On the measurement precision of solar p-mode eigenfrequencies

We make use of 3456 d of observations of the low-ℓ p-mode oscillations of the Sun in order to study the evolution over time of the measurement precision of the radial eigenfrequencies. These data were collected by the ground-based Birmingham Solar-Oscillations Network (BiSON) between 1991 January and 2000 June. When the power spectrum of the complete time series is fitted, the analysis yields frequency uncertainties that are close to those expected from the returned coherence times of the modes. The slightly elevated levels compared with the prediction appear to be consistent with a degradation of the signal-to-noise ratio in the spectrum that is the result of the influence of the window function of the observations (duty cycle 71 per cent). The fractional frequency precision reaches levels of a several parts in 10⁶ for many of the modes. The corresponding errors reported from observations made by the GOLF instrument on board the ESA/NASA SOHO satellite, when extrapolated to the length of the BiSON data set, are shown to be (on average) about ∼25 per cent smaller than their BiSON counterparts owing to the uninterrupted nature of the data from which they were derived.
An analysis of the BiSON data in contiguous segments of different lengths, T , demonstrates that the frequency uncertainties scale as T ^−1/2. This is to be expected in the regime where the coherence (life) times of the modes, τ _{n ℓ}, are smaller than the observing time T (the 'oversampled' regime). We show that mode detections are only now beginning to encroach on the 'undersampled' regime (where   T < τ _{n ℓ})  .     

Oscillatory motions in the sun corresponding to the solar cycle

Die mittleren Geschwindigkeiten, abgeleitet aus den Eigenbewegungen von Sonnenfleckengruppen, zeigen ein ähnliches Verhalten wie die von HOWARD und LABONTE (1980) gefundenen Torsionschwingungen und haben ebenfalls eine meridionale Komponente, die mit dem Sonnenzyklus variiert. Berechnungen der Lorentzkraft aus kinematischen Dynamomodellen zeigen, daß beide Komponenten eine natürliche Konsequenz eines in der Sonnenkonvektionszone wirkenden αω-Dynamos sind.     

A convenient method to obtain stellar eigenfrequencies

The differential equations describing stellar oscillations are transformed into an algebraic eigenvalue problem. Frequencies of adiabatic oscillations are obtained as the eigenvalues of a banded real symmetric matrix. We employ the Cowling-approximation, i.e. neglect the Eulerian perturbation of the gravitational potential, and, in order to preserve selfadjointness, require that the Eulerian pressure perturbation vanishes at the outer boundary. For a solar model, comparison of first results with results obtained from a Henyey method shows that the matrix method is convenient, accurate, and fast.     

Timing of the 1984 total solar eclipse and the size of the sun

We report accurate timing of second and third contacts made from videotape of the total solar eclipse of 23 November, 1984, observed in Papua New Guinea. The magnitude of the discrepancies between predicted and observed times indicates that the secular change in the size of the Sun reported by some observers is within the uncertainty.     

The effect of finite electrical conductivity on the angular-momentum loss of the sun due to the solar wind

In general the solutions to the azimuthal equations of motion of the solar wind possess a singularity at the radial Alfvénic critical point if the fluid is non-viscous and has an infinite electrical conductivity. This singularity can only be removed by a proper choice of boundary conditions. If a plasma with a large but finite conductivity is considered, the singularity is removed in the mathematical sense. However, it is shown that for this latter case the actual solution does not differ significantly from the former model and that the boundary condition is still determined from the behavior of the solution at or near the Alfvénic critical point.Kitt Peak National Observatory Contribution No. 411.Operated by The Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Small-scale background magnetic field on the sun in solar cycle 23

Based on SOHO/MDI data (an archive of magnetic maps with a resolution of ～2″), we have investigated the dynamics of the small-scale background magnetic field on the Sun in solar cycle 23. The cyclic variations and surface structure of the background magnetic field have been analyzed using the mean estimates of 〈B〉 and 〈B ²〉 of the observed magnetic field strength B for various solar surface areas and at various B levels. We have established that the cyclic variations of 〈2〉 at latitudes below 30° are essentially similar to those of the total radio flux F _10.7. A significant difference between the background magnetic fields in the northern and southern solar hemispheres persisting throughout the solar cycle has been detected. We have found the effect of background magnetic field growth toward the solar limb and concluded that the transversal component in the background magnetic field is significant. The relatively weak small-scale background magnetic fields are shown to form a special population with its own special laws of cyclic variation.     

