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1.
Giant planets in circumstellar disks can migrate inward from their initial (formation) positions at several AUs. Inward radial migration of the planet is caused by torques between the planet and the disk; outward radial migration of the planet is caused by torques between the planet and the spinning star, and by torques due to Roche lobe overflow and consequent mass loss from the planet. We present self-consistent numerical considerations of the problem of migrating giant planets by summing torques on planets for various physical parameters of the disk and of planets. We find that Jupiter-mass planets can stably arrive and survive at small heliocentric distances, thus reproducing observed properties of some of the recently discovered extra-solar planets. The range of fates of massive planets is broad, and some perish by losing all their mass onto the central star during Roche lobe overflow, while others survive for the lifetime of the central star. Surviving planets cluster into two groups when examined in terms of final mass and final heliocentric distance: those which have lost mass and those which have not. Some of the observed extrasolar planets fall into each of these two exclusive classes. We also find that there is an inner boundary for planets' final heliocentric distances, caused by tidal torques with the central star. Planets in small orbits are shown to be stable against atmospheric loss.  相似文献   

2.
We have performed N-body simulation on final accretion stage of terrestrial planets, including the effect of damping of eccentricity and inclination caused by tidal interaction with a remnant gas disk. As a result of runway and oligarchic accretion, about 20 Mars-sized protoplanets would be formed in nearly circular orbits with orbital separation of several to ten Hill radius. The orbits of the protoplanets would be eventually destabilized by long-term mutual gravity and/or secular resonance of giant gaseous planets. The protoplanets would coalesce with each other to form terrestrial planets through the orbital crossing. Previous N-body simulations, however, showed that the final eccentricities of planets are around 0.1, which are about 10 times higher than the present eccentricities of Earth and Venus. The obtained high eccentricities are the remnant of orbital crossing. We included the effect of eccentricity damping caused by gravitational interaction with disk gas as a drag force (“gravitational drag”) and carried out N-body simulation of accretion of protoplanets. We start with 15 protoplanets with 0.2M⊕ and integrate the orbits for 107 years, which is consistent with the observationally inferred disk lifetime (in some runs, we start with 30 protoplanets with 0.1M⊕). In most runs, the damping time scale, which is equivalent to the strength of the drag force, is kept constant throughout each run in order to clarify the effects of the damping. We found that the planets' final mass, spatial distribution, and eccentricities depend on the damping time scale. If the damping time scale for a 0.2M⊕ mass planet at 1 AU is longer than 108 years, planets grow to Earth's size, but the final eccentricities are too high as in gas-free cases. If it is shorter than 106 years, the eccentricities of the protoplanets cannot be pumped up, resulting in not enough orbital crossing to make Earth-sized planets. Small planets with low eccentricities are formed with small orbital separation. On the other hand, if it is between 106 and 108 years, which may correspond to a mostly depleted disk (0.01-0.1% of surface density of the minimum mass model), some protoplanets can grow to about the size of Earth and Venus, and the eccentricities of such surviving planets can be diminished within the disk lifetime. Furthermore, in innermost and outermost regions in the same system, we often find planets with smaller size and larger eccentricities too, which could be analogous to Mars and Mercury. This is partly because the gravitational drag is less effective for smaller mass planets, and partly due to the “edge effect,” which means the innermost and outermost planets tend to remain without collision. We also carried out several runs with time-dependent drag force according to depletion of a gas disk. In these runs, we used exponential decay model with e-folding time of 3×106 years. The orbits of protoplanets are stablized by the eccentricity damping in the early time. When disk surface density decays to ?1% of the minimum mass disk model, the damping force is no longer strong enough to inhibit the increase of the eccentricity by distant perturbations among protoplanets so that the orbital crossing starts. In this disk decay model, a gas disk with 10−4-10−3 times the minimum mass model still remains after the orbital crossing and accretional events, which is enough to damp the eccentricities of the Earth-sized planets to the order of 0.01. Using these results, we discuss a possible scenario for the last stage of terrestrial planet formation.  相似文献   

