The Kepler Mission: Astrophysics and Eclipsing Binaries

The Kepler Mission is a photometric space mission that will continuously observe a single 100 square degree field of view (FOV) of the sky of more than 100,000 stars in the Cygnus-Lyra region for four or more years with a precision of 14 parts per million (ppm) for a 6.5 hour integration including shot noise for a twelfth magnitude star. The primary goal of the mission is to detect Earth-size planets in the habitable zone of solar-like stars. In the process, many eclipsing binaries (EB) will also be detected. Prior to launch, the stellar characteristics will have been determined for all the stars in the FOV with K<14.5. As part of the verification process, stars with transits (about 5%) will need to have follow-up radial velocity observations performed to determine the component masses and thereby separate grazing eclipses caused by stellar companions from transits caused by planets. The result will be a rich database on EBs. The community will have access to the archive for uses such as for EB modeling of the high-precision light curves. A guest observer program is also planned for objects not already on the target list.     

Dynamics of Two Planets in the 3/2 Mean-motion Resonance: Application to the Planetary System of the Pulsar PSR B1257+12

This paper considers the dynamics of two planets, as the planets B and C of the pulsar PSR B1257+12, near a 3/2 mean-motion resonance. A two-degrees-of-freedom model, in the framework of the general three-body planar problem, is used and the solutions are analyzed through surfaces of section and Fourier techniques in the full phase space of the system.On the possibility of existence of a fourth planet in distant orbit, see Wolszczan et al., 2000     

Dynamics and circulation regimes of terrestrial planets

By the study of simple analogues, either in the form of simplified numerical models or laboratory experiments, considerable insights may be gained as to the likely roles of planetary size, rotation, thermal stratification and other factors in determining the principal length scales, styles of global circulation and dominant waves and instability processes active in the respective climate systems of Earth, Mars, Venus and Titan. In this review, we explore aspects of these analogues and demonstrate the importance of a number of key dimensionless parameters, most notably thermal Rossby and Rhines numbers and a measure of the dominant frictional or radiative timescale, in defining the type of circulation regime to be expected in a prototype planetary atmosphere subject to axisymmetric driving. These considerations help to place Mars, Venus, Titan and Earth into an appropriate context, and may also lay the foundations for predicting and understanding the climate and circulation regimes of (as yet undiscovered) Earth-like extra-solar planets. However, as recent discoveries of ‘super-Earth’ planets around some nearby stars are beginning to reveal, the parameter space determined from axisymmetrically forced prototype atmospheres may be incomplete and other factors, such as the possibility of tidally locked rotation and tidal forcing, may also need to be taken into account for some classes of extra-solar planet.     

Secular dynamics of the three-body problem: application to the υ Andromedae planetary system

The discovery of extra-solar planetary systems with multiple planets in highly eccentric orbits (∼0.1-0.6), in contrast with our own Solar System, makes classical secular perturbation analysis very limited. In this paper, we use a semi-numerical approach to study the secular behavior of a system composed of a central star and two massive planets in co-planar orbits. We show that the secular dynamics of this system can be described using only two parameters, the ratios of the semi-major axes and the planetary masses. The main dynamical features of the system are presented in geometrical pictures that allows us to investigate a large domain of the phase space of this three-body problem without time-expensive numerical integrations of the equations of motion, and without any restriction on the magnitude of the planetary eccentricities. The topology of the phase space is also investigated in detail by means of spectral map techniques, which allow us to detect the separatrix of a non-linear secular apsidal resonance. Finally, the qualitative study is supplemented by direct numerical integrations. Three different regimes of secular motion with respect to the secular angle Δ? are possible: they are circulation, oscillation (around 0° and 180°), and high eccentricity libration in a non-linear secular resonance. The first two regimes are a continuous extension of the classical linear secular perturbation theory; the last is a new feature, hitherto unknown, in the secular dynamics of the three-body problem. We apply the analysis to the case of the two outer planets in the υ Andromedae system, and obtain its periodic and ordinary orbits, the general structure of its secular phase space, and the boundaries of its secular stability; we find that this system is secularly stable over a large domain of eccentricities. Applying this analysis to a wide range of planetary mass and semi-major axis ratios (centered about the υ Andromedae parameters), we find that apsidal oscillation dominates the secular phase space of the three-body coplanar system, and that the non-linear secular resonance is also a common feature.     

Solar, interplanetary, planetary, and related extra-solar system science for LOFAR

The low frequency array (LOFAR) radiotelescope will be a powerful instrument for answering fundamental, unresolved scientific questions concerning solar system radio phenomena and related emissions from nearby stellar systems. This paper reviews the phenomena, emission mechanisms, open scientific questions, and LOFAR's capabilities. LOFAR will detect metric solar radio bursts in the corona and interplanetary medium, out to distances of order 10 solar radii, as well as Jovian radio emissions. Arguments are given that LOFAR may be sufficiently sensitive to detect stellar analoges of solar type II and III bursts, and may detect cyclotron-maser emissions from extra-solar planets. LOFAR may also aid space weather research, by passively detecting coronal mass ejections (CMEs) via scintillation and Faraday rotation effects, or by detecting radar signals bounced off CMEs and coronal density structures if a suitable solar radar is developed.     

