A new estimate of the solar meridional flow

We present a new method for measuring the solar magnetic meridional flow, and provide a comparison with other recent work. We have performed a least-squares fit to azimuthally averaged Mount Wilson Observatory synoptic data encompassing Carrington rotations 1722 to 1929 to produce an estimate of the solar meridional flow. A parametric fit to our results expresses the solar meridional flow as v() = 28.5 sin2.5 cos.     

The asymptotic limit of the form-factors α and β product for celestial bodies

The applicability of the properties of central configurations proceeding from the many-body problem to study of gaseous sphere cloud evolution during its gravitational contraction is justified. It is shown that the product runs to a constant value in the asymptotic time limit of simultaneous collision of all the particles of the cloud where is a form-factor of the potential energy and is a form-factor of the moment of inertia.The spherical bodies as well as ellipsoids of rotation and general ellipsoids with a one-dimensional mass distribution (k),k[0, 1] are found to possess the property =const.

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. , - , , ., , - =const., , (k),k[0, 1].

     

Sunspots: Their rotation,their expansion in the activity zone,their links with the giant convective cells

The rotational properties of sunspots during the time interval 1977–1986 (solar cycle 21) are studied; only sunspot groups older than 4 days have been the object of this research. We have looked systematically for any kind of anomaly or fine structure in the differential rotation latitudinal profile and any significant change occurring during the course of the solar cycle.Some latitudinal bands are found where the angular rotation rate, rather than decreases according to its overall tendency, increases or is constant with the latitude. The differential rotation profile is, therefore, finely structured. The whole fine-structure pattern is affected by a slow equatorward shift. It is suggested that these fine structure features are due to the Coriolis forces acting on the meridional motions associated with giant toroidal convective cells. Some of the properties of such cells are inferred.Moreover, while the spot zone shifts equatorward, it is found to expand poleward; this expansion occurs by the addition of new belts of activity on the poleward side of the pre-existing active zone. The active zone is therefore found to consist, at the maximum activity epoch, of three different belts of spot production, each of them being centered around a local maximum-activity latitude; each of these centroids of activity is hypothesized to lie where a couple of meridional streams - associated with giant cells - converge. The activity belts are independent of each other as far as their activation, maximum, and end time, as well as their lifetime and level of activity are concerned. The angular rotation rate is correlated, in each belt, with the local level of activity.     

Telluric water vapor contamination of the Mount Wilson solar Doppler measurements

It has been shown that the solar line 5250.2 (Fei) is weakly blended with a telluric line in the water vapor spectrum, and that magnetograms taken using this line are therefore inaccurate. We investigate the effects of this contamination on the Mount Wilson synoptic magnetograph data, which is based on 5250.2. Using spectrum scans taken at Kitt Peak, we model the contamination and develop a procedure that would correct for it, whenever the slant water vapor along the line of sight to the Sun is known. As this information is not available for the data collected thus far at Mount Wilson, we use the variation of determined quantities with airmass to obtain an average, or first-order, correction. Concentrating on the fitted coefficients for the solar rotation, the correction is found to be very slight, 0.5%, raising the value for the A coefficient, averaged over the period 3 December, 1985 to 22 July, 1990, from 2.8289 to 2.8422 rad s^-1, The correction also removes a slight annual variation that has become discernible in the data collected since 1986.Now at Oregon Heath Sciences University, Portland, OR, U.S.A.Now at Department of Astronomy, University of Minnesota, U.S.A.     

Resolution of the Hα double-limb controversy

The discussion of the H double limb had reached the point where the question of its existence as a real solar phenomenon could not be resolved without new observations made with the Lockheed filter and the Mount Wilson spectroheliograph. A study of the instrumental profiles had indicated that there was sufficient off-band light to produce the observed inner limb step in the Mount Wilson instrument, but this analysis was not completely satisfactory because of limitations inherent in the measurement of instrument functions with a Hg-198 source. The instrumental profile work did indicate, however, that the spectral purity of the instruments in question could be substantially improved by the use of narrow-band interference filters. An experimental program was thus launched to determine the effect of such a blocking filter on the appearance of the H limb. The results of these observations with three Halle filter systems and the Mount Wilson spectroheliograph are that the inner limb completely disappears at the center of H when a blocking filter is used to reduce unwanted light, which originates at wavelengths beyond ±0.8 Å. In addition, the contrast and visibility of the chromospheric fine structure is increased by eliminating the off-band light. Thus the experiment conclusively demonstrates that the apparent inner limb is not a solar feature but is due entirely to instrumental parasitic light.     

