STATISTICAL PROPERTIES OF THE PULSES IN THE SOLAR p-MODE POWER

We have revealed the periods of good visibility for each individual mode of low spherical degree using irradiance data from the IPHIR experiment. Their statistical properties and the influence on the resulting line shapes are discussed. The analysis of the temporal change of each mode power by Fourier transform with a running temporal window was performed. The running mean power of p-modes (=0, n=17–24 and =1, n=16–23) apparently changes with the rotation of the Sun. There is well visible an anticorrelation of the p-mode power with the mean solar magnetic field and less significant correlation with daily sunspot number.     

Properties of r-modes in the Sun

Global oscillations of the Sun (r-modes) with very long periods 1 month are reviewed and studied. Such modes would be trapped in an acoustic cavity formed either by most of the convective envelope or by most of the radiative interior. A turning point frequency giving cavity boundaries is defined and the run of eigenvalues for angular harmonics l 3 are plotted for a conventional solar convection zone. The r-modes show equipartition of oscillatory energy among shells which each contain one antinode in the radial dimension. Toroidal motion is dominant to at least the 14^th radial harmonic mode. Viscosity from convective turbulence is strong and would damp any mode in just a few solar rotations if it were the only significant nonadiabatic effect. Radial fine splitting which lifts the degeneracy in n is very small (20 nHz or less) for all n 14 trapped in the envelope. But, if splitting could be detected, we would have a valuable new constraint on solar convection theories.     

Photoelectrons and solar wind/lunar limb interaction

It is suggested that boundary conditions for solar wind/lunar limb interactions are active. The whole-Moon limb does not evoke a shock cone because warm (13 eV/electron) solar wind electrons are replaced by cool (2 eV/electron) photoelectrons that are ejected from the generally smooth areas of the lunar terminator illuminated at glazing angles by the Sun. A localized volume of low thermal pressure is created in the solar wind by these cool photoelectrons. The solar wind expands into this turbulence-suppressive volume without shock production. Conversely, directly illuminated highland areas exchange hot photoelectrons (> 20 eV/electron) for warm solar wind electrons. The hot electrons generate a localized pressure increase (p) in the adjacent solar wind flow which evokes a shock streamer in the solar wind. Shock streamers are identifiable by a coincident increase in the magnitude (B p) of the solar wind magnetic field immediately external to the lunar wake. Shock occurrence is controlled by lunar topography, solar activity in the hard ultraviolet (> 20 eV), solar wind electron density and thermal velocity, and the intensity of the solar wind magnetic field.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April 1973.The Lunar Science Institute is operated by the Universities Space Research Association under Contract No. NSR 09-051-001 with the National Aeronautics and Space Administration.     

Theoretical Clues for Mode Identification - Instability Ranges and Rotational Splitting Patterns

Frequency spectra of unstable modes for typical models of Cephei, SPBand Scuti variables are presented. Comparison of theoretical andobserved instability ranges allows to constrain possible parameters of thestellar models. As an example, models of ² Tau are considered. Mainuncertainties in the determination of the theoretical frequency ranges for Sct variables are due to unsatisfactory treatment of convection.The structure of rotationally split multiplets for the low-order modesexcited in Sct stars is discussed. The rotational coupling betweenclose modes of spherical harmonic degree, , differing by 2, cansignificantly disturb the frequency spectrum.     

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.     

Analysis of the solar low-ℓ p-mode asymmetries using wavelets

It is presently widely accepted that the solar low p modes show asymmetric profiles when their power spectrum is analysed and that the fact of fitting symmetric profiles yields systematic effects in the obtained frequencies which could affect the results of inversions. In this paper the low p-mode profiles are analysed using wavelets to denoise the power spectra of the modes. This denoising method is applied both to artificial data generated by Kosovichev (the Hare and Hound exercise) and to real data obtained with the GOLF instrument. The asymmetries as well as the frequencies obtained are studied in both cases. The results show that although the obtained p-mode profiles present a slightly negative asymmetry, the use of symmetric profiles to fit the power spectra does not introduce any systematic effect in the obtained frequencies.     

