The secular modulation of solar rotation from 1943 to 1992 and its time-delayed correlation with the 55-year grand cycle of the 11-year solar cycle

We devised a new method, which we call the running-segment method, to achieve high-resolution time series of indices of solar rotation for determining the latitude dependence of the differential rotation by a least-squares fitting of the daily translation of positions of sunspot groups during a fixed time segment of 11 years. The segment is moved by an amount of one year to determine the differential profile of the next point of time. Time of the determined rotation data is defined by an arithmetic mean of the beginning and ending years of the segment. The rotation underwent an acceleration from 1948 to 1974 and a deceleration from 1974 to 1987. We found that the time profile of the indexM, the angular momentum surface layer density defined by integration of the angular momentum volume density over the whole surface, follows almost exactly the time profile of the 11-year running mean of the yearly mean of the sunspot relative number with a delay time of about 20 years. The acceleration (deceleration) phase corresponds to the ascending (descending) phase of amplitude of the 11-year solar cycle of cycle 16 (19) to cycle 19 (20) with a delay time of about 20 years. The cycles 15–20 correspond to the 55-year grand cycle V of the 11-year cycle. The delay time of about 20 years agrees well with the delay time predicted by a nonlinear dynamo theory of the solar cycle for driving the 55-year modulation of the 11-year solar cycle. The agreement suggests that the Lorentz force of the magnetic field of the solar cycle during grand cycle V drives the solar rotation modulation from 1948 to 1987 and that the force needed about 20 years to modify the rotation during 1943–1992.     

Investigation of the solar differential rotation by hydrogen filaments in 1976–1986

Based on observational data on chromosphere filaments, certain characteristics of solar differential rotation during solar activity cycle No. 21 are determined at Abastumani Astrophysical Observatory.In the northern hemisphere of the Sun, propagation of a quasi-bi-annual impulse of the rotation residual from high latitudes to the equator is found in 1979–1981. It is supposed that this phenomenon might be related to the polarity reversal in the northern hemisphere of the Sun in 1981.0.     

The solar differential rotation from the eightteenth solar cycle

The sidereal daily rotation of the Sun, (), depends on the data used. From an appropriate selection of the data — sunspots with regular motion — it is found that ()=14.31–2.70 sin² , where denotes the heliographic latitude. Moreover, it seems that there is a variation, of the order of 3%, with the solar activity.     

Secular acceleration of Phobos and Q of Mars

Reductions of Mariner 9 TV data of Phobos and Deimos tend to corroborate the existence of a secular acceleration of Phobos commensurate with two recently reported values based on a reprocessing of Earth-based data. These values of secular acceleration have been used together with Mariner 9 data on the physical size of Phobos and Earth-based photoelectric observations which infer a carbonaceous composition for Phobos to place bounds of 50 < Q < 150 on the tidal dissipation function of Mars. The corresponding bounds on the tidal lag angle are 0.19° < Φ < 0.57°.     

Deceleration of the Earth's rotation from old solar tables

The solar tables of ibn Yunis and of King Alfonso, those of Kepler, of G. D. and J.-J. Cassini, and of Lalande are compared with Newcomb's theory of the Sun to determine the deceleration of the Earth's rotation. Comparisons of mean motion and of longitude lead to separate determinations. A value for the deceleration, , assumed to be independent of time is obtained for the period — 146 through 1892. This result is based on the assumption that Newcomb's theory converts the Earth's orbital motion into a perfect clock, and the result is independent of lunar and tidal theory. The deceleration seems greater than that obtained from the literature for the tidal deceleration caused by the Moon.     

Secular resonances in the primitive solar nebula

We present here a very simple model that could explain the relatively high eccentricities and inclinations observed in the minor planet belt. This model is based upon the sweeping of the secular resonances ₆ and ₁₆ through the belt due to the gravitational effect of the dissipation of a primitive solar nebula. The sweeping of the ₁₆ secular resonance (responsible for the high inclinations) is very sensitive to the density profile of the nebula. For the model to work we need a density profile proportional to ^–k with between 1.0 and 1.5.     

