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We investigate the distribution of mass M and orbital period P of extrasolar planets, taking account of selection effects caused by the limited velocity precision and duration of existing surveys. We fit the data on 72 planets to a power-law distribution of the form  d n = CM −α P −β(d M / M )(d P / P )  , and find  α= 0.11 ± 0.10  ,  β=−0.27 ± 0.06  for   M ≲ 10 M J  , where   M J  is the mass of Jupiter. The correlation coefficient between these two exponents is −0.31, indicating that uncertainties in the two distributions are coupled. We estimate that 4 per cent of solar-type stars have companions in the range  1 M J < M < 10 M J  ,  2d < P < 10 yr  .  相似文献   

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Most transiting planets orbit very close to their parent star, causing strong tidal forces between the two bodies. Tidal interaction can modify the dynamics of the system through orbital alignment, circularization, synchronization and orbital decay by exchange of angular moment. Evidence for tidal circularization in close-in giant planet is well known. Here, we review the evidence for excess rotation of the parent stars due to the pull of tidal forces towards spin-orbit synchronization. We find suggestive empirical evidence for such a process in the present sample of transiting planetary systems. The corresponding angular momentum exchange would imply that some planets have spiralled towards their star by substantial amounts since the dissipation of the protoplanetary disc. We suggest that this could quantitatively account for the observed mass–period relation of close-in gas giants. We discuss how this scenario can be further tested and point out some consequences for theoretical studies of tidal interactions and for the detection and confirmation of transiting planets from radial velocity and photometric surveys.  相似文献   

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We point out an intriguing relation between the masses of the transiting planets and their orbital periods. For the six currently known transiting planets, the data are consistent with a decreasing linear relation. The other known short-period planets, discovered through radial-velocity techniques, seem to agree with this relation. We briefly speculate about a tentative physical model to explain such a dependence.  相似文献   

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Natural systems tend to minimize their energy. Hence an important problem in astrophysics is the parametrization of the ground state. In this context a quantum statistical approach is very useful. The problem of the variational approximation of the density matrix is extended towards a parametrization of the ground state. With an analogy to the semiclassical approach, a classical approach to the variational principle in the parametrization of the ground state is elucidated and its applications are discussed. We find that planetary systems tend to have circular orbits in an effort to attain the ground state. The results of this paper may be useful for the modern problem of detecting planets around bright stars.  相似文献   

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The TrES‐2 system harbors one planet which was discovered with the transit technique. In this work we investigate the dynamical behavior of possible additional, lower‐mass planets. We identify the regions where such planets can move on stable orbits and show how they depend on the initial eccentricity and inclination. We find, that there are stable regions inside and outside the orbit of TrES‐2b where additional, smaller planets can move. We also show that those planets can have a large orbital inclination which makes a detection with the transit technique very difficult (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

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Planets orbiting a planetesimal circumstellar disc can migrate inward from their initial positions because of dynamical friction between planets and planetesimals. The migration rate depends on the disc mass and on its time evolution. Planets that are embedded in long-lived planetesimal discs, having total mass of 10−4– 0.01 M , can migrate inward a large distance and can survive only if the inner disc is truncated or as a result of tidal interaction with the star. In this case the semimajor axis, a , of the planetary orbit is less than 0.1 au. Orbits with larger a are obtained for smaller values of the disc mass or for a rapid evolution (depletion) of the disc. This model may explain not only several of the orbital features of the giant planets that have been discovered in recent years orbiting nearby stars, but also the metallicity enhancement found in several stars associated with short-period planets.  相似文献   

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Dynamical relaxation and massive extrasolar planets   总被引:1,自引:0,他引:1  
Following the suggestion of Black that some massive extrasolar planets may be associated with the tail of the distribution of stellar companions, we investigate a scenario in which 5 N 100 planetary mass objects are assumed to form rapidly through a fragmentation process occuring in a disc or protostellar envelope on a scale of 100 au. These are assumed to have formed rapidly enough through gravitational instability or fragmentation that their orbits can undergo dynamical relaxation on a time-scale of ∼100 orbits.
Under a wide range of initial conditions and assumptions, the relaxation process ends with either (i) one potential 'hot Jupiter' plus up to two 'external' companions, i.e. planets orbiting near the outer edge of the initial distribution; (ii) one or two 'external' planets or even none at all; (iii) one planet on an orbit with a semi-major axis of 10 to 100 times smaller than the outer boundary radius of the inital distribution together with an 'external' companion. Most of the other objects are ejected and could contribute to a population of free-floating planets. Apart from the potential 'hot Jupiters', all the bound objects are on orbits with high eccentricity, and also with a range of inclination with respect to the stellar equatorial plane. We found that, apart from the close orbiters, the probability of ending up with a planet orbiting at a given distance from the central star increases with the distance. This is because of the tendency of the relaxation process to lead to collisions with the central star. The scenario we envision here does not impose any upper limit on the mass of the planets. We discuss the application of these results to some of the more massive extrasolar planets.  相似文献   

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张旭东  周济林 《天文学报》2006,47(2):175-185
最近的多普勒观测表明恒星HD 12661周围存在两颗中等偏心率轨道上运行的行星,内行星的最小质量为2.3木星质量,轨道周期为263.6天;外行星的最小质量为1.57木星质量,轨道周期为1444.5天.该系统的稳定性要求两颗行星处在平运动轨道共振.用数值方法研究了该系统形成初期在恒星气体盘作用下的轨道迁移与稳定性,计算了行星在迁移中被平运动共振俘获的概率.发现这两颗行星目前很可能正处在11:2平运动共振边缘,且运动是混沌的,从而澄清了关于系统目前构形的不同说法,并且很可能在系统形成后行星迁移到目前构形时,气体盘几乎消失了.  相似文献   

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We investigate the populations of main-sequence stars within 25 pc that have debris discs and/or giant planets detected by Doppler shift. The metallicity distribution of the debris sample is a very close match to that of stars in general, but differs with >99 per cent confidence from the giant planet sample, which favours stars of above average metallicity. This result is not due to differences in age of the two samples. The formation of debris-generating planetesimals at tens of au thus appears independent of the metal fraction of the primordial disc, in contrast to the growth and migration history of giant planets within a few au. The data generally fit a core accumulation model, with outer planetesimals forming eventually even from a disc low in solids, while inner planets require fast core growth for gas to still be present to make an atmosphere.  相似文献   

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