Solar irradiance changes caused by g-modes and large scale convection

Solar irradiance measurements from the ACRIM experiment show a clear response to the rotation periods of g-mode oscillations (l = 1, 2, and 3) and their first harmonics. Peaks in the ACRIM spectrum at 16.6, 18.3, 20.7, 36.5, and - 71 days all lie within about 1% of periods arising from g-mode rotation. This means that the g-modes are a fundamental cause of irradiance fluctuations. On time scales of months and less they modulate the irradiance by means of transient flows of global scale which they stimulate in the Sun's convective envelope. Dimensional arguments indicate that the flows carry up heat at an average rate 10^-3 L which is not in conflict with observed changes in the irradiance. Five additional tests for g-modes and large-scale convection are given. An instability is described which undermines diffusion models of sunspot energy storage.     

Pitch angle scattering of solar particles: Comparison of ‘particle’ and ‘field’ approach

In the quasi-linear theory of pitch angle scattering the power spectrum of magnetic field fluctuations is related to the shape of the pitch angle diffusion coefficient D(), the absolute value of the mean free path , and the rigidity dependence of the mean free path (R). We discuss these relations in detail during the solar particle event of 11 April, 1978 which was observed on HELIOS-2 at a distance of 0.49 AU from the Sun. Magnetic field measurements obtained during the time of the event are used as a basis for the layer model in which the method of particle trajectories in an actually measured field is used to simulate pitch angle diffusion. The values of D() and based on the trajectory simulation for 100 MeV protons (field approach) are compared with results obtained from solar proton data (particle approach) and with predictions from quasi-linear theory based on the additional assumption of the slab model for magnetic field fluctuations (QLT approach). The time of the event is characterized by a high level of field fluctuations, the observed mean free path of about 0.03 AU for 100 MeV protons is smaller than the average value near 1 AU. Results from the field and particle approaches agree surprisingly well. The remaining difference in the mean free path of about a factor of 2 could be due to tangential discontinuities which are measured by the magnetometer, but not seen by the real particles traveling along the average field. The results from the field and QLT approaches based on the same set of magnetic field measurements differ by about a factor of 4. One of the reasons for this discrepancy is that the conditions for resonance scattering are only marginally valid. In addition, the wave vectors representing Alfvén-type fluctuations may not be totally field aligned. This deviation from the slab model would cause an increase of the theoretically predicted mean free path and lead to better agreement with the other two approaches.     

On the Power in the Legendre Modes of the Solar Radial Magnetic Field

The power in the different modes of an expansion of the solar radial magnetic field at the surface in terms of Legendre polynomials,P , is calculated with the help of a solar dynamo model studied earlier. The model is of the Babcock–Leighton type, i.e., the surface eruptions of the toroidal magnetic field – through the tilt angle, , formed by the magnetic axis of a bipolar magnetic region with the east-west line – are the sources for the poloidal field. In this paper it is assumed that the tilt angle is subject to fluctuations of the form, = ()+ <> where <> is the average value and () is a random normal fluctuation with standard deviation which is taken from Howard's observations of the distribution of tilt angles. For numerical considerations, negative values of were not allowed. If this occurred, was recalculated. The numerical integrations were started with a toroidal magnetic field antisymmetric across the equator, large enough to generate eruptions, and a negligible poloidal field. The fluctuations in the tilt angle destroy the antisymmetry as time increases. The power of the antisymmetric modes across the equator (i.e., odd values of ) is concentrated in frequencies, _p, corresponding to the cycle period. The maximum power lies in the =3 mode with considerable power in the =5 mode, in broad agreement with Stenflo's results who finds a maximum power at =5. For the symmetric modes, there is considerable power in frequencies larger than _p, again in broad agreement with Stenflo's power spectrum.     

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.     

An integrable case of a rotational motion analogous to that of Lagrange and Poisson for a gyrostat in a Newtonian force field

The scope of the present paper is to provide analytic solutions to the problem of the attitude evolution of a symmetric gyrostat about a fixed point in a central Newtonian force field when the potential function isV ⁽²⁾.We assume that the center of mass and the gyrostatic moment are on the axis of symmetry and that the initial conditions are the following: (t ₀)=₀, (t ₀)=₀, (t ₀)=(t ₀)=₀, ₁(t ₀)=0, ₂(t ₀)=0 and ₃(t ₀)= ₃ ⁰ .The problem is integrated when the third component of the total angular momentum is different from zero (B ₁ 0). There now appear equilibrium solutions that did not exist in the caseB ₁=0, which can be determined in function of the value ofl ₃ ^r (the third component of the gyrostatic momentum).The possible types of solutions (elliptic, trigonometric, stationary) depend upon the nature of the roots of the functiong(u). The solutions for Euler angles are given in terms of functions of the timet. If we cancel the third component of the gyrostatic momentum (l ₃ ^r =0), the obtained solutions are valid for rigid bodies.     

