Photometric search for extrasolar planets

The searches for extrasolar planetary systems by different methods based on the photometric monitoring of stars are reviewed. The search for extra-solar planets is, more or less consciously, the first step toward the search for other Minds in the Universe. A rational approach leads to the search for planets where structures with high complexity can emerge. In absence of any positive indication, it is safer to start this search by looking for planets within the habitable zone around main sequence stars where liquid water can be present. Of course, even if this future goal would fail, the detection of terrestrial planets would contribute to the characterization of other planetary systems and would constitute an interesting astrophysical goal by itself.     

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.     

Mass-radius curve for extrasolar Earth-like planets and ocean planets

By comparison with the Earth-like planets and the large icy satellites of the Solar System, one can model the internal structure of extrasolar planets. The input parameters are the composition of the star (Fe/Si and Mg/Si), the Mg content of the mantle (Mg# = Mg/[Mg + Fe]), the amount of H₂O and the total mass of the planet. Equation of State (EoS) of the different materials that are likely to be present within such planets have been obtained thanks to recent progress in high-pressure experiments. They are used to compute the planetary radius as a function of the total mass. Based on accretion models and data on planetary differentiation, the internal structure is likely to consist of an iron-rich core, a silicate mantle and an outer silicate crust resulting from magma formation in the mantle. The amount of H₂O and the surface temperature control the possibility for these planets to harbor an ocean. In preparation to the interpretation of the forthcoming data from the CNES led CoRoT (Convection Rotation and Transit) mission and from ground-based observations, this paper investigates the relationship between radius and mass. If H₂O is not an important component (less than 0.1%) of the total mass of the planet, then a relation (R/REarth)=ab(M/MEarth) is calculated with (a,b)=(1,0.306) and (a,b)=(1,0.274) for ¹⁰⁻²MEarth<M<MEarth and MEarth<M<10MEarth, respectively. Calculations for a planet that contains 50% H₂O suggest that the radius would be more than 25% larger than that based on the Earth-like model, with (a,b)=(1.258,0.302) for ¹⁰⁻²MEarth<M<MEarth and (a,b)=(1.262,0.275) for MEarth<M<10MEarth, respectively. For a surface temperature of 300 K, the thickness of the ocean varies from 150 to 50 km for planets 1 to 10 times the Earth's mass, respectively. Application of this algorithm to bodies of the Solar System provides not only a good fit to most terrestrial planets and large icy satellites, but also insights for discussing future observations of exoplanets.     

Luminosity and temperature relationships for extrasolar planets

A simple discussion of the final equilibrium state of extrasolar planetary evolution allows the determination of the luminosity and effective temperature of each planet which, in turn, allows the construction of a Hertzsprung–Russell diagram. The slope of the resulting line is found to be 4.5, similar to that which might be expected for isolated low-mass stars.     

Colour-differential interferometry for the observation of extrasolar planets

We present the high angular resolution technique of colour-differential interferometry for direct detection of extrasolar giant planets (EGPs). The measurement of differential phase with long-baseline ground-based interferometers in the near-infrared could allow the observation of several hot giant extrasolar planets in tight orbit around the nearby stars, and thus yield their low- or mid-resolution spectroscopy, complete orbital data set and mass. Estimates of potentially achievable signal-to-noise ratios are presented for a number of planets already discovered by indirect methods. The limits from the instrumental and atmospheric instability are discussed, and a subsequent observational strategy is proposed.     

Stable satellites around extrasolar giant planets

In this work, we study the stability of hypothetical satellites of extrasolar planets. Through numerical simulations of the restricted elliptic three-body problem we found the borders of the stable regions around the secondary body. From the empirical results, we derived analytical expressions of the critical semimajor axis beyond which the satellites would not remain stable. The expressions are given as a function of the eccentricities of the planet, e _P, and of the satellite, e _sat. In the case of prograde satellites, the critical semimajor axis, in the units of Hill's radius, is given by a _E≈ 0.4895   (1.0000 − 1.0305 e _P− 0.2738 e _sat). In the case of retrograde satellites, it is given by a _E≈ 0.9309  (1.0000 − 1.0764 e _P− 0.9812 e _sat). We also computed the satellite stability region ( a _E) for a set of extrasolar planets. The results indicate that extrasolar planets in the habitable zone could harbour the Earth-like satellites.     