Basic Functions of the Light Curve Analysis of Eclipsing Variables in the Frequency Domain

An analytically tractable method of transforming the problem of light curve analysis of eclipsing binaries from the time domain into the frequency domain was introduced by Kopal (1975, 1979, 1990). This method uses a new general formulation of eclipse functions α, the so-called moments A _2m , and their combinations as g _2m = A _2m+2/(A _2m A _2m+4) functions for the basic spherical model. In this paper, I will review the use of these functions in the light curve analysis of eclipsing binaries.     

Investigation of Times of Minima of Selected Early-Type Eclipsing Binaries

New precise times of minimum light for several early-type eclipsing binaries were obtained at three observatories. The changes of period of the following measured binaries are discussed: V1182 Aql, LY Aur, SZ Cam, FZ CMa, QZ Car, LZ Cen, V606 Cen, AH Cep and TU~Mus.     

Light Curve Analysis of Early-Type Close Lmc Binaries

Results are presented of an analysis of eclipsing binaries in the Large Magellanic Cloud. The sample of close OB-type stars was taken from the MACHO microlensing survey. The present study was restricted to systems with orbital periods shorter than 2 days and V and R light curves with large eclipse amplitudes, high S/N and homogeneous and dense phase coverage. Problems encountered during the analysis are discussed, especially with respect to the degeneracy of photometric mass ratios and other parameter correlations.     

Investigation on Planetary Atmospheres Using Laboratory Simulation Experiments The Example of Saturn's Moon (Titan)

The main goals of experimental simulation in the laboratory of a planetary atmosphere are to feed the theoretical models, and to help the treatment of observations. This type of simulation permits the direct study of objects that space missions can't study or have not studied yet, through the production of laboratory analogues of gaseous or solid phases. But the representativity of these laboratory analogues is of crucial importance. This revised version was published online in July 2006 with corrections to the Cover Date.     

Accretion of terrestrial planets from oligarchs in a turbulent disk

We have investigated the final accretion stage of terrestrial planets from Mars-mass protoplanets that formed through oligarchic growth in a disk comparable to the minimum mass solar nebula (MMSN), through N-body simulation including random torques exerted by disk turbulence due to Magneto-Rotational Instability. For the torques, we used the semi-analytical formula developed by Laughlin et al. [Laughlin, G., Steinacker, A., Adams, F.C., 2004. Astrophys. J. 608, 489-496]. The damping of orbital eccentricities (in all runs) and type-I migration (in some runs) due to the tidal interactions with disk gas is also included. Without any effect of disk gas, Earth-mass planets are formed in terrestrial planet regions in a disk comparable to MMSN but with too large orbital eccentricities to be consistent with the present eccentricities of Earth and Venus in our Solar System. With the eccentricity damping caused by the tidal interaction with a remnant gas disk, Earth-mass planets with eccentricities consistent with those of Earth and Venus are formed in a limited range of disk gas surface density (∼10⁻⁴ times MMSN). However, in this case, on average, too many (?6) planets remain in terrestrial planet regions, because the damping leads to isolation between the planets. We have carried out a series of N-body simulations including the random torques with different disk surface density and strength of turbulence. We found that the orbital eccentricities pumped up by the turbulent torques and associated random walks in semimajor axes tend to delay isolation of planets, resulting in more coagulation of planets. The eccentricities are still damped after planets become isolated. As a result, the number of final planets decreases with increase in strength of the turbulence, while Earth-mass planets with small eccentricities are still formed. In the case of relatively strong turbulence, the number of final planets are 4-5 at 0.5-2 AU, which is more consistent with Solar System, for relatively wide range of disk gas surface density (∼¹⁰⁻⁴-¹⁰⁻² times MMSN).     

