S. Ferraz-Mello

Estimation of periods from unequally spaced observations

A better estimation of the power spectrum of a time series formed with unequally spaced observations may be obtained by means of a data-compensated discrete Fourier transform. This transform is defined so as to include the uneven spacing of the dates of observation and weighting of the corresponding data. The accurate determination of the peak heights allows one to design harmonic filters and thus to make a more certain choice among peaks of similar height and also to discriminate peaks that are just aliases of other peaks. The theory is applied to simulated time series and also to true observational data.

Transiting exoplanets from the CoRoT space mission - XXIV. CoRoT-25b and CoRoT-26b: two low-density giant planets

We report the discovery of two transiting exoplanets, CoRoT-25b and CoRoT-26b, both of low density, one of which is in the Saturn mass-regime. For each star, ground-based complementary observations through optical photometry and radial velocity measurements secured the planetary nature of the transiting body and allowed us to fully characterize them. For CoRoT-25b we found a planetary mass of 0.27 similar to 0.04 M-Jup, a radius of 1.08(-0.10)(+0.3) R-Jup and hence a mean density of 0.15(-0.06)(+ 0.15) g cm(-3). The planet orbits an F9 mainsequence star in a 4.86-day period, that has a V magnitude of 15.0, solar metallicity, and an age of 4.5(-2.0) (+1.8)-Gyr. CoRoT-26b orbits a slightly evolved G5 star of 9.06 +/- 1.5-Gyr age in a 4.20-day period that has solar metallicity and a V magnitude of 15.8. With a mass of 0.52 +/- 0.05 MJup, a radius of 1.26(-0.07)(+0.13) R-Jup, and a mean density of 0.28(-0.07)(+0.09) g cm(-3), it belongs to the low-mass hot-Jupiter population. Planetary evolution models allowed us to estimate a core mass of a few tens of Earth mass for the two planets with heavy-element mass fractions of 0.52(-0.15)(+0.08) and 0.26(-0.08)(+0.05), respectively, assuming that a small fraction of the incoming flux is dissipated at the center of the planet. In addition, these models indicate that CoRoT-26b is anomalously large compared with what standard models could account for, indicating that dissipation from stellar heating could cause this size.

Tidal friction in close-in satellites and exoplanets: The Darwin theory re-visited

This report is a review of Darwin’s classical theory of bodily tides in which we present the analytical expressions for the orbital and rotational evolution of the bodies and for the energy dissipation rates due to their tidal interaction. General formulas are given which do not depend on any assumption linking the tidal lags to the frequencies of the corresponding tidal waves (except that equal frequency harmonics are assumed to span equal lags). Emphasis is given to the cases of companions having reached one of the two possible final states: (1) the super-synchronous stationary rotation resulting from the vanishing of the average tidal torque; (2) capture into the 1:1 spin-orbit resonance (true synchronization). In these cases, the energy dissipation is controlled by the tidal harmonic with period equal to the orbital period (instead of the semi-diurnal tide) and the singularity due to the vanishing of the geometric phase lag does not exist. It is also shown that the true synchronization with non-zero eccentricity is only possible if an extra torque exists opposite to the tidal torque. The theory is developed assuming that this additional torque is produced by an equatorial permanent asymmetry in the companion. The results are model-dependent and the theory is developed only to the second degree in eccentricity and inclination (obliquity). It can easily be extended to higher orders, but formal accuracy will not be a real improvement as long as the physics of the processes leading to tidal lags is not better known.

Extrasolar Planets in Mean-Motion Resonance: Apses Alignment and Asymmetric Stationary Solutions

In recent years several pairs of extrasolar planets have been discovered in the vicinity of mean-motion commensurabilities. In some cases, such as the GJ 876 system, the planets seem to be trapped in a stationary solution, the system exhibiting a simultaneous libration of the resonant angle θ1 = 2λ2 - λ1 - 1 and of the relative position of the pericenters. In this paper we analyze the existence and location of these stable solutions, for the 2 : 1 and 3 : 1 resonances, as functions of the masses and orbital elements of both planets. This is undertaken via an analytical model for the resonant Hamiltonian function. The results are compared with those of numerical simulations of the exact equations. In the 2 : 1 commensurability, we show the existence of three principal families of stationary solutions: (1) aligned orbits, in which θ1 and 1 - 2 both librate around zero, (2) antialigned orbits, in which θ1 = 0 and the difference in pericenter is 180°, and (3) asymmetric stationary solutions, in which both the resonant angle and 1 - 2 are constants with values different from 0° or 180°. Each family exists in a different domain of values of the mass ratio and eccentricities of both planets. Similar results are also found in the 3 : 1 resonance. We discuss the application of these results to the extrasolar planetary systems and develop a chart of possible planetary orbits with apsidal corotation. We estimate, also, the maximum planetary masses in order for the stationary solutions to be dynamically stable.

Planetary migration and extrasolar planets in the 2/1 mean-motion resonance

In this paper, we present a new set of corotational solutions for the 2/1 commensurability, including previously known solutions and new results. Comparisons with observed exoplanets show that current orbital fits of three proposed resonant planetary systems are consistent with apsidal corotations. We also discuss the possible relationship between the current orbital elements fits of known exoplanets in the 2/1 mean-motion resonance and the expected orbital configuration due to migration. We find that, as long as the orbital decay was sufficiently slow to be approximated by an adiabatic process, all captured planets should be in apsidal corotations. In other words, they should show a simultaneous libration of both the resonant angle and the difference in longitudes of pericenter.