Dynamical relaxation and massive extrasolar planets

Following the suggestion of Black that some massive extrasolar planets may be associated with the tail of the distribution of stellar companions, we investigate a scenario in which 5 N 100 planetary mass objects are assumed to form rapidly through a fragmentation process occuring in a disc or protostellar envelope on a scale of 100 au. These are assumed to have formed rapidly enough through gravitational instability or fragmentation that their orbits can undergo dynamical relaxation on a time-scale of ∼100 orbits.
Under a wide range of initial conditions and assumptions, the relaxation process ends with either (i) one potential 'hot Jupiter' plus up to two 'external' companions, i.e. planets orbiting near the outer edge of the initial distribution; (ii) one or two 'external' planets or even none at all; (iii) one planet on an orbit with a semi-major axis of 10 to 100 times smaller than the outer boundary radius of the inital distribution together with an 'external' companion. Most of the other objects are ejected and could contribute to a population of free-floating planets. Apart from the potential 'hot Jupiters', all the bound objects are on orbits with high eccentricity, and also with a range of inclination with respect to the stellar equatorial plane. We found that, apart from the close orbiters, the probability of ending up with a planet orbiting at a given distance from the central star increases with the distance. This is because of the tendency of the relaxation process to lead to collisions with the central star. The scenario we envision here does not impose any upper limit on the mass of the planets. We discuss the application of these results to some of the more massive extrasolar planets.     

The radio search for extrasolar planets with LOFAR

The Low Frequency Array (LOFAR) will come on line with unprecedented radio sensitivity and resolution between 10 and 240 MHz. Such a system will provide a factor of 10–30 improvement in sensitivity in the pursuit of the weak radio emission from extrasolar planets. To date, previous examinations of extrasolar planetary systems with the most advanced radio telescopes have yielded a negative result. However, the improvement in sensitivity by LOFAR over current systems will increase the likelihood of extrasolar planet detection in the radio. We apply radiometric models derived previously from the study of planets in our solar system to the known extrasolar planets, and demonstrate that approximately 3–5 of them should emit in the proper frequency range and with enough power to possibly become detectable at Earth with LOFAR.     

Migration and evolution of extrasolar planets

Giant planets in circumstellar disks can migrate inward from their initial (formation) positions at several AUs. Inward radial migration of the planet is caused by torques between the planet and the disk; outward radial migration of the planet is caused by torques between the planet and the spinning star, and by torques due to Roche lobe overflow and consequent mass loss from the planet. We present self-consistent numerical considerations of the problem of migrating giant planets by summing torques on planets for various physical parameters of the disk and of planets. We find that Jupiter-mass planets can stably arrive and survive at small heliocentric distances, thus reproducing observed properties of some of the recently discovered extra-solar planets. The range of fates of massive planets is broad, and some perish by losing all their mass onto the central star during Roche lobe overflow, while others survive for the lifetime of the central star. Surviving planets cluster into two groups when examined in terms of final mass and final heliocentric distance: those which have lost mass and those which have not. Some of the observed extrasolar planets fall into each of these two exclusive classes. We also find that there is an inner boundary for planets' final heliocentric distances, caused by tidal torques with the central star. Planets in small orbits are shown to be stable against atmospheric loss.     

Obliquity evolution of extrasolar terrestrial planets

We have investigated the obliquity evolution of terrestrial planets in habitable zones (at ∼1 AU) in extrasolar planetary systems, due to tidal interactions with their satellite and host star with wide varieties of satellite-to-planet mass ratio (m/Mp) and initial obliquity (γ₀), through numerical calculations and analytical arguments. The obliquity, the angle between planetary spin axis and its orbit normal, of a terrestrial planet is one of the key factors in determining the planetary surface environments. A recent scenario of terrestrial planet accretion implies that giant impacts of Mars-sized or larger bodies determine the planetary spin and form satellites. Since the giant impacts would be isotropic, tilted spins (sinγ₀∼1) are more likely to be produced than straight ones (sinγ₀∼0). The ratio m/Mp is dependent on the impact parameters and impactors' mass. However, most of previous studies on tidal evolution of the planet-satellite systems have focused on a particular case of the Earth-Moon systems in which m/Mp?0.0125 and γ₀∼10° or the two-body planar problem in which γ₀=0° and stellar torque is neglected. We numerically integrated the evolution of planetary spin and a satellite orbit with various m/Mp (from 0.0025 to 0.05) and γ₀ (from 0° to 180°), taking into account the stellar torques and precessional motions of the spin and the orbit. We start with the spin axis that almost coincides with the satellite orbit normal, assuming that the spin and the satellite are formed by one dominant impact. With initially straight spins, the evolution is similar to that of the Earth-Moon system. The satellite monotonically recedes from the planet until synchronous state between the spin period and the satellite orbital period is realized. The obliquity gradually increases initially but it starts decreasing down to zero as approaching the synchronous state. However, we have found that the evolution with initially tiled spins is completely different. The satellite's orbit migrates outward with almost constant obliquity until the orbit reaches the critical radius ∼10-20 planetary radii, but then the migration is reversed to inward one. At the reversal, the obliquity starts oscillation with large amplitude. The oscillation gradually ceases and the obliquity is reduced to ∼0° during the inward migration. The satellite eventually falls onto the planetary surface or it is captured at the synchronous state at several planetary radii. We found that the character change of precession about total angular momentum vector into that about the planetary orbit normal is responsible for the oscillation with large amplitude and the reversal of migration. With the results of numerical integration and analytical arguments, we divided the m/Mp-γ₀ space into the regions of the qualitatively different evolution. The peculiar tidal evolution with initially tiled spins give deep insights into dynamics of extrasolar planet-satellite systems and discussions of surface environments of the planets.     

