Transits of extrasolar planets

In this paper, we consider the physical properties and characteristic features of extrasolar planets and planetary systems, those, for which the passage of low-orbit giant planets across the stellar disk (transits) are observed. The paper is mostly a review. The peculiarities of the search for transits are briefly considered. The main attention in this paper is given to the difference in the physical properties of low-orbit giant planets. A comparison of the data obtained during the transits of “hot Jupiters” points to the probable existence of several distinct subtypes of low-orbit extrasolar planets. “Hot Jupiters” of low density (HD 209458b), “hot Jupiters” with massive cores composed of heavy elements (HD 149026b), and “very hot Jupiters” (HD 189733b) are bodies that probably fall into different categories of exoplanets. Dissipation of the atmospheres of low-orbit giant planets estimated from the experimental data is compared with the calculated Jeans atmospheric losses. For “hot Jupiters”, the expected Jeans mass losses due to atmospheric escape on a cosmogonic time scale hardly exceed a few percent. Low-orbit giant planets should have a strong magnetic field. Since the orbital velocity of “hot Jupiters” is close to the magnetosonic velocity (or can even exceed it), the moving planet should actively interact with the “stellar wind” plasma. The possession of a magnetic field by extrasolar planets and the effects of their interaction with plasma can be used to search for extrasolar planets.     

Observation and Research of the Transits of Extrasolar Planets

In order to make more accurate estimates of the physical parameters of extrasolar planets, the observation and research on the phenomena of transits of the 7 known stars with the planetary systems TrES-1, TrES-3, XO-2, WASP-1, WASP-2, WASP-3 and HAT-P-7 are carried out with the 1-m reflecting telescope at Shandong University Weihai Astronomical Observatory/Weihai Municipal Astronomical Observatory. The fundamental conditions of the observation and data processing are introduced, and the transit light curves as well as the parameters of some planets derived from them are given. At the same time, when the results are summarized and analyzed, the prospects for the more in-depth and detailed researches which will be further carried out are also described.     

PLATO: PLAnetary Transits and Oscillations of stars

The PLAnetary Transits and Oscillations of stars Mission (PLATO), presented to ESA in the framework of its “Cosmic Vision” programme, will detect and characterize exoplanets by means of their transit signature in front of a very large sample of bright stars, and measure the seismic oscillations of the parent stars orbited by these planets in order to understand the properties of the exoplanetary systems. PLATO is the next-generation planet finder, building on the accomplishments of CoRoT and Kepler: i) it will observe significantly more stars, ii) its targets will be 2 to 3 magnitudes brighter (hence the precision of the measurements will be correspondingly greater as will be those of post-detection investigations, e.g. spectroscopy, asteroseismology, and eventually imaging), iii) it will be capable of observing significantly smaller exoplanets. The space-based observations will be complemented by ground- and space-based follow-up observations. These goals will be achieved by a long-term (4 years), high-precision, high-time-resolution, high-duty-cycle monitoring in visible photometry of a sample of more than 100,000 relatively bright (m _V  ≤ 12) stars and another 400,000 down to m _V  = 14. Two different mission concepts are proposed for PLATO: i) a “staring” concept with 100 small, very wide-field telescopes, assembled on a single platform and all looking at the same 26° diameter field, and ii) a “spinning” concept with three moderate-size telescopes covering more than 1400 degree². See for The PLATO Consortium.     

Neutral and ion-exospheres in the solar wind with applications to mercury

A model of planetary neutral and ion-exospheres in the solar wind is formulated for weak or lunar like solar-wind interaction with a planet. The neutral exosphere model allows for density and temperature variations and for rotation at the exobase. The ion-exosphere is produced by ionization of the neutral exosphere in the solar wind and its density distribution is obtained by solving the continuity equation in the drift approximation. Applying to Mercury a surface temperature distribution inferred from infra-red data and a vanishing bound neutral flux at the base, He and He⁺ density distributions are found. When the He atmosphere of Mercury is due entirely to the surface bombardment by solar wind He⁺⁺, the resulting He⁺ density is found to vary from 1.5 × 10⁻¹ to 10⁻³ cm⁻³ over the range 1.5–5 planetocentric radii on the dayside. These densities are found to be detectable by typical solar-wind plasma instruments. The possible effects of cyclotron-resonant scattering by interplanetary magnetic field fluctuations are examined and shown to be negligible. An electromagnetic plasma instability, triggered by the birth of ions in the exosphere, is shown to be important for the thermalization of the energy mode transverse to the interplanetary magnetic field, allowing more ions to be detected by solar-wind ion probes.     

