ترغب بنشر مسار تعليمي؟ اضغط هنا

Tidal evolution of the Keplerian elements

64   0   0.0 ( 0 )
 نشر من قبل Michael Efroimsky
 تاريخ النشر 2019
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

We address the expressions for the rates of the Keplerian orbital elements within a two-body problem perturbed by the tides in both partners. The formulae for these rates have appeared in the literature in various forms, at times with errors. We reconsider, from scratch, the derivation of these rates and arrive at the Lagrange-type equations which, in some details, differ from the corresponding equations obtained previously by Kaula (1964). We also write down detailed expressions for $da/dt$, $de/dt$ and $di/dt$, to order $e^4$. They differ from Kaulas expressions which contain a redundant factor of $M/(M+M^{prime}),$ with $M$ and $M^{prime}$ being the masses of the primary and the secondary. As Kaula was interested in the Earth-Moon system, this redundant factor was close to unity and was unimportant in his developments. This factor, however, must be reinstated when Kaulas theory is applied to a binary composed of partners of comparable masses. We have found that, while it is legitimate to simply sum the primarys and secondarys inputs in $da/dt$ or $de/dt$, this is not the case for $di/dt$. So our expression for $di/dt$ differs from that of Kaula in two regards. First, the contribution due to the dissipation in the secondary averages out when the apsidal precession is uniform. Second, we have obtained an additional term which emerges owing to the conservation of the angular momentum: a change in the inclination of the orbit causes a change of the primarys plane of equator.



قيم البحث

اقرأ أيضاً

We study the dynamical evolution of the TRAPPIST-1 system under the influence of orbital circularization through tidal interaction with the central star. We find that systems with parameters close to the observed one evolve into a state where consecu tive planets are linked by first order resonances and consecutive triples, apart from planets c, d and e, by connected three body Laplace resonances. The system expands with period ratios increasing and mean eccentricities decreasing with time. This evolution is largely driven by tides acting on the innermost planets which then influence the outer ones. In order that deviations from commensurability become significant only on $Gy$ time scales or longer, we require that the tidal parameter associated with the planets has to be such that $Q > sim 10^{2-3}.$ At the same time, if we start with two subsystems, with the inner three planets comprising the inner one, $Q$ associated with the planets has to be on the order (and not significantly exceeding) $10^{2-3}$ for the two subsystems to interact and end up in the observed configuration. This scenario is also supported by modelling of the evolution through disk migration which indicates that the whole system cannot have migrated inwards together. Also in order to avoid large departures from commensurabilities, the system cannot have stalled at a disk inner edge for significant time periods. We discuss the habitability consequences of the tidal dissipation implied by our modelling, concluding that planets d, e and f are potentially in habitable zones.
We present an extended version of the Constant Time Lag analytical approach for the tidal evolution of circumbinary planets introduced in our previous work. The model is self-consistent, in the sense that all tidal interactions between pairs are comp uted, regardless of their size. We derive analytical expressions for the variational equations governing the spin and orbital evolution, which are expressed as high-order elliptical expansions in the semimajor axis ratio but retain closed form in terms of the binary and planetary eccentricities. These are found to reproduce the results of the numerical simulations with arbitrary eccentricities very well, as well as reducing to our previous results in the low-eccentric case. Our model is then applied to the well-characterised Kepler circumbinary systems by analysing the tidal timescales and unveiling the tidal flow around each different system. In all cases we find that the spins reach stationary values much faster than the characteristic timescale of the orbital evolution, indicating that all Kepler circumbinary planets are expected to be in a sub-synchronous state. On the other hand, all systems are located in a tidal flow leading to outward migration; thus the proximity of the planets to the orbital instability limit may have been even greater in the past. Additionally, Kepler systems may have suffered a significant tidally induced eccentricity damping, which may be related to their proximity to the capture eccentricity. To help understand the predictions of our model, we also offer a simple geometrical interpretation of our results.
Since 1995, numerous close-in planets have been discovered around low-mass stars (M to A-type stars). These systems are susceptible to be tidally evolving, in particular the dissipation of the kinetic energy of tidal flows in the host star may modify its rotational evolution and also shape the orbital architecture of the surrounding planetary system. Recent theoretical studies have shown that the amplitude of the stellar dissipation can vary over several orders of magnitude as the star evolves, and that it also depends on the stellar mass and rotation. We present here one of the first studies of the dynamics of close-in planets orbiting low-mass stars (from $0.6~M_odot$ to $1.2~M_odot$) where we compute the simultaneous evolution of the stars structure, rotation and tidal dissipation in its external convective envelope. We demonstrate that tidal friction due to the stellar dynamical tide, i.e. tidal inertial waves (their restoring force is the Coriolis acceleration) excited in the convection zone, can be larger by several orders of magnitude than the one of the equilibrium tide currently used in celestial mechanics. This is particularly true during the Pre Main Sequence (PMS) phase and to a lesser extent during the Sub Giant (SG) phase. Numerical simulations show that only the high dissipation occurring during the PMS phase has a visible effect on the semi-major axis of close-in planets. We also investigate the effect of the metallicity of the star on the tidal evolution of planets. We find that the higher the metallicity of the star, the higher the dissipation and the larger the tidally-induced migration of the planet.
This is an erratum for the publication Bolmont & Mathis 2016 (Celestial Mechanics and Dynamical Astronomy, 126, 275-296, https://doi.org/10.1007/s10569-016-9690-3). There was a small mistake for the spin integration of our code which we corrected and we take advantage of this erratum to investigate a bit further the influence of a planet on the spin of its host star.
Exoplanets residing close to their stars can experience evolution of both their physical structures and their orbits due to the influence of their host stars. In this work, we present a coupled analysis of dynamical tidal dissipation and atmospheric mass loss for exoplanets in XUV irradiated environments. As our primary application, we use this model to study the TRAPPIST-1 system, and place constraints on the interior structure and orbital evolution of the planets. We start by reporting on a UV continuum flux measurement (centered around $sim1900$ Angstroms) for the star TRAPPIST-1, based on 300 ks of Neil Gehrels Swift Observatory data, and which enables an estimate of the XUV-driven thermal escape arising from XUV photo-dissociation for each planet. We find that the X-ray flaring luminosity, measured from our X-ray detections, of TRAPPIST-1 is 5.6 $times$10$^{-4} L_{*}$, while the full flux including non-flaring periods is 6.1 $times$10$^{-5} L_{*}$, when $L_{*}$ is TRAPPIST-1s bolometric luminosity. We then construct a model that includes both atmospheric mass-loss and tidal evolution, and requires the planets to attain their present-day orbital elements during this coupled evolution. We use this model to constrain the ratio $Q=3Q/2k_{2}$ for each planet. Finally, we use additional numerical models implemented with the Virtual Planet Simulator texttt{VPLanet} to study ocean retention for these planets using our derived system parameters.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا