Observable consequences of planet formation models in systems with close-in terrestrial planets

To date, two planetary systems have been discovered with close-in, terrestrial-mass planets     . Many more such discoveries are anticipated in the coming years with radial velocity and transit searches. Here we investigate the different mechanisms that could form 'hot Earths' and their observable predictions. Models include: (1) in situ accretion; (2) formation at larger orbital distance followed by inward 'type 1' migration; (3) formation from material being 'shepherded' inward by a migrating gas giant planet; (4) formation from material being shepherded by moving secular resonances during dispersal of the protoplanetary disc; (5) tidal circularization of eccentric terrestrial planets with close-in perihelion distances and (6) photoevaporative mass-loss of a close-in giant planet. Models 1–4 have been validated in previous work. We show that tidal circularization can form hot Earths, but only for relatively massive planets     with very close-in perihelion distances (≲0.025 au), and even then the net inward movement in orbital distance is at most only 0.1–0.15 au. For planets of less than     , photoevaporation can remove the planet's envelope and leave behind the solid core on a Gyr time-scale, but only for planets inside 0.025–0.05 au. Using two quantities that are observable by current and upcoming missions, we show that these models each produce unique signatures, and can be observationally distinguished. These observables are the planetary system architecture (detectable with radial velocities, transits and transit timing) and the bulk composition of transiting close-in terrestrial planets (measured by transits via the planet's radius).     

Planetary microlensing at high magnification

Simulations of planetary microlensing at high magnification that were carried out on a cluster computer are presented. It was found that the perturbations owing to two-thirds of all planets occur in the time interval  −0.5 t _FWHM,0.5 t _FWHM  with respect to the peak of the microlensing light curve, where   t _FWHM  is typically ∼14 h. This implies that only this restricted portion of the light curve need be intensively monitored for planets – a very significant practical advantage. Nearly all planetary detections in high-magnification events will not involve caustic crossings. We discuss the issues involved in determining the planetary parameters in high magnification events. Earth-mass planets may be detected with 1-m class telescopes if their projected orbital radii lie within about 1.5–2.5 au. Giant planets are detectable over a much larger region. For multiplanet systems the perturbations caused by individual planets can be separated under certain conditions. The size of the source star needs to be determined independently, but the presence of spots on the source star is likely to be negligible, as is the effect of planetary motion during an event.     

A dynamical analysis of the 14 Herculis planetary system

Precision radial velocity measurements of the Sun-like dwarf 14 Herculis published by Naef et al., Butler et al. and Wittenmyer, Endl & Cochran reveal a Jovian planet in a 1760-d orbit and a trend indicating the second distant object. On the grounds of dynamical considerations, we test a hypothesis that the trend can be explained by the presence of an additional giant planet. We derive dynamical limits to the orbital parameters of the putative outer Jovian companion in an orbit within ∼13 au. In this case, the mutual interactions between the Jovian planets are important for the long-term stability of the system. The best self-consistent and stable Newtonian fit to an edge-on configuration of Jovian planets has the outer planet in 9-au orbit with a moderate eccentricity of ∼0.2 and confined to a zone spanned by the low-order mean motion resonances 5:1 and 6:1. This solution lies in a shallow minimum of (χ²_ν)^1/2 and persists over a wide range of the system inclination. Other stable configurations within 1σ confidence interval of the best fit are possible for the semimajor axis of the outer planet in the range of (6,13) au and the eccentricity in the range of (0, 0.3). The orbital inclination cannot yet be determined but when it decreases, both planetary masses approach ∼10 m _J and for i ∼ 30° the hierarchy of the masses is reversed.     

Migration of giant planets in planetesimal discs

Planets orbiting a planetesimal circumstellar disc can migrate inward from their initial positions because of dynamical friction between planets and planetesimals. The migration rate depends on the disc mass and on its time evolution. Planets that are embedded in long-lived planetesimal discs, having total mass of 10⁻⁴– 0.01 M_⊙ , can migrate inward a large distance and can survive only if the inner disc is truncated or as a result of tidal interaction with the star. In this case the semimajor axis, a , of the planetary orbit is less than 0.1 au. Orbits with larger a are obtained for smaller values of the disc mass or for a rapid evolution (depletion) of the disc. This model may explain not only several of the orbital features of the giant planets that have been discovered in recent years orbiting nearby stars, but also the metallicity enhancement found in several stars associated with short-period planets.     

