A numerical study of local stellar motions

The orbits of over 10000 stars are integrated in a steady-state model of the Galaxy for a time 6.0×10⁸ yr. Initially, the stars are placed randomly inside spheres of 500 pc and 50 pc radius and are given random velocities, such that the sample has a Maxwellian or a spheroidal velocity distribution. The spheres are placed at the Sun's distance from the galactic centre (10 kpc) and are given a circular velocity of 250 km s^?1. The mean velocities and dispersions of stars within 1 kpc of an ‘observer’ moving at the circular velocity are calculated as functions of time. The quantities show a strong time-dependence with oscillations of period 10⁸ yr. The oscillations are independent of the mass model and occur also in an inverse square force field. A vertex deviation of the velocity ellipsoid, an asymmetric drift and aK-effect occur as natural consequences of the oscillations. Attempts to apply the Oort method for density determinations in the galactic plane are also influenced by the oscillations. Spiral density waves appear to have a small effect on the motions of the test stars.     

Kinematics of Gould's Belt: Model and Observations

Using the available data for nearby stars we derive the velocity ellipsoid of dwarf O-B5.5 stars belonging to the Gould Belt (GB). The resulting vertex deviation for the whole sample is negative (l _v ≈ −70^°) and this value is modified to l _v≈ 20^° when the members of the Pleiades moving group are removed from the sample. This implies the existence of, at least, two different kinematic groups defining the GB system. We also model the evolution of a supershell in the solar neighborhood, and obtain a fit to the shape and kinematics of the gas in GB. Assuming that the expanding shell is also forming stars, we obtain the corresponding velocity fields for the shell and its newly formed stars. The average vertex deviation value resulting from these models for the new stars is l _v≈ 20^°, and is consistent with the observed value when the Pleiades moving group members are excluded from the GB. This revised version was published online in July 2006 with corrections to the Cover Date.     

Galactic kinematics from a sample of young massive stars

Based on published sources, we have created a kinematic database on 220 massive (> 10 M _⊙) young Galactic star systems located within ≤3 kpc of the Sun. Out of them, ≈100 objects are spectroscopic binary and multiple star systems whose components are massive OB stars; the remaining objects are massive Hipparcos B stars with parallax errors of no more than 10%. Based on the entire sample, we have constructed the Galactic rotation curve, determined the circular rotation velocity of the solar neighborhood around the Galactic center at R ₀ = 8kpc, V ₀ = 259±16 km s^?1, and obtained the following spiral density wave parameters: the amplitudes of the radial and azimuthal velocity perturbations f _R = ?10.8 ± 1.2 km s^?1 and f _θ = 7.9 ± 1.3 km s^?1, respectively; the pitch angle for a two-armed spiral pattern i = ?6.0° ± 0.4°, with the wavelength of the spiral density wave near the Sun being λ = 2.6 ± 0.2 kpc; and the radial phase of the Sun in χ _⊙ = ?120° ± 4°. We show that such peculiarities of the Gould Belt as the local expansion of the system, the velocity ellipsoid vertex deviation, and the significant additional rotation can be explained in terms of the density wave theory. All these effects decrease noticeably once the influence of the spiral density wave on the velocities of nearby stars has been taken into account. The influence of Gould Belt stars on the Galactic parameter estimates has also been revealed. Eliminating them from the kinematic equations has led to the following new values of the spiral density wave parameters: f _θ = 2.9 ± 2.1 km s^?1 and χ _⊙ = ?104° ± 6°.     

Tidal flows in binary systems

The expressions of the tidal velocity in not very close binaries (double stars, the Sun and a planet, a planet and a satellite) are derived and applied in particular to white dwarfs and the giant planets of the solar system. The magnitude of the velocity on the surface of Jupiter is estimated to be about 0.5 cm s^?1. In white dwarfs the velocities of the order of tens m s^?1 may be encountered, and they can influence their evolution. The symmetry of the tidal flows is noted to be suitable for the magnetic field generation.     

Distribution of gravitational potential energy within the solar system

The orbital gravitational potential energies of the planets and of the satellites have been estimated and compared to the gravitational potential energies of the bodies themselves and to the gravitational potential energy of the Sun. From the point of view of the gravitational potential energy distribution two quite different groups of the planets can be distinguished clearly. However, the gravitational potential energy of the systems is mainly concentrated within the central bodies, only about 10^–5 in orbiting bodies.     

