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1.
We numerically model the evolution of dust in a protoplanetary disk using a two-phase (gas+dust) Smoothed Particle Hydrodynamics (SPH) code, which is non-self-gravitating and locally isothermal. The code follows the three dimensional distribution of dust in a protoplanetary disk as it interacts with the gas via aerodynamic drag. In this work, we present the evolution of a disk comprising 1% dust by mass in the presence of an embedded planet for two different disk configurations: a small, minimum mass solar nebular (MMSN) disk and a larger, more massive Classical T Tauri star (CTTS) disk. We then vary the grain size and planetary mass to see how they effect the resulting disk structure. We find that gap formation is much more rapid and striking in the dust layer than in the gaseous disk and that a system with a given stellar, disk and planetary mass will have a different appearance depending on the grain size and that such differences will be detectable in the millimetre domain with ALMA. For low mass planets in our MMSN models, a gap can open in the dust disk while not in the gas disk. We also note that dust accumulates at the external edge of the planetary gap and speculate that the presence of a planet in the disk may facilitate the growth of planetesimals in this high density region.  相似文献   

2.
The dynamics of circumbinary planetary systems (the systems in which the planets orbit a central binary) with a small binary mass ratio discovered to date is considered. The domains of chaotic motion have been revealed in the “pericentric distance–eccentricity” plane of initial conditions for the planetary orbits through numerical experiments. Based on an analytical criterion for the chaoticity of planetary orbits in binary star systems, we have constructed theoretical curves that describe the global boundary of the chaotic zone around the central binary for each of the systems. In addition, based on Mardling’s theory describing the separate resonance “teeth” (corresponding to integer resonances between the orbital periods of a planet and the binary), we have constructed the local boundaries of chaos. Both theoretical models are shown to describe adequately the boundaries of chaos on the numerically constructed stability diagrams, suggesting that these theories are efficient in providing analytical criteria for the chaoticity of planetary orbits.  相似文献   

3.
We investigate the gravitational interaction between a planet and an optically thin protoplanetary disc, performing local three-dimensional hydrodynamical simulations. In the present study, we take account of radiative energy transfer in optically thin discs. Before the stage of planetary accretion, dust opacity is expected to decrease significantly because of grain growth and planetesimal formation. Thus, it would be reasonable to consider optically thin discs in the disc–planet interaction. Furthermore, we focus on small planets that can neither capture disc gas nor open a disc gap. The one-sided torque exerted on a planet by an optically thin disc is examined for various values of the disc optical thickness (<1). In optically thin discs, the temperature behind the density waves is lower than the unperturbed value because of radiative cooling. Heating due to shock dissipation is less effective than radiative cooling. Because of radiative cooling, the density distribution around the planet is not axisymmetric, which exerts an additional torque on the planet. The torque enhancement becomes maximum when the cooling time is comparable with the Keplerian period. The enhancement is significant for low-mass planets. For planets with  3 M⊕  , the additional one-sided torque can be 40 per cent of the torque in the isothermal case. The radiative cooling is expected to change the differential torque and the migration speed of planets, too.  相似文献   

4.
Limits are placed on the range of orbits and masses of possible moons orbiting extrasolar planets which orbit single central stars. The Roche limiting radius determines how close the moon can approach the planet before tidal disruption occurs; while the Hill stability of the star–planet–moon system determines stable orbits of the moon around the planet. Here the full three-body Hill stability is derived for a system with the binary composed of the planet and moon moving on an inclined, elliptical orbit relative the central star. The approximation derived here in Eq. (17) assumes the binary mass is very small compared with the mass of the star and has not previously been applied to this problem and gives the criterion against disruption and component exchange in a closed form. This criterion was applied to transiting extrasolar planetary systems discovered since the last estimation of the critical separations (Donnison in Mon Not R Astron Soc 406:1918, 2010a) for a variety of planet/moon ratios including binary planets, with the moon moving on a circular orbit. The effects of eccentricity and inclination of the binary on the stability of the orbit of a moon is discussed and applied to the transiting extrasolar planets, assuming the same planet/moon ratios but with the moon moving with a variety of eccentricities and inclinations. For the non-zero values of the eccentricity of the moon, the critical separation distance decreased as the eccentricity increased in value. Similarly the critical separation decreased as the inclination increased. In both cases the changes though very small were significant.  相似文献   