Tidal Evolution of Low-mass Kepler Planets

The planets with a radius < 4 R_⊕ observed by the Kepler mission exhibit a unique feature, and propose a challenge for current planetary formation models. The tidal effect between a planet and its host star plays an essential role in reconfiguring the final orbits of the short-period planets. In this work, based on various initial Rayleigh distributions of the orbital elements, the final semi-major axis distributions of the planets with a radius < 4 R_⊕ after suffering tidal evolutions are investigated. Our simulations have qualitatively revealed some statistical properties: the semi-major axis and its peak value all increase with the increase of the initial semi-major axis and eccentricity. For the case that the initial mean semi-major axis is less than 0.1 au and the mean eccentricity is larger than 0.25, the results of numerical simulation are approximately consistent with the observation. In addition, the effects of other parameters, such as the tidal dissipation coefficient, stellar mass and planetary mass, etc., on the final semi-major axis distribution after tidal evolution are all relatively small. Based on the simulation results, we have tried to find some clues for the formation mechanism of low-mass planets. We speculate that these low-mass planets probably form in the far place of protoplanetary disk with a moderate eccentricity via the type I migration, and it is also possible to form in situ.     

A search for starlight reflected from HD 75289b

We have used a Doppler tomographic analysis to conduct a deep search for the starlight reflected from the planetary companion to HD 75289. In four nights on VLT(UT2)/UVES in 2003 January, we obtained 684 high-resolution echelle spectra with a total integration time of 26 h. We establish an upper limit on the geometric albedo of the planet   p < 0.12  (to the 99.9 per cent significance level) at the most probable orbital inclination   i ≃ 60°  , assuming a grey albedo, a Venus-like phase function and a planetary radius   R _p= 1.6 R_Jup  . We are able to rule out some combinations of the predicted planetary radius and atmospheric albedo models with high, reflective cloud decks.     

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.     

Precessing collimated outflows in the planetary nebula IC 4846

We present [N  ii ] and H α images and high-resolution long-slit spectra of the planetary nebula IC 4846, which reveal, for the first time, its complex structure and the existence of collimated outflows. The object consists of a moderately elongated shell, two (and probably three) pairs of collimated bipolar outflows at different orientations, and an attached circular shell. One of the collimated pairs is constituted by two curved, extended filaments the properties of which indicate a high-velocity, bipolar precessing jet. A difference of ≃10 km s⁻¹ is found between the systemic velocity of the precessing jets and the centroid velocity of the nebula, as recently reported for Hu 2-1. We propose that this difference is as a result of orbital motion of the ejection source in a binary central star. The orbital separation of 30 au and period 100 yr estimated for the binary are similar to those in Hu 2-1, linking the central stars of both planetary nebulae to interacting binaries. Extraordinary similarities also exist between IC 4846 and the bewildering planetary nebula NGC 6543, suggesting a similar formation history for both objects.     

Detecting planets in planetary nebulae

We examine the possibility of detecting signatures of surviving Uranus/Neptune-like planets inside planetary nebulae. Planets that are not too close to the stars (orbital separation larger than ∼5 au) are likely to survive the entire evolution of the star. As the star turns into a planetary nebula, it has a fast wind and strong ionizing radiation. The interaction of the radiation and wind with a planet may lead to the formation of a compact condensation or tail inside the planetary nebula, which emits strongly in H α , but not in [O  iii ]. The position of the condensation (or tail) will change over a time-scale of ∼10 yr. Such condensations might be detected with currently existing telescopes.     