Orbital stability of systems of closely-spaced planets

An investigation of the stability of systems of 1 M_⊕ (Earth-mass) bodies orbiting a Sun-like star has been conducted for virtual times reaching 10 billion years. For the majority of the tests, a symplectic integrator with a fixed timestep of between 1 and 10 days was employed; however, smaller timesteps and a Bulirsch-Stoer integrator were also selectively utilized to increase confidence in the results. In most cases, the planets were started on initially coplanar, circular orbits, and the longitudinal initial positions of neighboring planets were widely separated. The ratio of the semimajor axes of consecutive planets in each system was approximately uniform (so the spacing between consecutive planets increased slowly in terms of distance from the star). The stability time for a system was taken to be the time at which the orbits of two or more planets crossed. Our results show that, for a given class of system (e.g., three 1 M_⊕ planets), orbit crossing times vary with planetary spacing approximately as a power law over a wide range of separation in semimajor axis. Chaos tests indicate that deviations from this power law persist for changed initial longitudes and also for small but non-trivial changes in orbital spacing. We find that the stability time increases more rapidly at large initial orbital separations than the power-law dependence predicted from moderate initial orbital separations. Systems of five planets are less stable than systems of three planets for a specified semimajor axis spacing. Furthermore, systems of less massive planets can be packed more closely, being about as stable as 1 M_⊕ planets when the radial separation between planets is scaled using the mutual Hill radius. Finally, systems with retrograde planets can be packed substantially more closely than prograde systems with equal numbers of planets.     

A New Package of Computer Codes for Analyzing Light Curves of Eclipsing Pre-Cataclysmic Binaries

Using the new package of computer codes for analyzing light curves of the two eclipsing pre-cataclysmic binary systems (PCBs) UU Sge and V471 Lyr we find updated values of the physical parameters and discuss the evolutionary state of these PCBs.     

Monitoring Secular Orbital Period Variations of Some Eclipsing Binaries at the Ankara University Observatory

This study concerns the long-term monitoring of the secular variation character in the orbital period of some short-period eclipsing binaries observed at the Ankara University Observatory. Among the systems of our observing list are CK Boo, V502 Oph and V836 Cyg that show long-term secular variations in their orbital periods. We use classical O-C diagram analysis technique as a tool to reveal the character of the period variations of these binary systems.     

Analysis of disturbances in the Planetary Fourier Spectrometer through numerical modeling

Fourier transform spectrometers are instruments with high sensitivity to many kinds of disturbances. This study started from the analysis of the disturbances related to mechanical vibrations on the PFS FTIR spectrometer to show how the measured spectra can differ from the actual ones. The complete study, more in general, accounts for the characteristics of a real instrument and its operating environment to show, which can be the effects of many sources of disturbances on realistic measurements. The analysis is especially relevant when the spectra are used for the determination of parameters through “best fitting techniques” by matching with synthetic ones because it shows how spectral features used in these studies can be modified by disturbances. A previous work addressed the theoretical treatment of vibrations borne effects on FTIR spectrometers and is the ground work for the present; however, that study, being based on an analytical approach could only show examples of single effects on simplified input signals such as emission lines. This study conversely is based on a numerical model, developed in order to include altogether the effects addressed in the theoretical work to show combined effects on complex spectra like those expected from Mars. This allows not only to evaluate the linked effects of many kinds of disturbances but also to account for the real spectrometer characteristics. The use of synthetic spectra as input allows the comparison between expected spectra and measured ones. The simulation is tailored on the Planetary Fourier Spectrometer (PFS), onboard the ESA Mars Express spacecraft, from 2003 orbiting around Mars and in particular on its short wavelength (SW) channel, where many disturbances are more evident.     

The formation and habitability of terrestrial planets in the presence of close-in giant planets

‘Hot jupiters,’ giant planets with orbits very close to their parent stars, are thought to form farther away and migrate inward via interactions with a massive gas disk. If a giant planet forms and migrates quickly, the planetesimal population has time to re-generate in the lifetime of the disk and terrestrial planets may form [P.J. Armitage, A reduced efficiency of terrestrial planet formation following giant planet migration, Astrophys. J. 582 (2003) L47-L50]. We present results of simulations of terrestrial planet formation in the presence of hot/warm jupiters, broadly defined as having orbital radii ?0.5 AU. We show that terrestrial planets similar to those in the Solar System can form around stars with hot/warm jupiters, and can have water contents equal to or higher than the Earth's. For small orbital radii of hot jupiters (e.g., 0.15, 0.25 AU) potentially habitable planets can form, but for semi-major axes of 0.5 AU or greater their formation is suppressed. We show that the presence of an outer giant planet such as Jupiter does not enhance the water content of the terrestrial planets, but rather decreases their formation and water delivery timescales. We speculate that asteroid belts may exist interior to the terrestrial planets in systems with close-in giant planets.     

Secular apsidal configuration of non-resonant exoplanetary systems

Using a high-order (order 12) expansion of the perturbative potential in powers of eccentricities [Libert, A.-S., Henrard, J., 2005. Celest. Mech. Dynam. Astron. 93, 187-200], we study the secular effects of two coplanar planets which are not in mean motion resonances. The main results concern eccentricity variations, oscillation amplitude of the angular difference of the apsidal lines (Δ?) and frequency of such an oscillation. We show that this analytical approach describes correctly the behaviour of most of the exosystems and underlines the known limitations of the linear Laplace-Lagrange theory. Apsidal configuration of υ Andromedae, HD 168443, HD 169830, HD 38529, HD 74156 and HD 12661 are examined. We also point out the great sensitivity of the υ Andromedae system to the initial values (e₁(0), e₂(0) or Δ?(0)).     

