Surface studies of asteroids from earthbound observations

The angular diameter of minor planets compared with best observation conditions of about one arcsec (seeing) at ground-based observatories, though situated at high sea levels with best climate conditions, usually is too small to be resolved for surface studies or diameter determinations with direct photographic or similar imaging methods.Nevertheless the rough geometry and/or small scale structures on the asteroid's surface can be studied with light-curve observations using high precision photoelectric photometry and the fact that the rotation of an asteroid during a spin period is now determined for slightly more than 200 minor planets.On only a few selected asteroids (63 Ausonia, 88 Thisbe, 92 Undina, 110 Lydia, 118 Peitho, 128 Nemesis, 139 Juewa, 337 Devosa and 599 Luisa) do we show, from details detected in the light-curves, how observations of this type were carried out successfully. From the small scale features we get the rough linear extensions on the asteroid surface from differences in magnitude and time. Such observations will be more useful and important in future with respect to an optimum selection of objects for a possible direct asteroid spacecraft mission.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.Visiting Astronomer, Kitt Peak National Observatory, USA, Operated by the Association of Universities for Research in Astronomy Inc., under contract with the National Science Foundation. A part of the observations was carried out at the Observatoire de Haute Provence (OHP), France.     

Stability of the solar system

If the solar system is considered as a mechanical clockwork consisting of its present members which attract each other as mass-points, the extent of its present approach to secular stability (i.e., the state of minimum potential energy) — manifested by the existence of a number of nearcommensurabilities of the present orbital periods, not only of the planets, but also of their satellites —could not have been attained in a time-span of 4.6×10⁹ yr of its age by gravitational perturbations alone.The existence of such commensurabilities — striking in many instances— could then be understood only on the assumption that either (a) the solar system was actually born with the present 2-, 3- and 4-term couplings between the orbital period of the planets already built-in from the outset (which is improbable on any known grounds); or (b) that these couplings — in particular, the 25 Jupiter-Saturn commensurability — have arisen as a result of tidal interaction between proto-planetary globes of much larger dimensions than these planets possess today. For the present dimensions and mutual distances of these planets, their tidal interaction in 10⁹ yr would exert but negligible effects; and during that time neither their masses, nor the scale of the solar system underwent any essential change.Therefore, a hypothesis is proposed that the situation now obtaining had its origin in the early days of the formation of the solar system, when the planetary globes — in particular, those of Jupiter and Saturn (now in the terminal stage of Kelvin contraction) — were very much larger than they are today; and when, as a result, the tidal coupling between them operated at a much higher rate than at the present time.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.     

Effects of a close encounter with Jupiter on different populations of planet-crossing objects

The evolutions of different planet-crossing populations due to a close encounter with Jupiter are examined and the implications on materials displacement throughout the solar system are discussed. The effects of the encounter are shown to be very important for those planet-crossers that could be responsible of planets surface cratering.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.     

Predictions for the frequency and orbital radii of massive extrasolar planets

We investigate the migration of massive extrasolar planets caused by gravitational interaction with a viscous protoplanetary disc. We show that a model in which planets form at 5 au at a constant rate, before migrating, leads to a predicted distribution of planets that is a steeply rising function of log( a ), where a is the orbital radius. Between 1 and 3 au, the expected number of planets per logarithmic interval in a roughly doubles. We demonstrate that, once selection effects are accounted for, this is consistent with current data, and then extrapolate the observed planet fraction to masses and radii that are inaccessible to current observations. In total, approximately 15 per cent of stars targeted by existing radial velocity searches are predicted to possess planets with masses  0.3< M _p sin( i )<10 M _J  and radii  0.1< a <5 au  . A third of these planets (around 5 per cent of the target stars) lie at the radii most amenable to detection via microlensing. A further  5–10  per cent of stars could have planets at radii of  5< a <8 au  that have migrated outwards. We discuss the probability of forming a system (akin to the Solar system) in which significant radial migration of the most massive planet does not occur. Approximately  10–15  per cent of systems with a surviving massive planet are estimated to fall into this class. Finally, we note that a smaller fraction of low-mass planets than high-mass planets is expected to survive without being consumed by the star. The initial mass function for planets is thus predicted to rise more steeply towards small masses than the observed mass function.     

