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.     

On the origin of the Kirkwood Gaps

It is proposed that the Kirkwood Gaps are primordial, representing regions where asteroids failed to form by accretion. A brief scenario is presented to indicate the main features of a model for the early history of the asteroids. An analytical treatment is given for the effects of a solar nebula upon the eccentricity-pumping of asteroids, due to secular perturbations and to commensurability-type resonances associated with Jupiter. It is shown that nebular effects promote growth of main-belt asteroids; but in commensurability regions, growth is inhibited. A discussion is given of two related problems: the origin of asteroidal eccentricities and inclinations, and the likelihood that Jupiter suffered major changes in its semimajor axis during its formation. It is suggested that in view of these problems, the present theory should not be taken as necessarily correct, but should be regarded as illustrative of viewpoints which in time may yield a correct theory.     

On the formation of the rings of saturn

It is shown in this paper that a satellite which revolves round a primary in a circular orbit in tied revolution and which spirals within Roche's limit must form by its disintegration a ring of ellipse-like cross-section which is more than 11 times larger than the original spherical diameter of the disintegrating body. The individual particles have elliptic orbits with small eccentricities and revolve in different planes at small inclinations to each other. By inelastic collisions of particles in differently inclined orbits the original considerable thickness of the ring is very greatly reduced.

Applied to the system of Saturn it is assumed that the Rings A and B are formed by disintegration of two different satellites. It can be shown that the satellite A had an original diameter of 1721 km and a density of 0.95 g/cm³, the satellite B a diameter of 2463 km and a density of 1.95.

Thus the hypothesis of G. P. Kuiper, that the rings of Saturn are composed of H²O-snow contaminated by silicate dust (as Jupiter III), seems to fit very well.     

On the intrinsic relative accuracy of the positions in the vatican zone of the astrographic catalogue

Analytical models for the transformation of measured to standard coordinates in the Vatican Zone of the Astrographic Catalogue and the random error of star positions obtained from measurements published in that zone have been investigated. It turns out that a linear formula is the optimum, and that the mean error of a published pair of coordinates is 0″.39 in x and y.     

Distribution of Galaxies with Respect to the Directions of the Bars of SB Galaxies

The surroundings of 75 active SB galaxies are investigated. It is shown with a fairly high degree of certainty that more galaxies are observed in the direction of the bar than in other directions. It is concluded that this may be a consequence of the galaxy-forming activity of these galaxies. It is noted that the influence of the surroundings on a galaxy is traditionally discussed, although there is much evidence that the surroundings of a galaxy are shaped due to its activity.     

The use of the distribution of the orbital energy to investigate the evolution of the Perseid meteoroid stream

Numerical integration of a meteor stream over a long period is a very time consuming process, especially if a number of different models have to be investigated. In this paper we demonstrate that using the distribution of orbital energy as a vector in a Markov process can be a useful tool and that meaningful results can be obtained with far less computation than is normally required.     

On the stability of the solutions of the general problem of three bodies

The following question is investigated: By how much may the initial conditions of a given three-body system be varied before the subsequent evolution of the new system completely differs from that of the original? Stated somewhat differently, how big is the ‘island’ in the phase space of initial conditions throughout which the parameters describing the evolution of the systems are continuous functions of the initial conditions? The extent of one such island is determined numerically and found to be surprisingly large. It is conjectured, however, that this result is due to the fact that the corresponding systems have very short disintegration times, so that the total motion is not very complex.     

Computing the effects of YORP on the spin rate distribution of the NEO population

The overall change of NEO spin rate due to planetary encounters and YORP is evaluated by using a Monte Carlo model. A large sample of test objects mimicking a source population is evolved over a timescale comparable with the Solar System age until they reach a steady state spin distribution that should reproduce the current NEO distribution. The spin change due to YORP is computed for each body according to a simplified model based on Scheeres [Scheeres, D.J., 2007a. Icarus 188, 430-450].The steady state cumulative distribution of NEO spin rates obtained from our simulation nicely reproduces the observed one, once our results are biased to match the diameter distribution of the sample of objects included in the observational database. The excellent agreement strongly suggests that YORP is responsible for the concentration of spin at low rotation rates. In fact, in the absence of YORP the steady state population significantly deviates from the observed one. The spin evolution due to YORP is also so rapid for NEOs that the initial rotation rate distribution of any source population is quickly relaxed to that of the observed population. This has profound consequences for the study of NEO origin since we cannot trace the sources of NEOs from their rotation rate only.     

