Regularization of Motion Equations with L-Transformation and Numerical Integration of the Regular Equations

The sets of L-matrices of the second, fourth and eighth orders are constructed axiomatically. The defining relations are taken from the regularization of motion equations for Keplerian problem. In particular, the Levi-Civita matrix and KS-matrix are L-matrices of second and fourth order, respectively. A theorem on the ranks of L-transformations of different orders is proved. The notion of L-similarity transformation is introduced, certain sets of L-matrices are constructed, and their classification is given. An application of fourth order L-matrices for N-body problem regularization is given. A method of correction for regular coordinates in the Runge–Kutta–Fehlberg integration method for regular motion equations of a perturbed two-body problem is suggested. Comparison is given for the results of numerical integration in the problem of defining the orbit of a satellite, with and without the above correction method. The comparison is carried out with respect to the number of calls to the subroutine evaluating the perturbational accelerations vector. The results of integration using the correction turn out to be in a favorable position.     

Long Range Science Perspectives for the VLTI

VLTI interferometry will allow imaging of galactic and extragalactic sources with milliarcsecond angular resolution. For moderately bright sources the spectral resolution will be of the order of 10000. These capabilities will allow detailed studies of solar system objects, stars, proto-planetary systems and the detection of hot extra-solar planets. The observations of galactic nuclei will allow unprecedented measurements of physical parameters in these systems. VLTI will be a prime instrument to study the immediate environment of the massive black hole at the center of the Milky Way. With the exception of a few `self-referencing' sources the observations of extragalactic nuclei will benefit from an extended capability for simultaneous measurements of nearby reference sources for fringe tracking. With beam combination instruments like AMBER, MIDI, PRIMA, and GENIE the VLTI will reach full maturity at a time when other interferometric instruments at different wavelengths will be fully operational. Most important are ALMA (in the mm- and sub-mm-domain), LOFAR and SKA (in the radio meter to centimeter domain) and of course VLB-networks in the radio, and other – at that time –well developed interferometers in the optical. A major scientific potential of future scientific VLTI programs will lie in an efficient combination of these high angular resolution capabilities. This revised version was published online in July 2006 with corrections to the Cover Date.     

An Analysis of the Radio Light Variations of Blazars With Low Peak Frequencies

The data of light variations of six blazars with low peak frequencies (i.e., BL Lacerta, 0235+164, OQ530, 0716+714, 3C 345, and 3C 273) at 4.8, 8, 14.5, 22 and 37 GHz in the recent thirty years have been collected from immense amount of literature. By using the method of discrete correlation function the correlations and delays of the light curves of these six sources at the 5 wavebands are analyzed. With the method of structural function, the periods and timescales of the light variations of these six sources are analyzed, and their amplitudes of light variations are compared and analyzed. As revealed by the result of analysis, among the six blazars the amplitudes of light variations of 0716+714 and 0235+164 are relatively large, and those of 3C 345 and OQ 530 are less. The amplitudes of light variations of 3C 273 and BL Lacertae are relatively smaller. As shown by the multi-waveband analysis of delays between two neighboring wavebands, 0235+164 exhibits the tendency of variation that the high-frequency wavebands precede the low-frequency wavebands. On the whole, 3C 345 exhibits the tendency that the high-frequency wavebands lag be-hind the low-frequency wavebands. The analyses of the other blazars show that in a part of radio wavebands there appears the tendency of variation that the high-frequency waveband leads the low-frequency waveband. Yet in the other radio wavebands there appears the tendency that the high-frequency waveband lags behind the low-frequency waveband. As revealed by the results of analyses with the method of structural function, the timescale, fitted slope, and period of light variations of 3C 345 are larger than those of the other five blazars with low peak frequencies. This demonstrates that the activity of 3C 345 is comparatively weaker than the other five sources, and implies that in the interior of 3C 345 there may exist some physical processes which are different from those of the other five blazars with low peak frequencies.     