5.
In publications presenting analytical results on the non-coplanar motion of a circumbinary planet it was shown that the unperturbed elliptical orbit of the planet undergoes simultaneously two kinds of the precession: the precession of the orbital plane and the precession of the orbit in its own plane. It is also well-known that there is also the relativistic precession of the planetary orbit in its own plane. In the present paper we study a combined effect of the all of the above precessions. For the general case, where the planetary orbit is not coplanar with the stars orbits, we analyzed the dependence of the critical inclination angle ic, at which the precession of the planetary orbit in its own plane vanishes, on the angular momentum L of the planet. We showed that the larger the angular momentum, the smaller the critical inclination angle becomes. We presented the analytical result for ic(L) and calculated the value of L, for which the critical inclination value becomes zero. For the particular case, where the planetary orbit is not coplanar with the stars orbits, we demonstrated analytically that at a certain value of the angular momentum of the planet, the elliptical orbit of the planet would become stationary: no precession. In other words, at this value of the angular momentum, the relativistic precession of the planetary orbit and its precession, caused by the fact that the planet revolves around a binary (rather than single) star, cancel each other out. This is a counterintuitive result.  相似文献   

6.
We discuss the dynamical connection of long-period and nearly parabolic comets with hypothetical transplutonian planets. The statistics includes 792 comets with periods P > 200 years. The orbital plane of the parent planet can be determined from the observed distribution of the perihelia and poles of cometary orbits. The radius of a planetary orbit can be calculated using the Radzievsky-Tisseran criterion. We calculated the minimum distance of each of the 792 orbits to 11 hypothetical planetary orbits. Testing for the kinematic connection of comets with transplutonian planets yielded a negative result. The presence of the nodes of cometary orbits in the transplutonian region is shown to be the result of a geometric effect. We found a high concentration of the nodes and perihelia of cometary orbits in the zone of the terrestrial planets.  相似文献   

7.
Exploring the global dynamics of a planetary system involves computing integrations for an entire subset of its parameter space. This becomes time-consuming in presence of a planet close to the central star, and in practice this planet will be very often omitted. We derive for this problem an averaged Hamiltonian and the associated equations of motion that allow us to include the average interaction of the fast planet. We demonstrate the application of these equations in the case of the μ Arae system where the ratio of the two fastest periods exceeds 30. In this case, the effect of the inner planet is limited because the planet’s mass is one order of magnitude below the other planetary masses. When the inner planet is massive, considering its averaged interaction with the rest of the system becomes even more crucial.  相似文献   

8.
The role of radial velocity (RV) jitter in extrasolar planet search surveys is discussed. Based on the maximum-likelihood principle, improved statistical algorithms for RV fitting and period search are developed. These algorithms incorporate a built-in jitter determination, so that resulting estimations of planetary parameters account for this jitter automatically. This approach is applied to RV data for several extrasolar planetary systems. It is shown that many RV planet search surveys suffer from periodic systematic errors which increase effective RV jitter and can lead to erroneous conclusions. For instance, the planet candidate HD 74156 d may be a false detection made due to annual systematic errors.  相似文献   

9.
The magnetic cataclysmic variable HU Aquarii displayed pronounced quasi‐periodic modulations of its eclipse timing. These were interpreted in terms of the light‐travel time (LTT) effect caused by a circumbinary planet or planetary system. We report new photometric observations that revealed another precise eclipse timing for the October 2013 epoch, the first obtained in a high accretion state after many years in low or intermediate states. The eclipse was observed to occur earlier by 95.3 ± 2.0 s or 62.8 ± 2.0 s than expected for an assumed linear or quadratic ephemeris, respectively. The implied apparent strong evolution of the orbital period calls for a revision of the current planetary model or the planetary parameters. The object deserves further monitoring to uncover the true nature of the observed variability and to constrain the properties of the proposed planet or planetary system. The new observations prove that advanced amateur equipment can successfully be used in the growing field of planet search in wide circumbinary orbits via the LTT effect. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