On the model of the accumulation of the moon compatible with the data on the composition and the age of lunar rocks

It is suggested that the overall early melting of the lunar surface is not necessary for the explanation of facts and that the structure of highlands is more complicated than a solidified anorthositic ‘plot’. The early heating of the interior of the Moon up to 1000K is really needed for the subsequent thermal history with the maximum melting 3.5 × 10⁹ yr ago, to give the observed ages for mare basalts. This may be considered as an indication that the Moon during the accumulation retained a portion of its gravitational energy converted into heat, which may occur only at rapid processes. A rapid (t < 10³ yr) accretion of the Moon from the circumterrestrial swarm of small particles would give necessary temperature, but it is not compatible with the characteristic time 10⁸ yr of the replenishment of this swarm which is the same as the time-scale of the accumulation of the Earth. It is shown that there were conditions in the circumterrestial swarm for the formation at a first stage of a few large protomoons. Their number and position is evaluated from the simple formal laws of the growth of satellites in the vicinity of a planet. Such ‘systems’ of protomoons are compared with the observed multiple systems, and the conclusion is reached that there could have been not more than 2–3 large protomoons with the Earth. The tidal evolution of protomoon orbits was short not only for the present value of the tidal phase-lag but also for a considerably smaller value. The coalescence of protomoons into a single Moon had to occur before the formation of the observed relief on the Moon. If we accept the age 3.9 × 10⁹ yr for the excavation of the Imbrium basin and ascribe the latter to the impact of an Earth satellite, this collision had to be roughly at 30R, whereR is the radius of the Earth, because the Moon at that time had to be somewhere at this distance. Therefore, the protomoons had to be orbiting inside 20–25R, and their coalescence had to occur more than 4.0x10⁹ yr ago. The energy release at coalescence is equivalent to several hundred degrees and even 1000 K. The process is very rapid (of the order of one hour). Therefore, the model is valid for the initial conditions of the Moon.     

On the origin of the lunar smooth-plains

Before the Apollo 16 mission, the material of the Cayley Formation (a lunar smooth plains) was theorized to be of volcanic origin. Because Apollo 16 did not verify such interpretations, various theories have been published that consider the material to be ejecta of distant multiringed basins. Results presented in this paper indicate that the material cannot be solely basin ejecta. If smoothplains are a result of formation of these basins or other distant large craters, then the plains materials are mainly ejecta of secondary craters of these basins or craters with only minor contributions of primary-crater or basin ejecta. This hypothesis is based on synthesis of knowledge of the mechanics of ejection of material from impact craters, photogeologic evidence, remote measurements of surface chemistry, and petrology of lunar samples. Observations, simulations, and calculations presented in this paper show that ejecta thrown beyond the continuous deposits of large lunar craters produce secondary-impact craters that excavate and deposit masses of local material equal to multiples of that of the primary crater ejecta deposited at the same place. Therefore, the main influence of a large cratering event on terrain at great distances from such a crater is one of deposition of more material by secondary craters, rather than deposition of ejecta from the large crater. Examples of numerous secondary craters observed in and around the Cayley Formation and other smooth plains are presented. Evidence is given for significant lateral transport of highland debris by ejection from secondary craters and by landslides triggered by secondary impact. Primary-crater ejecta can be a significant fraction of a deposit emplaced by an impact crater only if the primary crater is nearby. Other proposed mechanisms for emplacement of smooth-plains formations are discussed, and implications regarding the origin of material in the continuous aprons surrounding large lunar craters is considered. It is emphasized that the importance of secondary-impact cratering in the highlands has in general been underestimated and that this process must have been important in the evolution of the lunar surface.     

