Eclipsing binary statistics - theory and observation

The expected distributions of eclipse-depth versus period for eclipsing binaries of different luminosities are derived from large-scale population synthesis experiments. Using the rapid Hurley et al. BSE binary evolution code, we have evolved several hundred million binaries, starting from various simple input distributions of masses and orbit-sizes. Eclipse probabilities and predicted distributions over period and eclipse-depth (P/dm) are given in a number of main-sequence intervals, from O-stars to brown dwarfs. The comparison between theory and Hipparcos observations shows that a standard (Duquennoy & Mayor) input distribution of orbit-sizes (a) gives reasonable numbers and P/dm-distributions, as long as the mass-ratio distribution is also close to the observed flat ones. A random pairing model, where the primary and secondary are drawn independently from the same IMF, gives more than an order of magnitude too few eclipsing binaries on the upper main sequence. For a set of eclipsing OB-systems in the LMC, the observed period-distribution is different from the theoretical one, and the input orbit distributions and/or the evolutionary environment in LMC has to be different compared with the Galaxy. A natural application of these methods are estimates of the numbers and properties of eclipsing binaries observed by large-scale surveys like Gaia.Comment: 11 pages, 16 figures, accepted for publication in A&

From Hipparcos to Gaia

The measurement of the positions, distances, motions and luminosities of stars represents the foundations of modern astronomical knowledge. Launched at the end of the eighties, the ESA Hipparcos satellite was the first space mission dedicated to such measurements. Hipparcos improved position accuracies by a factor of 100 compared to typical ground-based results and provided astrometric and photometric multi-epoch observations of 118,000 stars over the entire sky. The impact of Hipparcos on astrophysics has been extremely valuable and diverse. Building on this important European success, the ESA Gaia cornerstone mission promises an even more impressive advance. Compared to Hipparcos, it will bring a gain of a factor 50 to 100 in position accuracy and of a factor of 10,000 in star number, collecting photometric, spectrophotometric and spectroscopic data for one billion celestial objects. During its 5-year flight, Gaia will measure objects repeatedly, up to a few hundred times, providing an unprecedented database to study the variability of all types of celestial objects. Gaia will bring outstanding contributions, directly or indirectly, to most fields of research in astrophysics, such as the study of our Galaxy and of its stellar constituents, the search for planets outside the solar system.Comment: 6 pages. New Horizons in Time Domain Astronomy Proceedings IAU Symposium No. 285, 2012, E. Griffin, B. Hanisch & R. Seaman, ed

Tidal decay and circularization of the orbits of short-period planets

We analyze the long-term tidal evolution of a single-planet system through the use of numerical simulations and averaged equations giving the variations of semi-major axis and eccentricity of the relative orbit. For different types of planets, we compute the variations due to the planetary and stellar tides. Then, we calculate the critical value of the eccentricity for which the stellar tide becomes dominant over the planetary tide. The timescales for orbital decay and circularization are also discussed and compared.Comment: 8 pages, 3 figures, corrected typo

Tidal torques. A critical review of some techniques

We point out that the MacDonald formula for body-tide torques is valid only in the zeroth order of e/Q, while its time-average is valid in the first order. So the formula cannot be used for analysis in higher orders of e/Q. This necessitates corrections in the theory of tidal despinning and libration damping. We prove that when the inclination is low and phase lags are linear in frequency, the Kaula series is equivalent to a corrected version of the MacDonald method. The correction to MacDonald's approach would be to set the phase lag of the integral bulge proportional to the instantaneous frequency. The equivalence of descriptions gets violated by a nonlinear frequency-dependence of the lag. We explain that both the MacDonald- and Darwin-torque-based derivations of the popular formula for the tidal despinning rate are limited to low inclinations and to the phase lags being linear in frequency. The Darwin-torque-based derivation, though, is general enough to accommodate both a finite inclination and the actual rheology. Although rheologies with Q scaling as the frequency to a positive power make the torque diverge at a zero frequency, this reveals not the impossible nature of the rheology, but a flaw in mathematics, i.e., a common misassumption that damping merely provides lags to the terms of the Fourier series for the tidal potential. A hydrodynamical treatment (Darwin 1879) had demonstrated that the magnitudes of the terms, too, get changed. Reinstating of this detail tames the infinities and rehabilitates the "impossible" scaling law (which happens to be the actual law the terrestrial planets obey at low frequencies).Comment: arXiv admin note: sections 4 and 9 of this paper contain substantial text overlap with arXiv:0712.105

On planetary mass determination in the case of super-Earths orbiting active stars. The case of the CoRoT-7 system