Parameterized post-Newtonian orbital effects in extrasolar planets

Perturbative post-Newtonian variations of the standard osculating orbital elements are obtained by using the two-body equations of motion in the parameterized post-Newtonian theoretical framework. The results obtained are applied to the Einstein and Brans–Dicke theories. As a results, the semi-major axis and eccentricity exhibit periodic variation, but no secular changes. The longitude of periastron and mean longitude at epoch experience both secular and periodic shifts. The post-Newtonian effects are calculated and discussed for six extrasolar planets.     

On the search for O2 in extrasolar planets

The present work is a first attempt to investigate the feasibility of the optical detection of absorption lines in the atmosphere of extrasolar planets. Two cases are considered: (1) the reflection case, where the planet is observed by imaging via the light coming from the parent star and re-emitted by the planet; and (2) the occultation case, where the planet makes a partial occultation of the star. I find only in the latter case that there are planetary configurations where the absorption lines can effectively be detected with existing or forthcoming telescopes. The discussion is basically made for the O₂ A-band, which is of interest for exobiology.Paper presented at the Conference onPlanetary Systems: Formation, Evolution, and Detection held 7–10 December, 1992 at CalTech, Pasadena, California, U.S.A.     

On the topography of extrasolar earthlike planets

We consider a class of planets which have experienced early, nearly complete differentiation and outgassing, whose mantles are fully convective, and whose crusts are isostatically compensated. The evolutionary model of Hargraves [Science193, 363 (1976)] suggests that in the absence of a runaway greenhouse, such planets may usually possess continent/ocean topographies similar to that of Earth. But if the planet is significantly larger than Earth, and its star of spectral type earlier than G, it may ordinarily be completely water-covered.     

Model bond albedos of extrasolar giant planets

The atmospheres of extrasolar giant planets are modeled with various effective temperatures and gravities, with and without clouds. Bond albedos are computed by calculating the ratio of the flux reflected by a planet (integrated over wavelength) to the total stellar flux incident on the planet. This quantity is useful for estimating the effective temperature and evolution of a planet. We find it is sensitive to the stellar type of the primary. For a 5 M_Jup planet the Bond albedo varies from 0.4 to 0.3 to 0.6 as the primary star varies from A5V to G2V to M2V in spectral type. It is relatively insensitive to the effective temperature and gravity for cloud-free planets. Water clouds increase the reflectivity of the planet in the red, which increases the Bond albedo. The Bond albedo increases by an order of magnitude for a 13 M_Jup planet with an M2V primary when water clouds are present. Silicate clouds, on the other hand, can either increase or decrease the Bond albedo, depending on whether there are many small grains (the former) or few large grains (the latter).     

Speckle interferometry as a method for detecting nearby extrasolar planets

The applicability of the technique of speckle interferometry to the problem of detecting faint planetary and stellar objects around nearby stars is considered. Direct resolution could not be expected to reveal planetary objects, although many faint stellar objects should be detectable with a speckle camera of large dynamic range. The most promising possibilities lie with the approximately 100 nearby visual binaries with separations ?3 arcsec. Continued speckle interferometric observation of these systems could detect perturbations with amplitudes similar to those detectable by an ideal astrometric telescope. A simple scheme for measurement the fringe spacing in the composite spatial frequency power spectrum of the visual binary Eta Orionis indicates that relative separations with accuracies of 0″.002 in each coordinate are attainable. Use as reference stars of faint background stars lying within the isoplanatic patch of a nearby star is also considered.     