Ground-based detection of terrestrial extrasolar planets by photometry: the case for CM Draconis

The detection of extrasolar planets by measuring a photometric drop in the stellar brightness due to a planetary transit can be statistically improved by observing eclipsing binary systems and photometrically improved by observing small component systems. In particular the system CM Draconis, with two dM4 components, would allow the detection of extrasolar planets in the size range of Earth-to-Neptune requiring a ground-based photometric precision of about 0.08% to 1.1% (photometric precision of about 0.3% is routinely achievable with 1-meter class telescopes at the magnitude of CM Draconis, 11.07 inR-filter). In addition, the transit of extrasolar planets in a binary star system provides a unique, quasi-periodic signal that can be cross-correlated with the observational data to detect sub-noise signals. We examine the importance of making such observations to an understanding of the formation and evolution of terrestrial-type planets in main-sequence star systems. Terrestrial planets could have formed with substancially shorter periods in this lower luminosity system, for example, and might be expected to have accreted essentially in the binary orbital plane (however, non-coplanar planets may also eventually be detectable due to precession). We also report on a network of medium-sized telescopes at varying longitudes that have been organized to provide such constraints on terrestrial-planet formation processes and discuss the extention of near-term observations to other possible binary systems, as well. Finally, we discuss a more speculative, future observation that could be performed on the CM Draconis system that would be of exobiological as well as astrophysical interest.     

Origin and early evolution of the planetary system

It is shown by linear stability analysis that a preplanetary (presatellite) disk of dust and gas with Keplerian velocity field can become unstable due to the collective self-gravity of the disk. The radial distribution of rings, which may result from this instability, is derived. These rings later on can be the formation sites for planets around the Sun and for satellites around the planets. The derived orbits are shown to be in good agreement with that of the planets and the satellites (of Jupiter, Saturn, and Uranus). Predictions and conclusions seem to be possible for the existence of three yet unknown Uranian satellites, the origin of the early Moon and the possible radial extension of the planetary system.     

Giant planet migration through the action of disk torques and planet-planet scattering

This paper presents a parametric study of giant planet migration through the combined action of disk torques and planet-planet scattering. The torques exerted on planets during Type II migration in circumstellar disks readily decrease the semi-major axes a, whereas scattering between planets increases the orbital eccentricities ?. This paper presents a parametric exploration of the possible parameter space for this migration scenario using two (initial) planetary mass distributions and a range of values for the time scale of eccentricity damping (due to the disk). For each class of systems, many realizations of the simulations are performed in order to determine the distributions of the resulting orbital elements of the surviving planets; this paper presents the results of ∼8500 numerical experiments. Our goal is to study the physics of this particular migration mechanism and to test it against observations of extrasolar planets. The action of disk torques and planet-planet scattering results in a distribution of final orbital elements that fills the a-? plane, in rough agreement with the orbital elements of observed extrasolar planets. In addition to specifying the orbital elements, we characterize this migration mechanism by finding the percentages of ejected and accreted planets, the number of collisions, the dependence of outcomes on planetary masses, the time spent in 2:1 and 3:1 resonances, and the effects of the planetary IMF. We also determine the distribution of inclination angles of surviving planets and the distribution of ejection speeds for exiled planets.     

The mid-term and long-term solar quasi-periodic cycles and the possible relationship with planetary motions

This work investigates the solar quasi-periodic cycles with multi-timescales and the possible relationships with planetary motions. The solar cycles are derived from long-term observations of the relative sunspot number and microwave emission at frequency of 2.80 GHz. A series of solar quasi-periodic cycles with multi-timescales are registered. These cycles can be classified into three classes: (1) the strong PLC (PLC is defined as the solar cycle with a period very close to the ones of some planetary motions, named as planetary-like cycle) which is related strongly with planetary motions, including nine periodic modes with relatively short period (P<12 yr), and related to the motions of the inner planets and of Jupiter; (2) the weak PLC, which is related weakly to planetary motions, including two periodic modes with relatively long period (P>12 yr), and possibly related to the motions of outer planets; (3) the non-PLC, for which so far there has been found no clear evidence to show the relationship with any planetary motions. Among the planets, Jupiter plays a key role in most periodic modes due to its sidereal motion or spring tidal motions associated with other planets. Among planetary motions, the spring tidal motion of the inner planets and of Jupiter dominates the formation of most PLCs. The relationships between multi-timescale solar periodic modes and the planetary motions will help us to understand the essential nature and prediction of solar activities.     

