper (superadiabatic) part of the shell excites gravity waves in the lower (subadiabatic) part. Due to differential rotation and Coriolis forces, convective cell patterns propagate eastward with a latitudinally dependent phase velocity. The structure of the excited wave motions in the stable region is more time-dependent than of the convective motions above. The magnetic field tends to be concentrated over giant-cell downdrafts in the convective zone but is affected very little by the wave motion in the stable region.

Glatzmaier, G. A.↗

NASA NTRS1987

Rotational modulation and flares on RS CVn and BY Dra systems. II - IUE observations of BY Draconis and AU Microscopii

The modulation of the strong chromospheric and transition region lines over one cycle of the optical light curves of BY Dra and AU Mic is studied using IUE observations. The IUE observations were made from October 2-5, 1981 and include 7 short wavelength (SW) spectra and 13 long wavelength (LW) spectra. The integrated line flux data reveal that for BY Dra in the SW spectra there is modulation in the C IV, C II, O I, and He II lines and nonflare surface fluxes; and in the LW spectra, flares are detected in the Mg II and Fe II bands. It is observed that there is no modulation in AU Mic, and the optical photometry data reveal a poor correlation between optical flare strength and UV emission line enhancements. The differential emission measure curves for BY Dra and AU Mic are compared with solar curves. It is noted that both stars show the presence of hot material throughout their rotation period.

Butler, C. J.↗

NASA NTRS1990

Turbulent thermal convection in a differentially rotating channel

Differentially rotating disks of gases and solids occur in several astrophysical systems, in particular in the inner parts of protostellar nebulae, of which our own solar system is thought to be a relic. The objectives of this paper are to: (1) study localized turbulence in circumstances approximating those found in accretion disks using previously existing expertise in performing direct numerical simulation of turbulent, incompressible channel flows with low Reynolds numbers; (2) determine the limitations of such calculations; and (3) extend the type of numerical simulation (e.g., to include density and stratification and compressibility effects and to accommodate higher Reynolds numbers with sub-grid scale modeling) so that the relevant physical effects are realistically captured.

Cabot, W.↗

NASA NTRS1992

Multiple periodicities in the solar magnetic field - Possible origin in a multiple-mode solar dynamo

The solar magnetic field is generated in an oscillatory mode with a 22 yr full period and gives rise to the 11 yr sunspot cycle. However, analyses of contemporary solar records, as well as other surrogate indicators of solar activity, suggest the presence also of longer term periodicities in the solar magnetic cycle. This paper suggests that the solar dynamo can operate in a multiply periodic state, with several periodicites being generated simultaneously at different depths in the convection zone. A simple two-layer model of the solar convection zone is used to illustrate the physical mechanism of spatially localized, multiple-periodicity-mode dynamo regeneration. The two layers are characterized by differences in their respective turbulent magnetic diffusivities. Although the magnetic modes interact with one another, each mode is produced large in one layer or the other, and has an oscillation period approximately equal to the time characteristic of magnetic diffusion across the layer. The observed complicated periodicity pattern in the solar magnetic field could be a combination of two (or more) dynamo modes generated in this manner. The calculations are carried out using a differential rotation model consistent with recent helioseismological measurements, illustrating the challenge to dynamo theory raised by those observational results.

Boyer, D. W.↗

NASA NTRS1981

Solar radiation force modeling for TDRS orbit determination

The relative orbit determination accuracies resulting from several TDRS models are evaluated. These models include spherical, single-plate, and restricted two-plate models. The plate models can be adjusted in both area and reflectivity through differential correction. The restricted two-plate model has an Earth-pointing plate and a solar plate; the orientation of the solar plate is restricted to rotation about an axis perpendicular to the satellite's orbital plane.