3.
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   

4.
Most extrasolar planets discovered to date are more massive than Jupiter, in surprisingly small orbits (semimajor axes less than 3 AU). Many of these have significant orbital eccentricities. Such orbits may be the product of dynamical interactions in multiplanet systems. We examine outcomes of such evolution in systems of three Jupiter-mass planets around a solar-mass star by integration of their orbits in three dimensions. Such systems are unstable for a broad range of initial conditions, with mutual perturbations leading to crossing orbits and close encounters. The time scale for instability to develop depends on the initial orbital spacing; some configurations become chaotic after delays exceeding 108 y. The most common outcome of gravitational scattering by close encounters is hyperbolic ejection of one planet. Of the two survivors, one is moved closer to the star and the other is left in a distant orbit; for systems with equal-mass planets, there is no correlation between initial and final orbital positions. Both survivors may have significant eccentricities, and the mutual inclination of their orbits can be large. The inner survivor's semimajor axis is usually about half that of the innermost starting orbit. Gravitational scattering alone cannot produce the observed excess of “hot Jupiters” in close circular orbits. However, those scattered planets with large eccentricities and small periastron distances may become circularized if tidal dissipation is effective. Most stars with a massive planet in an eccentric orbit should have at least one additional planet of comparable mass in a more distant orbit.  相似文献   

5.
Planetesimals encountering with a planet cannot be captured permanently unless energy dissipation is taken into account, but some of them can be temporarily captured in the vicinity of the planet for an extended period of time. Such a process would be important for the origin and dynamical evolution of irregular satellites, short-period comets, and Kuiper-belt binaries. In this paper, we describe the basic formulation for the study of temporary capture of planetesimals from heliocentric orbits using three-body orbital integration, such as the definition of the duration and rate of temporary capture, and present results in the case of low random velocity of planetesimals. In the case of planetesimals initially on circular orbits, we find that planetesimals undergo a close encounter with the planet before they become temporarily captured. When planetesimals are scattered by the planet into the vicinity of one of periodic orbits around the planet, the duration of temporary capture tends to be extended. Typically, these capture orbits are in the retrograde direction around the planet. We evaluate the rate of temporary capture of planetesimals, and find that the ratio of this rate to their collision rate on to the planet increases with increasing semimajor axis of the planet. Similar results are obtained for planetesimals with non-zero but small random velocities, as long as Kepler shear dominates the relative velocity between the planet and planetesimals. For larger initial random velocities of planetesimals, temporary capture in both prograde and retrograde directions with much longer duration becomes possible.  相似文献   

6.
In this paper we extend the theory of close encounters of a giant planet on a parabolic orbit with a central star developed in our previous work (Ivanov and Papaloizou in MNRAS 347:437, 2004; MNRAS 376:682, 2007) to include the effects of tides induced on the central star. Stellar rotation and orbits with arbitrary inclination to the stellar rotation axis are considered. We obtain results both from an analytic treatment that incorporates first order corrections to normal mode frequencies arising from stellar rotation and numerical treatments that are in satisfactory agreement over the parameter space of interest. These results are applied to the initial phase of the tidal circularisation problem. We find that both tides induced in the star and planet can lead to a significant decrease of the orbital semi-major axis for orbits having periastron distances smaller than 5?C6 stellar radii with tides in the star being much stronger for retrograde orbits compared to prograde orbits. Assuming that combined action of dynamic and quasi-static tides could lead to the total circularisation of orbits this corresponds to observed periods up to 4?C5 days. We use the simple Skumanich law to characterise the rotational history of the star supposing that the star has its rotational period equal to one month at the age of 5 Gyr. The strength of tidal interactions is characterised by circularisation time scale, t ev , which is defined as a typical time scale of evolution of the planet??s semi-major axis due to tides. This is considered as a function of orbital period P obs , which the planet obtains after the process of tidal circularisation has been completed. We find that the ratio of the initial circularisation time scales corresponding to prograde and retrograde orbits, respectively, is of order 1.5?C2 for a planet of one Jupiter mass having P obs ~ 4 days. The ratio grows with the mass of the planet, being of order five for a five Jupiter mass planet with the same P orb . Note, however, this result might change for more realistic stellar rotation histories. Thus, the effect of stellar rotation may provide a bias in the formation of planetary systems having planets on close orbits around their host stars, as a consequence of planet?Cplanet scattering, which favours systems with retrograde orbits. The results reported in the paper may also be applied to the problem of tidal capture of stars in young stellar clusters.  相似文献   

