Empirical evidence for tidal evolution in transiting planetary systems

Most transiting planets orbit very close to their parent star, causing strong tidal forces between the two bodies. Tidal interaction can modify the dynamics of the system through orbital alignment, circularization, synchronization and orbital decay by exchange of angular moment. Evidence for tidal circularization in close-in giant planet is well known. Here, we review the evidence for excess rotation of the parent stars due to the pull of tidal forces towards spin-orbit synchronization. We find suggestive empirical evidence for such a process in the present sample of transiting planetary systems. The corresponding angular momentum exchange would imply that some planets have spiralled towards their star by substantial amounts since the dissipation of the protoplanetary disc. We suggest that this could quantitatively account for the observed mass–period relation of close-in gas giants. We discuss how this scenario can be further tested and point out some consequences for theoretical studies of tidal interactions and for the detection and confirmation of transiting planets from radial velocity and photometric surveys.     

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.     

A SuperWASP search for additional transiting planets in 24 known systems

We present results from a search for additional transiting planets in 24 systems already known to contain a transiting planet. We model the transits due to the known planet in each system and subtract these models from light curves obtained with the SuperWASP (Wide Angle Search for Planets) survey instruments. These residual light curves are then searched for evidence of additional periodic transit events. Although we do not find any evidence for additional planets in any of the planetary systems studied, we are able to characterize our ability to find such planets by means of Monte Carlo simulations. Artificially generated transit signals corresponding to planets with a range of sizes and orbital periods were injected into the SuperWASP photometry and the resulting light curves searched for planets. As a result, the detection efficiency as a function of both the radius and orbital period of any second planet is calculated. We determine that there is a good (>50 per cent) chance of detecting additional, Saturn-sized planets in   P ∼  10 d orbits around planet-hosting stars that have several seasons of SuperWASP photometry. Additionally, we confirm previous evidence of the rotational stellar variability of WASP-10, and refine the period of rotation. We find that the period of the rotation is  11.91 ± 0.05  d, and the false alarm probability for this period is extremely low  (∼10⁻¹³)  .     

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.     

Periastron precession measurements in transiting extrasolar planetary systems at the level of general relativity

Transiting exoplanetary systems are surpassingly important among the planetary systems since they provide the widest spectrum of information for both the planet and the host star. If a transiting planet is on an eccentric orbit, the duration of transits T _D is sensitive to the orientation of the orbital ellipse relative to the line of sight. The precession of the orbit results in a systematic variation in both the duration of individual transit events and the observed period between successive transits,   P _obs  . The periastron of the ellipse slowly precesses due to general relativity and possibly the presence of other planets in the system. This secular precession can be detected through the long-term change in   P _obs  (transit timing variations, TTV) or in T _D (transit duration variations, TDV). We estimate the corresponding precession measurement precision for repeated future observations of the known eccentric transiting exoplanetary systems (XO-3b, HD 147506b, GJ 436b and HD 17156b) using existing or planned space-borne instruments. The TDV measurement improves the precession detection sensitivity by orders of magnitude over the TTV measurement. We find that TDV measurements over a approximately 4 yr period can typically detect the precession rate to a precision well exceeding the level predicted by general relativity.     

WASP-1b and WASP-2b: two new transiting exoplanets detected with SuperWASP and SOPHIE

We have detected low-amplitude radial-velocity variations in two stars, USNO-B1.0 1219–0005465 (GSC  02265–00107 = WASP–1  ) and USNO-B1.0 0964–0543604 (GSC  00522–01199 = WASP–2  ). Both stars were identified as being likely host stars of transiting exoplanets in the 2004 SuperWASP wide-field transit survey. Using the newly commissioned radial-velocity spectrograph SOPHIE at the Observatoire de Haute-Provence, we found that both objects exhibit reflex orbital radial-velocity variations with amplitudes characteristic of planetary-mass companions and in-phase with the photometric orbits. Line-bisector studies rule out faint blended binaries as the cause of either the radial-velocity variations or the transits. We perform preliminary spectral analyses of the host stars, which together with their radial-velocity variations and fits to the transit light curves yield estimates of the planetary masses and radii. WASP-1b and WASP-2b have orbital periods of 2.52 and 2.15 d, respectively. Given mass estimates for their F7V and K1V primaries, we derive planet masses 0.80–0.98 and 0.81–0.95 times that of Jupiter, respectively. WASP-1b appears to have an inflated radius of at least 1.33 R _Jup, whereas WASP-2b has a radius in the range 0.65–1.26 R _Jup.     

Using long-term transit timing to detect terrestrial planets

We propose that the presence of additional planets in extrasolar planetary systems can be detected by long-term transit timing studies. If a transiting planet is on an eccentric orbit then the presence of another planet causes a secular advance of the transiting planet's pericentre over and above the effect of general relativity. Although this secular effect is impractical to detect over a small number of orbits, it causes long-term differences when future transits occur, much like the long-term decay observed in pulsars. Measuring this transit-timing delay would thus allow the detection of either one or more additional planets in the system or the first measurements of non-zero oblateness ( J ₂) of the central stars.     

