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°.     

Polar coronal holes and the sunspot cycle. A new method to predict sunspot numbers

Twenty years ago, Ohl (1966, 1968) found a correlation between geomagnetic activity around the minimum of the solar cycle and the Wolf sunspot number in the maximum of the following solar cycle. In this paper we shall show that such a relation means indeed a relation between the polar coronal holes area around the minimum of the solar cycle and the sunspot number in the maximum of the next. In fact, a very high positive correlation exists between the temporal evolution of the size of polar coronal holes and the Wolf sunspot number 6.3. years later.     

The influence of sunspot canopies on magnetic inclination measurements in solar plages

Sunspots are known to have large, low-lying magnetic canopies, i.e. horizontal magnetic fields overlying a field-free medium, that cover substantial fractions of active region plage. In this paper we consider the influence of such canopies on the inclination of plage magnetic fields. We find that for observations in spectral lines like 5250.2Å the neglect of a sunspot canopy when determining magnetic inclination angles of plage fields can introduce errors exceeding 5–10°. This is particularly true if the observations do not have high spatial resolution. Thus this effect may explain some of the measurements of substantially inclined fields in solar plages. Furthermore we find that the Fe I 15648 Å line is far superior in giving correct flux-tube inclinations in the presence of a sunspot magnetic canopy. Finally, the inversion of full Stokes profiles is shown to produce more reliable results than results obtained by considering only ratios of individual Stokes profile parameters.     

A digital method to calculate the true areas of sunspot groups

The areas of sunspots are the most prominent feature of the development of sunspot groups. Since the size of sunspot areas depend on the strength of the magnetic field, accurate measurements of these areas are important. In this study, a method which allows to measure true areas of the sunspots is introduced. A Stonyhurst disk is created by using a computer program and is coincided with solar images. By doing this, an accurate heliographic coordinate system is formed. Then, the true area of the whole sunspot group is calculated in square degrees with the aid of the heliographic coordinates of each picture element forming the image of the sunspot group. This technique’s use is not limited with sunspot areas only. The areas of the flare and filaments observed on the chromospheric disk can also be calculated with the same method. In addition to this, it is possible to calculate the area of any occurrence on the solar disk, whether it is related to an activity or not.     

A search for sunspot canopies using a vector magnetograph

Using a magnetograph, we examine four sunspots for evidence of a magnetic canopy at the penumbra/photosphere boundary. The penumbral edge is determined from the photometric intensity and is defined to correspond to the value of the average intensity minus twice the standard deviation from the average. From a comparison of the location of this boundary with the location of contours of the vertical and horizontal components of the magnetic field, we conclude that the data are best represented by canopy-type fields close to all four sunspots. There is some evidence that the magnetic inclination in the canopies is 5°–15° with respect to the horizontal and that the canopy base height lies in the middle/upper photosphere. The observations further suggest that the magnetic canopy of a sunspot begins at its outer penumbral boundary.     

A sunspot with a peculiar motion

The development and the motion of a sunspot are described that has crossed the Sun's equator.     

A possible relationship between spectral bands in sunspot number and the space-time organization of our planetary system

For the particular purpose of this paper, Zürich relative sunspot numbers of the time spans 1749–1982, 1749–1865, and 1866–1982, have been analysed anew by two different methos. It is shown that the spectral bands in the power spectra of sunspot numbers between 1 and 234 years obtained from these analyses can be clearly related to the modified configuration frequencies of the giant planets and their harmonics. In particular, the clearly dominant spectral band in sunspot number, the solar cycle of 10.8 years, is given by the configuration period of Jupiter and Saturn (19.859 yr) times the ratio of their distances from the Sun (0.545).     

The use of abnormal quiet days in Sq(H) for predicting the magnitude of sunspot maximum at the time of preceding sunspot minimum

The previously established connection between the occurence of AQDs (“abnormal quiet days” when the phase of the solar diurnal variation of horizontal magnetic field, Sq(H), at a mid-latitude northern hemisphere station is anomalous) at sunspot minimum and the magnitude of the following sunspot maximum is examined in the light of our recent improved understanding of the nature and cause of AQDs. A small contribution to the relationship is found to arise from variations from cycle to cycle in the additional northward field which is characteristic of AQDs and leads to a reduced Sq(H) amplitude at stations poleward of the Sq focus. However, the main factor which determines the connection is a variation from one sunspot minimum to another of the amplitude of the small southward bay-like field perturbations which constitute the AQD events, and evidence is presented which suggests that this parameter may be quantitatively related to the extent of southward swing of the B_z component of the interplanetary magnetic field which determines the energy transfer from the solar wind into the magnetospheric tail. It thus appears that the magnitude of southward swing in B_z might be another solar parameter which anticipates the size of a forthcoming sunspot cycle during its build-up over the declining phase of the previous cycle and at the minimum.     

A new method of determining the inclination angle in interacting binaries

We describe a method of determining the system parameters in non-eclipsing interacting binaries. We find that the extent to which an observer sees the shape of the Roche lobe of the secondary star governs the amount of distortion of the absorption-line profiles. The width and degree of asymmetry of the phase-resolved absorption-line profiles show a characteristic shape, which depends primarily on the binary inclination and gravity darkening exponent. We show that, in principle, by obtaining high spectral and time resolution spectra of quiescent cataclysmic variables or low-mass X-ray binaries in which the mass-losing star is visible, fitting the shape of absorption-line profiles will allow one to determine not only the mass function of the binary, but also the binary inclination and hence the mass of the binary components.     