7.
In this paper we develop further the model for the migration of planets introduced in Del Popolo et al. We first model the protoplanetary nebula as a time-dependent accretion disc, and find self-similar solutions to the equations of the accretion disc that give us explicit formulae for the spatial structure and the temporal evolution of the nebula. These equations are then used to obtain the migration rate of the planet in the planetesimal disc, and to study how the migration rate depends on the disc mass, on its time evolution and on some values of the dimensionless viscosity parameter α . We find that planets that are embedded in planetesimal discs, having total mass of  10-4-0.1 M  , can migrate inward a large distance for low values of α (e.g.,   α ≃10-3-10-2)  and/or large disc mass, and can survive only if the inner disc is truncated or because of tidal interaction with the star. Orbits with larger a are obtained for smaller values of the disc mass and/or for larger values of α . This model may explain several orbital features of the recently discovered giant planets orbiting nearby stars.  相似文献   

8.
Potentially habitable planets can orbit close enough to their host star that the differential gravity across their diameters can produce an elongated shape. Frictional forces inside the planet prevent the bulges from aligning perfectly with the host star and result in torques that alter the planet’s rotational angular momentum. Eventually the tidal torques fix the rotation rate at a specific frequency, a process called tidal locking. Tidally locked planets on circular orbits will rotate synchronously, but those on eccentric orbits will either librate or rotate super-synchronously. Although these features of tidal theory are well known, a systematic survey of the rotational evolution of potentially habitable exoplanets using classic equilibrium tide theories has not been undertaken. I calculate how habitable planets evolve under two commonly used models and find, for example, that one model predicts that the Earth’s rotation rate would have synchronized after 4.5 Gyr if its initial rotation period was 3 days, it had no satellites, and it always maintained the modern Earth’s tidal properties. Lower mass stellar hosts will induce stronger tidal effects on potentially habitable planets, and tidal locking is possible for most planets in the habitable zones of GKM dwarf stars. For fast-rotating planets, both models predict eccentricity growth and that circularization can only occur once the rotational frequency is similar to the orbital frequency. The orbits of potentially habitable planets of very late M dwarfs ( Open image in new window ) are very likely to be circularized within 1 Gyr, and hence, those planets will be synchronous rotators. Proxima b is almost assuredly tidally locked, but its orbit may not have circularized yet, so the planet could be rotating super-synchronously today. The evolution of the isolated and potentially habitable Kepler planet candidates is computed and about half could be tidally locked. Finally, projected TESS planets are simulated over a wide range of assumptions, and the vast majority of potentially habitable cases are found to tidally lock within 1 Gyr. These results suggest that the process of tidal locking is a major factor in the evolution of most of the potentially habitable exoplanets to be discovered in the near future.  相似文献   

