Effects of the orbital eccentricity on the equipotential surfaces in binary systems

Todoran, I.

doi:10.1007/bf00613199

Cited by 3 publications

(3 citation statements)

References 2 publications

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“…For eccentric orbit binary star systems, the accretion from a circumbinary disk onto the stars pulsates over the orbital period of the binary (Artymowicz & Lubow 1996;Günther & Kley 2002). This effect is related to the pulsating character of the equipotential surfaces of the elliptical restricted threebody problem (Todoran 1993).…”

Section: Pulsed Accretionmentioning

confidence: 99%

Evolution of Giant Planets in Eccentric Disks

D’Angelo

Lubow

Bate

2006

ApJ

158

121

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We investigate the interaction between a giant planet and a viscous circumstellar disk by means of high-resolution, two-dimensional hydrodynamical simulations. We consider planet masses that range from 1 to 3 Jupiter masses (Mjup) and initial orbital eccentricities that range from 0 to 0.4. We find that a planet can cause eccentricity growth in a disk region adjacent to the planet's orbit, even if the planet's orbit is circular. Disk-planet interactions lead to growth in a planet's orbital eccentricity. The orbital eccentricities of a 2 Mjup and a 3 Mjup planet increase from 0 to 0.11 within about 3000 orbits. Over a similar time period, the orbital eccentricity of a 1 Mjup planet grows from 0 to 0.02. For a case of a 1 Mjup planet with an initial eccentricity of 0.01, the orbital eccentricity grows to 0.09 over 4000 orbits. Radial migration is directed inwards, but slows considerably as a planet's orbit becomes eccentric. If a planet's orbital eccentricity becomes sufficiently large, e > ~0.2, migration can reverse and so be directed outwards. The accretion rate towards a planet depends on both the disk and the planet orbital eccentricity and is pulsed over the orbital period. Planet mass growth rates increase with planet orbital eccentricity. For e~0.2 the mass growth rate of a planet increases by approximately 30% above the value for e=0. For e > ~0.1, most of the accretion within the planet's Roche lobe occurs when the planet is near the apocenter. Similar accretion modulation occurs for flow at the inner disk boundary which represents accretion toward the star.Comment: 20 pages 16 figures, 3 tables. To appear in The Astrophysical Journal vol.652 (December 1, 2006 issue

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Section: Pulsed Accretionmentioning

confidence: 99%

Evolution of Giant Planets in Eccentric Disks

D’Angelo

Lubow

Bate

2006

ApJ

158

121

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“…Gu et al (2003) assumed that the Roche lobe overflow occurs around perihelion and made an approximation that R l = (M p /3M * ) 1/3 a(1 − e). Here we investigate the validity of the approximation by employing the expression for the L1 point in the elliptical restricted three-body problem (Todoran 1993). The exact values of the Roche radius in units of a are calculated using the equations in Todoran (1993) and are shown in Table 1 for various mass ratios and eccentricities relevant to our problem.…”

Section: A Appendixmentioning

confidence: 99%

“…Here we investigate the validity of the approximation by employing the expression for the L1 point in the elliptical restricted three-body problem (Todoran 1993). The exact values of the Roche radius in units of a are calculated using the equations in Todoran (1993) and are shown in Table 1 for various mass ratios and eccentricities relevant to our problem. The table shows that the Roche radius at perihelion is larger than that at aphelion in some of the cases.…”

Section: A Appendixmentioning

confidence: 99%

Tidal and Magnetic Interactions Between a Hot Jupiter and Its Host Star in the Magnetospheric Cavity of a Protoplanetary Disk

Chang

Bodenheimer

2009

ApJ

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We present a simplified model to study the orbital evolution of a young hot Jupiter inside the magnetospheric cavity of a proto-planetary disk. The model takes into account the disk locking of stellar spin as well as the tidal and magnetic interactions between the star and the planet. We focus on the orbital evolution starting from the orbit in the 2:1 resonance with the inner edge of the disk, followed by the inward and then outward orbital migration driven by the tidal and magnetic torques as well as the Roche-lobe overflow of the tidally inflated planet. The goal in this paper is to study how the orbital evolution inside the magnetospheric cavity depends on the cavity size, planet mass, and orbital eccentricity. In the present work, we only target the mass range from 0.7 to 2 Jupiter masses. In the case of the large cavity corresponding to the rotational period ≈ 7 days, the planet of mass > 1 Jupiter mass with moderate initial eccentricities ( 0.3) can move to the region < 0.03 AU from its central star in 10 7 years, while the planet of mass < 1 Jupiter mass cannot. We estimate the critical eccentricity beyond which the planet of a given mass will overflow its Roche radius and finally lose all of its gas onto the star due to runaway mass loss. In the case of the small cavity corresponding to the rotational period ≈ 3 days, all of the simulated planets lose all of their gas even in circular orbits. Our results for the orbital evolution of young hot Jupiters may have the potential to explain the absence of low-mass giant planets inside ∼ 0.03 AU from their dwarf stars revealed by transit surveys.

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The elliptical three‐body problem. Triangular solution

Todoran¹,

Roman²

1992

Astron Nachr

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The restricted three-body problem with eccentric orbit is reviewed and the positions of the triangular Lagrangian points ( L 4 , L 5 ) are determined. I t is put in evidence the fact that L4 and L5 are situated at the corners of an isoscales triangle:1 -e Z I n t r o d u c t i o nIn a previous paper (Todoran 1992) we have analysed the effects of the orbital eccentricity on the shape of the equi-potential surfaces in a close binary system. So it was put in evidence the pulsational character and the variable positions of the linear Lagrangian points. In the frame of the same problem in the present note we shall discuss the positions of the triangular Lagrangian points. 2. E q u a t i o n s of the p r o b l e mLet us consider a non-uniform rotating barycentric coordinate system (X, Y , 2 ) assumed in rotation with the binary system. Here the true anomaly v will be an "angular" function, reckoned from the periastron passage. In such conditions for the double point positions the following equations are established (see Todoran 1992, eqs. (16) - (18)):Equations (1)-(4) are written for a fixed value of the true anomaly v and the following system of units is considered: the semi-major axis ( A = 1) as unit of length, the sum of the masses (rnl + r n 2 = 1) unit of mass, and the reciprocal 1/wk of the mean angular velocity as unit of time. Therefore, we have P = 27r for the orbital period and G = 1. In such conditions we have

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Effects of the orbital eccentricity on the equipotential surfaces in binary systems

Cited by 3 publications

References 2 publications

Evolution of Giant Planets in Eccentric Disks

Evolution of Giant Planets in Eccentric Disks

Tidal and Magnetic Interactions Between a Hot Jupiter and Its Host Star in the Magnetospheric Cavity of a Protoplanetary Disk

The elliptical three‐body problem. Triangular solution

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