Lee, T.↗

NASA NTRS1998

A Search for Giant Convection Cells on the Sun

Giant convection cells (slow, long-lived cellular flows in the Sun's convection zone with typical diameters greater than about 100,000 km) have been the subject of many searches over the last 30 years. If such flows exist, they should play a key role in structuring the Sun's large scale magnetic field and in driving the large scale axisymmetric flows: the differential rotation and meridional circulation. Detailed observations of the flows in these cells may also allow us to better predict future magnetic field configurations and the solar activity associated with them. Line-of-sight velocity data from the Michelson Doppler Interferometer on the ESA/NASA Solar and Heliospheric Observatory provides us with new opportunities to search for giant cells. This data is free of any atmospheric distortion and has been obtained continuously without any day/night gaps for more than two months at a time. These two-month datasets are important because giant cells are expected to have lifetimes somewhat longer that the Sun's 27 day rotation period. Any reappearance of a flow pattern after 27 days would be an important confirmation of the existence of these cells. The approach taken in this search is to separate the giant cell velocity signal from the other, stronger velocity signals by using a spherical harmonic representation of the spatial structures and a fourier decomposition of the temporal behavior. Any giant cell signal should be characterized by low spatial wavenumbers with temporal frequencies appropriate to the solar rotation of these patterns.

Hathaway, David H.↗

NASA NTRS1994

Improvement of the photometric sunspot index and changes of the disk-integrated sunspot contrast with time

The photometric sunspot index (PSI) was developed to study the effects of sunspots on solar irradiance. It is calculated from the sunspot data published in the Solar-Geophysical Data catalog. It has been shown that the former PSI models overestimate the effect of dark sunspots on solar irradiance; furthermore results of direct sunspot photometry indicate that the contrast of spots depends on their area. An improved PSI calculation is presented; it takes into account the area dependence of the contrast and calculates `true' daily means for each observation using the differential rotation of the spots. Moreover, the observations are screened for outliers which improves the homogeneity of the data set substantially, at least for the period after December 1981 when NOAA started to report data from a few instead of one to two stations. A detailed description of the method is provided. The correlation between the newly calculated PSI and total solar irradiance is studied for different phases of the solar cycles 21 and 22 using bi-variate spectral analysis. The results can be used as a `calibration' of PSI in terms of gain, the factor by which PSI has to be multiplied to yield the observed irradiance change. The factor changes with time from about 0.6 in 1980 to 1.1 in 1990. This unexpected result cannot be interpreted by a change of the contrast relative to the quiet Sun (as it is normally defined and determined by direct photometry) but rather as a change of the contrast between the spots and their surrounding as seen in total irradiance (integrated over the solar disk). This may partly be explained by a change in the ratio between the areas of the spots and the surrounding faculae.

Froehlich, Claus↗

NASA NTRS1994

VLA stereoscopy of solar active regions. 1: Method and tests

We develop a new technique for extracting three-dimensional information from multiday solar Very Large Array (VLA) observations. While standard stereoscopic methods provide a three-dimensional view of an object by combining simultaneous observations from two different aspect angles, we relax the condition of simultaneity and exploit solar rotation to vary the aspect angle. The solar radio images are decomposed into Gaussian source components, which are then cross-correlated in maps from preceding and following days. This provides measurements of the three-dimensional position of correlated source centroids. In this first paper, we describe the stereoscopic method and perform tests with simulated and real radio maps (from the VLA at 20 cm), in order to study the accuracy of altitude measurements, and the limitations introduced by (i) source confusion, (ii) source motion, and (iii) the assumed differential rotation rate. The tests demonstrate that (i) the information content of a VLA map relevant for stereoscopic correlation can be conveniently represented in terms of a small number of Gaussian components; (ii) the fitting of the three-dimensional source position is stable within a numerical accuracy of less than or approximately equal to 0.02 map pixels, (iii) the relative accuracy of the altitude determination is uniform over the solar disk, and (iv) source confusion does not affect the accuracy of stereoscopic position measurements for sources with a signal-to-noise ratio of greater than or approximately equal to 36.

Aschwanden, Markus J.↗

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 NTRS1985

Torsional oscillations of the sun

The sun's differential rotation has a cyclic pattern of change that is tightly correlated with the sunspot, or magnetic activity, cycle. This pattern can be described as a torsional oscillation, in which the solar rotation is periodically sped up or slowed down in certain zones of latitude while elsewhere the rotation remains essentially steady. The zones of anomalous rotation move on the sun in wavelike fashion, keeping pace with and flanking the zones of magnetic activity. It is uncertain whether this torsional oscillation is a globally coherent ringing of the sun or whether it is a local pattern caused by and causing local changes in the magnetic fields. In either case, it may be an important link in the connection between the rotation and the cycle that is widely believed to exist but is not yet understood.

