On the Sun's differential rotation and pole-equator temperature difference

The Sun's differential rotation can be understood in terms of a preferential stabilization of convection (by rotation) in the polar regions of the lower part of the convection zone (where the Taylor number is large). A significant pole-equator difference in flux () can develop deep inside the convection zone which would be unobservable at the surface, because can be very efficiently reduced by large scale meridional motions rising at the poles and sinking at the equator. This is the sense of circulation needed to produce the observed equatorial acceleration of the Sun. Differential rotation is generated, therefore, in the upper part of the convection zone (where the interaction of rotation with convection is small) and results as the convection zone adjusts to a state of negligible Taylor number.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Two-dimensional stochastic motions and the problem of differential rotation

This paper deals with the spatial dependence of the angular velocity in a rotating turbulent fluid sphere. The original turbulence unaffected by the global rotation is assumed to be two-dimensional where the stochastic force field producing the turbulence does not possess a radial component. By using results of earlier papers we proceed to the treatment of a rotational rate, , no longer small compared to _c (frequency of turbulent mode). It is shown that for _c the angular velocity increases with increasing radius but no latitudinal dependence exists. Contrary to this, for 2 _c an equatorial acceleration is possible and related to negativity of the two-dimensional eddy viscosity. Furthermore, the outer layers rotate faster than the inner ones. These findings coincide with Gilman's numerical results. Ward's observations, as well as the characteristic scales of supergranulation and giant cells, suggest the presence of negative two-dimensional eddy viscosity on the Sun.     

Spectral-spatial analysis of wave motions in the region of temperature minimum of the Sun's atmosphere

Solar Physics - A spectral-spatial analysis is made in the region of temperature minimum of the Sun's atmosphere. Filtergrams in the Baii 4554 + 0.05 Å line have been used. The wavelengths...     

The maintenance of solar differential rotation by two-dimensional turbulence

A numerical model has been made to test the theory that solar differential rotation is maintained by the Countergradient transport of energy peculiar to two-dimensional turbulence. After a brief discussion of this turbulent process, the numerical methods employed and their application to the sun are reviewed. The results of one problem are presented, indicating that this model can represent the observed large-scale nature of the sun's surface. The reader is referred to the author's dissertation for complete details of the methods and calculations.     

On the REYNOLDS stresses in mean-field hydrodynamics III. Two-dimensional turbulence and the problem of differential rotation

It is well-known that, in a rotating star, a meridional circulation directed from pole to equator contributes a latitude dependence to the law of rotation, as it is observed on the Sun. It is also known that such a circulation is produced by a radial dependence of the original angular velocity if the outer parts of the convective zone possess a higher angular velocity than the inner parts. In this paper it is shown that a two-dimensional turbulence with velocity vectors perpendicular to the radial direction, necessarily leads to the required relation dω₀/dr > 0. This also holds when there is an additional three-dimensional homogeneous and isotropic turbulent field. The characteristic lengths of the two turbulences would, however, have to have different orders of magnitude whenever the horizontal turbulence should not be strictly two-dimensional but posses correlation lengths finite in all directions. The application of this to explaining also the phenomenon of the superrotation of the Earth's upper atmosphere is suggested. In the final chapter the possibility of the occurrence of negative viscosity on the Sun is discussed.     

Differential rotation of the solar atmosphere as determined from millimeter data

Radiospectroheliograms obtained at millimeter wavelengths were used to determine the rotation of the solar atmosphere. Regions observed in both emission as well as absorption (associated with H dark filaments) were followed across the disk. The average sidereal rotation rate deduced from emissive regions is given by (deg day^-1)=14.152(±0.270)-4.194(±3.017)sin² B, where B is the heliographic latitude and the quoted errors are the standard deviations of a least squares fit to the data. The rate deduced from absorption regions is given by =14.729(±0.286)-1.050(±1.611)sin² B. This rate is larger than that of emissive regions at all latitudes and shows smaller differential rotation. This apparent difference in the rotation rates is probably due to the difference in the height of formation of the emissive and absorption regions. This difference could be used to estimate the difference in height between an emissive region and an absorption feature in millimeter radiation.     

