Equilibrium Structures of Rotationally and Tidally Distorted Polytropic Models of Stars

Lal, A. K.; Saini, Seema; Mohan, C.; Singh, V. P.

doi:10.1007/s10509-006-9209-6

Cited by 8 publications

(5 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…While the envelope is highly susceptible to applied centrifugal and tidal forces, the distortion of the core is assumed to be small even in the case of critical rotation. Depending on the method to calculate the distortion of the core, the double-approximation method has several different branches: Monaghan & Roxburgh (1965), Jackson (1970), Durney & Roxburgh (1970), and Naylor & Anand (1972a,b) used first-order perturbation theory of Chandrasekhar (1933a); Martin (1970) and Singh & Singh (1984) included terms up to of second order; Meynet & Maeder (1997) and Lal et al (2006) employed the quasispherical method.…”

Section: Introductionmentioning

confidence: 99%

Internal Structure and Apsidal Motions of Polytropic Stars in Close Binaries

Sirotkin

Kim

2009

ApJ

View full text Add to dashboard Cite

We consider a synchronized, circular-orbit binary consisting of a polytrope with index n and a point-mass object, and use a self-consistent field method to construct the equilibrium structure of the polytrope under rotational and tidal perturbations. Our self-consistent field method is distinct from others in that the equilibrium orbital angular velocity is calculated automatically rather than being prescribed, which is crucial for obtaining apsidal motion rates accurately. We find that the centrifugal and tidal forces make perturbed stars more centrally condensed and larger in size. For n = 1.5 polytopes with fixed entropy, the enhancement factor in stellar radii is about 23% and 4 − 8% for µ = 1 and ∼ 0.1 − 0.9, respectively, where µ is the fractional mass of the polytrope relative to the total. The centrifugal force dominates the tidal force in determining the equilibrium structure provided µ > ∼ 0.13 − 0.14 for n > ∼ 1.5. The shape and size of rotationally-and tidally-perturbed polytropes are well described by the corresponding Roche models as long as n > ∼ 2. The apsidal motion rates calculated for circular-orbit binaries under the equilibrium tide condition agree well with the predictions of the classical formula only when the rotational and tidal perturbations are weak. When the perturbations are strong as in critical configurations, the classical theory underestimates the real apsidal motion rates by as much as 50% for n = 1.5 polytropes, although the discrepancy becomes smaller as n increases. For practical uses, we provide fitting formulae for the density concentration, volume radius, coefficient of the mass-radius relation, moment of inertia, spin angular momentum, critical rotation parameter, effective internal structure constant, etc., as functions of µ and the perturbation parameters.

show abstract

Section: Introductionmentioning

confidence: 99%

Internal Structure and Apsidal Motions of Polytropic Stars in Close Binaries

Sirotkin

Kim

2009

ApJ

View full text Add to dashboard Cite

show abstract

“…Kopal (1972) introduced the concept of Roche equipotentials to analyze the problems of rotating stars and stars in binary systems. Since then several authors such as Kopal (1978Kopal ( , 1980Kopal ( , 1981Kopal ( , 1989, Kopal and Song (1983), Eggleton (1983), Mohan and Singh (1978), Mohan and Saxena (1983), Mohan et al (1990Mohan et al ( , 1992Mohan et al ( , 1997, Lal et al (2001Lal et al ( , 2006 have used this concept to analyze the problems of rotationally and/or tidally distorted stars. In this approach Roche approximation for the inner structure of a star is used to obtain an expression for the potential of a rotating star and star in a binary system.…”

Section: Introductionmentioning

confidence: 99%

Effect of Coriolis force on the shapes of rotating stars and stars in binary systems

Lal

Pathania

Mohan

2008

Astrophys Space Sci

Self Cite

View full text Add to dashboard Cite

In this paper an attempt has been made to determine the effect of Coriolis force on the shapes of Roche equipotential surfaces of rotating stars and stars in binary systems. Equations of Roche equipotential surfaces have been obtained for rotating and binary stars which take into account the effects of Coriolis force besides the centrifugal and gravitational forces. Shapes of Roche equipotentials and values of Roche limits are obtained for different values of angular velocity of rotation for rotating stars and for different values of mass ratios for the binary stars. The obtained results have been compared with the corresponding results in which the effect of Coriolis force has not been considered.

show abstract

“…Kopal (1972Kopal ( , 1978Kopal ( , 1983 and Mohan et al (1978aMohan et al ( , 1978bMohan et al ( , 1982Mohan et al ( , 1990Mohan et al ( , 1991Mohan et al ( , 1992Mohan et al ( , 1997Mohan et al ( , 1998 used this approach to analytically investigate the problems of the structure and oscillations of rotating stars and stars in binary systems. Some other authors who have also made use of the concept of Roche equipotentials in the study of the problems of rotating stars and stars in binary systems are Kitamura and Kopal (1968), Eggleton (1983), Mochnacki (1984), Morris (1994), Kahler (1997), Claret (1999), Seidov (2004, and Lal et al (2006).…”

Section: Introductionmentioning

confidence: 99%

On the validity of series expansion being used for the position of a point on a Roche equipotential

Lal

Saini

Mohan³

et al. 2007

Astrophys Space Sci

Self Cite

View full text Add to dashboard Cite

The concept of Roche equipotentials has been frequently used in literature to study the problems of rotating stars and stars in binary systems. However in spite of using this simplifying concept, it is still not possible to express the position of a point in the potential field of such a system in a closed analytic form. In order to carry out further analytic studies, Kopal (Adv. Astron. Astrophys. 9:1-65, 1972), therefore, developed a series expansion for it. The series expansion of Kopal has often been used in the analysis of the problem of equilibrium structure and the periods of oscillations of rotating stars and stars in binary systems, but its validity and convergence has not been analytically established. It is important that this aspect of the problem is checked so that one is sure of the correctness of subsequent analysis and results based on this series expansion. In the present brief note, we have addressed ourselves to this problem and validated the correctness of the numerical results obtained through the use of this series expansion.

show abstract

Equilibrium Structures of Rotationally and Tidally Distorted Polytropic Models of Stars

Cited by 8 publications

References 16 publications

Internal Structure and Apsidal Motions of Polytropic Stars in Close Binaries

Internal Structure and Apsidal Motions of Polytropic Stars in Close Binaries

Effect of Coriolis force on the shapes of rotating stars and stars in binary systems

On the validity of series expansion being used for the position of a point on a Roche equipotential

Contact Info

Product

Resources

About