Planetary dynamics in stellar clusters

We investigate how the formation and evolution of extrasolar planetary systems can be affected by stellar encounters that occur in the crowded conditions of a stellar cluster. Using plausible estimates of cluster evolution, we show how planet formation may be suppressed in globular clusters while planets wider than ≳0.1 au that do form in such environments can be ejected from their stellar system. Less crowded systems such as open clusters have a much reduced effect on any planetary system. Planet formation is unaffected in open clusters and only the wider planetary systems will be disrupted during the cluster's lifetime. The potential for free-floating planets in these environments is also discussed.     

The Effect of Sweeping Secular Resonances on the Classical Kuiper Belt

Abstract The Kuiper Belt is a disk of small icy objects orbiting the Sun beyond Neptune. The region between 40-48AU in this disk is supposed to consist of dynamical “cold” objects on low-inclination orbits and is called the “Classical Kuiper Belt”. Recent observations reveal that there is a “hot” population with inclinations being as large as 30? residing in this region. Secular resonance sweeping, which took place in the late stage of formation of the planetary system when the residual nebula gas was dispersing, is a possible mechanism that can excite the orbits in this region. In this paper, we investigate in detail the excitation of orbital inclination by this mechanism. It is shown that the excitation depends sensitively on the angle δ between the midplane of the nebula gas and the invariable plane of the solar system. The excitation is very small when δ = 0?, but if the gas midplane coincides with the ecliptic, i.e. if δ ≈ 1.6?, then objects in the region of classical Kuiper belt can be excited to orbital inclinations as high as 30?, provided the nebula gas has the proper initial density and disperses at a proper rate. We also considered the orbital excitation by secular resonance sweeping with Jupiter on an inclined orbit and with migrating Jovian planets, and found the excitation is only slightly affected.     

Data analysis on the extrasolar planets using robust clustering

We use both the conventional and more recently developed methods of cluster analysis to study the data of extrasolar planets (exoplanets). Using the data set with planetary mass M , orbital period P and orbital eccentricity e , we investigate the possible clustering in the  ln  M ,  ln  P ,  ln  P –ln  M ,   e   and ln   P – e spaces. There are two main implications: (1) mass distribution is continuous, and (2) orbital population could be classified into three clusters, which correspond to the exoplanets in the regimes of tidal, ongoing tidal and disc interaction, respectively.     

Why are there so few hot Jupiters?

We use numerical simulations to model the migration of massive planets at small radii and compare the results with the known properties of 'hot Jupiters' (extrasolar planets with semimajor axes   a < 0.1  au). For planet masses   M _pl sin  i > 0.5 M _J  , the evidence for any 'pile-up' at small radii is weak (statistically insignificant), and although the mass function of hot Jupiters is deficient in high-mass planets as compared to a reference sample located further out, the small sample size precludes definitive conclusions. We suggest that these properties are consistent with disc migration followed by entry into a magnetospheric cavity close to the star. Entry into the cavity results in a slowing of migration, accompanied by a growth in orbital eccentricity. For planet masses in excess of 1 Jupiter mass we find eccentricity growth time-scales of a few ×10⁵ yr, suggesting that these planets may often be rapidly destroyed. Eccentricity growth appears to be faster for more massive planets which may explain changes in the planetary mass function at small radii and may also predict a pile-up of lower mass planets, the sample of which is still incomplete.     

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.     

On the habitability of the OGLE-2006-BLG-109L planetary system

We investigate the dynamics of putative Earth-mass planets in the habitable zone (HZ) of the extrasolar planetary system OGLE-2006-BLG-109L, a close analogue of the Solar system. Our work is inspired by the work of Malhotra & Minton. Using the linear Laplace–Lagrange theory, they identified a strong secular resonance that may excite large eccentricity of orbits in the HZ. However, due to uncertain or unconstrained orbital parameters, the subsystem of Jupiters may be found in a dynamically active region of the phase space spanned by low-order mean-motion resonances. To generalize this secular model, we construct a semi-analytical averaging method in terms of the restricted problem. The secular orbits of large planets are approximated by numerically averaged osculating elements. They are used to calculate the mean orbits of terrestrial planets by means of a high-order analytic secular theory developed in our previous works. We found regions in the parameter space of the problem in which stable, quasi-circular orbits in the HZ are permitted. The excitation of eccentricity in the HZ strongly depends on the apsidal angle of jovian orbits. For some combinations of that angle, eccentricities and semimajor axes consistent with the observations, a terrestrial planet may survive in low eccentric orbits. We also study the effect of post-Newtonian gravity correction on the innermost secular resonance.     