Survival of Trojan-type companions of Neptune during primordial planet migration

We investigate the survivability of Trojan-type companions of Neptune during primordial radial migration of the giant planets Jupiter, Saturn, Uranus, and Neptune. We adopt the usual planet migration model in which the migration speed decreases exponentially with a characteristic time scale τ (the e-folding time). We perform a series of numerical simulations, each involving the migrating giant planets plus ∼1000 test particle Neptune Trojans with initial distributions of orbital eccentricity, inclination, and libration amplitude similar to those of the known jovian Trojans asteroids. We analyze these simulations to measure the survivability of Neptune's Trojans as a function of migration rate. We find that orbital migration with the characteristic time scale τ=10⁶ years allows about 35% of preexisting Neptune Trojans to survive to 5τ, by which time the giant planets have essentially reached their final orbits. In contrast, slower migration with τ=10⁷ years yields only a ∼5% probability of Neptune Trojans surviving to a time of 5τ. Interestingly, we find that the loss of Neptune Trojans during planetary migration is not a random diffusion process. Rather, losses occur almost exclusively during discrete prolonged episodes when Trojan particles are swept by secondary resonances associated with mean-motion commensurabilities of Uranus with Neptune. These secondary resonances arise when the circulation frequencies, f, of critical arguments for Uranus-Neptune mean-motion near-resonances (e.g., f^UN_1:2, f^UN_4:7) are commensurate with harmonics of the libration frequency of the critical argument for the Neptune-Trojan 1:1 mean-motion resonance (f^NT_1:1). Trojans trapped in the secondary resonances typically have their libration amplitudes amplified until they escape the 1:1 resonance with Neptune. Trojans with large libration amplitudes are susceptible to loss during sweeping by numerous high-order secondary resonances (e.g., f^UN_1:2≈11f^NT_1:1). However, for the slower migration, with τ=10⁷ years, even tightly bound Neptune Trojans with libration amplitudes below 10° can be lost when they become trapped in 1:3 or 1:2 secondary resonances between f^UN_1:2 and f^NT_1:1. With τ=10⁷ years the 1:2 secondary resonance was responsible for the single greatest episode of loss, ejecting nearly 75% of existing Neptune Trojans. This episode occurred during the late stages of planetary migration when the remnant planetesimal disk would have been largely dissipated. We speculate that if the number of bodies liberated during this event was sufficiently high they could have caused a spike in the impact rate throughout the Solar System.     

太阳质量损失对高阶行星轨道的长期影响

在文[1]研究的基础上给出了太阳质量损失对三阶行星轨道的影响解,并计算了二、三阶解的长期效应的数值结果。理论结果表明,在三阶解中对于质量变化模型k=3的情形,太阳质量损失对轨道半长轴继续产生长期项、混合项和周期项,但对轨道偏心率和近点角距只产生周期项,三阶解的效应值虽小,但有定性意义。     

On the stability of a planet between Mars and the asteroid belt: Implications for the Planet V hypothesis

The stability of an additional planet between the orbit of Mars and the asteroid belt is examined in the context of the Planet V hypothesis. In this model, the Solar System initially contained a fifth terrestrial planet, “Planet V,” which was removed after ∼700 Myr, a possible trigger for the late heavy bombardment on the inner planets. The model is investigated using 96 N-body integrations of the 8 major planets with an additional body between Mars and the asteroid belt. In more than 1/4 of simulations, Planet V survives for 1000 Myr. In most other cases, Planet V collides with the Sun or hits another planet after several hundred Myr, leaving 4 surviving terrestrial planets. In 24/96 simulations, Planet V is lost by ejection or collision with the Sun while the other four terrestrial planets survive without undergoing a collision. In 18 cases, Planet V is removed at least 200 Myr after the beginning of the simulation. The endstate depends sensitively on the mass of Planet V. Collision with the Sun is likely when Planet V's mass is 0.25 Mars masses or less. When Planet V is more massive than this, collisions involving it and/or other terrestrial planets become commonplace. In unstable systems, the times of first encounter and first collision/ejection depend on the initial aphelion distance of Mars. Reducing Mars's aphelion distance increases these times and also increases the fraction of systems surviving for 1000 Myr. When Mars's current orbit is used, the stability of Planet V increases when these two planets are widely separated initially. Planet V's aphelion distance Q typically begins to cross the asteroid belt within a few tens to a few hundred Myr, and its orbit last leaves the belt several hundred Myr later in most cases. The total time spent with Q>2.1 AU is typically less than 200 Myr.