A Reconnection Model for the Distribution of Flare Energies

A physically based explanation is given for the distribution of flare energies N(E)E ^– where 1.5. In contrast to previous approaches, the present treatment is based on a physical theory of the flare reconnection site. The central assumption is that topological flare energy, although released explosively, is slowly accumulated over several hundred Alfvén timescales. When coupled to the geometric properties of the reconnective flare source, this assumption is shown to lead naturally to a deduction of the flare energy distribution. Current sheet models yield the exponent whereas more compact current structures imply steeper spectra .     

Distribution of Flare Energies Based on Independent Reconnecting Structures

A model is presented to explain the observed frequency distribution of flare energies, based on independent flaring at a number of distinct topological structures (separators) within active-region magnetic fields. The model is a modification and generalization of a recent model due to Craig (2001), and reconciles that model with the observed flare waiting-time distribution, and the observed absence of a flare waiting-time versus energy relationship. The basic assumptions of the model are that flares of energy E ² occur at separators of length , and that the frequency of flaring at a separator is defined by the Alfvén transit time of the structure. To reproduce the observed distribution of flare energies the model requires a probability distribution P( ) ^–1 of separator lengths within active regions. This prediction of the model is in principle testable. A theoretical origin for this distribution is also discussed.     

Two Sets of Improved Approximate Expressions of the Gyrosynchrotron Radiation

In this paper two sets of improved approximate expressions of emissivity , absorptivity , effective temperature T_eff, and frequency of peak brightness _p of gyrosynchrotron radiation are presented respectively for the ranges from 5 to 10 and 10 to 100 of harmonic numbers s(= /_B). The expressions are designed for the range from 20° to 80° of viewing angle , and the range 2 to 7 of electron energy spectral index . They are expressed by a power-law function in which the indexes are fitted by polynomial expressions of . Their statistical errors are, respectively, 24% and 32% for and for and 28% for . Their accuracies are much better than those of linear fitting of the power-law index.     

POWER SPECTRA OF SOLAR NETWORK AND NON-NETWORK FIELDS

We report new properties of solar magnetic fields in a quiet region as found from their magnetic power spectra. The power spectra of network and intranetwork fields (non-network fields) are separately calculated from a Big Bear magnetogram obtained with moderately high spatial resolution of 1.5 arc sec and a high sensitivity reaching 2 Mx cm^-2. The effect of seeing on the power spectrum has been corrected using Fried's (1966) Modulation Transfer Function with the seeing parameter determined in our previous analysis of the magnetogram. As a result, it is found that the two-dimensional power spectra of network and non-network fields appear in a form: ( ₁) ^-1 and ( ₁) ^-3.5. Here ₀ 0.47 Mm^-1 for network fields and ₀ 0.69 Mm^-1 for non-network fields, the latter of which corresponds to the size of mesogranulation; ₁ 3.0 Mm^-1 for both, which is about the size of a large granule. The network field spectrum below ₀ appears nearly flat, whereas that of non-network fields instead decreases towards lower wave numbers as ( ) ^1.3. The turnover behavior of magnetic field spectra around ₁ coincides with that found for the velocity power spectrum, which may justify the kinetic approach taken in previous theoretical studies of the solar magnetic power spectra.     

The Search for Solar Gravity-Mode Oscillations in the Solar Wind Using it Ulysses Plasma Data

A recent report that energetic particles measured in the solar wind may be influenced by solar gravity-mode ( -mode) oscillations motivated the search for -mode signatures in the Ulysses solar wind plasma data. Ulysses solar wind plasma data from 1 March 1992 through the 12 April 1996 were examined in this study for signs of possible solar oscillations. The multi-taper method for spectral analysis was used to look for significant spectral peaks in the entire four-year data set, as well as in the smaller, more heliographically homogenous data set over the solar poles. Several frequencies satisfying certain significance requirements were found in the -mode frequency range in both data sets that also agree with the previously published findings. However, these identifications are shown to be false detections, and hence the frequencies found cannot be identified as solar modes.     

