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تسجيل مستخدم جديدModels of the formation of the planets in the 47 UMa system
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Formation of planets in the 47 UMa system is followed in an evolving protoplanetary disk composed of gas and solids. The evolution of the disk is calculated from an early stage, when all solids, assumed to be high-temperature silicates, are in the dust form, to the stage when most solids are locked in planetesimals. The simulation of planetary evolution starts with a solid embryo of ~1 Earth mass, and proceeds according to the core accretion -- gas capture model. Orbital parameters are kept constant, and it is assumed that the environment of each planet is not perturbed by the second planet. It is found that conditions suitable for both planets to form within several Myr are easily created, and maintained throughout the formation time, in disks with $alpha approx 0.01$. In such disks, a planet of 2.6 Jupiter masses (the minimum for the inner planet of the 47 UMa system) may be formed at 2.1 AU from the star in ~3 Myr, while a planet of 0.89 Jupiter masses (the minimum for the outer planet) may be formed at 3.95 AU from the star in about the same time. The formation of planets is possible as a result of a significant enhancement of the surface density of solids between 1.0 and 4.0 AU, which results from the evolution of a disk with an initially uniform gas-to-dust ratio of 167 and an initial radius of 40 AU.
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(Abridged)We numerically investigated the dynamical architecture of 47 UMa with the planetary configuration of the best-fit orbital solutions by Fischer et al. We systematically studied the existence of Earth-like planets in the region 0.05 AU $leq a
leq 2.0$ AU for 47 UMa with numerical simulations, and we also explored the packed planetary geometry and Trojan planets in the system. In the simulations, we found that hot Earths at 0.05 AU $leq a < $ 0.4 AU can dynamically survive at least for 1 Myr. The Earth-like planets can eventually remain in the system for 10 Myr in areas involved in the mean motion resonances (MMR) (e.g., 3:2 MMR) with the inner companion. Moreover, we showed that the 2:1 and 3:1 resonances are on the fringe of stability, while the 5:2 MMR is unstable. Additionally, the 2:1 MMR marks out a remarkable boundary between chaotic and regular motions, inside, most of the orbits can survive, outside, they are mostly lost in the orbital evolution. In a dynamical sense, the most likely candidate for habitable environment is Earth-like planets with orbits in the ranges 0.8 AU $leq a < 1.0$ AU and 1.0 AU $ < a < 1.30$ AU (except several unstable cases) with relatively low eccentricities. The Trojan planets with low eccentricities and inclinations can secularly last at the triangular equilibrium points of two massive planets. Hence, the 47 UMa planetary system may be a close analog to our solar system.
To reproduce the orbits and masses of the terrestrial planets (analogs) of the solar system, most studies scrutinize simulations for success as a batch. However, there is insufficient discussion in the literature on the likelihood of forming planet a
nalogs simultaneously in the same system (analog system). To address this issue, we performed 540 N-body simulations of protoplanetary disks representative of typical models in the literature. We identified a total of 194 analog systems containing at least three analogs, but only 17 systems simultaneously contained analogs of the four terrestrial planets. From an analysis of our analog systems, we found that, compared to the real planets, truncated disks based on typical outcomes of the Grand Tack model produced analogs of Mercury and Mars that were too dynamically cold and located too close to the Venus and Earth analogs. Additionally, all the Mercury analogs were too massive, while most of the Mars analogs were more massive than Mars. Furthermore, the timing of the Moon-forming impact was too early in these systems, and the amount of additional mass accreted after the event was too great. Therefore, such truncated disks cannot explain the formation of the terrestrial planets. Our results suggest that forming the four terrestrial planets requires disks with the following properties: 1) Mass concentrated in narrow core regions between ~0.7-0.9 and ~1.0-1.2 au; 2) an inner region component starting at ~0.3-0.4 au; 3) a less massive component beginning at ~1.0-1.2 au; 4) embryos rather than planetesimals carrying most of the disk mass; and 5) Jupiter and Saturn placed on eccentric orbits.