9.
To date, no accretion model has succeeded in reproducing all observed constraints in the inner Solar System. These constraints include: (1) the orbits, in particular the small eccentricities, and (2) the masses of the terrestrial planets - Mars’ relatively small mass in particular has not been adequately reproduced in previous simulations; (3) the formation timescales of Earth and Mars, as interpreted from Hf/W isotopes; (4) the bulk structure of the asteroid belt, in particular the lack of an imprint of planetary embryo-sized objects; and (5) Earth’s relatively large water content, assuming that it was delivered in the form of water-rich primitive asteroidal material. Here we present results of 40 high-resolution (N = 1000-2000) dynamical simulations of late-stage planetary accretion with the goal of reproducing these constraints, although neglecting the planet Mercury. We assume that Jupiter and Saturn are fully-formed at the start of each simulation, and test orbital configurations that are both consistent with and contrary to the “Nice model”. We find that a configuration with Jupiter and Saturn on circular orbits forms low-eccentricity terrestrial planets and a water-rich Earth on the correct timescale, but Mars’ mass is too large by a factor of 5-10 and embryos are often stranded in the asteroid belt. A configuration with Jupiter and Saturn in their current locations but with slightly higher initial eccentricities (e = 0.07-0.1) produces a small Mars, an embryo-free asteroid belt, and a reasonable Earth analog but rarely allows water delivery to Earth. None of the configurations we tested reproduced all the observed constraints. Our simulations leave us with a problem: we can reasonably satisfy the observed constraints (except for Earth’s water) with a configuration of Jupiter and Saturn that is at best marginally consistent with models of the outer Solar System, as it does not allow for any outer planet migration after a few Myr. Alternately, giant planet configurations which are consistent with the Nice model fail to reproduce Mars’ small size.  相似文献   

10.
The significant orbital eccentricities of most giant extrasolar planets may have their origin in the gravitational dynamics of initially unstable multiple planet systems. In this work, we explore the dynamics of two close planets on inclined orbits through both analytical techniques and extensive numerical scattering experiments. We derive a criterion for two equal mass planets on circular inclined orbits to achieve Hill stability, and conclude that significant radial migration and eccentricity pumping of both planets occurs predominantly by 2:1 and 5:3 mean motion resonant interactions. Using Laplace-Lagrange secular theory, we obtain analytical secular solutions for the orbital inclinations and longitudes of ascending nodes, and use those solutions to distinguish between the secular and resonant dynamics which arise in numerical simulations. We also illustrate how encounter maps, typically used to trace the motion of massless particles, may be modified to reproduce the gross instability seen by the numerical integrations. Such a correlation suggests promising future use of such maps to model the dynamics of more coplanar massive planet systems.  相似文献   

11.
In long-term stability studies of terrestrial planets moving in the habitable zone (HZ) of a sun-like star, we distinguish four different configurations: (i) planets moving in binary star systems, (ii) the inner type (where the gas giant moves outside the HZ), (iii) the outer type (where the gas giant is closer to the star, than the HZ) and (iv) the Trojan type (where the gas giant moves in the HZ). Since earlier calculations indicated, that the stability of the motion in the HZ also depends on the inclination of the terrestrial planet orbits, we present a detailed numerical investigation to show correlations between the eccentricity, the mass and the distance of the giant planet for various inclinations of the terrestrial planets. The orbital stability of the HZ was examined for all four configurations stated above. While we could find hardly any stable orbits for the first three types for inclinations higher than 40°, the Trojan planets can be stable up to an inclination of 60°. Additionally, we could also find some stabilizing effects of the inclination for the first three types. As dynamical model we used the elliptic restricted three-body problem, which consists of two massive and one mass-less body. This allows an application to all detected and future extrasolar single planet systems.  相似文献   

12.
在掩星法发现的系外行星系统中,如果存在其他未知的伴星绕同一颗恒星运动,掩星行星由于受到伴星引力的影响,运动轨道将发生变化,轨道周期不再是常数,而是变化的。利用这种变化探测掩星系统中的其他行星,已成为一种新的方法。主要介绍了未知行星与掩星行星之间的引力作用引起的掩星周期变化效应,以及掩星周期变化法探测系外行星的理论和研究进展状况,最后简要讨论了几种影响掩星周期变化的其他因素:共轨行星、卫星、潮汐效应、相对论效应及恒星的引力四极矩等。  相似文献   

