On mass flow in a complex sunspot

The velocity field in a large complex sunspot is investigated in Fe i 6302.5 Å and in H with a spatial resolution of about 2.5. The Evershed flow is almost parallel to the solar surface. For the inclination angle between the velocity and the horizontal = 4.4°±1.3° is estimated; = 11° is the definite upper limit.     

Additional measurements of the high-latitude sunspot rotation rate

We report measurements of the sunspot rotation rate at high sunspot latitutdes for the years 1966–1968. Ten spots at ¦latitude¦ 28 deg were found in our Mees Solar Observatory H patrol records for this period that are suitable for such a study. On the average we find a sidereal rotation rate of 13.70 ± 0.07 deg day^-1 at 31.05 ± 0.01 deg. This result is essentially the same as that obtained by Tang (1980) for the succeeding solar cycle, and significantly larger than Newton and Nunn's (1951) results for the 1934–1944 cycle. Taken together, the full set of measurements in this latitude regime yield a rotation rate in excellent agreement with the result =14^°.37₇–2^°.77 sin², derived by Newton and Nunn from recurrent spots predominatly at lower latitudes throughout the six cycles from 1878–1944.Summer Research Assistant.     

Sunspots Observed to Physically Weaken in 2000–2001

The strength of a sunspot depends on its magnetic field and umbral darkness, factors which go together. The strongest field in an umbra is always found at the darkest position. We use this relationship, B=f(1/T), to demonstrate that at the maximum of cycle 22 (1990–1991) sunspots were statistically stronger than at the same phase of cycle 23 (2000–2001). Within our sample of 195 spots, cycle 23 exhibits an excess of small bright spots, and possibly, a dearth of large dark spots. This could alter the total solar irradiance (TSI)–sunspot number relationship.     

The abelian higgs sunspot endowed with a local conformal symmetry

We show that the requirement of alocal conformal symmetry of the Abelian Higgs sunspot leads, at least formally, to a complex-valued electromagnetic potential, whose imaginary part is a conformal compensating potential. It is shown that there exists a fundamental difference between conformal and ordinary electromagnetic fields; whereas the ordinary total magnetic flux of a spot is quantized its conformal analogue has to vanish if the Higgs field is to be single-valued. We further stress that such a complex-valued Abelian Higgs field configuration mimics quite well, under certain conditions (all the salient features of) the classical Abelian Higgs sunspot.     

A new technique for the determination of coronal magnetic fields: A fixed mesh solution to Laplace's equation using line-of-sight boundary conditions

A new method for computing potential magnetic field configurations in the solar atmosphere is described. A discrete approximation to Laplace's equation is solved in the domain R r R ₁, 0 , 0 2 (R ₁being an arbitrary radial distance from the solar center). The method utilizes the measured line-of-sight magnetic fields directly as the boundary condition at the solar surface and constrains the field to become radial at the outer boundary, R ₁. First the differential equation and boundary conditions are reduced to a set of two-dimensional equations in r, by Fourier transforming out the periodic dependence. Next each transformed boundary condition is converted to a Dirichlet surface condition. Then each two-dimensional equation with standard Dirichlet-Dirichlet boundary conditions is solved for the Fourier coefficient it determines. Finally, the solution of the original three dimensional equation is obtained through inverse Fourier transformation. The primary numerical tools in this technique are the use of a finite fast Fourier transform technique and also a generalized cyclic reduction algorithm developed at NCAR. Any extraneous monopole component present in the data can be removed if so desired.The code was developed for the HAO solar-interplanetary modeling effort in response to the following specific requirements:

Transformation of the absolute solar radiation data into the ‘International Practical Temperature Scale of 1968’

Corrections are given which transform the Tables of the solar radiation data (Labs and Neckel, 1968) into the International Practical Temperature Scale of 1968. Additionally, for the adjustment of the data of the true continuum and the corresponding line blanketing as well, the veiled line effect mentioned first by Carbon et al. (1968), but studied in more detail by Holweger (1970a), has been considered also.The corresponding corrections of the solar irradiance result in an improved value of the spectrophotometric solar constant: S = 1.947 cal cm^-2 min^-1 or 0.1358 W cm^-2. Two Tables presenting the highest (window-) intensities and the corrected irradiance data have been added.     