3He enrichments by magnetosonic waves in current-driven instabilities

A theoretical model for³He enrichments in solar energetic particles is developed. First, current-driven, electrostatic instabilities that have frequencies ( is the cyclotron frequency of³He) are investigated for a plasma consisting of H,⁴He,³He, and electrons with the density of³He much lower than those of H and⁴He. It is found that in many cases the oblique ion-acoustic waves can have positive growth rates at frequencies and, at the same time, negative growth rates at and at _H. This can occur near the marginal state of the instability. The wave damping at these frequencies is caused by the cyclotron resonances of⁴He and H. The cyclotron damping at is negligible, however, because the abundance of³He is very small. The H cyclotron waves can be unstable at for a wide region of plasma parameters; the electron-to-ion temperature ratio must beT _e /T _H 1.5. To destabilize the₄He cyclotron waves with , high⁴He density and high electron temperature are both required. Then,³He enrichments are studied on the basis of the theory of nonlinear magnetosonic waves, which can promptly accelerate ions. The current-driven electrostatic waves with can enhance fluctuation velocities of³He. Thus, in the presence of these waves, magnetosonic waves can selectively accelerate³He particles to high energies. Finally, cyclotron resonances of heavy ions with the waves or are briefly discussed.     

Longitudinal distribution of X-bremsstrahlung on the solar disc

In this paper, the dependence of the intensity of solar bremsstrahlung in the spectral range from 1–60 keV on heliographic longitude is investigated. Considering a flare mechanism, which assumes that the electrons move in a preferred direction in the course of their acceleration (according to the model of Takakura and Kai (1966) the electrons move parallel to the solar surface), we come to the conclusion that the maximum of the bremsstrahlung intensity is shifted with increasing electron velocity towards the direction of motion of electron beams. In the case of the Takakura and Kai flare mechanism, the slow electrons ( ), i.e. with small energies of 1–10 keV, reach the maximum of the bremsstrahlung intensity round the CM; for higher velocities ( ), i.e. for higher energies of 10–60 keV, the direction of the maximum is shifted away from the CM towards the disc limb. These theoretical conclusions were proved by experimental research conducted by means of satellites.     

PERIODICITIES IN THE NORTH–SOUTH ASYMMETRY OF THE SOLAR DIFFERENTIAL ROTATION AND SURFACE MAGNETIC FIELD

We have studied the temporal variations in the north–south asymmetries of the differential rotation parameters A, B, and the mean rotation rate , by determining their values from Greenwich data for sunspot groups (1879–1976) in the northern and southern hemispheres, during moving time intervals of lengths 3 yr and 5 yr, successively displaced by 1 yr. The variation in the north–south asymmetry ( ) of is similar to the variation in the asymmetry (B ) of B but with opposite sign. These variations of and B may represent components of an anti-symmetric torsional oscillation which are in opposite phase with each other.The FFT and MEM analyses of the temporal variations of B , , and the north–south asymmetry (A ) of A, show existence of significant periodicities: 45.5 ± 11.5 yr,21.3 ± 4.5 yr, 13.3 ± 1.5 yr, and 10.5 ± 0.5 yr. These analyses also show a few other possible periodicities in A , B , and . All these periodicities are also seen in the north–south asymmetry of sunspot activity (with similar relative magnitudes). The 22-yr periodicity was seen in even-parity modes of magnetic field inferred from sunspot data.     

Temporal properties of He I 1083 nm dark points

The intensity of a sample of large, high-contrast and isolated dark points has been observed with full-disk images in the light of Hei 1083 nm from the Chromospheric Helium line Intensity Photometer (CHIP) on Mauna Loa, Hawaii. Temporal variations in the intensity encompassing a broad range of time scales have been recorded. Long-term changes in the intensity, although highly variable, are characterized by e-folding times on the order of 5 h. Superposed on these variations are frequent intensity variations, which occur over time scales ranging from the typical observing cadence of 3 min, to tens of minutes. Microflares-involving intensity changes of at least 50% over periods of minutes are observed frequently. Rapid cadence ( min) observations reveal differences between rise and decay times and shorter-term variations in the intensity profiles of these microflares.     