Constrained estimates of low-degree mode frequencies and the determination of the interior structure of the Sun

Low-degreep-modes penetrate to the solar centre and provide direct information about the core. However, the high observational accuracy that is required to resolve the details of the structure of the core is difficult to achieve because the oscillation power spectrum is significantly distorted by stochastic forcing of the oscillations, which appears as multiplicative noise. Here, an attempt is reported to reduce uncertainties of spectral parameter estimation by incorporating constraints imposed by smooth behaviour of some of the parameters (e.g., linewidths, background noise, rotational splitting) over a group of lines. Instead of estimating these parameters independently for each line, we determine them as smooth functions of frequency. It is expected that this procedure gives more accurate estimates of the average frequencies of any multiplet in the power spectrum, to which we have applied no constraints. We give some examples of the procedure for whole-disk measurements by the IPHIR space experiment. It is shown that the additional constraints do not result in significant changes in the frequency estimates, except for one mode whose peak in the power spectrum has the lowest signal-to-noise ratio. However, the uncertainty in the frequency of that mode does not influence substantially the results of the structure inversion in the core. Inversions of the IPHIR datasets are compared with corresponding inversions of data from the Birmingham Solar Oscillation Network (BISON). The IPHIR data indicate a sharp increase towards the centre of the deviation of the squared sound speed of the sun from that of a standard solar model, whereas the BISON data show a decrease. The difference between the IPHIR and BISON inversions is significant, preventing any definite conclusion about the deviation of the structure of the solar core from that of the model.     

The relationship between the strength of the IMF and the frequency of magnetic pulsations on the ground and in the solar wind

It has been established for some time that there is a correlation between the frequency of Pc 3–4 geomagnetic pulsations observed on the ground and the strength of the interplanetary magnetic field (IMF). The recent discovery of an apparently similar relationship between pulsations in the same frequency band in the solar wind and the strength of the IMF led to the suggestion that some magnetospheric Pc 3–4 pulsations have an exogenic source.In this paper we offer a statistical reappraisal of some of the earlier results, and an analysis of newly available ground and solar wind pulsation data sets, which suggest that on the basis of a frequency-field strength relationship alone, the case for an exogenic source is still unproven.We do, however, find support for the frequency-field strength relationship (for ground pulsations), which was the original basis for the Borok B index for prediction of the strength of the IMF. We also confirm that pulsation frequency is, at best, an imprecise predictor and show that any derived relationship is strongly dependent on the data sets used.     

Capture of comets during the evolution of a star cluster and the origin of the Oort Cloud

It is generally assumed that the Solar System is surrounded by a swarm of comets, the so-called Oort Cloud, which contains approximately 10¹¹ members. The observed comets belong to a small subsection of the Cloud, and they have very elongated orbits. The origin of the Cloud is presently unclear. Here we consider the possibility that the comets were born in a star cluster together with the Sun. We follow the evolution of the star cluster with its embedded swarm of comets and calculate the rate at which stars accumulate stable comet companions. We conclude that if the Oort Cloud of comets was born in this process, then the present day density of comets in interstellar space has to be high, and that comets make a significant contribution to the overall mass density of the Galaxy.     

On the early history of the asteroids

Among the major features of the asteroids as a group is the fact that they are small and numerous rather than being a single planet, and that they have unusually high eccentricities and inclinations. Regarding the first, this paper presents two lines of argument concerning the concept that the asteroids formed with a mass-distribution similar to what we observe today. Considerations of planet accretion are used to clarify the role of Jupiter in preventing coalescence of asteroids into a single planet. Regarding the eccentricities and inclinations, it is proposed that they were excited by secular resonances associated with the presence of Jupiter within a dissipating solar nebula.     

Generation of the Stressed State of the Lithosphere of the Earth and Mars Caused by the Reorientation of Their Figures

The computer simulation of the reorientation of the Earth and Mars lithosphere figure has been performed, which due to the dynamic redistribution of masses, allowed to reveal certain regularities of the structure-forming processes. It has been shown that the shape of the lithosphere surface has a different orientation relatively to the geoids’ (aroids) figure. This causes redistribution of masses leading to a strained state of the lithosphere as a result of endogenous and gravitational-rotational forces action in the evolutionary processes of planet’s self-development. The solution of this problem is considered on the example of lithosphere surface heights approximation by a biaxial ellipsoid with seven parameters. The acting horizontal forces in the upper shell of the planet has been calculated, introducing the concept of “evolutionary deviation of the plumb” and assuming that the tangential forces are proportional to the angle, which is defined as the angle between the direction of the plumb line in the past geological epoch and the plumb line direction at a given point. The calculated fields of tangential force vectors show good consistency with the direction of space-time displacement of Earth’s continents and tectonic plates and consistent with the results of the horizontal movements of GNSS stations. This is quite convincing evidence that under the long-term action of vortex rotationalgravitational forces, the lithospheres masses acquire the properties of creep. All this leads to the fact that interacting blocks and plates within the vortex rotational-gravitational model can be interconnected to elastic fields that creates a single planetary geodynamic field that forms the evolutionary state of the geo-environment.     