Essential features of the 11-year solar cycle

Investigation of sunspots, coronal lines intensity, flares and other solar and geophysical data have confirmed the fact that the 11-year cycle consists of two events (maxima) having different features.During the first maximum (it coincides in time with the maximum of the Wolf numbers) the solar activity increases in all heliographic latitudes but it is maximal in latitude 25° in each hemisphere. The far UV radiation and number of small spots, flares and geomagnetic disturbances with sudden commencements and without 27-day recurrences are maximum at this time.During the second maximum, which appears 2–3 years after the first one, the activity is maximal in latitudes ± 10°. At this time the biggest spots, big flares, aurora and geomagnetic disturbances with the gradual commencements and long series of 27-day recurrences appear.The variations of averaged 5303 and 6374 Å coronal line intensities may be interpreted as an increase of coronal density and temperature during the first maximum and a sharp decrease of density and temperature rise during the second one. The temperature during the second maximum is higher than that during the first one.The distribution of activity on time-latitude diagrams (so-called butterflies) is a result of superposition of two random distributions corresponding to the two maxima mentioned above.     

Variation of sodium on mercury with solar radiation pressure

Sodium atoms in the atmosphere of Mercury can be accelarated by solar radiation pressure, and several authors have suggested that radiation pressure could sweep sodium off the planet, provided that the sodium is nonthermal, with velocities in excess of 2.1 km/sec. As a consequence, the sodium abundance might be expected to decrease as the radiation pressure increases. We have measured the average sodium abundance over a range of solar radiation pressures and found that the sodium abundance does decrease with increasing radiation pressure. However, high-resolution line profile measurements of the sodium emission show that little, if any of the sodium is nonthermal, with the bulk at a temperature approximating that of the surface. Models which assume that the bulk of the sodium is nonthermal are ruled out. Possible explanations for the observed variation are (1) that radiation pressure sweeps away transient high-velocity sodium atoms generated upon meteoric material impacts, thus reducing the supply rate of sodium, or (2) that the accommodation coefficient of sodium for surface interactions is less than unity, so that radiation pressure can effectively push sodium to the dark side of the planet, where it cannot be detected by scattered sunlight.     

Migration of small bodies in the solar system

We investigate several parts of the process of migration of small bodies to the Earth from the asteroid and transneptunian belts. The obtained characteristic times up to collisions of near-Earth objects with the Earth are less than those obtained by other scientists.     

Shape of small solar system bodies

The morphometric parameters are examined for the shape of fragments of ordinary chondrites, iron meteorites, S- and C-class stony asteroids, metallic asteroids, and icy small bodies of the Solar System. All small Solar System bodies are shown to have, depending on their composition and, hence, physical and mechanical properties, a specific shape that is unique to a given composition. C-class asteroids, the strength of which is almost three times less than that of S asteroids, differ from the latter in their less elongated shape. No systematic change is observed in the morphometric parameters (increased roundness or sphericity) of small bodies of differing compositions depending on their mass, which suggests that the hypothesis of creep in small Solar System bodies is unlikely to be true. The absence of creep confirms that, regardless of their composition, all small Solar System bodies are solid elastic bodies having an ultimate strength (tensile strength and compressive strength) and a yield strength.     