Snodgrass, H. B.↗

NASA NTRS1975

Upper mass limits for stable rotating white dwarfs

Models of nonmagnetic axisymmetric differentially rotating zero-temperature white dwarfs are constructed and tested for stability. Upper mass limits, beyond which models become secularly and dynamically unstable to growth of nonaxisymmetric perturbations, are found at 2.5 solar masses and 4.6 solar masses, respectively. The upper mass limit for secular stability is practically the same for the two angular momentum distributions considered. Crude growth rates due to gravitational radiation and degenerate-electron viscosity are calculated for the secularly unstable models. Except for a narrow parameter range, gravitational radiation is the dominant destabilizing mechanism. For masses between 3.5 and 4.6 solar masses, the secular instability grows on a time scale of about 10 to 1000 years; for masses exceeding about 4.6 solar masses, the dynamic instability grows on a time scale of seconds. Implications of these results for mass-transfer binary star systems and degenerate stellar cores are discussed.

Durisen, R. H.↗

NASA NTRS1997

Evidence from Quasi-Periodic Oscillations for a Millisecond Pulsar in the Low Mass X-Ray Binary 4U 0614+091

We have detected quasi-periodic oscillations (QPOs) near 1 kHz from the low mass X-ray binary 4U 0614+091 in observations with RXTE. The observations span several months and sample the source over a large range of X-ray luminosity. In every interval QPOs are present above 400 Hz with fractional RMS amplitudes from 3 to 12% over the full PCA band. At high count rates, two high frequency QPOs are detected simultaneously. The difference of their frequency centroids is consistent with a constant value of 323 Hz in all observations. During one interval a third signal is detected at 328 +/- 2 Hz. This suggests the system has a stable 'clock' which is most likely the neutron star with spin period 3.1 msec. Thus, our observations of 4U 0614+091 and those of 4U 1728-34 provide the first evidence for millisecond pulsars within low-mass X-ray binary systems and reveal the 'missing-link' between millisecond radiopulsars and the late stages of binary evolution in low mass X-ray binaries. The constant difference of the high frequency QPOs sug,,ests a beat-frequency interpretation. In this model, the high frequency QPO is associated with the Keplerian frequency of the inner accretion disk and the lower frequency QPO is a 'beat' between the differential rotation frequency of the inner disk and the spinning neutron star. Assuming the high frequency QPO is a Keplerian orbital frequency for the accretion disk, we find a maximum mass of 1.9 solar mass and a maximum radius of 17 km for the neutron star.

Ford, E.↗

NASA NTRS1998

Mars Atmospheric Dynamics

The Martian atmosphere is dynamically similar to the Earth's. Its spin-axis rotation rate is only minutes longer than Earth's so the Coriolois force is nearly identical to Earth's. The inclination of its spin axis is also similar to Earth's giving it similarity in seasonal change. And the Martian atmosphere is nearly transparent to solar radiation (except during dust periods) such that it is heated primarily by upwelling infrared radiation from the surface. These characteristics make Mars an ideal laboratory for studying the dynamics of rapidly rotating differentially heated atmospheres. This talk reviews what we have learned about Mars atmospheric dynamics and how if compares with Earth. The source of information to make such a comparison comes from observations and models. The former are sparse and that the latter have played a major role in shaping our thinking about the general circulation on Mars. However, the models need validation. Fortunately, the first two orbiters in NASA's Mars Surveyor Program have instrumentation to address many of the issues related to the general circulation and climate of Mars. The first, Mars Global Surveyor, is already at Mars gathering data. The second, the Mars 98 Orbiter to be launched later this year, carries a dedicated atmospheric sounder. Thus, much will be learned about Mars' atmosphere in the next few years.

Haberle, Robert↗

NASA NTRS1976

The physical properties of coronal holes

Coronal hole data obtained by Skylab during the period May 1973 to February 1974 are reviewed for the region from the photosphere out through the low corona. Coronal holes have a significantly lower density and temperature than the typical background corona, possess an open divergent magnetic field structure, and are the source of the high-speed solar wind stream which give rise to recurrent geomagnetic storms. The photospheric, chromospheric, and coronal signatures of coronal holes are described, and the evolution of coronal holes is examined, with attention to the lifetimes, the differential rotation, and the areas covered by the holes. The association of coronal holes to large-scale magnetic fields and to disk activity is considered.

Bohlin, J. D.↗