10.
Previous studies have shown that extrasolar Earth-like planets in close-in habitable zones around M-stars are weakly protected against galactic cosmic rays (GCRs), leading to a strongly increased particle flux to the top of the planetary atmosphere. Two main effects were held responsible for the weak shielding of such an exoplanet: (a) For a close-in planet, the planetary magnetic moment is strongly reduced by tidal locking. Therefore, such a close-in extrasolar planet is not protected by an extended magnetosphere. (b) The small orbital distance of the planet exposes it to a much denser stellar wind than that prevailing at larger orbital distances. This dense stellar wind leads to additional compression of the magnetosphere, which can further reduce the shielding efficiency against GCRs. In this work, we analyse and compare the effect of (a) and (b), showing that the stellar wind variation with orbital distance has little influence on the cosmic ray shielding. Instead, the weak shielding of M star planets can be attributed to their small magnetic moment. We further analyse how the planetary mass and composition influence the planetary magnetic moment, and thus modify the cosmic ray shielding efficiency. We show that more massive planets are not necessarily better protected against galactic cosmic rays, but that the planetary bulk composition can play an important role.  相似文献   

11.
Three major geometric factors which are likely to influence theoretical interpretation of planetary polarization measurements, viz., observer—planet distance, horizontal inhomogeneity of planetary disk, and deviation from a spherical body, are investigated.The distance effect is examined for regional as well as global polarizations. For convenience of analysis, the expressions for zenith and azimuth angles of incident and emergent light appropriate for a snap-shot observation are derived as explicit functions of distance between observer and planet. Sample computations for Venus indicate that regional polarization near the planetary limb is significantly affected by the observer's distance. This effect should be particularly noticeable when an observation is made at a phase angle around which the single scattering polarization of atmospheric scattering agents exhibits a steep variation. The global polarization at large phase angles (measured at disk-center) is gradually moved toward smaller phase angles, as the observer approaches the planet. Any narrow polarization features such as rainbow and glory at small phase angles are heavily smoothed out.The effects of horizontal inhomogeneity are investigated with a planetary disk having highly polarizing regions at high latitudes. Comparison of theoretical global polarization computed for such a disk with the Pioneer Venus OCPP measurements shows a possible change in cloud-haze stratification approximately at 50° latitude, consistent with other imaging observations. An approximate analytical representation of residual polarization at zero phase angle is then derived to compare to the numerical results for Venus. An attempt is also made to explain the relatively large magnitude of residual polarization observed on Jupiter.Finally, to study the effects of nonsphericity of planetary body, the global polarizations are computed for a spheroidal planet. The global polarization tends to increase as the planet's oblateness increases. However, for Jupiter and Saturn, such effect may be of secondary importance.  相似文献   

12.
We present a search for the near-infrared spectroscopic signature of the close orbiting extrasolar giant planet HD 75289b. We obtained ∼230 spectra in the wavelength range 2.18–2.19 μm using the Phoenix spectrograph at Gemini South. By considering the direct spectrum, derived from irradiated model atmospheres, we search for the absorption profile signature present in the combined star and planet light. Since the planetary spectrum is separated from the stellar spectrum at most phases, we apply a phase-dependent orbital model and tomographic techniques to search for absorption signatures.
Because the absorption signature lies buried in the noise of a single exposure we apply a multiline deconvolution to the spectral lines available in order to boost the effective signal-to-noise ratio (S/N) of the data. The wavelength coverage of 80 Å is expected to contain ∼100 planetary lines, enabling a mean line with S/N of 800 to be achieved after deconvolution. We are nevertheless unable to detect the presence of the planet in the data and carry out further simulations to show that broader wavelength coverage should enable a planet like HD 75289b to be detected with 99.9 per cent confidence. We investigate the sensitivity of our method and estimate detection tolerances for mismatches between observed and model planetary atmospheres.  相似文献   

13.
The dynamical stability of a triple system composed of a binary or planetary system and a bound third body moving on a orbit inclined to the system is discussed in terms of Hill stability for the full three-body problem. The situation arises in the determination of stability of triple star systems against disruption and component exchange and the determination of stability of planetary systems against disruption, component exchange or capture. It is found that increasing the inclination of the third body decreases the Hill regions of stability. Increasing the eccentricity of the binary also produces similar effects. These type of changes make exchange or disruption of the component masses more likely. Increasing the eccentricity of the third body initially increases the stability of the system then decreases stability as the eccentricity reaches higher values.The Hill stability criterion is applied to extrasolar planetary systems to determine the critical distances at which planets of the same mass as the observed extrasolar planet moving on a circular orbit could remain on a stable orbit. It was found that these distances were sufficiently short suggesting that the presence of further as yet unobserved stable extrasolar planets in observed systems was very likely.  相似文献   