The solar differential rotation from the eightteenth solar cycle

The sidereal daily rotation of the Sun, (), depends on the data used. From an appropriate selection of the data — sunspots with regular motion — it is found that ()=14.31–2.70 sin² , where denotes the heliographic latitude. Moreover, it seems that there is a variation, of the order of 3%, with the solar activity.     

An atmospheric rotation period of Neptune determined from methane-band imaging

Direct imaging of Neptune through an 8900-Å methane-band filter with the University of Hawaii 2.24-m telescope at Mauna Kea Observatory shows discrete atmospheric cloud features. A rotation period of 17.86 ± 0.02 hr is derived from the observations of two transits of a bright feature in the southern hemisphere during May and June 1986. This period is consistent with earlier observations of cloud motion on Neptune. The imaging also shows that bright features in Neptune's northern hemisphere seen as recently as in 1983 by earlier investigations have disappeared, markedly changing the overall distribution of reflected light from the planetary disk.     

An analysis of full-disk observations of facular contrast in the blue and red

Full-disk images from the Cartesian Full-Disk Telescope no. 2 (CFDT2) were used to study the center-to-limb (CLV) variation of facular contrast in two colors. The CFDT2 images, which have 2.5 arc sec pixels, were obtained during the summer months of 1993, 1994 and 1995. In order to minimize the bias in finding faint facular features in continuum images, we have used coaligned images obtained in the Ca K-line to identify faculae. Faculae were sorted into 20 annular bins of equal width. To reduce the effects of seeing, faculae were not identified closer to the limb than =0.2. The facular pixel contrasts were fitted to various trial functions. The contrast in the blue filter (470.6 nm) rose from 0.122% at disk center to 12.2% at =0.2. The contrast in the red filter (672.3 nm) rose from 0.13% at disk center to 8.16% at =0.2. We have also analyzed the facular contrasts multiplied by their -value to obtain an estimate of facular flux tube contrasts. These flux tube contrasts increased roughly linearly from =0.95 to 0.25. The blue flux tube contrast reached a maximum of 2.48% near =0.25. The red flux tube contrast reached a maximum of 1.59% at =0.2. These contrast values are not corrected for the filling factor. The blue curve leveled off slightly betwen =0.25 and 0.2 while the red curve showed no deviation from its linear trend. These results may provide some support for the hot wall model of facular flux tubes.     

On the depth dependence of the solar rotation velocity determined from fraunhofer lines

From 63 mostly unblended Fraunhofer lines measured along the solar east-west diameter the rotation velocity has been determined. The mean value is 1986 km s^#X2212;1. The velocity decreases with the optical depth in the photosphere. Over a range of 700 km the difference of the velocities is 41 m s^#X2212;1 for the Holweger-Müller atmosphere or 34 m s^#X2212;1 for the Harvard Smithsonian reference atmosphere.     

Rotating convection and the solar differential rotation

We discuss the implication of a numerical experiment on rotating convection and its relevance to the construction of a model for the solar differential rotation.     

Observations from 1982 of facular limb darkening and excess solar oblateness

Observations of facular regions on 35 days during 1982 obtained with the Extreme Limb Photometer are reported. The data were obtained at a wavelength of 0.53 m with two apertures, No. 1 covering 36 arc sec and No. 2 covering 11 arc sec, inwards from the limb. The mean contrasts for all regions detected are 1.05 ± 0.12% and 1.59 ± 0.16%, respectively. The mean contrast of the faculae closer to the limb (aperture 2) is 1.51 ± 0.23 times that from aperture No. 1. This contrast ratio can be fit to a ^–1-curve. These results are consistent with those from 1975 and 1979 observations and may be consistent with the facular limb-darkening function determined by Libbrecht and Kuhn (1984, 1985) if our data are normalized by the area of the solar surface. However, no calibrations or corrections are required to obtain the mean facular contrast presented here.     