Analysis of historical meteor and meteor shower records: Korea, China, and Japan

We have compiled and analyzed historical Korean meteor and meteor shower records in three Korean official history books, Samguksagi which covers the three Kingdoms period (57 B.C.-A.D. 935), Goryeosa of Goryeo dynasty (A.D. 918-1392), and Joseonwangjosillok of Joseon dynasty (A.D. 1392-1910). We have found 3861 meteor and 31 meteor shower records. We have confirmed the peaks of Perseids and an excess due to the mixture of Orionids, north-Taurids, or Leonids through the Monte Carlo test. The peaks persist from the period of Goryeo dynasty to that of Joseon dynasty, for almost one thousand years. Korean records show a decrease of Perseids activity and an increase of Orionids/north-Taurids/Leonids activity. We have also analyzed seasonal variation of sporadic meteors from Korean records. We confirm the seasonal variation of sporadic meteors from the records of Joseon dynasty with the maximum number of events being roughly 1.7 times the minimum. The Korean records are compared with Chinese and Japanese records for the same periods. Major features in Chinese meteor shower records are quite consistent with those of Korean records, particularly for the last millennium. Japanese records also show Perseids feature and Orionids/north-Taurids/Leonids feature, although they are less prominent compared to those of Korean or Chinese records.     

Analyses of the Light Variations of OJ 287, 0716+714 and BL Lacertae

OJ 287 is a BL Lac object which exhibits intense activities of low peak-frequencies. Its energy spectrum in low frequency band is quite similar with those of two other TeV BL Lac objects (i.e., 0716+714 and BL Lacertae). However, the Cerenkov telescope did not detect its TeV rays. By using the observational data of these three heavenly bodies and comparing the discrepan- cies of their minimal periods of light variations and delays at 22 GHz, 37 GHz and B-waveband, we have further investigated the possible reason why the TeV gamma-rays of OJ 287 have not been observed. The results of analyses are as fol- lows. (1) For the minimal periods of light variations, the periods of OJ 287 at 37 GHZ and B-waveband are short. At 22 GHz the results of OJ 287 and 0716+714 are comparable, but the period of OJ 287 is much shorter in comparison with that of BL Lacertae, and this shows that its activity is more intense. However, the TeV gamma-rays of OJ 287 have not been detected, which implies that the radiation of OJ 287 in TeV waveband may have no connection with the minimal periods of light variations in these three low-energy wavebands. (2) In respect of delays, the delay of OJ 287 in the B waveband with respect to 37 GHz is longer than that of 0716+714, but shorter than that of BL Lacertae. Its delay at 37 GHz in respect to 22 GHz is shorter than that of 0716+714. Meanwhile, the delay of BL Lacertae at 37 GHz in respect to 22 GHz is negative, which implies that 22 GHz precedes 37 GHz. Via the comparison and analysis of delays, no obvious differences between OJ 287 and 0716+714 as well as BL Lacertae have been found. On the side of energy spectra, it is quite possible that due to the steep energy spectrum of OJ 287 in TeV waveband, the Cerenkov telescope has not detected the gamma radiation of OJ 287. However, nowadays it is still not clear whether the steep energy spectrum in TeV energy range has some influence on the light variations in low energy realm.     

Dynamics of Enceladus and Dione inside the 2:1 mean-motion resonance under tidal dissipation

In a previous work (Callegari and Yokoyama, Celest. Mech. Dyn. Astr. 98:5–30, 2007), the main features of the motion of the pair Enceladus–Dione were analyzed in the frozen regime, i.e., without considering the tidal evolution. Here, the results of a great deal of numerical simulations of a pair of satellites similar to Enceladus and Dione crossing the 2:1 mean-motion resonance are shown. The resonance crossing is modeled with a linear tidal theory, considering a two-degrees-of-freedom model written in the framework of the general three-body planar problem. The main regimes of motion of the system during the passage through resonance are studied in detail. We discuss our results comparing them with classical scenarios of tidal evolution of the system. We show new scenarios of evolution of the Enceladus–Dione system through resonance not shown in previous approaches of the problem.     