The solar radius derived from limb-darkening scans obtained in 1981 and from 1986 to 1990

Solar-radius data are presented which result from observations made in 1981 and from 1986 to 1990. These data, which are a by-product of the limb-darkening observations made by Neckel and Labs (1984, 1994), do not show significant deviations from the value which is adopted from Auwers (1891) for computations of solar eclipses and of the Sun's ephemeris in theAstronomical Almanac.     

Particle acceleration in solar flares

Particle acceleration during solar flares is a complex process where the main actors (Direct (D.C.) or turbulent electric fields) are hidden from us. It is easy to construct a successful particle accelertion model if we are allowed to impose on the flaring region arbitrary conditions (e.g., strength and scale length of the D.C. or turbulent electric fields), but then we have not solved the acceleration problem; we have simply re-defined it. We outline in this review three recent observations which indicate that the following physical processes may happen during solar flares: (1) Release of energy in a large number of microflares; (2) short time-scales; (3) small length scales; and (4) coherent radiation and acceleration sources. We propose that these new findings force us to reformulate the acceleration process inside a flaring active region assuming that a large number of reconnection sites will burst almost simultaneously. All the well-known acceleration mechanisms (electric fields, turbulent fields, shock waves, etc.) reviewed briefly here, can be used in a statistical model where each particle is gaining energy through its interaction with many small reconnection sites.     

Electron acceleration in solar flares

We present observations of an intense solar flare hard X-ray burst on 1980 June 27, made with a balloon-borne array of liquid nitrogen-cooled germanium detectors which provided unprecedented spectral resolution (1 keV FWHM). The hard X-ray spectra throughout the impulsive phase burst fitted well to a double power-law form, and emission from an isothermal 10⁸–10⁹K plasma can be specifically excluded. The temporal variations of the spectrum indicate that the hard X-ray burst is made up of two superposed components: individual spikes lasting 3–15 s, whch have a hard spectrum and a break energy of 30–65 keV; and a slowly varying component characterized by a soft spectrum with a constant low-energy slope and a break energy which increases from 25 keV to 100 keV through the event. The double power-law shape indicates that acceleration by DC electric fields parallel to the magnetic field, similar to that occurring in the Earth's auroral zone, may be the source of the energetic electrons which produce the hard X-ray emission. The total potential drop required for flares is typically 10² kV compared to 10 kV for auroral substorms.     

Electron acceleration in solar flares

We present observations of an intense solar flare hard X-ray burst on 1980 June 27, made with a balloon-borne array of liquid nitrogen-cooled germanium detectors which provided unprecedented spectral resolution (≲1 keV FWHM). The hard X-ray spectra throughout the impulsive phase burst fitted well to a double power-law form, and emission from an isothermal 10⁸–10⁹K plasma can be specifically excluded. The temporal variations of the spectrum indicate that the hard X-ray burst is made up of two superposed components: individual spikes lasting ∼3–15 s, whch have a hard spectrum and a break energy of 30–65 keV; and a slowly varying component characterized by a soft spectrum with a constant low-energy slope and a break energy which increases from 25 keV to ≳100 keV through the event. The double power-law shape indicates that acceleration by DC electric fields parallel to the magnetic field, similar to that occurring in the Earth's auroral zone, may be the source of the energetic electrons which produce the hard X-ray emission. The total potential drop required for flares is typically ∼10² kV compared to ∼10 kV for auroral substorms.

     

Electron acceleration in solar flares

For the period September 1978 to December 1982 we have identified 55 solar flare particle events for which our instruments on board the ISEE-3 (ICE) spacecraft detected electrons above 10 MeV. Combining our data with those from the ULEWAT spectrometer (MPI Garching and University of Maryland) electron spectra in the range from 0.1 to 100 MeV were obtained. The observed spectral shapes can be divided into two classes. The spectra of the one class can be fit by a single power law in rigidity over the entire observed range. The spectra of the other class deviate from a power law, instead exhibiting a steepening at low rigidities and a flattening at high rigidities. Events with power-law spectra are associated with impulsive (&#x003C;1 hr duration) soft X-ray emission, whereas events with hardening spectra are associated with long-duration (&#x003c;1 hr) soft X-ray emission. The characteristics of long-duration events are consistent with diffusive shock acceleration taking place high in the corona. Electron spectra of short-duration flares are well reproduced by the distribution functions derived from a model assuming simultaneous second-order Fermi acceleration and Coulomb losses operating in closed flare loops.     