Dynamics of the TrES‐2 system

The TrES‐2 system harbors one planet which was discovered with the transit technique. In this work we investigate the dynamical behavior of possible additional, lower‐mass planets. We identify the regions where such planets can move on stable orbits and show how they depend on the initial eccentricity and inclination. We find, that there are stable regions inside and outside the orbit of TrES‐2b where additional, smaller planets can move. We also show that those planets can have a large orbital inclination which makes a detection with the transit technique very difficult (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Detecting the glint of starlight on the oceans of distant planets

We propose that astronomers will be eventually be able to discriminate between extrasolar Earth-like planets with surface oceans and those without using the shape of phase light curves in the visible and near-IR spectrum. We model the visible light curves of planets having Earth-like surfaces, seasons, and optically-thin atmospheres with idealized diffuse-scattering clouds. We show that planets partially covered by water will appear measurably brighter near crescent phase (relative to Lambertian planets) because of the efficient specular reflection (“glint”) of starlight incident on their surfaces at a highly oblique angle. Planets on orbits within 30° of edge-on orientation (50% of all planets) will show pronounced glint over a sizeable range of orbital longitudes, from quadrature to crescent, all outside the glare of their parent stars. Also, water-covered planets will appear darker than a Lambertian disk near full illumination. Finally, we show that planets with a mixed land/water surface will polarize the reflected signal by as much as 30-70%. These results suggest several new ways of directly identifying water on distant planets.     

Study of dynamical processes at the final stages of planetary system formation: Resonance motion of giant planets

According to current observational data, planets of many exoplanetary systems have resonant motion. The formation of resonance configurations is studied within a unified model of planetary migration. Planets in the observed systems 24 Sex, HD 37124, HD 73526, HD 82943, HD 128311, HD 160691, Kepler 9, NN Ser, which are moving in the 2: 1 resonance, could have been captured into this resonance due to both the Type I and II migration with a wide range of parameters. The migration conditions are defined for the formation of HD 45364 and HD 200964 that are in the 3: 2 and 4: 3 first-order resonances, correspondingly. The results obtained for HD 200964 show that planets can be captured in the first-order resonances, when the outer-to-inner orbital period ratios for the planets are less than 3: 2, only if Type I migration rates are large, and the mass of at least one planet is substantially less than the modern masses of the observed giant planets. The formation of the HD 102272, HD 108874, HD 181433 and HD 202206 systems with planets in high-order resonances is considered. The capture into these resonances can be realized with very slow Type II migration. Possible bounds for migration parameters are considered. In particular, it has been found that the capture of HD 108874 into the 4: 1 resonance is possible only if the angle between the plane of planetary orbits and the plane of sky is appreciably less than 90°, i.e., the planetary masses are a few times larger than the minimum values. The capture of HD 202206 into the 5: 1 resonance is possible at low migration rates; however, another mechanism is required to explain the high observed eccentricity of the inner planet (for example, strong gravitational interaction between the planets). Resonant configurations can be disrupted due to the interaction between planets and remaining fragments of the planetesimal disk as, for example, may occur in the three-planet system 47 UMa. The specific orbital features observed for this system are explained.     

The planetary masses and the orbits of the first four minor planets

Numerical tests are the basis of a study about the effects caused in the orbits of the planets (1)–(4) by possible errors in the system of planetary masses. The masses of five major and three minor planets are considered. Especially, the effects caused by (1) Ceres in the orbit of (2) Pallas since the time of discovery are found to be large enough for a determination of the mass of Ceres. A first result for this mass is (6.7±0.4)×10^–10 solar masses.     

Resonant structures in the solar system

The resonance theory is discussed with respect to the Solar System with a view to show that every triad of successive planets in the Solar System follows Laplace's resonance relation. With rings now known to exist around three of the four major planets, scientists have begun to speculate about the possible existence of ring structure and one or two small planets going around the Sun itself. It is also believed that the ring systems may exist around the planets Neptune and Mars. In this paper an attempt is made to provide a basis to these beliefs using Laplace's resonance relation. The triads of successive innermost objects (rings and/or satellites) in the satellite — systems of Jupiter, Saturn and Uranus are also shown to follow Laplace's resonance relation.     