A new method to calculate the resonant response of a sunspot model atmosphere to magneto-atmospheric waves

In order to understand the observed oscillations in sunspots we present a new method for calculating the resonant response of a realistic semi-empirical model of the sunspot umbral atmosphere and subphotosphere to magneto-atmospheric waves in a vertical magnetic field. The depth dependence of both the adiabatic coefficient and the turbulent pressure is taken into account. This requires an extension of the wave equations by Ferraro & Plumpton (1958). We compare the coefficients of wave transmission, re flection, and conversion between fast mode and slow mode waves for different assumptions, compare the results with those from earlier modelling efforts, and point out possible sources of mistakes. The depth dependence of the adiabatic coefficient strongly influences the resulting spectrum of resonance frequencies. The condition of a conservation of wave flux is violated if the depth dependence of the turbulent pressure is not properly considered.     

The possible presence of C2 lines in sunspot spectra

Indirect evidence against the presence of C₂ lines in umbral spectra is discussed. The dominant role of CO in the molecular equilibrium of C at umbral temperatures ensures that CN, CH and C₂ lines are formed in the same atmospheric regions. Observations of CN and CH umbral lines are in good accord with predictions based on accepted umbral model atmospheres. This implies that C₂ must follow the predictions and that it is too weak to contribute to the umbral spectrum. C₂ lines in the photosphere and penumbrae are in excellent quantitative agreement with predictions. Additional tests are proposed.     

A method for the determination of cosmic distances

In this paper, a general method is developed for the determination of cosmic distances. The method is based on the assumption that the members of a cosmic group scatter around a mean absolute magnitude in a Gaussian distribution. The basic formula of the method is obtained as a least-squares fit of the solution of a highly transcendental equation as a function of a given apparent magnitude parameter α. For each range of α, the precision criteria of this formula, and also the absolute relative uncertainty in the derived distance, are very satisfactory. Some illustrative examples of the usages of the method are included.     

A model of the sunspot umbra

Equations governing the structure of the umbra of a single spot have been integrated on the spot-axis. It is shown that a consistent umbral model can be obtained only for a narrow range of the electron pressures at the spot surface. The spot center is found to be at a depth of about 400 km below the normal solar surface. The reduced energy flux observed at the surface is assumed to be due to the effect of the spot-magnetic field on subphotospheric convection and an empirical factor is introduced to take into account the reduction in the convective energy flux. With an inferred expression for as a function of the internal and magnetic-energy density it is shown that in a consistent model the physical variables in the spot approach their ambient values at about 2330 km below the undisturbed solar surface and at the same depth the energy flux approaches the normal solar value and the magnetic interference with convection vanishes. The present investigation is a refinement of an earlier paper by Chitre (1963).Supported in part by the Office of Naval Research [Nonr-220(47)] and the National Science Foundation [GP-5391].     

The limits of possible values of inclination of Mercury's equator

The method of estimation of the limits, containing the equator inclination of a celestial body, had been developed. In this method it is necessary to know the orbital elements and the mass of a celestial body. Another condition is that the axial rotation of a body should be in the resonance with its orbital motion. It has been found that the equator inclinations should have the values between 1 .7 and 2 .6 for Mercury and between 1 .0 and 1 .8 for the Moon. It also has been found that largest harmonics in Mercury's physical libration are the harmonics sin( – 3g), cos( – 3g), sin g and sin 2.     

A new empirical model of a sunspot umbra

H and K-line spectra of quiescent prominences, taken with the slit placed normal to the limb, commonly reveal a gas streaming (5–50 km/s) that is peculiar to the upper edge of these objects. On the average this streaming is uni-directional and consistent with a hypothetical east-west wind.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Structure of a sunspot

From enlargements of patrol photographs of the disk passage of the sunspot of July 20 – August 2, 1966, intensity profiles across the spot are obtained at several positions near the disk-center and at each limb. It is found that these profiles show asymmetric features near each limb (increasingly sharp limb-side penumbra and poorly resolved disk-side penumbra) which are similar to those reported in Paper III of this series. It is suggested that these profile asymmetries are the essential feature of the center-limb variations in the appearance of a sunspot which have become known as the Wilson effect.Conventionally the Wilson effect is described as the extreme foreshortening and eventual disappearance of the disk-side penumbra and, recently, Suzuki has referred to this as the occultation of the penumbra by the photosphere. We find no evidence at all for the disappearance of the disk-side penumbra at the limb in this spot. Defining half-height points on the profile curves as the umbral and penumbral boundaries, we find that, near the west limb where the spot is stable and regular, the limb-side penumbra increases by about 10% at the expense of the umbra. This result qualitatively supports the results reported in Paper III although it is smaller in magnitude.Other observations of sunspots which appear to exhibit the conventional Wilson effect are discussed and it is concluded that in no case yet published is the resolution and seeing of sufficient quality to demonstrate unambiguously the disappearance of the disk-side penumbra.     

A recurrence relation for inclination functions

When the terms of the series expansion for the gravitational potential of the Earth are expressed in terms of the orbital elements of an arbitrary Earth satellite, the orbital inclination,i, appears in each, term as the argument of a function of inclination only. For the special case when the field is axi-symmetric, studied in an earlier paper, a recurrence relation was given for a normalized inclination function,A ^k l(i), with two parameters. The present paper gives a recurrence relation for a general normalized function,K ^k lm(i), with three parameters.     

Relationship between sunspot numbers during years of sunspot maximum and sunspot minimum

A correlation analysis shows that the sunspot numbers at the peaks of the last eight solar cycles are well-correlated with the sunspot numbers in heliolatitudes 20°–40° (specially in the southern hemisphere) occurring in the solar minimum years immediately preceding the solar maximum years.On leave from Physical Research Laboratory, Ahmedabad, India.