Secular variations in the spectrum of solar p-modes

The solar p-mode spectrum of very low I is measured with high accuracy for a long enough period of time so as to allow the search for solar cycle variations. In this paper solar cycle variations of the frequency and energy of the modes are confirmed. Moreover, a slight variation,within errors, of its rotational splitting with the solar cycle, is suggested.     

The solar surface differential rotation from disk-integrated chromospheric fluxes

Disk-integrated solar chromospheric Caii K-line (3933.68 ) fluxes have been measured almost daily at Sacramento Peak Observatory since 1977. Using observing windows selected to mimic seasonal windows for chromospheric measurements of lower Main-Sequence stars such as those observed by Mount Wilson Observatory's HK Project, we have measured the solar rotation from the modulation of the Caii K-line flux. We track the change of rotation period from the decline of cycle 21 through the maximum of cycle 22. This variation in rotation period is shown to behave as expected from the migration of active regions in latitude according to Maunder's butterfly diagram, including an abrupt change in rotation period at the transition from cycle 21 to cycle 22. These results indicate the successful detection of solar surface differential rotation from disk-integrated observations. We argue that the success of our study compared to previous investigations of the solar surface differential rotation from disk-integrated fluxes lies primarily with the choice of the length of the time-series window. Our selection of 200 days is shorter than in previous studies whose windows are typically on the order of one year. The 200-day window is long enough to permit an accurate determination of the rotation period, yet short enough to avoid complications arising from active region evolution. Thus, measurements of the variation of rotation period in lower Main-Sequence stars, especially those that appear to be correlated with long-term changes in chromospheric activity (i.e., cycles), are probably evidence for stellar surface differential rotation.     

Shock acceleration of solar cosmic rays

The solar cosmic ray (SCR) acceleration by the shocks driven by coronal mass ejections is studied by taking into account the generation of Alfvén waves by accelerated particles. Detailed numerical calculations of the SCR spectra produced during the shock propagation through the solar corona have been performed within a quasi-linear approach with a realistic set of coronal parameters. The resultant SCR energy spectrum is shown to include a power-law part N ∝ ?^-γ with an index γ = 1.7–3.5 that ends with an exponential tail. The maximum SCR energy lies within the range ? _max = 0.01–10 GeV, depending on the shock velocity V _S = 750–2500 km s^?1. The decrease of the shock Alfvénic Mach number due to the increase Alfvén velocity with heliocentric distance r leads to the end of the efficient SCR acceleration when the shock size reaches R _S ≈ 4R _⊙. In this case, the diffusive SCR propagation begins to exceed the shock velocity; as a result, SCRs escape intensively from the shock vicinity. The self-consistent generation of Alfvén waves by accelerated particles is accompanied by a steepening of the particle spectrum and an increase of their maximum energy. Comparison of the calculated SCR fluxes expected near the Earth’s orbit with the available experimental data shows that the theory explains the main observed features.     

Shock acceleration of solar cosmic rays

We investigated the acceleration of solar cosmic rays (SCRs) by the shock waves produced by coronal mass ejections. We performed detailed numerical calculations of the SCR spectra produced during the shock propagation in the solar corona in terms of a model based on the diffusive transport equation using a realistic set of physical parameters for the corona. The resulting SCR energy spectrum N(ε) ∝ ε^?γ exp [? (ε/ε_max)^α] is shown to include a power-law portion with an index γ?2 that ends with an exponential tail with α ? 2.5 ? β, where β is the spectral index of the background Alfvén turbulence. The maximum SCR energy lies within the range ε_max = 1–300 MeV, depending on the shock velocity. Because of the steep spectrum of the SCRs, their backreaction on the shock structure is negligible. The decrease in the Alfvén Mach number of the shock due to the increase in the Alfvén velocity with heliocentric distance r causes the efficient SCR acceleration to terminate when the shock reaches a distance of r = 2–3R_⊙. Since the diffusive SCR propagation in this case is faster than the shock expansion, SCR particles intensively escape from the shock vicinity. A comparison of the calculated SCR fluxes expected near the Earth’s orbit with available experimental data indicates that the theory satisfactorily explains all of the main observed features.     