Solar activity and the variations of the geomagnetic Kp-index

A careful correlation analysis is made between various types of solar activity as observed at photospheric levels and the daily variations of the geomagnetic K_p-index which, in turn, is a measure of the solar wind speed. We find that in no case does a significant enough correlation exist to pin-point a physical relation between some aspect of photospheric activity and the solar wind speed. It is concluded that the physical processes that do determine the wind speed occur at coronal heights.     

On the evolution of the lunar orbit

It is generally accepted that the Earth-Moon separation is at present increasing due to tidal dissipation. Values for the corresponding lunar deceleration and the related slowing of the Earth's rotation are obtained from astronomical observations and by studies of ancient eclipses. Extrapolation of these values leads to a close approach of the Earth and Moon 1–3 b.y. BP. However, justification for such an extrapolation is required. It has been hypothesized that periodicities in the Precambrian stromatolites can be used to determine the number of solar days in a lunar month prior to 500 m.y. BP. These data combined with dynamic constraints on the number of solar days in a lunar month indicate a close approach of the Earth and Moon at 2.85 ± 0.25 b.y. BP. It is suggested that the mare volcanism on the Moon and high-temperature Archean volcanism on the Earth prior to this date were caused by tidal heating. It is also suggested that the strong tidal heating during a close approach could have contributed to the formation of the first living organisms.     

Precise Determination of the Orientation of the Solar Image

Accurate heliographic coordinates of objects on the Sun have to be known in several fields of solar physics. One of the factors that affect the accuracy of the measurements of the heliographic coordinates is the accuracy of the orientation of a solar image. In this paper the well-known drift method for determining the orientation of the solar image is applied to data taken with a solar telescope equipped with a CCD camera. The factors that influence the accuracy of the method are systematically discussed, and the necessary corrections are determined. These factors are as follows: the trajectory of the center of the solar disk on the CCD with the telescope drive turned off, the astronomical refraction, the change of the declination of the Sun, and the optical distortion of the telescope. The method can be used on any solar telescope that is equipped with a CCD camera and is capable of taking solar full-disk images. As an example to illustrate the method and its application, the orientation of solar images taken with the Gyula heliograph is determined. As a byproduct, a new method to determine the optical distortion of a solar telescope is proposed.     

On the stability of the solar wind

The stability of the solar wind is studied in the case of spherical symmetry and constant temperature. It is shown that the stability problem must be formulated as a mixed initial and boundary-value problem in which are prescribed the perturbation values of velocity and density at an initial time and additionally the velocity perturbation at the base of the corona for all times. The solution is constructed by linear superposition of normal solutions, which contain the time only in an exponential factor. The stability problem becomes a singular eigenvalue problem for the amplitudes of the velocity and pressure perturbations, since additionally to the boundary condition at the base of the corona one must add the condition that the amplitudes behave regularly at the critical point. It is proved that only stable eigenvalues exist.     

A model of the origin of the Jovian ring

Starting with the assumption that the micron-sized particles which make up the bright Jovian ring are fragments of erosive collisions between micrometeoroid projectiles and large parent bodies, a physical model of the ring is calculated. The physics of high-velocity impacts leads to a well-defined size distribution for the ejecta, the optical properties of which can be compared with observation. This gives information on the ejecta material (very likely silicates) and on the maximum size of the projectiles, which turns out to be about 0.1 μm. The origin of these projectiles is discussed, and it is concluded that dust particles ejected in volcanic activity from Io are the most likely source. The impact model leads quite naturally to a distribution in ejecta sizes, which in turn determines the structure of the ring. The largest ejecta form the bright ring, medium-sized ejecta form a disk extending all the way to the Jovian atmosphere, and the small ejecta form a faint halo, the structure of which is dominated by electromagnetic forces. In addition to the Io particles, interaction with interplanetary micrometeoroids is also considered. It is concluded that μm-sized ejecta from this source have ejection velocities which are several orders of magnitude too large, and thus cannot contribute significantly to the observed bright ring. However, the total mass ejection rate is significant. Destruction of these ejecta by the Io particles may provide additional particles for the halo.