14.
Keiko Atobe  Shigeru Ida 《Icarus》2004,168(2):223-236
We have investigated obliquity variations of possible terrestrial planets in habitable zones (HZs) perturbed by a giant planet(s) in extrasolar planetary systems. All the extrasolar planets so far discovered are inferred to be jovian-type gas giants. However, terrestrial planets could also exist in extrasolar planetary systems. In order for life, in particular for land-based life, to evolve and survive on a possible terrestrial planet in an HZ, small obliquity variations of the planet may be required in addition to its orbital stability, because large obliquity variations would cause significant climate change. It is known that large obliquity variations are caused by spin-orbit resonances where the precession frequency of the planet's spin nearly coincides with one of the precession frequencies of the ascending node of the planet's orbit. Using analytical expressions, we evaluated the obliquity variations of terrestrial planets with prograde spins in HZs. We found that the obliquity of terrestrial planets suffers large variations when the giant planet's orbit is separated by several Hill radii from an edge of the HZ, in which the orbits of the terrestrial planets in the HZ are marginally stable. Applying these results to the known extrasolar planetary systems, we found that about half of these systems can have terrestrial planets with small obliquity variations (smaller than 10°) over their entire HZs. However, the systems with both small obliquity variations and stable orbits in their HZs are only 1/5 of known systems. Most such systems are comprised of short-period giant planets. If additional planets are found in the known planetary systems, they generally tend to enhance the obliquity variations. On the other hand, if a large/close satellite exists, it significantly enhances the precession rate of the spin axis of a terrestrial planet and is likely to reduce the obliquity variations of the planet. Moreover, if a terrestrial planet is in a retrograde spin state, the spin-orbit resonance does not occur. Retrograde spin, or a large/close satellite might be essential for land-based life to survive on a terrestrial planet in an HZ.  相似文献   

15.
A unique short‐period (P = 0.65356(1) d) Mercury‐size Kepler exoplanet candidate KIC012557548b has been discovered recently by Rappaport et al. (2012). This object is a transiting disintegrating exoplanet with a circum‐planetary material–comet‐like tail. Close‐in exoplanets, like KIC012557548b, are subjected to the greatest planet‐star interactions. This interaction may have various forms. In certain cases it may cause formation of the comet‐like tail. Strong interaction with the host star, and/or presence of an additional planet may lead to variations in the orbital period of the planet. Our main aim is to search for comet‐like tails similar to KIC012557548b and for long‐term orbital period variations. We are curious about frequency of comet‐like tail formation among short‐period Kepler exoplanet candidates. We concentrate on a sample of 20 close‐in candidates with a period similar to KIC012557548b from the Kepler mission. We first improved the preliminary orbital periods and obtained the transit light curves. Subsequently we searched for the signatures of a circum‐planetary material in these light curves. For this purpose the final transit light curve of each planet was fitted with a theoretical light curve, and the residuals were examined for abnormalities. We then searched for possible long‐term changes of the orbital periods using the method of phase dispersion minimization. In 8 cases out of 20 we found some interesting peculiarities, but none of the exoplanet candidates showed signs of a comet‐like tail. It seems that the frequency of comet‐like tail formation among short‐period Kepler exoplanet candidates is very low. We searched for comet‐like tails based on the period criterion. Based on our results we can conclude that the short‐period criterion is not enough to cause comet‐like tail formation. This result is in agreement with the theory of the thermal wind and planet evaporation (Perez‐Becker & Chiang 2013). We also found 3 cases of candidates which showed some changes of the orbital period. Based on our results we can see that orbital period changes are not caused by comet‐like tail disintegration processes, but rather by possible massive outer companions. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