This investigation uses the excellent HARPS radial velocity measurements of CoRoT-7 to re-determine the planet masses and to explore techniques able to determine mass and elements of planets discovered around active stars when the relative variation of the radial velocity due to the star activity cannot be considered as just noise and can exceed the variation due to the planets. The main technique used here is a self-consistent version of the high-pass filter used by Queloz et al. (2009) in the first mass determination of CoRoT-7b and CoRoT-7c. The results are compared to those given by two alternative techniques: (1) The approach proposed by Hatzes et al. (2010) using only those nights in which 2 or 3 observations were done; (2) A pure Fourier analysis. In all cases, the eccentricities are taken equal to zero as indicated by the study of the tidal evolution of the system; the periods are also kept fixed at the values given by Queloz et al. Only the observations done in the time interval BJD 2,454,847 - 873 are used because they include many nights with multiple observations; otherwise it is not possible to separate the effects of the rotation fourth harmonic (5.91d = Prot/4) from the alias of the orbital period of CoRoT-7b (0.853585 d). The results of the various approaches are combined to give for the planet masses the values 8.0 \pm 1.2 MEarth for CoRoT-7b and 13.6 \pm 1.4 MEarth for CoRoT 7c. An estimation of the variation of the radial velocity of the star due to its activity is also given.The results obtained with 3 different approaches agree to give masses larger than those in previous determinations. From the existing internal structure models they indicate that CoRoT-7b is a much denser super-Earth. The bulk density is 11 \pm 3.5 g.cm-3 . CoRoT-7b may be rocky with a large iron core.Comment: 12 pages, 11 figure

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) the capture into a 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.Comment: 30 pages, 7 figures, corrected typo

The effect of the motion of the Sun on the light-time in interplanetary relativistic experiments

In 2002 a measurement of the effect of solar gravity upon the phase of coherent microwave beams passing near the Sun has been carried out with the Cassini mission, allowing a very accurate measurement of the PPN parameter $\gamma$. The data have been analyzed with NASA's Orbit Determination Program (ODP) in the Barycentric Celestial Reference System, in which the Sun moves around the centre of mass of the solar system with a velocity $v_\odot$ of about 10 m/sec; the question arises, what correction this implies for the predicted phase shift. After a review of the way the ODP works, we set the problem in the framework of Lorentz (and Galilean) transformations and evaluate the correction; it is several orders of magnitude below our experimental accuracy. We also discuss a recent paper \cite{kopeikin07}, which claims wrong and much larger corrections, and clarify the reasons for the discrepancy.Comment: Final version accepted by Classical and Quantum Gravity (8 Jan. 2008

Tidal decay and orbital circularization in close-in two-planet systems

The motion of two planets around a Sun-like star under the combined effects of mutual interaction and tidal dissipation is investigated. The secular behaviour of the system is analyzed using two different approaches. First, we solve the exact equations of motion through the numerical simulation of the system evolution. In addition to the orbital decay and circularization, we show that the final configuration of the system is affected by the shrink of the inner orbit. Our second approach consist in the analysis of the stationary solutions of mean equations of motion based on a Hamiltonian formalism. We consider the case of a hot super-Earth planet with a more massive outer companion. As a real example, the CoRoT-7 system is analyzed solving the exact and mean equations of motion. The star-planet tidal interaction produces orbital decay and circularization of the orbit of CoRoT-7b. In addition, the long-term tidal evolution is such that the eccentricity of CoRoT-7c is also circularized and a pair of final circular orbits is obtained. A curve in the space of eccentricities can be constructed through the computation of stationary solutions of mean equations including dissipation. The application to CoRoT-7 system shows that the stationary curve agrees with the result of numerical simulations of exact equations. A similar investigation performed in a super-Earth-Jupiter two-planet system shows that the doubly circular state is accelerated when there is a significant orbital migration of the inner planet, in comparison with previous results were migration is neglected.Comment: Accepted for publication in MNRAS; 10 pages, 13 figure

Proper Motions in the Galactic Bulge: Plaut's Window

A proper motion study of a field of 20' x 20' inside Plaut's low extinction window (l,b)=(0 deg,-8 deg), has been completed. Relative proper motions and photographic BV photometry have been derived for ~21,000 stars reaching to V~20.5 mag, based on the astrometric reduction of 43 photographic plates, spanning over 21 years of epoch difference. Proper motion errors are typically 1 mas/yr and field dependent systematics are below 0.2 mas/yr. Cross-referencing with the 2MASS catalog yielded a sample of ~8,700 stars, from which predominantly disk and bulge subsamples were selected photometrically from the JH color-magnitude diagram. The two samples exhibited different proper-motion distributions, with the disk displaying the expected reflex solar motion as a function of magnitude. Galactic rotation was also detected for stars between ~2 and ~3 kpc from us. The bulge sample, represented by red giants, has an intrinsic proper motion dispersion of (sigma_l,sigma_b)=(3.39, 2.91)+/-(0.11,0.09) mas/yr, which is in good agreement with previous results, and indicates a velocity anisotropy consistent with either rotational broadening or tri-axiality. A mean distance of 6.37^{+0.87}_{-0.77} kpc has been estimated for the bulge sample, based on the observed K magnitude of the horizontal branch red clump. The metallicity [M/H] distribution was also obtained for a subsample of 60 bulge giants stars, based on calibrated photometric indices. The observed [M/H] shows a peak value at [M/H]~-0.1 with an extended metal poor tail and around 30% of the stars with supersolar metallicity. No change in proper motion dispersion was observed as a function of [M/H]. We are currently in the process of obtaining CCD UBVRI photometry for the entire proper-motion sample of ~21,000 stars.Comment: Submitted to AJ April 17th 2007. Accepted June 8th 2007. 45 pages, 14 figure