Computing with certainty individual members of families of periodic orbits of a given period

The accurate computation of families of periodic orbits is very important in the analysis of various celestial mechanics systems. The main difficulty for the computation of a family of periodic orbits of a given period is the determination within a given region of an individual member of this family which corresponds to a periodic orbit. To compute with certainty accurate individual members of a specific family we apply an efficient method using the Poincaré map on a surface of section of the considered problem. This method converges rapidly, within relatively large regions of the initial conditions. It is also independent of the local dynamics near periodic orbits which is especially useful in the case of conservative dynamical systems that possess many periodic orbits, often of the same period, close to each other in phase space. The only computable information required by this method is the signs of various function evaluations carried out during the integration of the equations of motion. This method can be applied to any system of celestial mechanics. In this contribution we apply it to the photogravitational problem.     

Spectral Investigation of Two Asteroidal Fireballs

High resolution photographic spectra of two fireballs have been analyzed. The fireballs were produced by meteoroids of asteroidal origin of the mass of the order of 1 kg. Temperature, size, and mass of the vapor cloud around the meteoroid was derived at selected points along the trajectory. Abundances of 11 elements, including lithium, were determined. The abundances of refractory elements in the vapors of the first meteoroid indicate that only 90–95% of the ablated material was vaporized. The meteoroid was likely a chondritic body. Relative stability of the vapor cloud was disturbed for 0.1 s after a major fragmentation of the meteoroid at the height of 42 km. Size and mass of the cloud decreased after the fragmentation and this enabled more intensive heat transfer from the incoming airflow. Both the vapor temperature and the vaporization temperature of the ablated melt increased. A brief millisecond flare of the fireball was produced under these conditions by a violent vaporization of small amount of material. The composition of the vapors of the second meteoroid can be explained either by an anomalous meteoroid composition with severely depleted Al, Ca, and Mg or by highly incomplete evaporation of the ablated material reaching only about 50%.     

Copper Mosaic Crystals for Laue Lenses

Large single crystals of copper with an uniform and very narrow mosaic spread between 25 seconds and 1 minute of arc are now available at I.L.L. This result is of great interest in the construction of a Laue lens for astrophysical applications for which such quality copper single crystals may be used. The X-ray diffraction properties of copper single crystals produced at I.L.L. were studied for x-ray energies ranging from 100 keV to 400 keV. Several monocrystalline plates with different thicknesses and mosaic distributions were then prepared from the as-grown crystals in order to measure their diffraction efficiency as a function of energy. As expected, the value of the peak reflectivity depends on the crystal thickness. Reflectivity measurements show the excellent properties of copper crystals for gamma-ray diffraction. A peak reflectivity of 24% was measured at 220 keV from a copper single crystal of 3.75 mm thickness having a mosaic spread of 1.5 minutes of arc. Some technical aspects on the preparation of copper single crystal plates are also discussed.     

Fitting X-ray Afterglow Light curves of Gamma-ray Bursts by Using the Magnetar Energy Injection Model

The central compact object for some gamma-ray bursts (GRBs) may be a strongly magnetized millisecond pulsar. It can inject energy to the outer shock of the GRB by through the magnetic dipole radiation, and therefore causes the shallow decay of the early afterglow. Recently, from a large number of GRB X-ray afterglows observed by Swift/XRT(X-ray telescope), it is revealed that many of them exhibit the shallow decay about 10²∼10⁴ s after the burst prompt emission. We have fitted the X-ray afterglow light curves of 11 GRBs by using the energy injection model of a magnetar with the rotation period in the millisecond order of magnitude. The obtained result shows the validity and universality of the magnetar energy injection model in explaining the shallow decay of afterglows, and simultaneously provides some constraints on the magnetic field strength and rotation period of the central magnetar.     

