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 Physics , 2002, DOI: 10.1046/j.1365-8711.2002.05343.x Abstract: In this paper, we further develop the model for the migration of planets introduced in Del Popolo et al. (2001). 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 to us explicit formulas 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 alpha. We find that planets that are embedded in planetesimal discs, having total mass of 10^{-4}-0.1 M_{\odot}, can migrate inward a large distance for low values of alpha (e.g., alpha \simeq 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 value of the disc mass and/or for larger values of alpha. This model may explain several orbital features of the recently discovered giant planets orbiting nearby stars.
 Stefano Meschiari Physics , 2012, DOI: 10.1088/2041-8205/761/1/L7 Abstract: The existence of planets born in environments highly perturbed by a stellar companion represents a major challenge to the paradigm of planet formation. In numerical simulations, the presence of a close binary companion stirs up the relative velocity between planetesimals, which is fundamental in determining the balance between accretion and erosion. However, the recent discovery of circumbinary planets by Kepler establishes that planet formation in binary systems is clearly viable. We perform N-body simulations of planetesimals embedded in a protoplanetary disk, where planetesimal phasing is frustrated by the presence of stochastic torques, modeling the expected perturbations of turbulence driven by the magnetorotational instability (MRI). We examine perturbation amplitudes relevant to dead zones in the midplane (conducive to planet formation in single stars), and find that planetesimal accretion can be inhibited even in the outer disk (4-10 AU) far from the central binary, a location previously thought to be a plausible starting point for the formation of circumbinary planets.
 Physics , 2009, DOI: 10.1088/0004-637X/698/2/2066 Abstract: Recent observations show that planet can reside in close binary systems with stellar separation of only about 20 AU. However, planet formation in such close binary systems is a challenge to current theory. One of the major theoretical problems occurs in the intermediate stage-planetesimals accretion into planetary embryos-during which the companion's perturbations can stir up the relative velocites(dV) of planetesimals and thus slow down or even cease their growth. However, all previous studies assumed a 2-dimentional (2D) disk and a coplanar binary orbit. Extending previous studies by including a 3D gas disk and an inclined binary orbit with small relative inclination of i_B=0.1-5 deg, we numerically investigate the conditions for planetesimal accretion at 1-2 AU, an extension of the habitable zone(1-1.3 AU), around alpha Centauri A in this paper. Inclusion of the binary inclination leads to: (1) differential orbital phasing is realized in the 3D space, and thus different-sized bodies are separated from each other; (2) total impact rate becomes lower, and impacts mainly occur between similar-sized bodies; (3) accretion is more favored, but the balance between accretion and erosion remains uncertain, and the "possible accretion region" extends up to 2AU when assuming an optimistic Q*(critical specific energy that leads to catastrophic fragmentation); and (4) impact velocities (dV) are significantly reduced but still much larger than their escape velocities, which infers that planetesimals grow by means of type II runaway mode. As a conclusion, inclusion of a small binary inclination is a promising mechanism that favors accretion, opening a possibility that planet formation in close binary systems can go through the difficult stage of planetesimals accretion into planetary embryos.
 Physics , 2015, DOI: 10.1088/0004-637X/809/1/94 Abstract: We present a model in which planetesimal disks are built from the combination of planetesimal formation and accretion of radially drifting pebbles onto existing planetesimals. In this model, the rate of accretion of pebbles onto planetesimals quickly outpaces the rate of direct planetesimal formation in the inner disk. This allows for the formation of a high mass inner disk without the need for enhanced planetesimal formation or a massive protoplanetary disk. Our proposed mechanism for planetesimal disk growth does not require any special conditions to operate. Consequently, we expect that high mass planetesimal disks form naturally in nearly all systems. The extent of this growth is controlled by the total mass in pebbles that drifts through the inner disk. Anything that reduces the rate or duration of pebble delivery will correspondingly reduce the final mass of the planetesimal disk. Therefore, we expect that low mass stars (with less massive protoplanetary disks), low metallicity stars and stars with giant planets should all grow less massive planetesimal disks. The evolution of planetesimal disks into planetary systems remains a mystery. However, we argue that late stage planet formation models should begin with a massive disk. This reinforces the idea that massive and compact planetary systems could form in situ but does not exclude the possibility that significant migration occurs post-planet formation.
 Physics , 2014, DOI: 10.1088/0004-637X/798/2/70 Abstract: Planet formation in small-separation (~20 AU) eccentric binaries such as gamma Cephei or alpha Centauri is believed to be adversely affected by the presence of the stellar companion. Strong dynamical excitation of planetesimals by the eccentric companion can result in collisional destruction (rather than growth) of 1-100 km objects, giving rise to the "fragmentation barrier" for planet formation. We revise this issue using a novel description of secular dynamics of planetesimals in binaries, which accounts for the gravity of the eccentric, coplanar protoplanetary disk, as well as gas drag. By studying planetesimal collision outcomes we show, in contrast to many previous studies, that planetesimal growth and subsequent formation of planets (including gas giants) in AU-scale orbits within ~20 AU separation binaries may be possible, provided that the protoplanetary disks are massive (>10^{-2}M_\odot) and only weakly eccentric (disk eccentricity <0.01). These requirements are compatible with both the existence of massive (several M_J) planets in gamma Cep-like systems and the results of recent simulations of gaseous disks in eccentric binaries. Terrestrial and Neptune-like planets can also form in lower-mass disks at small (sub-AU) radii. We find that fragmentation barrier is less of a problem in eccentric disks which are apsidally aligned with the binary orbit. Alignment gives rise to special locations, where (1) relative planetesimal velocities are low and (2) the timescale of their drag-induced radial drift is long. This causes planetesimal pileup at such locations in the disk and promotes their growth.