On the difference between low-ℓ p-mode frequencies seen in velocity and in intensity

We compare the line profiles and frequencies of low =0, 1, 2 acoustic oscillations seen in observations in velocity (by the GOLF and GONG experiments) and in intensity (LOI instrument). Our study indicates that the systematic shift between the frequencies of low- pmodes in intensity and in velocity measurements recently discovered by Toutain and co-workers is merely an artifact of their reduction techniques. The results obtained agree perfectly with the theoretical expectation that solar oscillations are the global eigenmodes simultaneously visible in velocity and intensity with the frequencies and line profiles coinciding within the error bars.     

Comparative Solar Seeing and Scintillation Studies at the Fuxian Lake Solar Station

Starting November 1999 we are carrying out simultaneous seeing observations with the Solar Differential Image Motion Monitor (S-DIMM) at the Fuxian Lake station of the Yunnan Observatory and a solar scintillometer of the type used in the recent site survey by one of us (Beckers et al., 1997). The purpose was to compare the two methods of assessing the daytime atmospheric seeing for a lake site. We report here the first results of this comparison. We find that the relation between the seeing as measured by the S-DIMM (the Fried parameter r ₀) and the scintillation in the solar irradiance (_I) differs greatly from the relation found by Seykora (1993) for NSO/Sac Peak. We conclude that the _I measurements give a good indication for the amount of near-Earth seeing but that they are a poor proxy for the total atmospheric seeing. We interpret the simultaneous (r ₀, _I) observations in terms of an atmospheric seeing model and find good quantitative agreement with a model in which a fraction () of the seeing originated near the Earth (ground or water) and the rest (1–) originates at higher layers. For lake sites is small all day and the seeing is determined primarily by the refractive index variations at higher atmospheric layers. For land sites is small in the early morning but rapidly increases as the day progresses, near-Earth seeing dominating there most of the time.     

Geometrical dynamics: A new approach to periodic orbits aroundL 4

Geometrical dynamics is the study of the geometry of the orbits in configuration space of a dynamical system without reference to the system's motion in time.Generalized coordinates for the circular restricted problem of three bodies are taken as polar coordinatesr, centered at the triangular libration pointL ₄. A time-independent nonlinear second order ordinary differential equation forr as a function of is derived. Approximations to periodic solutions are obtained by perturbations and Fourier series.     

Solar particle propagation from 1 to 5 AU

A statistical analysis of solar particle events, observed by the GSFC-UNH charged particle detector on board Pioneer 10 and Pioneer 11 from March 1972 to December 1974 (from 1 to 5 AU for each spacecraft), is carried out with the goal of experimentally determining the statistical average interplanetary propagation conditions from 3 to 30 MeV. A numerical propagation model is developed that includes diffusion with a diffusion coefficient of the form k _r =k _o r , convection, adiabatic deceleration, and a variable coronal injection profile. The statistical analysis is carried out by individually analyzing each of five parameters (t _max, (t_max), t ₅, ) that are uniquely defined in a solar particle event. Each of the five parameter data sets were analyzed in terms of both a spacecraft-solar flare connection longitude 50°, and a numerical model that employed a variable exponential decaying coronal injection profile.The five individual parameter analyses are combined with the results that the statistical average radial interplanetary diffusion coefficient from 1 to 5 AU is given by k _r = (1.2 ± 0.4) × 10²¹ cm² s^-1 with = 0.0± 0.3 for 3.4 to 5.2 MeV protons and k _r = (2.6 ± 0.6) × 10²¹ cm² s^-1 with () = 0.0± 0.3 for 24 to 30 MeV protons. Using the classical relationship for the radial scattering mean free path _r, i.e. k _r = _r/3, we obtain _r = 0.09 ± 0.03 AU and 0.075 ± 0.020 AU for the low and high energy data, respectively. These results show, from 1 to 5 AU and from 3 to 30 MeV, that _r is both independent of radial distance and approximately independent of rigidity (for _r~P , where P = rigidity, = -0.15 ± 0.20).The above diffusion coefficients are inconsistent With both the predictions of the diffusion coefficient from present theoretical transport models and with the diffusion coefficient used in modulation studies at low energies.     