Testing the Distance Scale of the Gaia TGAS Catalogue by the Kinematic Method

We have studied the simultaneous and separate solutions of the basic kinematic equations obtained using the stellar velocities calculated on the basis of data from the Gaia TGAS and RAVE5 catalogues. By comparing the values of Ω'₀ found by separately analyzing only the line-of-sight velocities of stars and only their proper motions, we have determined the distance scale correction factor p to be close to unity, 0.97 ± 0.04. Based on the proper motions of stars from the Gaia TGAS catalogue with relative trigonometric parallax errors less than 10% (they are at a mean distance of 226 pc), we have found the components of the group velocity vector for the sample stars relative to the Sun (U, V,W)_⊙ = (9.28, 20.35, 7.36) ± (0.05, 0.07, 0.05) km s^?1, the angular velocity of Galactic rotation Ω⁰ = 27.24 ± 0.30 km s?1 kpc?1, and its first derivative Ω'₀ = ?3.77 ± 0.06 km s^?1 kpc^?2; here, the circular rotation velocity of the Sun around the Galactic center is V₀ = 218 ± 6 km s^?1 kpc (for the adopted distance R₀ = 8.0 ± 0.2 kpc), while the Oort constants are A = 15.07 ± 0.25 km s^?1 kpc^?1 and B = ?12.17 ± 0.39 km s^?1 kpc^?1, p = 0.98 ± 0.08. The kinematics of Gaia TGAS stars with parallax errors more than 10% has been studied by invoking the distances from a paper by Astraatmadja and Bailer-Jones that were corrected for the Lutz–Kelker bias. We show that the second derivative of the angular velocity of Galactic rotation Ω'₀ = 0.864 ± 0.021 km s^?1 kpc^?3 is well determined from stars at a mean distance of 537 pc. On the whole, we have found that the distances of stars from the Gaia TGAS catalogue calculated using their trigonometric parallaxes do not require any additional correction factor.     

Rotation, planets, and the 'second parameter' of the horizontal branch

We analyse the angular momentum evolution from the red giant branch (RGB) to the horizontal branch (HB) and along the HB. Using rotation velocities for stars in the globular cluster M13, we find that the required angular momentum for the fast rotators is up to 1–3 orders of magnitude (depending on some assumptions) larger than that of the Sun. Planets of masses up to 5 times Jupiter's mass and up to an initial orbital separation of ~2 au are sufficient to spin-up the RGB progenitors of most of these fast rotators. Other stars have been spun-up by brown dwarfs or low-mass main-sequence stars. Our results show that the fast rotating HB stars have been probably spun-up by planets, brown dwarfs or low-mass main-sequence stars while they evolved on the RGB. We argue that the angular momentum considerations presented in this paper further support the 'planet second parameter' model. In this model, the 'second parameter' process, which determines the distribution of stars on the HB, is interaction with low-mass companions, in most cases with gas-giant planets, and in a minority of cases with brown dwarfs or low-mass main-sequence stars. The masses and initial orbital separations of the planets (or brown dwarfs or low-mass main-sequence stars) form a rich spectrum of different physical parameters, which manifests itself in the rich varieties of HB morphologies observed in the different globular clusters.     

