arXiv subjects

Sylvio Ferraz-Mello

Publications and source records attributed to Sylvio Ferraz-Mello.

27 records · Page 2Linked to original sources

arXiv2013

Tidal synchronization of close-in satellites and exoplanets. A rheophysical approach

This paper presents a new theory of the dynamical tides of celestial bodies. It is founded on a Newtonian creep instead of the classical delaying approach of the standard viscoelastic theories and the results of the theory derive mainly from the solution of a non-homogeneous ordinary differential equation. Lags appear in the solution but as quantities determined from the solution of the equation and are not arbitrary external quantities plugged in an elastic model. The resulting lags of the tide components are increasing functions of their frequencies (as in Darwin's theory), but not small quantities. The amplitudes of the tide components depend on the viscosity of the body and on their frequencies; they are not constants. The resulting stationary rotations (pseudo-synchronous) have an excess velocity roughly proportional to $6ne^2/(χ^2+1/χ^2)$ ($χ$ is the mean-motion in units of one critical frequency - the relaxation factor - inversely proportional to the viscosity) instead of the exact $6ne^2$ of standard theories. The dissipation in the pseudo-synchronous solution is inversely proportional to $(χ+1/χ)$. In the inviscid limit it is roughly proportional to the frequency (as in standard theories), but that behavior is inverted when the viscosity is high and the tide frequency larger than the critical frequency. For free rotating bodies, the dissipation is given by the same law, but now $χ$ is the frequency of the semi-diurnal tide in units of the critical frequency. This approach fails to reproduce the actual tidal lags on Earth. In this case, to reconcile theory and observations, we need to assume the existence of an elastic tide superposed to the creeping tide. The theory is applied to several Solar System and extrasolar bodies and currently available data are used to estimate the relaxation factor $γ$ (i.e. the critical frequency) of these bodies.

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arXiv2011

The periodic and chaotic regimes of motion in the exoplanet 2/1 mean-motion resonance

We present the dynamical structure of the phase space of the planar planetary 2/1 mean-motion resonance (MMR). Inside the resonant domain, there exist two families of periodic orbits, one associated to the librational motion of the critical angle ($σ$-family) and the other related to the circulatory motion of the angle between the pericentres ($Δ\varpi$-family). The well-known apsidal corotation resonances (ACR) appear at the intersections of these families. A complex web of secondary resonances exists also for low eccentricities, whose strengths and positions are dependent on the individual masses and spatial scale of the system. Depending on initial conditions, a resonant system is found in one of the two topologically different states, referred to as \textit{internal} and \textit{external} resonances. The internal resonance is characterized by symmetric ACR and its resonant angle is $2\,λ_2-λ_1-\varpi_1$, where $λ_i$ and $\varpi_i$ stand for the planetary mean longitudes and longitudes of pericentre, respectively. In contrast, the external resonance is characterized by asymmetric ACR and the resonant angle is $2\,λ_2-λ_1-\varpi_2$. We show that systems with more massive outer planets always envolve inside internal resonances. The limit case is the well-known asteroidal resonances with Jupiter. At variance, systems with more massive inner planets may evolve in either internal or external resonances; the internal resonances are typical for low-to-moderate eccentricity configurations, whereas the external ones for high eccentricity configurations of the systems. In the limit case, analogous to Kuiper belt objects in resonances with Neptune, the systems are always in the external resonances characterized by asymmetric equilibria.