Meridional motions of magnetic features in the solar photosphere

We cross-correlate pairs of Mt. Wilson magnetograms spaced at intervals of 24–38 days to investigate the meridional motions of small magnetic features in the photosphere. Our study spans the 26-yr period July 1967–August 1993, and the correlations determine longitude averages of these motions, as functions of latitude and time. The time-average of our results over the entire 26-yr period is, as expected, antisymmetric about the equator. It is poleward between 10° and 60°, with a maximum rate of 13 m s^–1, but for latitudes below ±10° it is markedly equatorward, and it is weakly equatorward for latitudes above 60°. A running 1-yr average shows that this complex latitude dependence of the long-term time average comes from a pattern of motions that changes dramatically during the course of the activity cycle. At low latitudes the motion is equatorward during the active phase of the cycle. It tends to increase as the zones of activity move toward the equator, but it reverses briefly to become poleward at solar minimum. On the poleward sides of the activity zones the motion is most strongly poleward when the activity is greatest. At high latitudes, where the results are more uncertain, the motion seems to be equatorward except around the times of polar field reversal. The difference-from-average meridional motions pattern is remarkably similar to the pattern of the magnetic rotation torsional oscillations. The correspondence is such that the zones in which the difference-from-average motion is poleward are the zones where the magnetic rotation is slower than average, and the zones in which it is equatorward are the zones where the rotation is faster.Our results suggest the following characterization: there is a constant and generally prevailing motion which is perhaps everywhere poleward and varies smoothly with latitude. On this is superimposed a cycle-dependent pattern of similar amplitude in which the meridional motions of the small magnetic features are directed away from regions of magnetic flux concentration. This is suggestive of simple diffusion, and of the models of Leighton (1964) and Sheeley, Nash, and Wang (1987). The correspondence between the meridional motions pattern and the torsional oscillations pattern in the magnetic rotation suggests that the latter may be an artifact of the combination of meridional motion and differential rotation.     

Analysis of Extra-Solar Planetary Transits Using Tools from Eclipsing Binaries

Analytical formulae for the computation of the photometric elements of extra-solar planetary transits are presented. They were initially derived for the study of well-detached eclipsing binaries and are valid for any degree of limb darkening and type of transit as well as for eccentric orbits. The only assumption is that the projections of the star and the planet on the plane of the sky are well represented by circular discs. The procedure to get valid ranges for the involved parameters, as well as to make precise estimations of initial parameters, using the analytical nature of the equations is given together with some discussion on their practical application. Examples are shown for OGLE-TR-113, representative of a light curve obtained with ground-based telescopes, and HD 209458 with a precise light curve obtained with the Hubble Space Telescope.     

Comment on lifetime determination of solar features

We propose a modification to a commonly used technique for lifetime determination of solar features. Suggestions for practical implementation of the method are presented. In addition, a serious source of bias in lifetime determination from time-ordered data is discussed.     

太阳系外行星的凌星观测研究

为对太阳系外行星的物理参数进行更精确估算,利用山东大学威海天文台/威海市天文台的1 m反射望远镜,对7颗已知具有行星系统的恒星:TrES-1、TrES-3、XO-2、WASP-1、WASP-2、WASP-3、HAT-P-7,进行了凌星现象的观测研究.介绍观测和数据处理的基本情况,给出凌星光变曲线结果及由之推算出的一些行星参数.在总结结果并加以分析的同时,展望下一步将进行的更为深入细致的研究.     

Tracking of kilometric-wave type III solar bursts in elevation and elongation and apparent source sizes

With our experiment on the satellite IMP-6 (Explorer 43) we are able to track the position of type III solar bursts in elevation as well as elongation. We do this by measuring the correlations between signals on an electric dipole antenna which is approximately normal to the plane of the ecliptic, and either of two antennas rotating in the ecliptic plane. The result is that the sources are generally close to the ecliptic plane, close enough that their elevation above the ecliptic cannot account for the large apparent width which we and others observe, and that this width must therefore be real.     