Planetary microlensing signals from the orbital motion of the source star around the common barycentre

With several detections, the technique of gravitational microlensing has proven useful for studying planets that orbit stars at Galactic distances, and it can even be applied to detect planets in neighbouring galaxies. So far, planet detections by microlensing have been considered to result from a change in the bending of light and the resulting magnification caused by a planet around the foreground lens star. However, in complete analogy to the annual parallax effect caused by the revolution of the Earth around the Sun, the motion of the source star around the common barycentre with an orbiting planet can also lead to observable deviations in microlensing light curves that can provide evidence for the unseen companion. We discuss this effect in some detail and study the prospects of microlensing observations for revealing planets through this alternative detection channel. Given that small distances between lens and source star are favoured, and that the effect becomes nearly independent of the source distance, planets would remain detectable even if their host star is located outside the Milky Way with a sufficiently good photometry (exceeding present-day technology) being possible. From synthetic light curves arising from a Monte Carlo simulation, we find that the chances for such detections are not overwhelming and appear practically limited to the most massive planets (at least with current observational set-ups), but they are large enough for leaving the possibility that one or the other signal has already been observed. However, it may remain undetermined whether the planet actually orbits the source star or rather the lens star, which leaves us with an ambiguity not only with respect to its location, but also to its properties.     

The full set of gas giant structures: I: On the origin of planetary masses and the planetary initial mass function

Context

Current planet search programs are detecting extrasolar planets at a rate of 60 planets per year. These planets show more diverse properties than was expected.

Aims

We try to get an overview of possible gas giant (proto-) planets for a full range of orbital periods and stellar masses. This allows the prediction of the full range of possible planetary properties which might be discovered in the near future.

Methods

We calculate the purely hydrostatic structure of the envelopes of proto-planets that are embedded in protoplanetary disks for all conceivable locations: combinations of different planetesimal accretion rates, host star masses, and orbital separations. At each location all hydrostatic equilibrium solutions to the planetary structure equations are determined by variation of core mass and pressure over many orders of magnitude. For each location we analyze the distribution of planetary masses.

Results

We get a wide spectrum of core-envelope structures. However, practically all calculated proto-planets are in the planetary mass range. Furthermore, the planet masses show a characteristic bimodal, sometimes trimodal, distribution. For the first time, we identify three physical processes that are responsible for the three characteristic planet masses: self-gravity in the Hill sphere, compact objects, and a region of very low adiabatic pressure gradient in the hydrogen equation of state. Using these processes, we can explain the dependence of the characteristic masses on the planet’s location: orbital period, host star mass, and planetesimal accretion rate (luminosity). The characteristic mass caused by the self-gravity effect at close proximity to the host star is typically one Neptune mass, thus producing the so-called hot Neptunes.

Conclusions

Our results suggest that hot Jupiters with orbital period less than 64 days (the exact location of the boundary depends on stellar type and accretion rate) have quite distinct properties which we expect to be reflected in a different mass distribution of these planets when compared to the “normal” planetary population. We use our theoretical survey to produce an upper mass limit for embedded planets: the maximum embedded equilibrium mass (MEEM). This naturally explains the lack of high mass planets between 3 and 64 days orbital period.     

A new family of planets? “Ocean-Planets”

A new family of planets is considered which is in between the rocky terrestrial planets and the gaseous giants, “Ocean-Planets.” We present the possible formation, composition and internal structure of these putative planets. We consider their oceans, as well as their possible Exobiology interest. These exoplanets should be detectable by Space missions such as Eddington, Kepler, and possibly COROT (launch scheduled in 2006). They have a density lower than that of rocky planets. Their rather large radius would make them attractive targets for exoplanet spectroscopic missions such as Darwin/TPF, all the more because a robust biosignature appears to exist.     