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arXiv2011

On the Mass of CoRoT-7b

The mass of CoRoT-7b, the first transiting superearth exoplanet, is still a subject of debate. A wide range of masses have been reported in the literature ranging from as high as 8 M_Earth to as low as 2.3 M_Earth. Although most mass determinations give a density consistent with a rocky planet, the lower value permits a bulk composition that can be up to 50% water. We present an analysis of the CoRoT-7b radial velocity measurements that uses very few and simple assumptions in treating the activity signal. By only analyzing those radial velocity data for which multiple measurements were made in a given night we remove the activity related radial velocity contribution without any a priori model. We demonstrate that the contribution of activity to the final radial velocity curve is negligible and that the K-amplitude due to the planet is well constrained. This yields a mass of 7.42 +/- 1.21 M_Earth and a mean density of rho = 10.4 +/- 1.8 gm cm^-3. CoRoT-7b is similar in mass and radius to the second rocky planet to be discovered, Kepler-10b, and within the errors they have identical bulk densities - they are virtual twins. These bulk densities lie close to the density - radius relationship for terrestrial planets similar to what is seen for Mercury. CoRoT-7b and Kepler-10b may have an internal structure more like Mercury than the Earth.

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arXiv2011

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.

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arXiv2010

Chirikov Diffusion in the Asteroidal Three-Body Resonance (5,-2,-2)

The theory of diffusion in many-dimensional Hamiltonian system is applied to asteroidal dynamics. The general formulations developed by Chirikov is applied to the Nesvorný-Morbidelli analytic model of three-body (three-orbit) mean-motion resonances (Jupiter-Saturn-asteroid system). In particular, we investigate the diffusion \emph{along} and \emph{across} the separatrices of the (5,-2,-2) resonance of the (490) Veritas asteroidal family and their relationship to diffusion in semi-major axis and eccentricity. The estimations of diffusion were obtained using the Melnikov integral, a Hadjidemetriou-type sympletic map and numerical integrations for times up to $10^{8}$ years.

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arXiv2009

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.

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arXiv2009

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.

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arXiv2007

Formation and transformation of the 3:1 mean-motion resonance in 55 Cancri System

We report in this paper the numerical simulations of the capture into the 3:1 mean-motion resonance between the planet b and c in the 55 Cancri system. The results show that this resonance can be obtained by a differential planetary migration. The moderate initial eccentricities, relatively slower migration and suitable eccentricity damping rate increase significantly the probability of being trapped in this resonance. Otherwise, the system crosses the 3:1 commensurability avoiding resonance capture, to be eventually captured into a 2:1 resonance or some other higher-order resonances. After the resonance capture, the system could jump from one orbital configuration to another one if the migration continues, making a large region of the configuration space accessible for a resonance system. These investigations help us understand the diversity of resonance configurations and put some constrains on the early dynamical evolution of orbits in the extra-solar planetary systems.

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arXiv2005

On the V-type asteroids outside the Vesta family. I. Interplay of nonlinear secular resonances and the Yarkovsky effect: the cases of 956 Elisa and 809 Lundia

Among the largest objects in the main belt, asteroid 4 Vesta is unique in showing a basaltic crust. It is also the biggest member of the Vesta family, which is supposed to originate from a large cratering event about 1 Gyr ago (Marzari et al. 1996). Most of the members of the Vesta family for which a spectral classification is available show a V-type spectra. Before the discovery of 1459 Magnya (Lazzaro et al. 2000) and of several V-type NEA (Xu 1995), all the known V-type asteroids were members of the Vesta family. Recently two V-type asteroids, 809 Lundia and 956 Elisa, (Florczak et al. 2002) have been discovered well outside the limits of the family, near the Flora family. We currently know 22 V-type asteroids outside the family, in the inner asteroid belt. In this work we investigate the possibility that these objects are former family members that migrated to their current positions via the interplay of Yarkovsky effect and nonlinear secular resonances. The main dynamical feature of 956 Elisa and 809 Lundia is that they are currently inside the 2(g-g6)+s-s6 (z2 by Milani and Knezevic, 1993) secular resonance. Our investigations show that members of the Vesta dynamical family may drift in three-body and weak secular resonances until they are captured in the strong z2 secular resonance. Only asteroids with diameters larger than 16 km can remain in one of the three-body or secular resonances long enough to reach the region of the z2 resonance. This two-step mechanism of capture into the z2 resonance could explain: i) the current resonant orbits of 956 Elisa and 809 Lundia, ii) why their size is significantly larger than that of the typical member of the Vesta family, and iii) provide a lower limit on the Vesta family age.

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