Study by MOA of extrasolar planets in gravitational microlensing events of high magnification

A search for extrasolar planets was carried out in three gravitational microlensing events of high magnification, MACHO  98–BLG–35  , MACHO  99–LMC–2  and OGLE  00–BUL–12  . Photometry was derived from observational images by the MOA and OGLE groups using an image subtraction technique. For MACHO  98–BLG–35  , additional photometry derived from the MPS and PLANET groups was included. Planetary modelling of the three events was carried out in a supercluster computing environment. The estimated probability for explaining the data on MACHO  98–BLG–35  without a planet is <1 per cent. The best planetary model has a planet of mass ∼(0.4–1.5)× M _Earth at a projected radius of either ∼1.5 or ∼2.3 au. We show how multiplanet models can be applied to the data. We calculate exclusion regions for the three events and find that Jupiter-mass planets can be excluded with projected radii from as wide as about 30 au to as close as around 0.5 au for MACHO  98–BLG–35  and OGLE  00–BUL–12  . For MACHO  99–LMC–2  , the exclusion region extends out to around 10 au and constitutes the first limit placed on a planetary companion to an extragalactic star. We derive a particularly high peak magnification of ∼160 for OGLE  00–BUL–12  . We discuss the detectability of planets with masses as low as Mercury in this and similar events.     

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.     

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.     

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.     

Detectability of exoplanetary transits from radial velocity surveys

Of the known transiting extrasolar planets, a few have been detected through photometric follow-up observations of radial velocity planets. Perhaps the best known of these is the transiting exoplanet HD 209458b. For hot Jupiters (periods less than ∼5 d), the a priori information that 10 per cent of these planets will transit their parent star due to the geometric transit probability leads to an estimate of the expected transit yields from radial velocity surveys. The radial velocity information can be used to construct an effective photometric follow-up strategy which will provide optimal detection of possible transits. Since the planet-harbouring stars are already known in this case, one is only limited by the photometric precision achievable by the chosen telescope/instrument. The radial velocity modelling code presented here automatically produces a transit ephemeris for each planet data set fitted by the program. Since the transit duration is brief compared with the fitted period, we calculate the maximum window for obtaining photometric transit observations after the radial velocity data have been obtained, generalizing for eccentric orbits. We discuss a typically employed survey strategy which may contribute to a possible radial velocity bias against detection of the very hot Jupiters which have dominated the transit discoveries. Finally, we describe how these methods can be applied to current and future radial velocity surveys.     

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.     

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.     

Migration of giant planets in a time-dependent planetesimal accretion disc

In this paper we develop further the model for the migration of planets introduced in Del Popolo et al. We first model the protoplanetary nebula as a time-dependent accretion disc, and find self-similar solutions to the equations of the accretion disc that give us explicit formulae for the spatial structure and the temporal evolution of the nebula. These equations are then used to obtain the migration rate of the planet in the planetesimal disc, and to study how the migration rate depends on the disc mass, on its time evolution and on some values of the dimensionless viscosity parameter α . We find that planets that are embedded in planetesimal discs, having total mass of  10^-4-0.1 M_⊙  , can migrate inward a large distance for low values of α (e.g.,   α ≃10^-3-10^-2)  and/or large disc mass, and can survive only if the inner disc is truncated or because of tidal interaction with the star. Orbits with larger a are obtained for smaller values of the disc mass and/or for larger values of α . This model may explain several orbital features of the recently discovered giant planets orbiting nearby stars.     

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 Radii of Close-in Giant Planets

The recent discovery that the close-in extrasolar giant planet HD 209458b transits its star has provided a first-of-its-kind measurement of the planet's radius and mass. In addition, there is a provocative detection of the light reflected off of the giant planet tau Bootis b. Including the effects of stellar irradiation, we estimate the general behavior of radius/age trajectories for such planets and interpret the large measured radii of HD 209458b and tau Boo b in that context. We find that HD 209458b must be a hydrogen-rich gas giant. Furthermore, the large radius of a close-in gas giant is not due to the thermal expansion of its atmosphere but to the high residual entropy that remains throughout its bulk by dint of its early proximity to a luminous primary. The large stellar flux does not inflate the planet but retards its otherwise inexorable contraction from a more extended configuration at birth. This implies either that such a planet was formed near its current orbital distance or that it migrated in from larger distances (>/=0.5 AU), no later than a few times 107 yr of birth.     

Debris disc stirring by secular perturbations from giant planets

Detectable debris discs are thought to require dynamical excitation ('stirring'), so that planetesimal collisions release large quantities of dust. We investigate the effects of the secular perturbations of a planet, which may lie at a significant distance from the planetesimal disc, to see if these perturbations can stir the disc, and if so over what time-scale. The secular perturbations cause orbits at different semimajor axes to precess at different rates, and after some time   t _cross  initially non-intersecting orbits begin to cross. We show that   t _cross∝ a ^9/2_disc/( m _pl e _pl a ³_pl)  , where   m _pl, e _pl  and   a _pl  are the mass, eccentricity and semimajor axis of the planet, and   a _disc  is the semimajor axis of the disc. This time-scale can be faster than that for the growth of planetesimals to Pluto's size within the outer disc. We also calculate the magnitude of the relative velocities induced among planetesimals and infer that a planet's perturbations can typically cause destructive collisions out to 100 s of au. Recently formed planets can thus have a significant impact on planet formation in the outer disc which may be curtailed by the formation of giant planets much closer to the star. The presence of an observed debris disc does not require the presence of Pluto-sized objects within it, since it can also have been stirred by a planet not in the disc. For the star ε Eridani, we find that the known radial velocity planet can excite the planetesimal belt at 60 au sufficiently to cause destructive collisions of bodies up to 100 km in size, on a time-scale of 40 Myr.     

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.