Stars resembling the Sun

Summary. This review is primarily directed to the question whether photometric solar analogues remain such when subjected to detailed spectroscopic analyses and interpreted with the help of internal stucture models. In other words, whether the physical parameters: mass, chemical composition, age (determining effective temperature and luminosity), chromospheric activity, equatorial rotation, lithium abundance, velocity fields etc., we derive from the spectral analysis of a photometric solar analogue, are really close to those of the Sun. We start from 109 photometric solar analogues extracted from different authors. The stars selected had to satisfy three conditions: i) their colour index must be contained in the interval: –0.69, ii) they must possess a trigonometric parallax, iii) they must have undergone a high resolution detailed spectroscopic analysis. First, this review presents photometric and spectrophotometric researches on solar analogues and recalls the pionneering work on these stars by the late Johannes Hardorp. After a brief discussion on low and high resolution spectroscopic researches, a comparison is made between effective temperatures as obtained, directly, from detailed spectral analyses and those obtained, indirectly, from different photometric relations. An interesting point in this review is the discussion on the tantalilizing value of the of the Sun, and the presentation of a new reliable value of this index. A short restatement of the kinematic properties of the sample of solar analogues is also made. And, finally, the observational diagram, obtained with 99 of the initially presented 109 analogues, is compared to a theoretical diagram. This latter has been constructed with a grid of internal structure models for which, (very important for this investigation), the Sun was used as gauge. In analysing the position, with respect to the Sun, of each star we hoped to find a certain number of stars tightly neighbouring the Sun in mass, chemical composition and state of evolution. The surprising result is that the stars occupy in this HR Diagram a rather extended region around the Sun, many of them seem more evolved and older than the Sun, and only 4 of the evolved stars seem younger. The age of some stars in the sample is also discussed in terms of chromospheric activity and Li-content. Our conclusion is much the same as that contained in previous papers we have written on the subject: in spite of a much larger number of stars, we have not been able to nominate a single star of the sample for a “perfect good solar twin”. Another aim in beginning, 25 years ago, this search for solar analogues, was to have ready a bunch of stars resembling the Sun and analysed spectroscopically in detail, in order that, when planets hunters of solar type stars, finally would have found such a specimen, we would have been able to immediately compare the physical parameters of this star to those of the Sun. We have been lucky enough: one of the good solar analogues we present herewith, is 51 Pegasi (HD 217014) which, according to the very recent observations by Mayor and Queloz (1995), has a planet orbiting around it. And what is more: two other stars possessing planets: 47 Ursae Majoris (HD 95128) and 70 Virginis (HD 117176), have just been discovered by Marcy and Butler (187 Meeting of the AAS, January 1996). One of them, 47 Ursae Majoris, is also included in the list of photometric solar analogues. The other star, 70 Virginis, has only been included after the “Planets News”, because the colour index of this star is slightly higher than the prescribted limit of the selection, (, instead, 0.69). It would have been a pity to leave the third ” planet star out of the competition.     

Distribution of Matter in the Solar System

A new formula for the distribution of matter in the solar system is derived by assuming that the planets were formed from trapped particles of a cosmic dust disk attached to the Sun. Contrary to Boltzmann's distribution which predicts thermal collapse of this cloud on the Sun, it is found that if the primeval particles move on circular orbits according to Kepler's law, then their velocities obey a 2-D global Maxwellian and their distribution in space is given by p ₀ (r)=(α r ²)\exp(-α r) (Km^-1); α = 888.73 × 10⁶ Km. The form ofp ₀ (r) agrees with the observed mass distribution of the planets and explains their present large angular momentum. PACS numbers: 96.35.Cp, 96.35.Fs This revised version was published online in July 2006 with corrections to the Cover Date.     

Three-dimensional reddening map for stars from 2MASS photometry: The method and the first results

The first results of the construction of a three-dimensional reddening map for stars within 1600 pc of the Sun are presented. Analysis of the distribution of 70 million stars from the 2MASS catalog with the most accurate photometry on the (J-Ks)-Ks diagram supplemented with Monte Carlo simulations has shown that one of the maxima of this distribution corresponds to F-type dwarfs and subgiants with a mean absolute magnitude M _Ks = 2_⊙ ^m 5. The shift of this maximum toward large J-Ks with increasing Ks reflects the reddening of these stars with increasing heliocentric distance. The distribution of the sample of stars over Ks, l, and b cells with a statistically significant number of stars in each cell corresponds to their distribution over three-dimensional spatial cells. As a result, the reddening E(J-Ks) has been determined with an accuracy of 0_· ^m 03 for spatial cells with a side of 100 pc. All of the known large absorbing clouds within 1600 pc of the Sun have manifested themselves in the results obtained. The distances to the near and far edges of the clouds have been determined with a relative accuracy of 15%. The cases where unknown clouds are hidden behind known ones on the same line of sight have been found. The distance dependence of reddening is considered for various Galactic latitudes and longitudes. The absorbing matter of the Gould Belt is shown to manifest itself at latitudes up to 40° and within 600 pc of the Sun. The size and influence of the Gould Belt may have been underestimated thus far. The absorbing matter at latitudes up to 60° and within 1600 pc of the Sun has been found to be distributed predominantly in the first and second quadrants in the southern hemisphere and in the third and fourth quadrants in the northern hemisphere. The warping of the absorbing layer in the near Galaxy apparently manifests itself in this way. A nonrandom orientation of the clouds relative to the Sun is possible. The mass of the baryonic dark matter in solar neighborhoods can then be considerably larger than is generally believed.     