Secular tidal changes in lunar orbit and Earth rotation

Small tidal forces in the Earth–Moon system cause detectable changes in the orbit. Tidal energy dissipation causes secular rates in the lunar mean motion n, semimajor axis a, and eccentricity e. Terrestrial dissipation causes most of the tidal change in n and a, but lunar dissipation decreases eccentricity rate. Terrestrial tidal dissipation also slows the rotation of the Earth and increases obliquity. A tidal acceleration model is used for integration of the lunar orbit. Analysis of lunar laser ranging (LLR) data provides two or three terrestrial and two lunar dissipation parameters. Additional parameters come from geophysical knowledge of terrestrial tides. When those parameters are converted to secular rates for orbit elements, one obtains dn/dt = \(-25.97\pm 0.05 ''/\)cent\(^{2}\), da/dt = 38.30 ± 0.08 mm/year, and di/dt = ?0.5 ± 0.1 \(\upmu \)as/year. Solving for two terrestrial time delays and an extra de/dt from unspecified causes gives \(\sim \) \(3\times 10^{-12}\)/year for the latter; solving for three LLR tidal time delays without the extra de/dt gives a larger phase lag of the N2 tide so that total de/dt = \((1.50 \pm 0.10)\times 10^{-11}\)/year. For total dn/dt, there is \(\le \)1 % difference between geophysical models of average tidal dissipation in oceans and solid Earth and LLR results, and most of that difference comes from diurnal tides. The geophysical model predicts that tidal deceleration of Earth rotation is \(-1316 ''\)/cent\(^{2}\) or 87.5 s/cent\(^{2}\) for UT1-AT, a 2.395 ms/cent increase in the length of day, and an obliquity rate of 9 \(\upmu \)as/year. For evolution during past times of slow recession, the eccentricity rate can be negative.     

Spectroscopic determinations of solar rotation

Spectral line shift data obtained from full-disk magnetograms recorded at Mt. Wilson are analyzed for differential rotation. The method of analysis is discussed and the results from the data for 1966 through 1968 are presented. The average equatorial velocity over this period is found to be 1.93 km/sec or 13.76 deg/day (sidereal). This corresponds to a sidereal period of 26.16 days. The average results are = 2.78 × 10^-6 - 3.51 × 10^-7 sin² B - 4.43 × 10^-7 sin⁴ B rad/sec, whereB is the solar latitude. This indicates a smaller decrease of angular velocity with latitude than found by earlier investigators. Variations from day to day are caused by large-scale short-lived velocity fields on the solar surface. There also appear to be secular variations.Currently at the Kitt Peak National Observatory, Tucson, Arizona.     

Differential rotation of solar filaments

The latitudinal component of solar differential rotation and the possibility of a radial component are discussed and compared to the observed rotational velocities of solar filaments. Our values of rotational rate versus heliographic latitude for 100 points in the solar atmosphere derived from 17 quiescent filaments are comparable to the rates found by d'Azambuja and d'Azambuja (1948). The filament rate is significantly greater than the spot rate (Newton and Nunn, 1951); the difference cannot be accounted for by the poleward migration of filaments and seems to reflect a true radial gradient of rotational velocity in the Sun. We show that filaments in closer proximity to active regions usually exhibit no differential rotation, while those far from active regions generally show it clearly. Comparison with Mt. Wilson photospheric Doppler measurements shows that filaments rotate faster than the general photosphere and that, as is well known, the spot rate exceeds that for the general photosphere.     

Non-rigid rotation of solar spicules

Hα profiles of chromospheric spicules computed for a variety of rotational behavior are compared with an observed profile, which was derived by averaging 11 Hα profiles taken near times of maximum spicule intensity. If turbulent velocity is small or equals zero, calculated profiles are in good agreement with the observed one under the conditions that rotation is non-rigid (faster rotation further away from the axis of the spicule) and the source function decreases in the direction from the spicule axis to the periphery. The comparison of calculated and observed tilts of spicule spectra relative to the direction of dispersion seems to corraborate the non-rigid character of spicular rotation.