The solar wind cycle,the sunspot cycle,and the corona

Recent theories of the solar cycle and of coronal heating strongly suggest that solar cycle variations of different quantities (i.e. sunspots, coronal green line, etc.) ought not to be expected to be in phase with one another. In agreement with this notion we note that the shape of the corona typical of a maximum eclipse occurs 1.5yr before sunspot maximum, compared with 2 yr as might be expected from Leighton's standard model. Further, we argue that the phase of the solar wind cycle can be determined from geomagnetic observations. Using this phase, a solar cycle variation of 100 km s^–1 in the solar wind velocity and 1 in the magnetic field intensity becomes apparent. In general, the solar wind cycle lags the coronal-eclipse-form cycle by 3 yr, compared with the 2 yr that might be expected from model calculations.     

Modelling solar irradiance variations with an area dependent photometric sunspot index

The He 1083 nm line equivalent width and the 10.7 cm radio flux are employed to model the total solar irradiance corrected for sunspot deficit. A new area dependent photometric sunspot index (APSI) based on sunspot photometry by Steinegger et al. (1990) is used to correct the irradiance data for sunspot deficits. Two periods of time are investigated: firstly, the 1980–1989 period between the maxima of solar cycles 21 and 22; this period is covered by ACRIM I irradiance data. Secondly, the 1978–92 period which includes both maxima; here, the revised Nimbus-7 ERB data are used.For both He 1083 nm and 10.7 cm radio flux irradiance models as well as ACRIM I and ERB irradiance data, the APSI yields an improved fit compared to the one obtained with the standard Photometric Sunspot Index (PSI) which uses a constant bolometric spot contrast. With APSI, the standard deviation calculated from daily values is 0.461 Wm^–2 for the period 1980–89 modelling ACRIM I vs. He 1083 nm, as compared to 0.478 when PSI is used, and to 0.531 for the uncorrected ACRIM series. A similar improvement is obtained for the same period modelling ERB vs. He 1083 nm, while there is almost no improvement for the long period.As a general result the models provide a good fit with the spot-deficit.-corrected irradiance only during the period between the maxima. If both maxima are included (period 1978–92) the He 1083 nm and 10.7 cm radio flux models show appreciably larger discrepancies to the irradiances corrected for PSI or APSI.     

Solar irradiance variations from photometry of active regions

The Extreme Limb Photometer (ELP) has been used to measure the irradiance fluctuation of the Sun due to selected active regions. Forty-five active regions that were completely scanned at various disk positions are included in the analysis. The contribution of these active regions to a global solar irradiance fluctuation has been correlated with photometric sunspot and facular indices (PSI and PFI) using published values of sunspot and calcium plage areas. The measured ELP fluctuations are converted to a global brightness fluctuation, B/B. The sunspot component of B/B correlates with PSI with r = 0.95. The facular component of B/B correlates with PFI with r - 0.72. The expression for PFI is important to the question of energy balance between sunspots and faculae and the results presented here are not incompatible with energy balance between the two phenomena; that is the energy deficit of sunspots may be balanced by the energy excess of faculae.     

The oscillatory velocity field observed in a unipolar sunspot region

The velocity field has been mapped for 42 min in an area 80 by 85 containing a unipolar sunspot. Apparent shifts of Fe i 5233 were measured photoelectrically using a rectangular scanning aperture 1.6 × 4.0. The sunspot did not exert a marked influence on the generally random pattern of oscillations at a period of 300 s. Discrete periods of oscillation both longer and shorter than 300 s were excited within the enhanced magnetic field boundaries of this spot. Umbral oscillations at periods near 180 s were detected in agreement with independent observations of the same spot during the previous solar rotation.NRC Postdoctoral Fellow, 1969–71.     

On the presence of SH in the sunspot spectrum

The expected equivalent widths of individual rotational lines of the most intense Q ₂ branch of the 0-0 band of the A ²-X²_i; system of S³²H and S³⁴H have been calculated in the umbral spectrum for five disk positions using Zwaan's (1974) sunspot model. Percentage abundance of S³⁴ in the terrestrial case has been considered valid in our calculations.Strong lines of S³²H and S³⁴H of the A-X band system should be detectable in the sunspot spectrum. The molecule SH may play a possible role as a major opacity source in the ultraviolet spectrum of sunspots along with the molecule OH in the upper layers (up to _0.5m = 1.0) wherefrom most of the continuum arises. Study of this molecule in the umbral spectrum may also provide the solar isotopic abundance ratio N(S³²)/N(S³⁴).     