The extreme physical properties of the CoRoT-7b super-Earth

Photospheric stellar activity (i.e. dark spots or bright pl ages) might be an important source of noise and confusion in s tellar radialvelocity (RV) measurements. Radial-velocimetry planet se arch surveys as well as follow-up of photometric transit sur veys require a deeper understanding and characterization of the e ffects of stellar activities to di fferentiate them from planetary signals. We simulate dark spots on a rotating stellar photosphere. The variation s in the photometry, RV, and spectral line shapes are charact erized and analyzed according to the stellar inclination, the latitud e, and the number of spots. We show that the anti-correlation between RV and bisector span, known to be a signature of activity, requi s a good sampling to be resolved when there are several spot s on the photosphere. The Lomb-Scargle periodograms of the RV varia tions induced by activity present power at the rotational pe riod Prot of the star and its two first harmonics Prot/2 andProt/3. Three adjusted sinusoids fixed at the fundamental period a nd its two-first harmonics allow us to remove about 90% of the RV jitter amplit ude. We apply and validate our approach on four known active p lanethost stars: HD 189733, GJ 674, CoRoT-7, and ιHor. We succeed in fitting simultaneously activity and plane t ry signals on GJ674 and CoRoT-7. This simultaneous modeling of the activity and planetary parameters leads to slightly higher masses of CoR oT-7b and c of respectively, 5.7± 2.5 MEarth and 13.1± 4.1 MEarth. The larger uncertainties properly take into account the st ellar active jitter. We exclude short-period low-mass exoplanets around ιHor. For data with realistic time-sampling and white Gaussi an noise, we use simulations to show that our approach is e ffective in distinguishing reflex-motion due to a planetary co mpanion and stellar-activityinduced RV variations provided that 1) the planetary orbita l period is not close to that of the stellar rotation or one of i ts two first harmonics, 2) the semi-amplitude of the planet exceeds ∼30% of the semi-amplitude of the active signal, 3) the rotati nal period of the star is accurately known, and 4) the data cover more than o ne stellar rotational period.

A transiting giant planet with a temperature between 250 K and 430 K

Of the over 400 known exoplanets, there are about 70 planets that transit their central star, a situation that permits the derivation of their basic parameters and facilitates investigations of their atmospheres. Some short-period planets, including the first terrestrial exoplanet (CoRoT-7b), have been discovered using a space mission designed to find smaller and more distant planets than can be seen from the ground. Here we report transit observations of CoRoT-9b, which orbits with a period of 95.274 days on a low eccentricity of 0.11 ± 0.04 around a solar-like star. Its periastron distance of 0.36 astronomical units is by far the largest of all transiting planets, yielding a ‘temperate’ photospheric temperature estimated to be between 250 and 430 K. Unlike previously known transiting planets, the present size of CoRoT-9b should not have been affected by tidal heat dissipation processes. Indeed, the planet is found to be well described by standard evolution models with an inferred interior composition consistent with that of Jupiter and Saturn.

Evolution of Migrating Planet Pairs in Resonance

Numerical simulations of the evolution of planets or massive satellites captured in the 2/1 and 3/1 resonances, under the action of an anti-dissipative tidal force. The evolution of resonant trapped bodies show a richness of solutions: librations around stationary symmetric solutions with aligned periapses (Δϖ = 0) or anti-aligned periapses (Δϖ = π), librations around stationary asymmetric solutions in which the periapses configuration is fixed, but with Δϖ taking values in a wide range of angles. Many of these solutions exist for large values of the eccentricities and, during the semimajor axes drift, the solutions show turnabouts from one configuration to another. The presented results are valid for other non-conservative anti-dissipative forces leading to adiabatic convergent migration and capture into one of these resonances.

Transiting exoplanets from the CoRoT space mission - XV. CoRoT-15b: a brown-dwarf transiting companion

We report the discovery by the CoRoT space mission of a transiting brown dwarf orbiting a F7V star with an orbital period of 3.06 days. CoRoT-15b has a radius of 1.12 +0.30 ―0.15 R Jup and a mass of 63.3 ± 4.1 M Jup , and is thus the second transiting companion lying in the theoretical mass domain of brown dwarfs. CoRoT-15b is either very young or inflated compared to standard evolution models, a situation similar to that of M-dwarf stars orbiting close to solar-type stars. Spectroscopic constraints and an analysis of the lightcurve imply a spin period in the range 2.9-3.1 days for the central star, which is compatible with a double-synchronisation of the system.

Transiting exoplanets from the CoRoT space mission X. CoRoT-10b: a giant planet in a 13.24 day eccentric orbit

Context. The space telescope CoRoT searches for transiting extrasolar planets by continuously monitoring the optical flux of thousands of stars in several fields of view. Aims. We report the discovery of CoRoT-10b, a giant planet on a highly eccentric orbit (e = 0.53 ± 0.04) revolving in 13.24 days around a faint (V = 15.22) metal-rich K1V star. Methods. We used CoRoT photometry, radial velocity observations taken with the HARPS spectrograph, and UVES spectra of the parent star to derive the orbital, stellar, and planetary parameters. Results. We derive a radius of the planet of 0.97 ± 0.07 RJup and a mass of 2.75 ± 0.16 MJup. The bulk density, ρp = 3.70 ± 0. 83 gc m −3 ,i s∼2.8 that of Jupiter. The core of CoRoT-10b could contain up to 240 M⊕ of heavy elements. Moving along its eccentric orbit, the planet experiences a 10.6-fold variation in insolation. Owing to the long circularisation time, τcirc > 7G yr, a resonant perturber is not required to excite and maintain the high eccentricity of CoRoT-10b.