Formation of the FeI 5324.19 line in the sun and theoretical calibration of solar magnetic telescope

Using the Unno-Beckers equations and the Rnnge-Kutta method with variable steplength, we calculated the formation in a magnetic field of the FeI λ 5324.19 line in the solar photosphere, sunspot penumbra and umbra, and determined various theoretical calibration parameters for the magnetic and radial velocity fields. These parameters for the transverse and velocity fields have good linearity and stability and adequate sensitivity, making the line very suitable for the study of solar active regions. When observing the transverse field, the filter should best be placed 0.10 – 0.11 A away from the line centre. The calibration is rather complicated when magneto-optical effects are considered. Temperature sensitivity effects of this line should not be serious.     

Kinematics and age of 15 stars-photometric solar analogs

The radial and space velocities are inferred for 15 stars that are photometric analogs of the Sun. The space velocity components (U, V, W) of most of these stars lie within the 10–60 km/s interval. The star HD 225239, which in our previous papers we classified as a subgiant, has a space velocity exceeding 100 km/s, and belongs to the thick disk. The inferred fundamental parameters of the atmospheres of solar analogs are combined with published evolutionary tracks to estimate the masses and ages of the stars studied. The kinematics of photometric analogs is compared to the data for a large group of solar-type stars.     

Dependence of kinematics on the age of stars in the solar neighborhood

The variations of kinematic parameters with age are considered for a sample of 15 402 thin-disk O-F stars with accurate ??, ??, ??, and ?? > 3 mas from the Hipparcos catalogue and radial velocities from the PCRV catalogue. The ages have been calculated from the positions of the stars on the Hertzsprung-Russell diagram relative to the isochrones from the Padova database by taking into account the extinction from the previously constructed 3D analytical model and extinction coefficient R _V from the 3D map of its variations. Smooth, mutually reconciled variations of the velocity dispersions ??(U), ??(V), ??(W), solar motion components U _??, V _??, W _??, Ogorodnikov-Milne model parameters, Oort constants, and vertex deviation l _xy consistent with all of the extraneous results for which the stellar ages were determined have been found. The velocity dispersion variations are well fitted by power laws the deviations from which are explained by the influence of predominantly radial stellar streams: Sirius, Hyades, ?? Cet/Wolf 630, and Hercules. The accuracy of determining the solar motion relative to the local standard of rest is shown to be fundamentally limited due to these variations of stellar kinematics. The deviations of our results from those of Dehnen and Binney (1998), the Geneva-Copenhagen survey of dwarfs, and the Besan con model of the Galaxy are explained by the use of PCRV radial velocities with corrected systematic errors.     

Period and phase of the 88-year solar cycle and the Maunder minimum: Evidence for a chaotic sun

The problem of whether the solar dynamo is quasi-periodic or chaotic is addressed by examining 1500 years of sunspot, geomagnetic and auroral activity cycles. We find sub-harmonics of the fundamental solar cycle period during the years preceding the Maunder minimum and loss of phase of the subharmonic on emergence from it. These phenomena are indicative of chaos. They indicate that the solar dynamo is chaotic and is operating in a region close to the transition between period doubling and chaos. Since Maunder type minima reoccur irregularly for millennia, it appears that the Sun remains close to this transition to and from chaos. We postulate this as a universal characteristic of solar type stars caused by feedback in the dynamo number.     

The numerical determination of the eigenfrequencies of a rotating star

A technique for finding the oscillation spectrum of a rotating star based on the solution of two simultaneous ordinary differential equations is described. Results are presented for someg-modes of the polytrope of index 2. It appears that the functional dependence of frequency on rotational velocity is different for different azimuthal wave numbersm.     

The adapted solar wind system as cause for a momentum transfer to the sun and its consequences for the orbital motions of keplerian objects