A search for Ca ii emission enhancement in stars resulting from nearby giant planets

We present a search for periodicities ( P _chr) in the chromospheric Ca  ii infrared triplet emission of several stars ( τ Boo, 51 Peg, υ And, ρ ¹ Cnc, ρ CrB, 70 Vir and GL 876) which may be directly attributable to interaction with close-in giant planets. Activity enhancements could arise from increased non-radiative heating and dynamo action in planet-induced tidal bulges (with P _chr≈ P _orb/2), or from interactions between the stellar and planetary magnetic fields (with P _chr≈ P _orb). We compare both P _chr and the phase dependence of the activity with the planetary orbital period P _orb, the orbital phase, and models. No significant P _chr or phase dependence attributable to planets can be clearly identified. We place approximate upper limits on the amplitude of any planet-induced activity. We identify a possible stellar rotation period for GL 876, and support previous period determinations for four other stars. We discuss the results and possible directions of future research.     

Transit timing effects due to an exomoon – II

In our previous paper, we evaluated the transit duration variation (TDV) effect for a co-aligned planet-moon system at an orbital inclination of   i = 90°  . Here, we will consider the effect for the more general case of   i ≤ 90°  and an exomoon inclined from the planet-star plane by Euler rotation angles  α, β  and γ. We find that the TDV signal has two major components, one due to the velocity variation effect described in our first paper and one new component due to transit impact parameter variation. By evaluating the dominant terms, we find the two effects are additive for prograde exomoon orbits, and deductive for retrograde orbits. This asymmetry could allow for future determination of the orbital sense of motion. We re-evaluate the ratio of TDV and transit timing variation effects, η, in the more general case of an inclined planetary orbit with a circular orbiting moon and find that it is still possible to directly determine the moon's orbital separation from just the ratio of the two amplitudes, as first proposed in our previous paper.     

Upper limits on the hot Jupiter fraction in the field of NGC 7789

We describe a method of estimating the abundance of short-period extra-solar planets based on the results of a photometric survey for planetary transits. We apply the method to a 21-night survey with the 2.5-m Isaac Newton Telescope of ∼32 000 stars in a ∼0.5 × 0.5 deg² field including the open cluster NGC 7789. From the colour–magnitude diagram, we estimate the mass and radius of each star by comparison with the cluster main sequence. We search for injected synthetic transits throughout the light curve of each star in order to determine their recovery rate, and thus calculate the expected number of transit detections and false alarms in the survey. We take proper account of the photometric accuracy, time sampling of the observations and criteria (signal-to-noise ratio and number of transits) adopted for transit detection. Assuming that none of the transit candidates found in the survey will be confirmed as real planets, we place conservative upper limits on the abundance of planets as a function of planet radius, orbital period and spectral type.     

uvbyβ photometry of the short-period binary VV Ursae Majoris

We present well-sampled uvby light curves, supplemented by a few β filter measurements, of the Algol binary VV UMa. The light curves are analysed using two different codes to derive the orbital and absolute stellar parameters of this binary. We find reasonably good fits to the light curves and determine the stellar effective temperatures T _eff,1≃9000–9600 K , and T _eff,2≃5300–5600 K with a mass ratio q ≃0.35 . From the light-curve fits we discard the possibility of an anomalous gravity-darkening exponent for the secondary star of this system, as previously suggested.
We find evidence of short-term, small-amplitude variations in the brightness of the system. Two periodicities of about 1.10 and 0.51 h seem to be present in the data for at least two different nights, even within the secondary eclipse. This suggests that VV UMa may be a new Algol binary with a low-amplitude variable primary star, but new data collected during longer observing runs are necessary to confirm the pulsating nature of the brightness variations.