16.
Mark J. Reid 《Icarus》1975,24(1):136-138
The stability of a satellite-orbiting object under the disturbing influence of the parent planet can be assessed by comparison with analogous three-body systems. The changes in the eccentricity and semimajor axis of a satellite-orbiting object (disturbed by the planet) and a planetary satellite (disturbed by the sun) scale equally if the dimensions of the systems are scaled by the sphere of influence of the orbited body. Thus, the apparent gravitational stability of planetary satellites supports theories of the gravitational stability of satellite-orbiting objects.  相似文献   

17.
We study orbits of planetary systems with two planets, for planar motion, at the 1/1 resonance. This means that the semimajor axes of the two planets are almost equal, but the eccentricities and the position of each planet on its orbit, at a certain epoch, take different values. We consider the general case of different planetary masses and, as a special case, we consider equal planetary masses. We start with the exact resonance, which we define as the 1/1 resonant periodic motion, in a rotating frame, and study the topology of the phase space and the long term evolution of the system in the vicinity of the exact resonance, by rotating the orbit of the outer planet, which implies that the resonance and the eccentricities are not affected, but the symmetry is destroyed. There exist, for each mass ratio of the planets, two families of symmetric periodic orbits, which differ in phase only. One is stable and the other is unstable. In the stable family the planetary orbits are in antialignment and in the unstable family the planetary orbits are in alignment. Along the stable resonant family there is a smooth transition from planetary orbits of the two planets, revolving around the Sun in eccentric orbits, to a close binary of the two planets, whose center of mass revolves around the Sun. Along the unstable family we start with a collinear Euler–Moulton central configuration solution and end to a planetary system where one planet has a circular orbit and the other a Keplerian rectilinear orbit, with unit eccentricity. It is conjectured that due to a migration process it could be possible to start with a 1/1 resonant periodic orbit of the planetary type and end up to a satellite-type orbit, or vice versa, moving along the stable family of periodic orbits.  相似文献   

18.
Szebehely's criterion for Hill stability of satellites is derived from Hill's problem and a more exact result is obtained. Direct, Hill stable, circular satellites can exist almost twice as far from the planet as retrograde satellites. For direct satellites the new result agrees with Kuiper's empirical estimate that such satellites are stable up to a distance of half the radius of action of the planet. Comparison with the results of numerical experiments shows that Hill 'stability is valid for direct satellites but meaningless for retrograde satellites. Further accuracy for the maximum distance of Hill stable orbits is obtained from the restricted problem formulation. This provides estimates for planetary distances in double star systems.  相似文献   

19.
A migrating planet can capture planetesimals into mean motion resonances. However, resonant trapping can be prevented when the drift or migration rate is sufficiently high. Using a simple Hamiltonian system for first- and second-order resonances, we explore how the capture probability depends on the order of the resonance, drift rate and initial particle eccentricity. We present scaling factors as a function of the planet mass and resonance strength to estimate the planetary migration rate above which the capture probability drops to less than half. Applying our framework to multiple extrasolar planetary systems that have two planets locked in resonance, we estimate lower limits for the outer planet's migration rate, allowing resonance capture of the inner planet.
Mean motion resonances are comprised of multiple resonant subterms. We find that the corotation subterm can reduce the probability of capture when the planet eccentricity is above a critical value. We present factors that can be used to estimate this critical planet eccentricity. Applying our framework to the migration of Neptune, we find that Neptune's eccentricity is near the critical value that would make its 2 : 1 resonance fail to capture twotinos. The capture probability is affected by the separation between resonant subterms and so is also a function of the precession rates of the longitudes of periapse of both planet and particle near resonance.  相似文献   

20.
Since the first extrasolar planet was discovered about 10 years ago, a major point of dynamical investigations was the determination of stable regions in extrasolar planetary systems where additional planets may exist. Using numerical methods, we investigate the dynamical stability in known multiple planetary systems (HD74156, HD38529, HD168443, HD169830) with special interest on the region between the two known planets and on the mean motion resonances inside this region. As a dynamical model we take the restricted 4-body problem containing the host star, the two planets and massless test-planets. For our numerical integrations, we used the Lie-integrator and additionally the Fast Lyapunov Indicators as a tool for detecting chaotic motion. We also investigated the inner resonances with the outer planet and the outer resonances with the inner planet with test-planets located inside the resonances.  相似文献   

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