In the following paper we argue that each wind-driving star in relative motion with respect to the ambient interstellar medium experiences a force exerted on its central wind-generating body. The exact magnitude of this force depends on the actual geometry of the counterflow configuration of stellar and interstellar winds for a particular kinematic situation which is especially sensitive to whether the interstellar flow is subsonic or supersonic. It will, however, be demonstrated here that this force is of an accelerating nature, i.e., it operates like a rocket-motor, as long as the peculiar motion of the wind-driving star with respect to the ambient interstellar medium remains subsonic.Here we use a specific analytical model to describe theoretically the specific counterflow configuration for the case of the solar system in a subsonic peculiar motion with respect to the local interstellar medium assuming irrotational and incompressible flows. We can work out a quantitative number for the accelerating force governing the Sun's motion at present. The net reaction force exerted on the solar body is then mediated by the asymmetric boundary conditions to which the distant solar wind field has to adapt.Next we study the indirect action of such a force on orbiting Keplerian objects like planets, planetesimals and comets. Since this force only influences the central solar body, but not the planets themselves, the problem is different from the treatment of a constant perturbation force perturbing the Keplerian orbits. We present a perturbation analysis treating the action of a corresponding position-dependent perturbation force resulting in secular changes of the orbital elements of Keplerian objects. It is found that changes are accumulating more rapidly in time the closer to the sun the orbiting bodies are. Main axis and perihelion distances are systematically increasing. Especially pronounced are changes in the perihelion position angle of the objects. For solar wind mass losses larger than the Sun's present value by a factor of 1000 (T-Tauri phase of the Sun,) the migration periods calculated for the planet Mercury are of the same order of magnitude as that for corresponding general relativistic migration.     

Electron groups traced from the sun to 1 AU

We trace electrons from the Sun by a variety of proxy methods - solar flare positions, and metric and kilometric type III radio bursts from the Sun until they can be observed in situ as electrons at the ISEE-3 spacecraft. Our study extends over the period of operation of the electron experiment on ISEE-3 from August 1978 to November 1979. By carefully restricting timing within the data sets involved, we find a peak in the number of flares associated with in situ electrons near 60° west solar longitude. This peak shows that type III bursts can be fairly limited in spatial extent, and that the best connection with the solar surface to the flare is along the Archimedean magnetic field spiral. We use this spatial determination to define an average beam shape for an event. We assume this average beam shape to be representative of the distribution in space of each electron group. The electron numbers at 2 and 29–45 keV energies combined with this average beam shape are used to approximate the total numbers of electrons and energy per burst for individual events. We find that the total number of electrons and total energy for events varies significantly with flare type; that on the average brighter flares are associated with more electrons.     

The association of flares to cancelling magnetic features on the sun

Previous work relating flares to evolutionary changes of photospheric solar magnetic fields are reviewed and reinterpreted in the light of recent observations of cancelling magnetic fields. In line-of-sight magnetograms and H-alpha filtergrams from Big Bear Solar Observatory, we confirm the following 3 associations: (a) the occurrence of many flares in the vicinity of emerging magnetic flux regions (Rust, 1974), but only at locations where cancellation has been observed or inferred; (b) the occurrence of flares at sites where the magnetic flux is increasing on one side of a polarity inversion line and concurrently decreasing on the other (Martres et al., 1968; Ribes, 1969); and (c) the occurrence of flares at sites where cancellation is the only observed change in the magnetograms for at least several hours before a flare (Martin, Livi, and Wang, 1985). Because cancellation (or the localized decrease in the line-of-sight component of magnetic flux) is the only common factor in all of these circumstances, suggest that cancellation is the more general association that includes the other associations as special cases. We propose the hypothesis that cancellation is a necessary, evolutionary precondition for flares. We also confirm the observation of Martin, Livi, and Wang (1985) that the initial parts of flares occur in close proximity to cancellation sites but that during later phases, the flare emission can spread to other parts of the magnetic field that are weak, strong, or not cancelling.     

On the influence of nonlinearities on the eigenfrequencies of five-minute oscillations of the Sun

Fitting the results of linear normal-mode analysis of the solar five-minute oscillations to the observed k - ω diagram selects a class of models of the Sun's envelope. It is a property of all the models in this class that their convection zones are too deep to permit substantial transmission of internal g modes of degree 20 or more. This is in apparent conflict with Hill and Caudell's (1979) claim to have detected such modes in the photosphere. A proposal to resolve the conflict was made by Rosenwald and Hill (1980). They pointed out that despite the impressive agreement between linearized theory and observation, nonlinear phenomena in the solar atmosphere might influence the eigenfrequencies considerably. In particular, they suggested that a correct nonlinear analysis could predict a shallow convection zone. This paper is an enquiry into whether their hypothesis is plausible. We construct k - ω diagrams assuming that the modes suffer local nonlinear distortions in the atmosphere that are insensitive to the amplitude of oscillation over the range of amplitudes that are observed. The effect of the nonlinearities on the eigenfrequencies is parameterized in a simple way. Taking a class of simple analytical models of the Sun's envelope, we compute the linear eigenfrequencies of one model and show that no other model can be found whose nonlinear eigenfrequencies agree with them. We show also that the nonlinear eigenfrequencies of a particular solar model with a shallow convective zone, computed with more realistic physics, cannot be made to agree with observation. We conclude, therefore, that the hypothesis of Rosenwald and Hill is unlikely to be correct.     