Motions, relative positions, and sizes of continua and bursts in solar noise storms

We present multifrequency radioheliograph observations of solar radio noise storms. The data base consists of observations carried out over 7 different days in the spring months of 1992 and 1993. In all, we present about 82 hours of data with 1 s time resolution at 4 different frequencies between 164 and 410 MHz. The spatial resolutions in the EW and NS directions vary with frequency from 1.2 to 0.8 and 3.7 to 1.5 arc min, respectively. In order to study the characteristics of bursts and continuum, we have developed a method for separating them in the time domain at each frequency. Our main results are: (i) there are no systematic large-scale motions of the continuum, the position is usually stable to within 2 of arc over durations of 3–4 hours and more; (ii) the positions of the continuum at different frequencies are often closer to each other than 1 of arc and have strongly correlated small-scale motions; (iii) the bursts have their positions scattered over the continuum extent and are slightly smaller in size than the underlying continuum; and (iv) there is no evidence for bipolar structures. We discuss the implications of these results for the current models of noise storm emission and for the trapping of suprathermal electrons.Presented at the CESRA Workshop in Potsdam, Germany, 16–20 May, 1994.     

Spectral features of burst radio emission over the solar cycle

We have investigated common burst spectral features for the 20th cycle of solar activity. The maximum daily radio fluxes in 8 frequency ranges are analysed. For every year the classification of these daily spectra is obtained by cluster analysis methods. There are two spectral minima for average spectra of clusters (in frequency ranges 4–3 and 0.5–0.25 GHz). As a rule their positions do not change during the solar cycle.Every annual spectrum of weak bursts has three minima (in frequency ranges 4–3, 2–1, and 0.5–0.25 GHz). The positions of these minima remain invariable during the solar cycle. But anuual spectra of strong bursts depend essentially on the phase of solar activity.The basic features of most burst spectra can be explained by gyrosynchrotron radiation of thermal and nonthermal electrons and plasma radiation at the plasma frequency and its second harmonic.     

Effects of solar radiation on the orbits of small particles

Revised equations of motion are formulated on more general assumptions than hitherto making allowance for some reflection of sunlight by a dust-particle, and from these the secular rates of change of the orbital elements of the particle are obtained. The equation for the eccentricity yields numerical results for the time taken for given changes in this element to occur. Other elements turn out to be expressible in terms of the eccentricity and thence are effectively also known in terms of the time. More general forms of earlier results are found, and some new mathematical results in the theory of the process are derived. The time of infall to the Sun associated with almost circular initial motion of a particle is calculated, and also the time from an orbit of initially high eccentricity. In this latter case, infall takes place much more rapidly than from a circular orbit of radius comparable with the average distance in the eccentric orbit. The effect on a particle of a long-period comet during a single return is negligible compared with the change in its binding-energy to the Sun that will in general result from planetary action. The possible history of a dust-particle from original capture by the Sun to final infall to the solar surface is briefly considered.     

Measuring the sizes, shapes, surface features and rotations of Solar System objects with interferometry

We consider the application of interferometry to measuring the sizes and shapes of small bodies in the Solar System that cannot be spatially resolved by today’s single-dish telescopes. Assuming ellipsoidal shapes, we provide a formalism to derive the shape parameters from visibility measurements along three different baseline orientations. Our results indicate that interferometers can measure the size of an object to better than 15% uncertainty if the limb-darkening is unknown. Assuming a Minnaert scattering model, one can theoretically derive the limb-darkening parameters from simultaneous measurements of visibilities at several different projected baseline lengths to improve the size and shape determination to an accuracy of a few percent. The best size measurement can be reached when one axis of the object’s projected disk is aligned with one baseline orientation, and the measurement of cross-sectional area is independent of baseline orientation. We construct a 3-D shape model for the dwarf planet Haumea and use it to synthesize interferometric data sets. Using the Haumea model, we demonstrate that when photometric light curve, visibility light curve, and visibility phase center displacement are combined, the rotational period and sense of rotation can all be derived, and the rotational pole can be estimated. Because of its elongated shape and the dark red spot, the rotation of Haumea causes its optical photocenter to move in a loop on the sky. Our simulations show that this loop has an extend of about 80 μas without the dark red spot, and about 200 μas with it. Such movements are easily detectable by space-based astrometric interferometer designed e.g. for planet detection. As an example, we consider the possible contributions to the study of small bodies in the Solar System by the Space Interferometry Mission. We show that such a mission could make substantial contributions in characterizing the fundamental physical properties of the brightest Kuiper Belt Objects and Centaurs as well as a large number of main belt asteroids. We compile a list of Kuiper Belt Objects and Centaurs that are potentially scientifically interesting and observable by such missions.     