A Re-Evaluation of the Abundance of Lutetium in the Sun

Lutetium is one of the few nonvolatile elements whose solar photospheric abundance departs significantly from that derived from CI chondrites. We have applied the Cowan code to compute new oscillator strengths for Luii, and have included a correction for core polarization. The results have been used in a synthesis of the solar spectrum in the vicinity of features at 3397.062 and 6221.72. We find that the majority of the absorption in the ultraviolet feature is due to NH, making it unsuitable for extracting a reliable lutetium abundance. Our best fit to the low-noise Jungfraujoch spectrum for the weak, nine-component hyperfine Luii line at 6221.87 yields an abundance of +0.06 on a scale where log(H) = 12.00. This value is within 0.07 dex of the meteoritic result (+0.13). (These figures reflect the note added in proof below.)     

Non-Homogeneous Charge-Consistent Model for Acceleration of Iron in the Solar Corona

Acceleration of iron ions by a spherical shock wave moving through non-homogeneous solar corona is considered. The energy dependence of the mean charge of iron, _Fe(E), is determined by the characteristic acceleration time, T _a, trapping time, T _tr, and time for charge changes, T _q. The latter varies along with plasma number density during the propagation of the shock wave in the corona. Our calculations have demonstrated that adiabatic energy changes, Coulomb losses and shock broadening do not sufficiently influence the dependence _Fe(E). According to our estimations, the photoionizing processes can scarcely affect the ionic states of accelerated iron, except probably for the most powerful X10 class events.     

Radio frequency emission in electron beam-plasma and beam-beam interaction

A linear excitation of electromagnetic modes at frequencies , in a plasma through which two electron beams are contra-streaming along the magnetic field is investigated. This may be a source of the observed emissions at auroral latitudes.     

The elimination of the critical terms of a first order Uranus-Neptune theory by Hori's method

In this part we determine the value ofS ₁, and in terms of the canonical variables of H. Poincaré. A complete solution of the auxiliary system of equations generated by the Hamiltonian is presented.     

Short-term periodicities of the sun's ‘mean’ and differential rotation

We have looked for periodicities in solar differential rotation on time scales shorter than the 11-year solar cycle through the power- spectrum analysis of the differential rotation parameters determined from Mt. Wilson velocity data (1969–1994) and Greenwich sunspot group data (1879–1976). We represent the differential rotation by a set of Gegenbauer polynomials (()= + (5sin₂–1)+ (21sin₄–14sin₂+1)). For the Mt. Wilson data, we focus on observations obtained after 1981 due to the reduced instrumental noise and have binned the data into intervals of 19 days. We calculated annual averages for the sunspot data to reduce the uncertainty and corrected for outliers occuring during solar cycle minima. The power spectrum of the photospheric mean rotation , determined from the velocity data during 1982–1994, shows peaks at the periods of 6.7–4.4 yr, 2.2 ± 0.4 yr, 1.2 ± 0.2 yr, and 243 ± 10 day with 99.9% confidence level, which are similar to periods found in other indicators of solar activity suggesting that they are of solar origin. However, this result has to be confirmed with other techniques and longer data sets. The 11-yr periodicity is insignificant or absent in . The power spectra of the differential rotation parameters and , determined from the same subset, show only the solar cycle period with a 99.9% confidence level.The time series of determined from the yearly sunspot group data obtained during 1879–1976 is very similar to the corresponding time series of . After correcting for data with large error bars (occurring during cycle minima), we find periods, which are most likely harmonics of the solar cycle, such as 18.3 ± 3.0 yr and 7.5 ± 0.5 yr in and confirmed these and the 3.0 ± 0.1 yr period in . The original time series show in addition some shorter periods, absent in the corrected data, representing temporal variations during cycle minimum. Given their large error bars, it is uncertain whether they represent a solar variation or not. The results presented here show considerable differences in the periodicities of and determined from the velocity data and the spot group data. These differences may be explained by assuming that the rotation rates determined from velocity and sunspot data represent the rotation rates of the Sun's surface layers and of somewhat deeper layers.     