The angle of inclination of the sunspot symmetry axis to the solar surface

The Wilson effect, used before only as a method of determining the physical depression of sunspots, is used here to estimate a quite different parameter - the sunspot symmetry axis inclination angle to the solar surface, this explains the observed negative Wilson effect.On the basis of photoheliograms taken with three telescopes of the High-Altitude Solar observatory Peak Alma-Ata, the Wilson effect for the whole solar disk is investigated, the east and west parts of the disk being studied separately. 111 sunspots of regular shape at different heliocentric angles were measured, eight of them being under observations from one limb to the other. To study the dependence of the Wilson effect on the heliocentric angle, all observations within an angular interval of 10° were averaged. The dependence thus derived is described by two sinusoids having the zero point shifted along both axes. The shift of the zero Wilson effect to the west, i.e., a shift along the heliocentric angle axis, can be caused by the deviation of the sunspot axis to the east from the normal to the solar surface. On the line of sight-normal plane the angle corresponding to this deviation is =34°±14°.     

The solar surface differential rotation from disk-integrated chromospheric fluxes

Disk-integrated solar chromospheric Caii K-line (3933.68 ) fluxes have been measured almost daily at Sacramento Peak Observatory since 1977. Using observing windows selected to mimic seasonal windows for chromospheric measurements of lower Main-Sequence stars such as those observed by Mount Wilson Observatory's HK Project, we have measured the solar rotation from the modulation of the Caii K-line flux. We track the change of rotation period from the decline of cycle 21 through the maximum of cycle 22. This variation in rotation period is shown to behave as expected from the migration of active regions in latitude according to Maunder's butterfly diagram, including an abrupt change in rotation period at the transition from cycle 21 to cycle 22. These results indicate the successful detection of solar surface differential rotation from disk-integrated observations. We argue that the success of our study compared to previous investigations of the solar surface differential rotation from disk-integrated fluxes lies primarily with the choice of the length of the time-series window. Our selection of 200 days is shorter than in previous studies whose windows are typically on the order of one year. The 200-day window is long enough to permit an accurate determination of the rotation period, yet short enough to avoid complications arising from active region evolution. Thus, measurements of the variation of rotation period in lower Main-Sequence stars, especially those that appear to be correlated with long-term changes in chromospheric activity (i.e., cycles), are probably evidence for stellar surface differential rotation.     

Numerical implementation of a perturbation theory up to the third order for rotating polytropic stars: Application to a solar model

Numerical treatment of a pertubation theory up to the third order yields quantitative estimates for an interesting polytropic solar model possessing differential rotation of Clement's type. A suitably defined reduction factor, otherwise referred to as strength, moderates the effects of the differential rotation and the so resulting limiting state represents efficiently uniform rotation of the model. The numerical results obtained are compared to respective ones derived from an original numerical implementation of a second-order perturbation theory.     

An Estimate of Microwave low-Brightness-Temperature Regions' Heights Obtained Measuring Their Rotation Velocity

Daily full-disk solar maps obtained at 37 GHz in the years 1979, 1980, 1981, 1982, 1987, 1988, 1989, 1990, and 1991 are analysed and compared with full-disk solar maps in H. A search for a difference in the measured angular rotation velocity for two classes of microwave low-brightness-temperature regions (LTRs), associated and not associated with H filaments, is performed. Procedures with and without statistical weights, assigned to angular rotation velocities according to the tracing time, are applied and the statistical significance of the results is discussed. A higher angular rotation velocity is measured for LTRs associated with H filaments than for the not-associated ones. This angular velocity difference is interpreted as a consequence of a height difference between these two types of LTR tracers. Changes of the solar differential rotation velocity during the activity cycle measured using LTRs as tracers are explained by the measured cycle-dependence of the association rate between LTRs and H filaments. Similarly, the north–south asymmetry in the solar rotation velocity measured tracing LTRs is explained by the measured north–south asymmetry in the association rate between LTRs and H filaments. The rotation velocity of LTRs and H filaments is on the average more rigid in comparison with sunspots.     