Radiation forces on small particles in the solar system

We present a new and more accurate expression for the radiation pressure and Poynting-Robertson drag forces; it is more complete than previous ones, which considered only perfectly absorbing particles or artificial scattering laws. Using a simple heuristic derivation, the equation of motion for a particle of mass m and geometrical cross section A, moving with velocity v through a radiation field of energy flux density S, is found to be (to terms of order $\text{v}\text{c}$)

$\text{m}\text{v}\text{?}\text{= (}\text{SA}\text{c}\text{)Q}{}_{\mathrm{<mtext>pr</mtext>}}\text{[(1 ?}\text{r}\text{?}\text{c}\text{)}\text{S}\text{?}\text{?}\text{v}\text{c}\text{]}$

, where ? is a unit vector in the direction of the incident radiation, $\text{r}\text{?}$ is the particle's radial velocity, and c is the speed of light; the radiation pressure efficiency factor Q_pr ≡ Q_abs + Q_sca(1 ? 〈cos α〉), where Q_abs and Q_sca are the efficiency factors for absorption and scattering, and 〈cos α〉 accounts for the asymmetry of the scattered radiation. This result is confirmed by a new formal derivation applying special relativistic transformations for the incoming and outgoing energy and momentum as seen in the particle and solar frames of reference. Q_pr is evaluated from Mie theory for small spherical particles with measured optical properties, irradiated by the actual solar spectrum. Of the eight materials studied, only for iron, magnetite , and graphite grains does the radiation pressure force exceed gravity and then just for sizes around 0.1 μm; very small particles are not easily blown out of the solar system nor are they rapidly dragged into the Sun by the Poynting-Robertson effect. The solar wind counterpart of the Poynting-Robertson drag may be effective, however, for these particles. The orbital consequences of these radiation forces-including ejection from the solar system by relatively small radiation pressures-and of the Poynting-Robertson drag are considered both for heliocentric and planetocentric orbiting particles. We discuss the coupling between the dynamics of particles and their sizes (which diminish due to sputtering and sublimation). A qualitative derivation is given for the differential Doppler effect, which occurs because the light received by an orbiting particle is slightly red-shifted by the solar rotation velocity when coming from the eastern hemisphere of the Sun but blue-shifted when from the western hemisphere; the ratio of this force to the Poynting-Robertson force is $\text{(}\text{R}{}_{\mathrm{\odot }}\text{r}\text{)}{}^2\text{[(}\text{w}{}_{\mathrm{\odot }}\text{n}\text{) ? 1]}$, where R_⊙ and w_⊙ are the solar radius and spin rate, and n is the particle's mean motion. The Yarkovsky effect, caused by the asymmetry in the reradiated thermal emission of a rotating body, is also developed relying on new physical arguments. Throughout the paper, representative calculations use the physical and orbital properties of interplanetary dust, as known from various recent measurements.     

Transits of Mercury: Results of Belgrade Observations in 1970 and 1973

Photographic observations of the transits of Mercury over the solar disk in 1970 and 1973 at the Belgrade Observatory were used not only in order to determine the classical parameters, as the times of contacts and least distances to determine the apparent radii of the Sun and Mercury. The mean value of the Sun's semi-diameter reduced to the distance unit differs from AUWERS value by about 1.3 while the Mercury's radius is in good agreement with LE VERRIER 's value. On the basis of quite homogenous observational material and precise observing data it was possible to derive the parallax of the Sun by means of the angular distance changes due to the parallactic effect in the course of transit. The values are determined as: 8.800 ± 0.008 (1970) and 8.788 ± 0.032 (1973). The mean value resulting from the two transits is πs = 8.794 ± 0.013, an amount in striking agreement with that currently used.