Achromatic interfero-coronagraph with variable rotation shearing for studying extrasolar planets

Direct observation of exoplanets will make it possible to clarify many principal questions connected both with extrasolar planets and planetary systems and to measure atmospheric spectra of the planets. Obtaining an exoplanet image not distorted by the light from a star is at the cutting edge of present-day optical technologies owing to the combination of tremendous brightness contrasts and small angular distances between the planet and star. To observe the exo-Earth, it is necessary to weaken the brightness of the parent star image by 9–10 orders of magnitude (in the optical and near-IR ranges). To compensate the influence of the atmosphere, ground-based (e.g., 8–10 m) telescopes intended for observing exoplanets are equipped with adaptive optics systems, the spatial and temporal resolutions of which are not yet sufficient. A meter-class space telescope equipped with a star coronagraph will make it possible to observe the nearest exoplanets. In this paper, an improved tool for star coronagraphy is considered, namely, the achromatic interferometric coronagraph with a variable rotational shear. It is fabricated according to the optical scheme of the common path interferometer for studying extrasolar planets by direct observations. Theoretical and experimental estimations for the main characteristics of the scheme were carried out. Laboratory experimental measurements were carried out on a coronagraph model.     

Space-borne global astrometric surveys: the hunt for extrasolar planets

The proposed global astrometry mission GAIA , recently recommended within the context of ESA's Horizon 2000 Plus long-term scientific programme, appears capable of surveying the solar neighbourhood within ∼200 pc for the astrometric signatures of planets around stars down to the magnitude limit of V =17 mag, which includes late M dwarfs at 100 pc.
Realistic end-to-end simulations of the GAIA global astrometric measurements have yielded the first quantitative estimates of the sensitivity to planetary perturbations and of the ability to measure their orbital parameters. Single Jupiter-mass planets around normal solar-type stars appear detectable out to 150 pc ( V ≤12 mag) with probabilities ≥50 per cent for orbital periods between ∼2.5 and ∼8 yr, and their orbital parameters are measurable with better than 30 per cent accuracy to about 100 pc. Jupiter-like objects (same mass and period as our giant planet) are found with similar probabilities out to 100 pc.
These first experiments indicate that the GAIA results would constitute an important addition to those that will come from the other ongoing and planned planet-search programmes. These data combined would provide a formidable testing ground on which to confront theories of planetary formation and evolution.     

Dynamic habitability for Earth-like planets in 86 extrasolar planetary systems

In this paper we estimate the likelihood to find habitable Earth-like planets on stable orbits for 86 selected extrasolar planetary systems, where luminosity, effective temperature and stellar age are known. For determining the habitable zone (HZ) an integrated system approach is used taking into account a variety of climatological, biogeochemical, and geodynamical processes. Habitability is linked to the photosynthetic activity on the planetary surface. We find that habitability strongly depends on the age of the stellar system and the characteristics of a virtual Earth-like planet. In particular, the portion of land/ocean coverages plays an important role. We approximated the conditions for orbital stability using a method based on the Hill radius. Almost 60% of the investigated systems could harbour habitable Earth-like planets on stable orbits. In 18 extrasolar systems we find even better prerequisites for dynamic habitability than in our own solar system. In general our results are comparable to those with an HZ determination based only on climatic constraints. However, there are remarkable differences for land worlds and for systems older than about 7 Gyr.     

Stability of fictitious Trojan planets in extrasolar systems

Our work deals with the dynamical possibility that in extrasolar planetary systems a terrestrial planet may have stable orbits in a 1:1 mean motion resonance with a Jovian like planet. We studied the motion of fictitious Trojans around the Lagrangian points L₄/L₅ and checked the stability and/or chaoticity of their motion with the aid of the Lyapunov Indicators and the maximum eccentricity. The computations were carried out using the dynamical model of the elliptic restricted three‐body problem that consists of a central star, a gas giant moving in the habitable zone, and a massless terrestrial planet. We found 3 new systems where the gas giant lies in the habitable zone, namely HD99109, HD101930, and HD33564. Additionally we investigated all known extrasolar planetary systems where the giant planet lies partly or fully in the habitable zone. The results show that the orbits around the Lagrangian points L₄/L₅ of all investigated systems are stable for long times (10⁷ revolutions). (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)