On the interpretation of the π-component splitting in sunspot spectra

It is shown that in order to explain the observed splitting of the -component in the sunspot umbra spectrum by the hypothesis of the coexistence in sunspots of weak- and strong-field regions with opposite polarities, one has to admit the additional assumption that in the weak-field regions the Doppler halfwidth ( _D) and the ratio between line opacity and continuum opacity ( ₀) are both less than those in the strong-field regions.     

Predicting the maximum amplitude for the sunspot cycle from the rate of rise in sunspot number

Examined are associational aspects as they relate the maximum amplitude R _M for the sunspot cycle to the rate of rise R _t during the ascending phase, where R _M is the smoothed sunspot number at cycle maximum and R _t is the sum of the monthly mean sunspot numbers for selected 6-month intervals (t) measured from cycle onset. One finds that, prior to about 2 yr into the cycle, the rate of rise is not a reliable predictor for maximum amplitude. Only during the latter half of the ascent do the fits display strong linearity, having a coefficient of correlation r 0.9 and a standard error S _yx 20. During the first four intervals, the expected R _M and the observed R _M were found to differ by no more than 20 units of smoothed sunspot number only 25, 42, 50, and 58 % of the time; during the latter four intervals, they differed by no more than 20 units 67, 83, 92, and 100% of the time.     

Facular models and the sunspot energy deficit

The problem of the energy deficit in a sunspot is shown to be critically related to the depth of a given sunspot model. Recent facular models are discussed and a new model is derived from recent data using a two-dimensional radiative transfer analysis. The excess non-radiative energy required by this and other models is evaluated and it is shown that in some models this may account for a considerable fraction of the sunspot energy deficit. For these models the Alfvén energy travelling along the closed flux loops from the sunspot is insufficient to supply the requirements of the faculae and it is suggested that excess energy flux from below the faculae is also required. These results provide further support for deep as opposed to shallow sunspot models.     

Facular excess radiation and the energy balance of solar active regions

Plage areas and intensities derived from CaII K spectroheliograms are used as a proxy for the facular irradiance excess of solar active regions for the period 19 August to 4 September 1980. Using a calibration method proposed by Vrnak et al. (1991), the photospheric facular index (PFI) with constant facular contrastC _p = 0.018 is replaced by a variableC _p , depending on the plage brightness. A sgnificant increase ofC _p from 0.015 to 0.025 is found for plage areas varying from a few to approx. 6 · 10³ millionths hemispheres.Combining the facular irradiance excess with sunspot deficits (as determined for the same period by Steinegger et al. 1990) yields good aggrement with the irradiance variations measured by ACRIM I, using a center-to-limb variation ofC _p according to Chapman and Meyer (1986). The ratio of facular excess to sunspot deficit (integrated over solid angle 2) decreases from values of 1.5 to 2 for regions with sunspot areas below 100 millionths hemispheres to 0.2 for sunspots of areas > 1000 millionths hemispheres,     

Activity of sunspots and solar constant variations during 1980

A strong inverse correlation is shown between the irradiance dips observed by the SMM/ACRIM radiometer and the projected areas of the active sunspots. This strong correlation and the results of a preliminary time series analysis indicate that the value of the solar constant decreased when quickly developing sunspot groups with complex structure occurred on the solar disk. On the other hand, when the old groups with simple structure were dominant the value of the solar constant increased slightly or these groups could reduce the effects of the active spots. On the basis of our investigations it seems that the formation of the sunspots and the new activity of the older ones as well as the decreases of the solar constant may be the common symptoms of such a physical process which takes place in deeper regions of the Sun through the interaction of magnetic fields with the convection.     