活动星系和类星体中的喷流（Ⅱ）

喷流的研究是天文学和天体物理学中最使人兴趣的课题之一。在本文中，陈述了河外射电源中喷流在现阶段的观测阶段，讨论了某些典型的高能天体中喷流的特性。第一部分所涉及的内容包括喷流的定义，产生和传播；也包括喷流的不对称性和统一的解释模式的讨论。     

A Semi-analytical Model of Quasar Formation

On the basis of Kang et al.’s semi-analytical model of galaxy formation and evolution, the joint formation and evolution of galaxies and their central massive black holes are studied. It is assumed that the activity of quasars is caused by merging of galaxies. Via the introduction of the mass accretion rate of black holes, the bolometric luminosity function of quasars with the redshifts in the region of 0 < z < 4.5 is ascertained. With the respective limitations of the three factors, i.e., the Eddington ratio, black-hole mass function and two-point correlation function, the luminosity function predicted by the model may coincide with observations in the entire range of luminosity. This result reveals that the constant Eddington ratio cannot well describe the accretion of black holes, so the Eddington ratio has to be increased with the redshift in a certain range of redshift. The major merging of galaxies is the effective mechanism of triggering the quasar activity, while the minor merging can merely affect the quasars with low and intermediate luminosities. Its effect on the high-luminosity quasars is very small. At the place of z=1, the quasars with extremely high luminosities possess more intense properties of clustering than other quasars.     

Digging deep for ice in Isidis Planitia—New constraints on subsurface volatile concentrations from thermal modeling

The Isidis Planitia region on Mars usually is regarded as a comparably attractive site for landing missions based on engineering constraints such as elevation and smooth regional topography. The Mars Express landed element Beagle 2 was deployed to this area, and the southern margin of the basin was selected as one of the backup landing sites for the NASA Mars Exploration Rovers.Especially in the context of the Beagle 2 mission, Isidis Planitia has been discussed as a place which might have experienced a volatile-rich history with associated potential for biological activity [e.g. Bridges et al., 2003. Selection of the landing site in Isidis Planitia of Mars Probe Beagle 2. J. Geophys. Res. 108(E1), 5001, doi: 10.1029/2001JE001820]. However the measurements of by the GRS instrument on Mars Odyssey indicate a maximum inferred water abundance of only 3 wt% in the upper few meters of the surface [Feldman et al., 2004. Global distribution of near-surface hydrogen on Mars. J. Geophys. Res. 109, E09006, doi: 10.1029/2003JE002160]. Based on these measurements this area seems to be one of the driest spots in the equatorial region of Mars.To support future landing site selections we took a more detailed look at the minimum burial depth of stable ice deposits in this area, focusing as an example on the planned Beagle 2 landing site. We are especially interested in the likelihood of ground ice deposits within the range of proposed subsurface sampling tools as drills or ‘mole’-like devices [Richter et al., 2002. Development and testing of subsurface sampling devices for the Beagle 2 Lander. Planet. Space Sci. 50, 903-913] given reasonable physical constraints for the surface and near surface material.For a mission like ExoMars [Kminek, G., Vago, J.L., 2005. The Aurora Exploration Program—The ExoMars Mission. In: Proceedings of the 35th Lunar and Planetary Science Conference, abstract no. 1111, 15-19 March 2004, League City, TX] with a focus on finding traces of fossil life the area might be of potential interest, because these traces would be better conserved in the dry soil. Modeling and measurement indicate that Isidis Planitia is indeed a dry place and any hypothetical ground ice deposits in this region are out of range of currently proposed sampling devices.     