Kinematics of Tycho-2 red giant clump stars

Based on the Ogorodnikov-Milne model, we analyze the proper motions of 95 633 red giant clump (RGC) stars from the Tycho-2 Catalogue. The following Oort constants have been found: A = 15.9 ± 0.2 km s^?1 kpc^?1 and B = ?12.0±0.2 km s^?1 kpc^?1. Using 3632 RGC stars with known proper motions, radial velocities, and photometric distances, we show that, apart from the star centroid velocity components relative to the Sun, only the model parameters that describe the stellar motions in the XY plane differ significantly from zero. We have studied the contraction (a negative K effect) of the system of RGC stars as a function of their heliocentric distance and elevation above the Galactic plane. For a sample of distant (500–1000 pc) RGC stars located near the Galactic plane (|z| < 200 pc) with an average distance of d = 0.7 kpc, the contraction velocity is shown to be Kd = ?3.5 ±0.9 km s^?1; a noticeable vertex deviation, l _xy = 9 _· ^o 1 ± 0 _· ^o 5, is also observed for them. For stars located well above the Galactic plane (|z| ≥200 pc), these effects are less pronounced, Kd = ?1.7 ± 0.5 km s^?1 and l _xy = 4 _· ^o 9 ± 0 _· ^o 6. Using RGC stars, we have found a rotation around the Galactic X axis directed toward the Galactic center with an angular velocity of ?2.5 ± 0.3 km s^?1 kpc^?1, which we associate with the warp of the Galactic stellar-gaseous disk.     

Pulkovo Compilation of Radial Velocities for 35 495 Hipparcos stars in a common system

The Pulkovo Compilation of Radial Velocities (PCRV) has been made to study the stellar kinematics in the local spiral arm. The PCRV contains weighted mean absolute radial velocities for 35 495 Hipparcos stars of various spectral types and luminosity classes over the entire celestial sphere mainly within 500 pc of the Sun. The median accuracy of the radial velocities obtained is 0.7 km s^?1. Results from 203 publications were used in the catalogue. Four of them were used to improve the radial velocities of standard stars from the IAU list. The radial velocities of 155 standard stars turned out to be constant within 0.3 km s^?1. These stars were used to analyze 47 768 mean radial velocities for 37 200 stars from 12 major publications (～80% of all the data used). Zero-point discrepancies and systematic dependences on radial velocity, B-V color index, right ascension, and declination were found in radial velocity differences of the form “publication minus IAU list of standards.” These discrepancies and dependences were approximated and taken into account when calculating the weighted mean radial velocities. 1128 stars whose independent radial-velocity determinations were available at least in three of these publications and agreed within 3 km s^?1 were chosen as the work list of secondary standards. Radial-velocity differences of the form “publication minus list of secondary standards” were used by analogy to correct the zero points and systematic dependences in the radial velocities from 33 more publications (～ 13% of the data used). In addition, the radial velocities from 154 minor publications (～7% of the data used) pertaining to well-known instruments were used without any corrections.     

The evolution of the z distribution of normal neutron stars in the Galaxy

Under the two initial 1‐D one parameter velocity distribution forms (one is normal, the other is exponential), the z direction scale height evolution of normal neutron stars in the Galaxy is studied by numerical simulation. We do statistics for the cases at different time segments, also do statistics for the cumulative cases made of each time segment. The results show in the cumulative cases the evolution curves of the scale heights are smoother than in the each time segment, i.e., the cumulation improve the signal‐to‐noise ratio. Certainly the evolution cases are different at different Galactic disk locations, which also have very large difference from the average cases in the whole disk. In the initial stages of z evolution of normal neutron stars, after the beginning transient states, the cumulative scale heights increase linearly with time, and the cumulative scale height increasing rates have linear relationship with the initial velocity distribution parameters, which have larger fluctuation in the vicinity of the Sun than in the whole disk. We utilize the linear relationship of the cumulative scale height increasing rates vs. the initial velocity distribution parameters in the vicinity of the Sun to make comparison with the observation near the Sun. The results show if there is no magnetic decay, then the deserved initial velocity parameters are obvious lower than the present well known results from some authors; whereas if introducing magnetic decay, for the 1‐D normal case we can make consistence among concerning results using magnetic decay time values which are supported by some authors, while for the 1‐D exponential case the results show the lackness of young pulsar samples in the larger z in the vicinity of the Sun (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A New Way that Planets Can Affect the Sun