We have undertaken a thorough dynamical investigation of five extrasolar planetary systems using extensive numerical experiments. The systems Gl 777 A, HD 72659, Gl 614, 47 Uma and HD 4208 were examined concerning the question of whether they could h
ost terrestrial like planets in their habitable zones (=HZ). First we investigated the mean motion resonances between fictitious terrestrial planets and the existing gas giants in these five extrasolar systems. Then a fine grid of initial conditions for a potential terrestrial planet within the HZ was chosen for each system, from which the stability of orbits was then assessed by direct integrations over a time interval of 1 million years. The computations were carried out using a Lie-series integration method with an adaptive step size control. This integration method achieves machine precision accuracy in a highly efficient and robust way, requiring no special adjustments when the orbits have large eccentricities. The stability of orbits was examined with a determination of the Renyi entropy, estimated from recurrence plots, and with a more straight forward method based on the maximum eccentricity achieved by the planet over the 1 million year integration. Additionally, the eccentricity is an indication of the habitability of a terrestrial planet in the HZ; any value of e>0.2 produces a significant temperature difference on a planets surface between apoapse and periapse. The results for possible stable orbits for terrestrial planets in habitable zones for the five systems are summarized as follows: for Gl 777 A nearly the entire HZ is stable, for 47 Uma, HD 72659 and HD 4208 terrestrial planets can survive for a sufficiently long time, while for Gl 614 our results exclude terrestrial planets moving in stable orbits within the HZ.
Exoplanet surveys have confirmed one of humanitys (and all teenagers) worst fears: we are weird. If our Solar System were observed with present-day Earth technology -- to put our system and exoplanets on the same footing -- Jupiter is the only planet
that would be detectable. The statistics of exo-Jupiters indicate that the Solar System is unusual at the ~1% level among Sun-like stars (or ~0.1% among all stars). But why are we different? Successful formation models for both the Solar System and exoplanet systems rely on two key processes: orbital migration and dynamical instability. Systems of close-in super-Earths or sub-Neptunes require substantial radial inward motion of solids either as drifting mm- to cm-sized pebbles or migrating Earth-mass or larger planetary embryos. We argue that, regardless of their formation mode, the late evolution of super-Earth systems involves migration into chains of mean motion resonances, generally followed by instability when the disk dissipates. This pattern is likely also ubiquitous in giant planet systems. We present three models for inner Solar System formation -- the low-mass asteroid belt, Grand Tack, and Early Instability models -- each invoking a combination of migration and instability. We identify bifurcation points in planetary system formation. We present a series of events to explain why our Solar System is so weird. Jupiters core must have formed fast enough to quench the growth of Earths building blocks by blocking the flux of inward-drifting pebbles. The large Jupiter/Saturn mass ratio is rare among giant exoplanets but may be required to maintain Jupiters wide orbit. The giant planets instability must have been gentle, with no close encounters between Jupiter and Saturn, also unusual in the larger (exoplanet) context. Our Solar System system is thus the outcome of multiple unusual, but not unheard of, events.
The presented work investigates the possible formation of terrestrial planets in the habitable zone (HZ) of the exoplanetary system HD 141399. In this system the HZ is located approximately between the planets c (a = 0.7 au) and d (a = 2.1 au). Exten
sive numerical integrations of the equations of motion in the pure Newtonian framework of small bodies with different initial conditions in the HZ are performed. Our investigations included several steps starting with 500 massless bodies distributed between planets c and d in order to model the development of the disk of small bodies. It turns out that after some 10^6 years a belt-like structure analogue to the main belt inside Jupiter in our Solar System appears. We then proceed with giving the small bodies masses (Moon-mass) and take into account the gravitational interaction between these planetesimal-like objects. The growing of the objects - with certain percentage of water - due to collisions is computed in order to look for the formation of terrestrial planets. We observe that planets form in regions connected to mean motion resonances (MMR). So far there is no observational evidence of terrestrial planets in the system of HD 141399 but from our results we can conclude that the formation of terrestrial planets - even with an appropriate amount of water necessary for being habitable - in the HZ would have been possible.
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