 Physics , 2012, DOI: 10.1088/2041-8205/763/1/L8 Abstract: According to the core accretion theory, circumbinary embryos can form only beyond a critical semimajor axis (CSMA). However, due to the relatively high density of solid materials in the inner disk, significant amount of small planetesimals must exist in the inner zone when embryos were forming outside this CSMA. So embryos migration induced by the planetesimal swarm is possible after the gas disk depletion. Through numerical simulations, we found (i) the scattering-driven inward migration of embryos is robust, planets can form in the habitable zone if we adopt a mass distribution of MMSN-like disk; (ii) the total mass of the planetesimals in the inner region and continuous embryo-embryo scattering are two key factors that cause significant embryo migrations; (iii) the scattering-driven migration of embryos is a natural water-deliver mechanism. We propose that planet detections should focus on the close binary with its habitable zone near CSMA.
 Physics , 2003, DOI: 10.1046/j.1365-8711.2003.06194.x Abstract: In this paper, we further develop the model for the migration of planets introduced in Del Popolo, Gambera and Ercan, and extended to time-dependent planetesimal accretion disks in Del Popolo and Eksi. More precisely, the assumption of Del Popolo and Eksi that the surface density in planetesimals is proportional to that of gas is released. Indeed, the evolution of the radial distribution of solids is governed by many processes: gas-solid coupling, coagulation, sedimentation, evaporation/condensation, so that the distribution of planetesimals emerging from a turbulent disk does not necessarily reflect that of gas. In order to describe this evolution we use a method developed in Stepinski and Valageas which, using a series of simplifying assumptions, is able to simultaneously follow the evolution of gas and solid particles for up to $10^7 {\rm yr}$. Then, the distribution of planetesimals obtained after $10^7 {\rm yr}$ is used to study the migration rate of a giant planet through the migration model introduced in \cite{DP1}. This allows us to investigate the dependence of the migration rate on the disk mass, on its time evolution and on the value of the dimensionless viscosity parameter alpha. We find that in the case of disks having a total mass of $10^{-3}-10^{-1} M_{\odot}$, and $10^{-4}<\alpha<10^{-1}$, planets can migrate inward over a large distance while if $M_{\rm d}<10^{-3} M_{\odot}$ the planets remain almost at their initial position for $\alpha>10^{-3}$ and only in the case $\alpha<10^{-3}$ the planets move to a minimum value of orbital radius of $\simeq 2 {\rm AU}$. Moreover, the observed distribution of planets in the period range 0-20 days can be easily obtained from our model.
 Physics , 2014, DOI: 10.1093/mnras/stu1591 Abstract: In this paper, we investigate whether hypothetical Earth-like planets have high probability of remaining on stable orbits inside the habitable zones around the stars A and B of {\alpha} Centauri, for lengths of time compatible with the evolution of life. We introduce a stability criterion based on the solution of the restricted three-body problem and apply it to the {\alpha} Centauri system. In this way, we determine the regions of the short-term stability of the satellite-type (S-type) planetary orbits, in both planar and three-dimensional cases. We also study the long-term stability of hypothetical planets through the dynamical mapping of the habitable zones of the stars. The topology of the maps is analyzed using the semi-analytical secular Hamiltonian model and possible processes responsible for long-lasting instabilities are identified. We verify that the planetary motion inside the habitable zones is regular, regardless of high eccentricities, for inclinations smaller than 40{\deg}. We show that the variation of the orbital distance of the planet located in the habitable zones of the binary is comparable to that of Earth, if the planet is close to the Mode I stationary solution. This result brings positive expectations for finding habitable planets in binary stars.
 Physics , 2001, DOI: 10.1046/j.1365-8711.2001.04517.x Abstract: 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 $10^{-4}-0.01 M_{\odot}$, can migrate inward a large distance and can survive only if the inner disc is truncated or because of tidal interaction with the star. In this case the semi-major axis, a, of the planetary orbit is less than 0.1 AU. Orbits with larger $a$ are obtained for smaller value of the disc mass or for a rapid evolution (depletion) of the disc. This model may explain several of the orbital features of the giant planets that were discovered in last years orbiting nearby stars as well as the metallicity enhancement found in several stars associated with short-period planets.
 Physics , 1996, DOI: 10.1086/118360 Abstract: This paper investigates the long-term orbital stability of small bodies near the central binary of the Alpha Centauri system. Test particles on circular orbits are integrated in the field of this binary for 32000 binary periods or approximately 2.5 Myr. In the region exterior to the binary, particles with semi-major axes less than roughly three times the binary's semi-major axis are unstable. Inside the binary, particles are unstable if further than 0.2 binary semimajor axes from the primary, with stablility closer in a strong function of inclination: orbits inclined near 90 degrees are unstable in as close as 0.01 binary semimajor axes from either star.
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