We derive a perturbation inside a rotating star that occurs when the star is accelerated by orbiting bodies. If a fluid element has rotational and orbital components of angular momentum with respect to the inertially fixed point of a planetary system that are of opposite sign, then the element may have potential energy that could be released by a suitable flow. We demonstrate the energy with a very simple model in which two fluid elements of equal mass exchange positions, calling to mind a turbulent field or natural convection. The exchange releases potential energy that, with a minor exception, is available only in the hemisphere facing the barycenter of the planetary system. We calculate its strength and spatial distribution for the strongest case (“vertical”) and for weaker horizontal cases whose motions are all perpendicular to gravity. The vertical cases can raise the kinetic energy of a few well positioned convecting elements in the Sun’s envelope by a factor ≤7. This is the first physical mechanism by which planets can have a nontrivial effect on internal solar motions. Occasional small mass exchanges near the solar center and in a recently proposed mixed shell centered at 0.16R _s would carry fresh fuel to deeper levels. This would cause stars like the Sun with appropriate planetary systems to burn somewhat more brightly and have shorter lifetimes than identical stars without planets. The helioseismic sound speed and the long record of sunspot activity offer several bits of evidence that the effect may have been active in the Sun’s core, its envelope, and in some vertically stable layers. Additional proof will require direct evidence from helioseismology or from transient waves on the solar surface.     

Evidence for cyclotron maser emission from the Sun and stars

In recent years radiation has been observed from planets, Sun and stars that is best explained by the cyclotron maser instability; in fact, all celestial bodies that might feasibly emit and be detected by their cyclotron maser radiation have been detected. Here we review those observations, the developments in the theory, the recent work on the effiency of energy transfer by cyclotron maser radiation, and some recent and future observations that might demonstrate whether the mechanism is energetically important in solar and stellar flares.

     

Searching for nonsolar planets

Existing instruments are unable to detect planets about stars other than the Sun but such detection would be important for the theory of origin of our solar system and in the search for extraterrestrial intelligence. Infrared offers an advantage of about 10⁵ over visible light as regards the ratio of power received from star and planet. Infrared interferometry from Earth orbit would allow discrimination against the stellar infrared by the placement of an interference null on the star and a spinning infrared interferometer would modulate the planetary emission to permit extraction by synchronous detection from the background level. The limit to sensitivity will be set by thermal emission from the zodiacal light particles near the Earth's orbit unless the interferometer is launched out of the ecliptic or out to the orbit of Jupiter, in which case instrumental limitations will dominate. Technological developments in several fields will be required as also with astrometry, spectroscopic radial velocity measurement, and direct photography from orbit, three approaches with which infrared interferometry should be carefully compared.     

Probability distribution of terrestrial planets in habitable zones around host stars

With more and more exoplanets being detected, it is paid closer attention to whether there are lives outside solar system. We try to obtain habitable zones and the probability distribution of terrestrial planets in habitable zones around host stars. Using Eggleton’s code, we calculate the evolution of stars with masses less than 4.00 M _⊙. We also use the fitting formulae of stellar luminosity and radius, the boundary flux of habitable zones, the distribution of semimajor axis and mass of planets and the initial mass function of stars. We obtain the luminosity and radius of stars with masses from 0.08 to 4.00 M _⊙, and calculate the habitable zones of host stars, affected by stellar effective temperature. We achieve the probability distribution of terrestrial planets in habitable zones around host stars. We also calculate that the number of terrestrial planets in habitable zones of host stars is 45.5 billion, and the number of terrestrial planets in habitable zones around K type stars is the most, in the Milky Way.     

太阳系外行星系统轨道参数的统计研究

自1995年第一颗类太阳恒星周围的系外行星发现以来,随着已发现的系外行星数目的增多,对系外行星性质的统计分析变得重要和有意义。截至2011年6月9日,共发现系外行星555颗。以这些系外行星的轨道参数为依据,对系外行星的性质进行统计分析,得出了一些有意义的结论。同时简要介绍现有的行星形成与演化模型并依据得出的行星统计性质对其进行检验,这对于系外行星的进一步探测具有一定的指导作用。     

Photoelectric study of the sky brightness along Sun’s meridian during the March 29, 2006 solar eclipse

Photoelectric observations of the sky brightness along Sun’s meridian have been carried out at Salloum during the March 29, 2006 total solar eclipse. The measurements have been taken at different zenith distances along the Sun’s meridian using yellow and red wide band glass filters centered at 5500 Å and 7900 Å, respectively. The present results of the sky brightness during the total solar eclipse have been compared with that of twilight, and night sky obtained by the same instrument at Abu-Simbel and Kottamia observatory sites respectively. The variation of V–R color index with zenith distance have been also studied. The visibility of planets and stars during the March 29, 2006 total solar eclipse is given.