13.
Sean N. Raymond  Thomas Quinn 《Icarus》2005,177(1):256-263
‘Hot jupiters,’ giant planets with orbits very close to their parent stars, are thought to form farther away and migrate inward via interactions with a massive gas disk. If a giant planet forms and migrates quickly, the planetesimal population has time to re-generate in the lifetime of the disk and terrestrial planets may form [P.J. Armitage, A reduced efficiency of terrestrial planet formation following giant planet migration, Astrophys. J. 582 (2003) L47-L50]. We present results of simulations of terrestrial planet formation in the presence of hot/warm jupiters, broadly defined as having orbital radii ?0.5 AU. We show that terrestrial planets similar to those in the Solar System can form around stars with hot/warm jupiters, and can have water contents equal to or higher than the Earth's. For small orbital radii of hot jupiters (e.g., 0.15, 0.25 AU) potentially habitable planets can form, but for semi-major axes of 0.5 AU or greater their formation is suppressed. We show that the presence of an outer giant planet such as Jupiter does not enhance the water content of the terrestrial planets, but rather decreases their formation and water delivery timescales. We speculate that asteroid belts may exist interior to the terrestrial planets in systems with close-in giant planets.  相似文献   

14.
S. Fred Singer 《Icarus》1975,25(3):484-488
Uranus exhibits an unusually large obliquity compared to other planets of the solar system; its equator is inclined by 98° to the plane of its orbit. However its five satellites are remarkably regular, with eccentricities and inclinations very nearly zero, but of course with orbit planes that are tilted by ~98° to the plane of the ecliptic. This circumstance is used here to relate the formation of satellites to planet formation. Six different cases are discussed, of which two can be ruled out and two others are highly improbable. In the analysis, use is made of the fact that satellites in near-equatorial orbits could not follow a rapid (“non-adiabatic”) change of the planet's obliquity. We assume, also, that the observed obliquity is the result of the last stages of planet accumulation. We can therefore exclude contemporaneous formation of planet and satellites, and conclude instead that the satellites were formed or acquired after the planet's axis had been tilted. A plausible scenario involves the tidal capture of a body having 5% to 10% of the planet's mass—sufficient to account for the tilt—followed by its accretion. However, tidal forces break up the body into chunks, slow the accretion, and allow ~1% of the chunks to form the satellites through interaction with a temporary dense atmosphere. The same reasoning may apply also for Saturn and Jupiter. It should be noted that the synchronous orbit it well within the Roche limit for all three planets.  相似文献   

15.
On the migration of a system of protoplanets   总被引:1,自引:0,他引:1  
The evolution of a system consisting of a protoplanetary disc with two embedded Jupiter-sized planets is studied numerically. The disc is assumed to be flat and non-self-gravitating; this is modelled by the planar (two-dimensional) Navier–Stokes equations. The mutual gravitational interaction of the planets and the star, and the gravitational torques of the disc acting on the planets and the central star are included. The planets have an initial mass of one Jupiter mass M Jup each, and the radial distances from the star are one and two semimajor axes of Jupiter, respectively.
During the evolution a joint wide annular gap is created by the planets. Both planets increase their mass owing to accretion of gas from the disc: after about 2500 orbital periods of the inner planet it has reached a mass of 2.3  M Jup, while the outer planet has reached a mass of 3.2  M Jup. The net gravitational torques exerted by the disc on the planets result in an inward migration of the outer planet on time-scales comparable to the viscous evolution time of the disc. The semimajor axis of the inner planet remains constant as there is very little gas left in its vicinity to induce any migration. When the distance of close approach eventually becomes smaller than the mutual Hill radius, the eccentricities increase strongly and the system may become unstable.
If disc depletion occurs rapidly enough before the planets come too close to each other, a stable system similar to our own Solar system may remain. Otherwise the orbits may become unstable and produce systems like υ And.  相似文献   