Obliquity variations of terrestrial planets in habitable zones

We have investigated obliquity variations of possible terrestrial planets in habitable zones (HZs) perturbed by a giant planet(s) in extrasolar planetary systems. All the extrasolar planets so far discovered are inferred to be jovian-type gas giants. However, terrestrial planets could also exist in extrasolar planetary systems. In order for life, in particular for land-based life, to evolve and survive on a possible terrestrial planet in an HZ, small obliquity variations of the planet may be required in addition to its orbital stability, because large obliquity variations would cause significant climate change. It is known that large obliquity variations are caused by spin-orbit resonances where the precession frequency of the planet's spin nearly coincides with one of the precession frequencies of the ascending node of the planet's orbit. Using analytical expressions, we evaluated the obliquity variations of terrestrial planets with prograde spins in HZs. We found that the obliquity of terrestrial planets suffers large variations when the giant planet's orbit is separated by several Hill radii from an edge of the HZ, in which the orbits of the terrestrial planets in the HZ are marginally stable. Applying these results to the known extrasolar planetary systems, we found that about half of these systems can have terrestrial planets with small obliquity variations (smaller than 10°) over their entire HZs. However, the systems with both small obliquity variations and stable orbits in their HZs are only 1/5 of known systems. Most such systems are comprised of short-period giant planets. If additional planets are found in the known planetary systems, they generally tend to enhance the obliquity variations. On the other hand, if a large/close satellite exists, it significantly enhances the precession rate of the spin axis of a terrestrial planet and is likely to reduce the obliquity variations of the planet. Moreover, if a terrestrial planet is in a retrograde spin state, the spin-orbit resonance does not occur. Retrograde spin, or a large/close satellite might be essential for land-based life to survive on a terrestrial planet in an HZ.     

Resonance capture and the evolution of the planets

The present nearly resonant orbital periods of the planets are explained in terms of past two-body resonance capture of planetesimals in the solar nebula. Planetary formation then occurs sequentially starting with Jupiter for the outer planets and Venus for the inner planets and propagates outward due to two-body orbital resonances. It might now be possible to reconstruct the evolutionary history of the planets from their nearly commensurable orbital periods and, hence, provide an explanation for the Titius-Bode law.     

Resonances of low orders in the planetary system of HD37124

The full set of published radial velocity data (52 measurements from Keck + 58 ones from ELODIE + 17 ones from CORALIE) for the star HD37124 is analysed. Two families of dynamically stable high-eccentricity orbital solutions for the planetary system are found. In the first one, the outer planets c and d are trapped in the 2/1 mean-motion resonance. The second family of solutions corresponds to the 5/2 mean-motion resonance between these planets. In both families, the planets are locked in (or close to) an apsidal corotation resonance. In the case of the 2/1 MMR, it is an asymmetric apsidal corotation (with the difference between the longitudes of periastra Δω ~ 60°), whereas in the case of the 5/2 MMR it is a symmetric antialigned one (Δω = 180°). It remains also possible that the two outer planets are not trapped in an orbital resonance. Then their orbital eccentricities should be relatively small (less than, say, 0.15) and the ratio of their orbital periods is unlikely to exceed 2.3 − 2.5.     

A matched filter method for ground-based sub-noise detection of terrestrial extrasolar planets in eclipsing binaries: application to CM Draconis

The photometric detection of extrasolar planets by transits in eclipsing binary systems can be significantly improved by cross-correlating the observational light curves with synthetic models of possible planetary transit features, essentially a matched filter approach. We demonstrate the utility and application of this transit detection algorithm for ground-based detections of terrestrial-sized (Earth-to-Neptune radii) extrasolar planets in the dwarf M-star eclipsing binary system CM Draconis. Preliminary photometric observational data of this system demonstrate that the observational noise is well characterized as white and Gaussian at the observational time steps required for precision photometric measurements. Depending on planet formation scenarios, terrestrial-sized planets may form quite close to this low-luminosity system. We demonstrate, for example, that planets as small as 1.4 Earth radii with periods on the order of a few months in the CM Draconis system could be detected at the 99.9% confidence level in less than a year using 1-m class telescopes from the ground. This result contradicts commonly held assumptions limiting present ground-based efforts to, at best, detections of gas giant planets after several years of observation. This method can be readily extended to a number of other larger star systems with the utilization of larger telescopes and longer observing times. Its extension to spacecraft observations should also allow the determination of the presence of terrestrial-sized planets in nearly 100 other known eclipsing binary systems.