On the possibility of constructing a radiative sunspot model in magnetohydrostatic equilibrium

It is currently believed that it is impossible to construct a radiative sunspot model in magnetohydrostatic equilibrium unless magnetic fields below the surface are excessively large (> 100 kG). This belief is based on results obtained using the mixing length theory of convection. We wish to point out that by using a different theory of convection, due to Öpik (1950), it is possible to compute a radiative sunspot model in which the field becomes no greater than 9000 G. By applying two boundary conditions, (i) depth of spot equals depth of convection zone, (ii) magnetic field has zero gradient at the base of the spot, we show that a radiative spot has a unique effective temperature for a given Wilson depression, . For = 650 km, we find T _e = 3800K ; for = 150 km, T _e = 3950K. According to our model, spots having T _e cooler than these values should not exist.     

Periodogram analysis of 240 years of sunspot records

We have analyzed the direct records of sunspot number between 1749 and 1990 with the same technique currently used in the study of stellar activity cycles observed with Mount Wilson Observatory's 60-inch telescope. In order to mimic the stellar time series, which span only two decades, we analyzed twenty- and fifty-year intervals of the sunspot data in comparison to the entire record. We also examined the reliability of the oldest (pre-1850) sunspot records. The mean solar cycle period determined from the entire record (1749–1990) is 11.04 yr with a computed precision of ± 0.01 yr, but an overall accuracy of only ±1.1 yr. The large uncertainty is caused by variation of the cycle period with time and not observational uncertainty.The correct sunspot period is found slightly more often (82%) in 50-year intervals compared to 20-year (74%). The cause is twofold: first, a more precise period results from the longer sample length, and second, other periodicities exist in the sunspot record, so that a more accurate determination of the dominant 11.0-year period results from the longer time series. As a guideline for cycle periodicities in other stars, the solar results indicate that the 50-year intervals would produce more precise and accurate periods than the 20-year time series. On the other hand, useful statistics concerning long-term activity could be obtained from a less-frequently sampled group of stars that is substantially larger than the group of 100 lower Main-Sequence stars currently observed at Mount Wilson, although knowledge of short-term variability would be sacrificed.Pre-doctoral fellow, Harvard-Smithsonian Center for Astrophysics.     

Polar faculae and sunspot cycles

The monthly number of polar faculae of the Sun were determined from white-light images at spectral band (eff) = (4100 ± 200) Å obtained at the Kislovodsk Solar Station during 1960–1994. Corrected monthly numbers were obtained with the help of the visibility function. The level of polar activity larger than 1 above the monthly running mean was calculated, and the relation between the polar faculae and sunspot cycle was studied. We confirmed earlier results (Makarov and Makarova, 1987) that the monthly number of polar faculae, NPF _m (t) correlates with the monthly sunspot area A _m (Sp)(t + T) with a time shift T 6 yr. The new polar faculae cycle began in the middle of 1991. Peculiarities of the first part of sunspot cycle 23 are discussed.Guest scientist with the University of Arizona and Zetetic Institute. Tucson, Arizona 85719, U.S.A.     

The intensity,velocity and magnetic structure of a sunspot region

The observational set-up for a detailed study of the velocity, intensity and magnetic-field fine structure in and around a sunspot is described. On highly resolved spectra we detected in the vicinity of a sunspot a large number of points with strong magnetic fields (magnetic knots). The magnetic field in these knots causes a striking decrease of the line depth (or a line gap after Sheeley, 1967). The properties of the magnetic knots are: (1) magnetic fields up to 1400 gauss; (2) diameter 1100 km; (3) coincidence with dark intergranular spaces; (4) generally downward material motion; (5) lifetime>30min; (6) estimated total number around an unipolar spot 2000; (7) combined magnetic flux comparable to the sunspot flux; (8) coincidence with Ca⁺ plages.For the smallest sunspots (pores) we obtained magnetic fields >1500 gauss. Hence a magnetic field of about 1400–1500 gauss appears to be a rather critical level for pore and spot formation.We found a large number of small areas producing line gaps without measurable magnetic field. These non-magnetic gap-regions coincide with bright continuum structures.Some aspects arising from the occurrence of hundreds of magnetic knots in an active region are discussed in the last section.Presently guest investigator at the Göttingen Observatory.Previously member of the High Altitude Observatory solar project at Sacramento Peak (Contract Nr. AF (628) - 4078).