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 mid-infrared spectrum of the zodiacal and exozodiacal light

The zodiacal light is the dominant source of the mid-infrared sky brightness seen from Earth, and exozodiacal light is the dominant emission from planetary and debris systems around other stars. We observed the zodiacal light spectrum with the mid-infrared camera ISOCAM over the wavelength range 5-16 μm and a wide range of orientations relative to the Sun (solar elongations 68°-113°) and the ecliptic (plane to pole). The temperature in the ecliptic ranged from 269 K at solar elongation 68° to 244 K at 113°, and the polar temperature, characteristic of dust 1 AU from the Sun, is 274 K. The observed temperature is exactly as expected for large (>10 μm radius), low-albedo (<0.08), rapidly-rotating, gray particles 1 AU from the Sun. Smaller particles (<10 μm radius) radiate inefficiently in the infrared and are warmer than observed. We present theoretical models for a wide range of particle size distributions and compositions; it is evident that the zodiacal light is produced by particles in the 10-100 μm radius range. In addition to the continuum, we detect a weak excess in the 9-11 μm range, with an amplitude of 6% of the continuum. The shape of the feature can be matched by a mixture of silicates: amorphous forsterite/olivine provides most of the continuum and some of the 9-11 μm silicate feature, dirty crystalline olivine provides the red wing of the silicate feature (and a bump at 11.35 μm), and a hydrous silicate (montmorillonite) provides the blue wing of the silicate feature. The presence of hydrous silicate suggests the parent bodies of those particles were formed in the inner solar nebula. Large particles dominate the size distribution, but at least some small particles (radii ∼1 μm) are required to produce the silicate emission feature. The strength of the feature may vary spatially, with the strongest features being at the lowest solar elongations as well as at high ecliptic latitudes; if confirmed, this would imply that the dust properties change such that dust further from the Sun has a weaker silicate feature. To compare the properties of zodiacal dust to dust around other main sequence stars, we reanalyzed the exozodiacal light spectrum for β Pic to derive the shape of its silicate feature. The zodiacal and exozodiacal spectra are very different. The exozodiacal spectra are dominated by cold dust, with emission peaking in the far-infrared, while the zodiacal spectrum peaks around 20 μm. We removed the debris disk continuum from the spectra by fitting a blackbody with a different temperature for each aperture (ranging from 3.7″ to 27″); the resulting silicate spectra for β Pic are identical for all apertures, indicating that the silicate feature arises close to the star. The shape of the silicate feature from β Pic is nearly identical to that derived from the ISO spectrum of 51 Oph; both exozodiacal features are very different from that of the zodiacal light. The exozodiacal features are roughly triangular, peaking at 10.3 μm, while the zodiacal feature is more boxy, indicating a different mineralogy.     

Maximum-likelihood method for estimating the mass and period distributions of extrasolar planets

We investigate the distribution of mass M and orbital period P of extrasolar planets, taking account of selection effects caused by the limited velocity precision and duration of existing surveys. We fit the data on 72 planets to a power-law distribution of the form  d n = CM ^−α P ^−β(d M / M )(d P / P )  , and find  α= 0.11 ± 0.10  ,  β=−0.27 ± 0.06  for   M ≲ 10 M _J  , where   M _J  is the mass of Jupiter. The correlation coefficient between these two exponents is −0.31, indicating that uncertainties in the two distributions are coupled. We estimate that 4 per cent of solar-type stars have companions in the range  1 M _J < M < 10 M _J  ,  2_d < P < 10 yr  .     

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.     

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)     

Dynamical relaxation and the orbits of low-mass extrasolar planets

We consider the evolution of a system containing a population of massive planets formed rapidly through a fragmentation process occurring on a scale on the order of 100 au and a lower mass planet that assembles in a disc on a much longer time-scale. During the formation phase, the inner planet is kept on a circular orbit owing to tidal interaction with the disc, while the outer planets undergo dynamical relaxation. Interaction with the massive planets left in the system after the inner planet forms may increase the eccentricity of the inner orbit to high values, producing systems similar to those observed.     

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.     

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.     

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.     

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.     