Epstein weight functions for non-radial oscillations of polytropes

Weight functions for the determination of the periods of linear adiabatic non-radial oscillations have been calculated in the same manner as Epstein's classic treatment of purely radial oscillations. Quadrupole (l=2) oscillations for thef and lower orderp andg-modes were considered. One group of static models were polytropes in the range 1.0n4.0 with ; thus included were configurations that were convectively stable, unstable and neutrally stable throughout. Another group consisted ofn=3.0 polytropes with convective shells or convective cores; ₁ was set at different values in each region in order to produce stability ( ) or instability ( ). The weight function provides a pictorial means for assessing the relative importance of each region of a given static model with respect to generating a given non-radial mode.     

Solution of Lambert's problem for short arcs

Approximation formulas are found for and , wherex(t) satisfies ,x(0)=x ₀,x(1)=x ₁. The results are applied to an example of two-body motion.     

Special Solutions in a Simplified Restricted Three-Body Problem with Gravitational Radiation Taken into Account

The distinctive feature of the relativistic restricted three-body problem within the c ^–5 order of accuracy (2 post-Newtonian approximation) is the presence of the gravitational radiation. To simplify the problem the motion of the massive binary components is assumed to be quasi-circular. In terms of time these orbits have linearly changing radii and quadratically changing phase angles. By substituting this motion into the Newtonian-like equations of motion one gets the quasi-Newtonian restricted quasi-circular three-body problem sufficient to take into account the main indirect perturbations caused by the binary radiation terms. Such problem admits the Lagrange-like quasi-libration solutions and rather simple quasi-circular orbits lying at large distance from the binary.     

[CII] Emission and Star Formation in Late-Type Galaxies

A linear correlation between the ratio of the[CII( $^{\text{2}}$ P A linear correlation between the ratio of the[CII( P → P )] line intensity to the [ CO(J:1 →0)] line emission, I /I and the equivalent width (EW) is found, over the range 2–71 ? in EW, for a sample of 21late-Type= galaxies. The latter is comprised of an optically selected sample of 12 normal Virgo Cluster spiral galaxies with [CII] detections obtained by us with ISOLWS, plus nine late-Type= galaxies with higher star formation rates (SFRs), for which [CII] data and, especially, EW data are available in the literature. As a result we infer I /I to be a reliable tracer of the current mass-normalized global SFR for non-starburst spiral galaxies. Moreover, the ratio of the [CII] line to the total far-infrared (FIR) continuum intensity, I /I , is found to decrease from ∼0.5% to ∼0.1% with decreasing SFR which we propose is due to a `[CII]-quiet' component of I from dust heated by the general interstellar radiation field (ISRF). The more `quiescent' galaxies in the sample have values of I /I different from those observed in `compact' Galactic interstellar regions. Their [CII]-emission is interpreted to be dominated by diffuse regions of the interstellar medium (ISM). For normal `star-forming' galaxies the diffuse component of the [CII] emission is estimated to account for at least 50% of the total. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the occurrence rate of high-speed solar wind events

We have investigated the rate of occurrence of solar wind phenomena observed between 1972–1984 using power-spectrum analysis. The data have been taken from the high-speed solar wind (HSSW) stream catalogue published by Mavromichalaki, Vassilaki, and Marmatsouri (1988). The power-spectrum analysis of HSSW events indicates that HSSW stream events have a periodicity of 9 days. This periodicity of HSSW events is of the 27-day period of coronal holes, which are major sources of solar wind events. In our opinion, the 9-day period may be the energy build-up time for coronal hole regions to produce the HSSW stream events.