16.
Using numerical simulations, we studied several coupled translational and rotational solutions of the two-finite-body problem with one spherical and one triaxial body. The aim was to investigate which types of orbits and planetary bodies could produce spin-induced orbital perturbations relevant enough to add to models dealing with other perturbations. To fully assess the strengths and consequences of this perturbation, we did not include any other perturbation even when a more realistic scenario would have required it. Interesting results concern planet–star mass ratios like a hot Jupiter or a super-Jupiter around a star like the Sun or the red dwarf Proxima Centauri. The short-period chaotic effect of the gravitational spin–orbit perturbation on highly eccentric orbits in the vicinity of the Roche limit can be a prominent feature. It should be taken into account when studying the tidal evolution of such a planet or its interactions with any companion in the neighborhood of the star.  相似文献   

17.
S. Elser  J. Stadel 《Icarus》2011,214(2):357-365
The Earth’s comparatively massive moon, formed via a giant impact on the proto-Earth, has played an important role in the development of life on our planet, both in the history and strength of the ocean tides and in stabilizing the chaotic spin of our planet. Here we show that massive moons orbiting terrestrial planets are not rare. A large set of simulations by Morishima et al. (Morishima, R., Stadel, J., Moore, B. [2010]. Icarus. 207, 517-535), where Earth-like planets in the habitable zone form, provides the raw simulation data for our study. We use limits on the collision parameters that may guarantee the formation of a circumplanetary disk after a protoplanet collision that could form a satellite and study the collision history and the long term evolution of the satellites qualitatively. In addition, we estimate and quantify the uncertainties in each step of our study. We find that giant impacts with the required energy and orbital parameters for producing a binary planetary system do occur with more than 1 in 12 terrestrial planets hosting a massive moon, with a low-end estimate of 1 in 45 and a high-end estimate of 1 in 4.  相似文献   

18.
There is evidence for the existence of massive planets at orbital radii of several hundred au from their parent stars where the time-scale for planet formation by core accretion is longer than the disc lifetime. These planets could have formed close to their star and then migrated outwards. We consider how the transfer of angular momentum by viscous disc interactions from a massive inner planet could cause significant outward migration of a smaller outer planet. We find that it is in principle possible for planets to migrate to large radii. We note, however, a number of effects which may render the process somewhat problematic.  相似文献   

19.
E.W. Thommes  M.J. Duncan 《Icarus》2003,161(2):431-455
Runaway growth ends when the largest protoplanets dominate the dynamics of the planetesimal disk; the subsequent self-limiting accretion mode is referred to as “oligarchic growth.” Here, we begin by expanding on the existing analytic model of the oligarchic growth regime. From this, we derive global estimates of the planet formation rate throughout a protoplanetary disk. We find that a relatively high-mass protoplanetary disk (∼10 × minimum-mass) is required to produce giant planet core-sized bodies (∼10 M) within the lifetime of the nebular gas (?10 million years). However, an implausibly massive disk is needed to produce even an Earth mass at the orbit of Uranus by 10 Myrs. Subsequent accretion without the dissipational effect of gas is even slower and less efficient. In the limit of noninteracting planetesimals, a reasonable-mass disk is unable to produce bodies the size of the Solar System’s two outer giant planets at their current locations on any timescale; if collisional damping of planetesimal random velocities is sufficiently effective, though, it may be possible for a Uranus/Neptune to form in situ in less than the age of the Solar System. We perform numerical simulations of oligarchic growth with gas and find that protoplanet growth rates agree reasonably well with the analytic model as long as protoplanet masses are well below their estimated final masses. However, accretion stalls earlier than predicted, so that the largest final protoplanet masses are smaller than those given by the model. Thus the oligarchic growth model, in the form developed here, appears to provide an upper limit for the efficiency of giant planet formation.  相似文献   

20.
A young hot Jupiter might have been tidally inflated beyond its Roche radius when its orbit was being circularized. This scenario has the potential to explain a couple of solid or tentative observations such as a pile‐up of hot Jupiters around 0.04‐0.05 AU, the mass‐period correlation of transiting planets, as well as the existence of hot Neptunes. Other scenarios such as tidal dissipation in a planet‐host star as well as the magnetic interaction will be also discussed. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

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