Physical properties of asteroid dust bands and their sources

Disruptive collisions in the main belt can liberate fragments from parent bodies ranging in size from several micrometers to tens of kilometers in diameter. These debris bodies group at initially similar orbital locations. Most asteroid-sized fragments remain at these locations and are presently observed as asteroid families. Small debris particles are quickly removed by Poynting-Robertson drag or comminution but their populations are replenished in the source locations by collisional cascade. Observations from the Infrared Astronomical Satellite (IRAS) showed that particles from particular families have thermal radiation signatures that appear as band pairs of infrared emission at roughly constant latitudes both above and below the Solar System plane. Here we apply a new physical model capable of linking the IRAS dust bands to families with characteristic inclinations. We use our results to constrain the physical properties of IRAS dust bands and their source families. Our results indicate that two prominent IRAS bands at inclinations ≈2.1° and ≈9.3° are byproducts of recent asteroid disruption events. The former is associated with a disruption of a ≈30-km asteroid occurring 5.8 Myr ago; this event gave birth to the Karin family. The latter came from the breakup of a large >100-km-diameter asteroid 8.3 Myr ago that produced the Veritas family. Using an N-body code, we tracked the dynamical evolution of ≈10⁶ particles, 1 μm to 1 cm in diameter, from both families. We then used these results in a Monte Carlo code to determine how small particles from each population undergo collisional evolution. By computing the thermal emission of particles, we were able to compare our results with IRAS observations. Our best-fit model results suggest the Karin and Veritas family particles contribute by 5-9% in 10-60-μm wavelengths to the zodiacal cloud's brightness within 50° latitudes around the ecliptic, and by 9-15% within 10° latitudes. The high brightness of the zodiacal cloud at large latitudes suggests that it is mainly produced by particles with higher inclinations than what would be expected for asteroidal particles produced by sources in the main belt. From these results, we infer that asteroidal dust represents a smaller fraction of the zodiacal cloud than previously thought. We estimate that the total mass accreted by the Earth in Karin and Veritas particles with diameters 20-400 μm is ≈15,000-20,000 tons per year (assuming 2 g cm⁻³ particles density). This is ≈30-50% of the terrestrial accretion rate of cosmic material measured by the Long Duration Exposure Facility. We hypothesize that up to ≈50% of our collected interplanetary dust particles and micrometeorites may be made up of particle species from the Veritas and Karin families. The Karin family IDPs should be about as abundant as Veritas family IDPs though this ratio may change if the contribution of third, near-ecliptic source is significant. Other sources of dust and/or large impact speeds must be invoked to explain the remaining ≈50-70%. The disproportional contribution of Karin/Veritas particles to the zodiacal cloud (only 5-9%) and to the terrestrial accretion rate (30-50%) suggests that the effects of gravitational focusing by the Earth enhance the accretion rate of Karin/Veritas particles relative to those in the background zodiacal cloud. From this result and from the latitudinal brightness of the zodiacal cloud, we infer that the zodiacal cloud emission may be dominated by high-speed cometary particles, while the terrestrial impactor flux contains a major contribution from asteroidal sources. Collisions and Poynting-Robertson drift produce the size-frequency distribution (SFD) of Karin and Veritas particles that becomes increasingly steeper closer to the Sun. At 1 AU, the SFD is relatively shallow for small particle diameters D (differential slope exponent of particles with D?100 μm is ≈2.2-2.5) and steep for D?100 μm. Most of the mass at 1 AU, as well as most of the cross-sectional area, is contributed by particles with D≈100-200 μm. Similar result has been found previously for the SFD of the zodiacal cloud particles at 1 AU. The fact that the SFD of Karin/Veritas particles is similar to that of the zodiacal cloud suggests that similar processes shaped these particle populations. We estimate that there are ≈5×¹⁰²⁴ Karin and ≈10²⁵ Veritas family particles with D>30 μm in the Solar System today. The IRAS observation of the dust bands may be satisfactorily modeled using ‘averaged’ SFDs that are constant with semimajor axis. These SFDs are best described by a broken power-law function with differential power index α≈2.1-2.4 for D?100 μm and by α?3.5 for 100 μm?D?1 cm. The total cross-sectional surface area of Veritas particles is a factor of ≈2 larger than the surface area of the particles producing the inner dust bands. The total volumes in Karin and Veritas family particles with 1 μm<D<1 cm correspond to D=11 km and D=14 km asteroids with equivalent masses ≈1.5×¹⁰¹⁸ g and ≈3.0×¹⁰¹⁸ g, respectively (assuming 2 g cm⁻³ bulk density). If the size-frequency and radial distribution of particles in the zodiacal cloud were similar to those in the asteroid dust bands, we estimate that the zodiacal cloud represents ∼3×¹⁰¹⁹ g of material (in particles with 1 μm<D<1 cm) at ±10° around the ecliptic and perhaps as much as ∼¹⁰²⁰ g in total. The later number corresponds to about a 23-km-radius sphere with 2 g cm⁻³ density.     

Parent stars of extrasolar planets – VIII. Chemical abundances for 18 elements in 31 stars

We present the results of detailed spectroscopic abundance analyses for 18 elements in 31 nearby stars with planets (SWPs). The resulting abundances are combined with other similar studies of nearby SWPs and compared to a sample of nearby stars without detected planets. We find some evidence for abundance differences between these two samples for Al, Si and Ti. Some of our results are in conflict with a recent study of SWPs in the SPOCS data base. We encourage continued study of the abundance patterns of SWPs to resolve these discrepancies.