Fast tidal cycling and the origin of life

Replicating prebiotic polymers are thought to predate the emergence of true life-forms. The initial mode of replication, a prerequisite for Darwinian selection, is unknown, but demands an explanation based on local physicochemistry. Dual consideration of the conditions of the early terrestrial surface, with the unusual physicochemical properties of nucleic acids like DNA, could explain the emergence of nucleic acids as key biomolecules. The early impact that produced the Moon, and fast terrestrial rotation, subjected coastal areas 3.9 Ga ago to rapid tidal flooding (dilution) and drying (concentration), with a likely periodicity in the range of 2-6 h, and could have provided a driving force for cyclic replication of early biomolecules. Such a mechanism applies only to molecules capable of association/polymerization at high salt concentration, and of dissociation at low salinity. Nucleic acids meet these criteria. It is suggested that tidal cycling, resembling the polymerase chain reaction (PCR) mechanism, could only replicate and amplify DNA-like polymers. This mechanism suggests constraints on the evolution of extra-terrestrial life.     

Report of the IAU/IAG Working Group on Cartographic Coordinates and Rotational Elements: 2003

Every three years the IAU/IAG Working Group on Cartographic Coordinates and Rotational Elements revises tables giving the directions of the north poles of rotation and the prime meridians of the planets, satellites, and asteroids. This report introduces a system of cartographic coordinates for asteroids and comets. A topographic reference surface for Mars is recommended. Tables for the rotational elements of the planets and satellites and size and shape of the planets and satellites are not included, since there were no changes to the values. They are available in the previous report (Celest. Mech. Dyn. Astron., 82, 83–110, 2002), a version of which is also available on a web site.     

Active hot star shells

Interferometry in the visible provides milliarcsecond spatial resolution and thus has been used for studying the circumstellar environment of active hot stars. In this paper I will illustrate how the visibility modulus and phase can be used to better constrain the physics of Be disks through results from the VLA, the MkII and the GI2T interferometers. I will insist on the importance and the potential of coupling high angular resolution with high spectral resolution to the study of Be shells. Finally I will present a possible study of the circumstellar disk of Be stars using the VLTI. This revised version was published online in July 2006 with corrections to the Cover Date.     

活动星系和类星体中的喷流（Ⅰ）

自从人们获得河外射电源的第一个结构图像以来，３０多年时间已经过去了。在这段时间的后半期，人们对许多源中的喷流状结构作了大量研究。目前，我们正在分析所获得的有关喷流的第一代结果。这包括高分辨率观测，数值模拟和理论研究等诸方面的成就。在本文 详细地讨论河外射电源中的喷流。     

A distinct class of avalanche scars on Mars

We report observations of a set of surface features on Mars that form a distinct class of avalanche scars. These features have a horizontal scale of hundreds of meters, but a depth scale of meters distinguishes them from the shallower features known as slope streaks. The meters-thick avalanche scars have escaped previous attention because of weak contrast between the interiors of the scarred regions and their surroundings. Often the most visible feature is a shadow cast by the trough wall, a band 1-3 pixels wide in Mars Orbiter Camera narrow angle images, indicating maximum depths of 4-10 m. We investigate the morphology of more than 500 such features. Slopes upon which the avalanches occur average about 27°. Impact craters are seen at the heads of some avalanche scars; this subset exhibits statistically wider opening angles. The scars span an estimated several Ma in age. Those found so far occurred mainly in the Olympus Mons lower aureole. We compare shapes of slope streaks to shapes of meters-thick avalanches, and the results support the notion that the two classes are distinct. The newly-discovered avalanches resemble some terrestrial flows of loose, dry material such as dry snow and glass beads. On the basis of these analogs, we suggest a physical model.     