The estimate of the deceleration in the earth's rotation due to the sun

The tidal long-term decrease in the angular velocity of the Earth's rotation has been estimated on the basis of the angular momentum tidal balance in the Earth-Moon-Sun system. The observed (LLR) tidal long-term decrease in the Moon's mean motion, the apparent secular acceleration in the mean longitude of the Sun and the long-term decrease in the 2nd degree zonal geopotential parameter were used.Presented at the XXth General Assembly of the I.A.G., Vienna, August 15, 1991.     

YO molecule in the sun

Vibrational transition probabilities, namely Franck—Condon factors and -centroids have been evaluated by an approximate analytical method for the (A–X), (A–X), and (A–X) system of YO molecule. Morse potential energy curves forX ²⁺,A ²₂,A²₂, andA²₂, states of YO have been constructed using the latest spectroscopic data. The value of -centroids for the band have been found to decrease linearly with the corresponding wavelengths. We show results for two new transitions of (A–X) and (A–X) and five new bands of (A–X) of YO in the umbral spectrum of the Sun.     

On convection in the sun

Convective motions driven by a superadiabatic temperature gradient in a viscous thermally conductive medium are considered. Approximate linearized equations governing the perturbation are derived under the following conditions: (i) The ratio of the excess temperature gradient over the adiabatic gradient is small compared with the gradient itself, (ii) The perturbation is of low-frequency type, (iii) The rotation is slow. Only the convective mode is described by these equations (as in the Boussinesq approximation), and the equations are valid for compressible configurations with any ratio between the scale heights of the equilibrium and perturbed quantities. Results of a numerical calculation of unstable perturbations for configurations with a large density stratification are given. They show that under conditions appropriate for the solar convection zone an extremely strong instability is expected to occur if the mixing length is assumed to be equal to 1.5 times the pressure scale height. The horizontal scale of the instability is intermediate between those of granulation and supergranulation. The larger the mixing length, the smaller the growth rate of the instability, and the larger its horizontal scale. Therefore it seems possible to adjust the mixing length to obtain the characteristics corresponding to those of the solar supergranulation. The possible origin of the granulation as an instability in a subsurface zone, where a local increase in the density scale height takes place, is also discussed. To achieve agreement with observations, it seems necessary to assume that the ratio of the mixing length to pressure scale height is an increasing function of the pressure.     

Grazing incidence spectra of the sun

Intensity calibrated grazing incidence spectrographs have been flown on three Skylark sounding rockets to record the solar soft X-ray and XUV spectra over a wide wavelength range. This paper describes the instrumentation and calibration procedures, and presents wavelength and intensity data, for each of the flights.     

Large-scale motions in the sun

Large-scale solar motions comprise differential rotation (with latitudinal, and perhaps radial gradients), axially symmetric meridional motions, and possible asymmetric motions (giant convective cells or Rossby-type waves or both). These motions must be basic in any satisfactory theory of the changing pattern of solar magnetic fields and of the 22-yr cycle. In the present paper available data are discussed and, as far as possible, evaluated and explained.Rotational measurements are based on the changing positions of discrete features such as sunspots, on Doppler shifts, on geophysical changes and on statistical evaluation of the motions of diffuse objects. The first mentioned, comprising faculae, sunspots, K-corona (to latitudes 45°) and filaments, show agreement better than 0.7 %. A new formula for surface rotation _s , based on faculae and sunspot data, is _s = 14.52 – 2.48 sin² b – 2.51 sin⁶ b deg day^–1, where b is latitude, and validity may extend to about 70°. Errors in Doppler shift measurements and statistical treatments are discussed. There is evidence of a much slower coronal rate at high latitudes, and of a slower sub-surface rate at lower latitudes.Ordered meridional motions have been revealed by statistical investigations of the positions of spot groups, of spots and of filaments. All these results seem explicable in terms of an oscillating hydro-magnetic circulation in each hemisphere. These have both 11-yr and 22-yr components, and these periods are provided by a general dipole field of about one gauss, together with a pair of toroidal fields centred at latitudes ±16° and of average strength of order 10 G.Evidence of large-scale (perhaps 3 × 10⁵ km), irregular surface motions is provided by the distribution of surface magnetic flux, the motions of sunspots, and Doppler-shift observations; it is supported by Ward's theory of the equatorial acceleration. The possibility is suggested that these asymmetric motions also drive the oscillatory meridional motions.