Modelling the differential rotation of F stars

We model stellar differential rotation based on the mean-field theory of fluid dynamics. DR is mainly driven by Reynolds stress, which is anisotropic and has a non-diffusive component because the Coriolis force affects the convection pattern. Likewise, the convective heat transport is not strictly radial but slightly tilted towards the rotation axis, causing the polar caps to be slightly warmer than the equator. This drives a flow opposite to that caused by differential rotation and so allows the system to avoid the Taylor-Proudman state. Our model reproduces the rotation pattern in the solar convection zone and allows predictions for other stars with outer convection zones. The surface shear turns out to depend mainly on the spectral type and only weakly on the rotation rate. We present results for stars of spectral type F which show signs of very strong differential rotation in some cases. Stars just below the mass limit for outer convection zones have shallow convection zones with short convective turnover times. We find solar-type rotation and meridional flow patterns at much shorter rotation periods and horizontal shear much larger than on the solar surface, in agreement with recent observations. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the differential rotation of the solar photosphere

It is shown that sunspots as tracers can give the same results for the differential rotation of the solar photosphere as the Doppler-shift measurements, if the sunspots used have only insignificant motion relative to their immediate photospheric surroundings.     

Differential rotation,meridional and random motions of the solar Ca+ network

From high precision computer controlled tracings of bright Ca⁺-mottles we investigated differential rotation, meridional and random motions of these chromospheric fine structures. The equatorial angular velocity of the Ca⁺-mottles agrees well with that of sunspots (14°.50 per day, sidereal) and is 5 % higher than for the photosphere. The slowing down with increasing latitude is larger than for sunspots. Hence in higher latitudes Ca⁺-mottles rotate as fast as the photospheric plasma. A systematic meridional motion of about 0.1 km s^–1 for latitudes around 10° was found. The Ca⁺-mottles show horizontal random motions due to the supergranular flow pattern with an rms velocity of about 0.15 km s^–1. We finally investigated the correctness of the solar rotation elements i and derived by Carrington (1863).     

Two types of differential rotation of the solar corona

The differential rotation of the solar corona has been analyzed using as the input data the brightness of the coronal green line Fe xiv 530.3 nm for more than five activity cycles. It is found that the character of rotation of the solar corona changes during the activity cycle. Approximately at the middle of the descending branch the differential rotation is weakly pronounced, while the greatest differential gradient is observed at the ascending branch and, occasionally, at the maximum of the cycle. An explanation of this difference has been suggested. The total rotation rate of the corona can be represented as a superposition of two rotation modes (components) – the fast and slow ones. The synodic period of the fast mode near the equator is about 27 days, increasing slightly with latitude. The synodic period of the slow mode exceeds 30 days. The changing relative fraction of these two modes results in variation of the latitude dependence of the observed rotation rate during the activity cycle. The characteristics of two principal types of differential rotation of the solar corona have been determined. The first type consists of the fast mode alone and is established approximately at the middle of the descending branch of the cycle. The second type is the sum of both modes with the fast mode dominating at low latitudes and the slow mode at high latitudes. The results obtained can be used for in-depth study of interaction of the velocity field and dynamo mechanism in the Sun and stars.     

On the Reynolds stresses in mean-field hydrodynamics II. Two-dimensional turbulence and the problem of negative viscosity

The methods proposed in a foregoing paper are used for the derivation of the eddy viscosity of a two-dimensional homogeneous isotropic turbulence. In contrast to three-dimensional isotropic turbulence is shown that for the two-dimensional case the eddy viscosity (i) has no definite sign, (ii) tends to zero if the molecular viscosity tends to zero, (iii) is negative for special cases. However, the modes with large wave numbers decay in any case as is shown by investigating a dispersion relation.