The climatic and physiographic controls of the eastern Mediterranean over the late Pleistocene climates in the southern Levant and its neighboring deserts

Modern-day synoptic-scale eastern Mediterranean climatology provides a useful context to synthesize the diverse late Pleistocene (60–12 ka) paleohydrologic and paleoenvironmental indicators of past climatic conditions in the Levant and the deserts to its south and east. We first critically evaluate, extract, and summarize paleoenvironmental and paleohydrologic records. Then, we propose a framework of eastern Mediterranean atmospheric circulation features interacting with the morphology and location of the southeast Mediterranean coast. Together they strongly control the spatial distribution of rainfall and wind pattern. This cyclone–physiography interaction enforces the observed rainfall patterns by hampering rainfall generation south and southeast of the latitude of the north Sinai coast, currently at 31°15′.The proposed framework explains the much-increased rains in Lebanon and northern Israel and Jordan as deduced from pollen, rise and maintenance of Lake Lisan, and speleothem formation in areas currently arid and semiarid. The proposed framework also accounts for the southward and eastward transition into semiarid, arid, and hyperarid deserts as expressed in thick loess accumulation at the deserts' margins, dune migration from west to east in the Sinai and the western Negev, and the formation of hyperarid (< 80 mm yr^− 1) gypsic–salic soils in the southern Negev and Sinai. Our climatic synthesis explains the hyperarid condition in the southern Negev, located only 200–250 km south of the much-increased rains in the north, probably reflecting a steeper rainfall gradient than the present-day gradient from the wetter Levant into its bordering southern and eastern deserts.At present, the rainiest winter seasons in Lebanon and northern and central Israel are associated with more frequent (+ 20%), deeper Cyprus Lows traversing the eastern Mediterranean at approximately the latitude of southern Turkey. Even these wettest years in northern Israel do not yield above average annual rainfall amounts in the hyperarid southern Negev. This region is mainly influenced by the Active Red Sea Troughs that produce only localized rains. The eastern Mediterranean Cyprus Lows also produce more dust storms and transport higher amounts of suspended dust to the loess area than any other atmospheric pattern. Concurrent rainfall and dust are essential to the late Pleistocene formation of the elongated thick loess zone along the desert northern margin. Even with existing dust storms, the lack of rain and very sparse vegetation account for the absence of late Pleistocene loess sequences from the southern Negev and the formation of hyperarid soils.When the north Sinai coast shifted 30–70 km northwest due to last glacial global sea level lowering, the newly exposed coastal areas supplied the sand and dust to these active eastern Mediterranean cyclones. This enforced the latitude of the northern boundary of the loess zone to be directly due east of the LGM shoreline. This shift of coast to the northwest inhibited rainfall in the southern Levant deserts and maintained their hyperaridity. Concurrently, frequent deep eastern Mediterranean Cyprus Lows were funneled along the northern Mediterranean increasing (probably doubling) the rains in central and northern Israel, Lebanon, southwestern Syria and northern Jordan. These storms and rains formed lakes, forests, and speleothems only a short distance north of the deserts in the southern Levant.     

Solar-cycle Time Delay of Rotating Sunspots

As shown by statistical results, in the 23rd solar activity cycle the variation of the latitudes of rotating sunspots with time exhibits a butterfly pattern. We have studied the variations with phase for the mean square errors among the 4 fitting curves of the 2 wings of the butterfly diagram of sunspots and the 2 wings of the butterfly diagram of rotating sunspots in the 23rd solar activity cycle. The results show that a systematic time delay exists not only between the northern and southern hemispheres of the butterfly diagram of sunspots, but also between the northern and southern hemispheres of the butterfly diagram of rotating sunspots, even between the butterfly diagrams of the sunspots and rotating sunspots in the same hemisphere. This means that the 23rd-cycle sunspot activities in the northern and southern hemispheres happened not simultaneously, that a systematic time delay or advance (phase difference) exists between the northern and southern hemispheres, that the southern hemisphere lags behind the northern hemisphere, that a phase difference exists between the butterfly diagram of rotating sunspots and the butterfly diagram of sunspots in the 23rd cycle, and that the butterfly diagram of rotating sunspots lags behind that of sunspots. The observed delay is a little less than the theoretical value predicted by the dynamo model.