Periodicities in the solar differential rotation,surface magnetic field and planetary configurations

Using Greenwich data on sunspot groups during 1874–1976, we have studied the temporal variations in the differential rotation parametersA andB by determining their values during moving time intervals of lengths 1–5 yr successively displaced by 1 yr. FFT analysis of the temporal variations ofB (orB/A) shows periodicities 18.3 ± 3 yr, 8.5 ± 1 yr, 3.9 ± 0.5 yr, 3.1 ± 0.2 yr, and 2.6 ± 0.2 yr at levels 2. This analysis also shows five more periodicities at levels 1–2. The maximum entropy method is used to set narrower limits on the values of these periods. The reality of the existence of all these periodicities ofB (orB/A ) except the one at 2.8 yr is confirmed by analyzing the simulated time series ofB andB/A with values ofA andB randomly distributed within the limits of their respective uncertainties. Four of the prominent periods ofB agree, within their uncertainties, with the known periods in the the large-scale photospheric magnetic field. The deviations from the average differential rotation are larger near the sunspot minima. On longer time scales, the variations in the amount of sunspot activity per unit time are well correlated to the variations in the amplitudes of the torsional oscillation represented by the 22-yr periodicity inB. All the periods inB found here are in good agreement with the synodic periods of two or more consecutive planets. The possibility of planetary configurations providing perturbations needed for the Sun's MHD torsional oscillations is speculated upon and briefly discussed.     

Electron density diagnostics for solar ultraviolet lines of O V

We determine the electron densities for a range of solar features using new calculations for the Ov line ratio, R=I(761.1)/I(760.4), in conjunction with observational data obtained with the Solar Ultraviolet Measurements of Emitted Radiation (SUMER) instrument on the Solar and Heliospheric Observatory (SOHO). The densities obtained from this diagnostic are in good agreement with earlier measured values. This provides support for the theoretical diagnostics presented in this paper, and hence the atomic data used in their derivation. We conclude from these results that this particular Ov ratio is a useful diagnostic for many types of solar features.     

The Coronal Mass Ejection Waiting-Time Distribution

The distribution of times t between coronal mass ejections (CMEs) in the Large Angle and Spectrometric Coronagraph (LASCO) CME catalog for the years 1996–2001 is examined. The distribution exhibits a power-law tail (t) with an index –2.36±0.11 for large waiting times (t>10 hours). The power-law index of the waiting-time distribution varies with the solar cycle: for the years 1996–1998 (a period of low activity), the power-law index is –1.86±0.14, and for the years 1999–2001 (a period of higher activity), the index is –2.98±0.20. The observed CME waiting-time distribution, and its variation with the cycle, may be understood in terms of CMEs occurring as a time-dependent Poisson process. The CME waiting-time distribution is compared with that for greater than C1 class solar flares in the Geostationary Operational Environmental Satellite (GOES) catalog for the same years. The flare and CME waiting-time distributions exhibit power-law tails with very similar indices and time variation.     

The equilibrium,stability and evolution of a rotating magnetized gaseous disk

The exact solutions for the equilibrium of rotating gaseous disk with poloidal magnetic field are obtained. The stability of the disk with respect to uniform expansion and contraction is investigated by means of the variational principle. It is shown that if the equilibrium is determined by gravitational and magnetic forces only, the disk is in neutral equilibrium with respect to perturbations of the form r=r. The instability to short-waves perturbations is studied by the quasi-classical method. The analysis shows that if the magnetic field isH>2G, where is the surface density, then these perturbations are stabilized. The configurations of the electrical field induced by the rotation of magnetized disk are found. In conclusion, the questions of the evolution of the disk are discussed in connection with the quasar model when pulsar-like radiation is taken into account.