Effect of perturbations on the stability of triangular points. In the restricted problem of three bodies with variable mass

The effect of small perturbations and in the coriolis and the centrifugal forces respectively on the stability of the triangular points in the restricted problem of three bodies with variable mass has been studied. It is found that the range of stability of triangular points increases or decreases depending upon whether the perturbation point (, ) lies in one or the other of the two parts in which the (, ) plane is divided by the line J₈–J₉=0 where J₈ and J₉ depend upon , the constant due to the variation in mass governed by Jeans' law.     

The Energy Equation in the Lower Solar Convection Zone

As a consequence of the Taylor–Proudman balance, a balance between the pressure, Coriolis and buoyancy forces in the radial and latitudinal momentum equations (that is expected to be amply satisfied in the lower solar convection zone), the superadiabatic gradient is determined by the rotation law and by an unspecified function of r, say, S(r), where r is the radial coordinate. If the rotation law and S(r) are known, then the solution of the energy equation, performed in this paper in the framework of the ML formalism, leads to a knowledge of the Reynolds stresses, convective fluxes, and meridional motions. The ML-formalism is an extension of the mixing length theory to rotating convection zones, and the calculations also involve the azimuthal momentum equation, from which an expression for the meridional motions in terms of the Reynolds stresses can be derived. The meridional motions are expanded as U _r(r,)=P ₂(cos)₂(r)/r ²+P ₄(cos)₄(r)/r ² +..., and a corresponding equation for U (r,). Here is the polar angle, is the density, and P ₂(cos), P ₄(cos) are Legendre polynomials. A good approximation to the meridional motion is obtained by setting ₄(r)=–H₂(r) with H–1.6, a constant. The value of ₂(r) is negative, i.e., the P ₂ flow rises at the equator and sinks at the poles. For the value of H obtained in the numerical calculations, the meridional motions have a narrow countercell at the poles, and the convective flux has a relative maximum at the poles, a minimum at mid latitudes and a larger maximum at the equator. Both results are in agreement with the observations.     

Synoptic Hα Full-Disk Observations of the Sun from Big Bear Solar Observatory – I. Instrumentation,Image Processing,Data Products,and First Results

The Big Bear Solar Observatory (BBSO) has a long tradition of synoptic full-disk observations. Synoptic observations of contrast enhanced full-disk images in the Caii K-line have been used with great success to reproduce the Hi L irradiance variability observed with the Upper Atmosphere Research Satellite (UARS). Recent improvements in data calibration procedures and image- processing techniques enable us now to provide contrast enhanced H full-disk images with a spatial resolution of approximately 2 and a temporal resolution of up to 3 frames min–1.In this first paper in a series, we describe the instruments, the data calibration procedures, and the image-processing techniques used to obtain our daily H full-disk observations. We also present the final data products such as low- and high-contrast images, and Carrington rotation charts. A time series of an erupting mini- filament further illustrates the quality of our H full-disk observations and motivate one of the future research projects. This lays a solid foundation for our subsequent studies of solar activity and chromospheric fine structures. The high quality and the sunrise- to-sunset operation of the H full-disk observations presented in this paper make them an ideal choice to study statistical properties of mini-filament eruptions, chromospheric differential rotation, and meridional flows within the chromosphere, as well as the evolution of active regions, filaments, flares, and prominences.     

Recalibration of Mount Wilson Doppler measurements

A new calibration of the spectrograph at the Mount Wilson 150-foot Tower Telescope demonstrates that all reported solar Doppler rates to date measured at 5250.2 with this instrument are too high by a factor of 0.55%.     

Solar rotation measurements at Mount Wilson

The ears velocity pattern described in Paper I (Howard et al., 1980) had no physical explanation. A reanalysis shows that the large scale solar velocity patterns are better described by a nonmonotonic limbshift and a meridional flow. The results of the new analysis imply that the study of solar velocity pattern at the level of a few ms^–1 required that magnetic regions be treated separately from nonmagnetic regions.Now at: Institute for Astronomy, University of Hawaii, Honolulu, Hawaii 96822, U.S.A.     

Cycle latitude effects for sunspot groups

Digitized Mount Wilson sunspot data from 1917 to 1985 are analyzed to examine meridional motion and rotation properties as a function of latitude and distance () from the average latitude of activity (₀) in each hemisphere. Latitude dependence similar to previous results is found, but only for spot groups whose areas are decreasing from one day to the next. A previous study of active region magnetic fields, using this technique of motions as a function of the average latitude of activity, had shown meridional motions on average toward ₀. In this analysis of spot data some evidence is seen for motion away from ₀, with some slight evidence for faster rotation equatorward of ₀ and slower motion poleward of ₀, similar to the torsional oscillation phenomenon. For reasons that are not clear, both of these effects are significantly more pronounced for sunspot groups whose areas are decreasing.Operated by the Association of Universities for Research in Astronomy, Inc., under Cooperative Agreement with the National Science Foundation.     

The virial-based solution for the velocity of gaseous sphere gravitational contraction

It is found that the relationship between the potential energy and the moment of the inertia independent of the radial mass distribution obtained earlier for the sphere also holds in the case of the ellipsoidal mass distribution for the ellipsoid of rotation.The possibility of application of the energy virial relations for solution of the evolutionary problems of the gravitating gaseous sphere, with the help of the relationship found earlier, is demonstrated. The physical conditions on the gaseous sphere boundary are introduced. The existence of two branches of evolution, the proton one and the electron one, is established. The problem of the gravitational contraction velocity during sphere evolution is solved. The relationship between the boundary temperature and the gaseous sphere radius as well as between the luminosity and the body mass is obtained. Some limiting relations for the final stage of the gaseous sphere evolution are found.

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, , , . . . — . . , . .

     

Phase relation between the poloidal and toroidal solar-cycle general magnetic fields and location of the origin of the surface magnetic fields

The phase relation of the poloidal and toroidal components of the solar-cycle general magnetic fields, which propagate along isorotation surfaces as dynamo waves, is investigated to infer the structure of the differential rotation and the direction of the regeneration action of the dynamo processes responsible for the solar cycle. It is shown that, from the phase relation alone, (i) the sign of the radial gradient of the differential rotation (/r) can be determined in the case that the radial gradient dominates the differential rotation, and (ii) the direction of the regeneration action can be determined in the case that the latitudinal gradient (/) dominates the differential rotation. Examining the observed poloidal and toroidal fields, it is concluded that (i) the / should dominate the differential rotation, and (ii) the determined sign of the regeneration factor (positive [negative] in the northern [southern] hemisphere) describing the direction of the regeneration action requires that the surface magnetic fields should originate from the upper part of the convection zone according to the model of the solar cycle driven by the dynamo action of the global convection.     

Magnetic-cloud chamber effects behind flare-generated shock waves

A mechanism explaining the generation of the helium-enriched plasma-condensation colud (HAE-events) behind the front of shock waves associated with mass-ejecting flares is presented. The mechanism is based on the occurence of physical conditions, analogous to those in a Wilson cloud chamber in a magnetic field, behind the front of a flare-generated shock wave propagation out into interplanetary space. Consequently, if the solar atmosphere above the flare active region is saturated with ejected helium plasma, conditions are created for the forming of the helium-enriched plasma-condensation colud in the temperature-depressed region behind the shock wave front.     

Solar surface velocity fields determined from small magnetic features

We describe a method for the analysis of magnetic data taken daily at the Vacuum Telescope at Kitt Peak. In this technique, accurate position differences of very small magnetic features on the solar surface outside active regions are determined from one day to the next by a cross-correlation analysis. In order to minimize systematic errors, a number of corrections are applied to the data for effects originating in the instrument and in the Earth's atmosphere. The resulting maps of solar latitude vs central meridian distance are cross-correlated from one day to the next to determine daily motions in longitude and latitude. Some examples of rotation and meridional motion results are presented. For the months of May 1988 and October–November 1987, we find rotation coefficients A = 2.894 ± 0.011, B = - 0.428 ± 0.070, and C = -0.370 ± 0.077 in rad s^–1 from the expansion = A + B sin² + C sin⁴, where is the latitude. The differential rotation curve for this interval is essentially flat within 20 deg of the equator in these intervals. For the same intervals we find a poleward meridional motion a = 16.0 ± 2.8 m sec ^-1 from the relation v = a sin, where v is the line-of-sight velocity.Operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation.