Roche Equipotentials Research Articles

Equilibrium Structure of Rotationally and Tidally Distorted Prasad Model Including the Effect of Mass Variation Inside the Star

In this paper we propose suitable modifications in the concept of Roche equipotentials to account for the effect of mass distribution inside the star on its equipotential surfaces and use this in conjunction with the approach of Kippenhahn and Thomas, in a manner earlier used by Prasad and Mohan, to incorporate the effects of rotational and tidal forces in the equations of stellar structure parameters. The proposed method has been used to compute the structure parameters of the rotationally and tidally distorted Prasad model of the star.

On the Use of Roche Equipotentials in Analysing the Problems of Binary and Rotating Stars

Kopal (Adv. Astron. Astrophys., 9, 1, 1972) introduced the concept of Roche equipotentials to analyse the effects of rotational and tidal distortions in case of stars in binary systems. In this approach a mathematical expression for the potential of a star in a binary system is obtained by approximating its inner structure with Roche model. This expression for the potential has been used in subsequent analysis by various authors to analyse the problems of structures and oscillations of synchronous and nonsynchronus binary stars as well as single rotating stars. Occasionally, doubts have been expressed regarding the validity of the use of this approach for analysing nonsynchronous binaries and rotationally and tidally distorted single stars. In this paper we have tried to clarify these doubts.

Study of Eclipsing Binary and Multiple Systems in OB Associations. I. Orion OB1a- IM Monocerotis

Abstract All available photometric and spectroscopic observations were collected and used as the basis of a detailed analysis of the close binary IM Mon. The orbital period of the binary was refined to 1$.\!\!\!^{\rm d}$19024249 (0.00000014). The Roche equipotentials, fractional luminosities (in $B$, $V$, and Hp-bands) and fractional radii for the component stars in addition to the mass ratio, $q$, inclination, $i$, of the orbit, and the effective temperature, $T_{\rm eff}$, of the secondary cooler less massive component were obtained by the analysis of light curves. IM Mon is classified to be a detached binary system in contrast to the contact configuration estimations in the literature. The absolute parameters of IM Mon were derived by the simultaneous solutions of light and radial-velocity curves as $M_{1,2}$$=$ 5.50 (0.24)$\ M_{\odot}$ and 3.32 (0.16)$\ M_{\odot}$, $R_{1,2}$$=$ 3.15 (0.04)$\ R_{\odot}$ and 2.36 (0.03)$\ R_{\odot}$, $T_{{\rm eff} 1,2}$$=$ 17500 (350) K and 14500 (550) K implying spectral types of B4 and B6.5 ZAMS stars for the primary and secondary components, respectively. The modelling of the high-resolution spectrum revealed the rotational velocities of the component stars as $V_{{\rm rot}1}$$=$ 147 (15) km s$^{-1}$ and $V_{{\rm rot}2}$$=$ 90 (25) km s$^{-1}$. The photometric distance of 353 (59) pc was found to be more precise and reliable than the Hipparcos distance of 341 (85) pc. An evolutionary age of 11.5 (1.5) Myr was obtained for IM Mon. Kinematical and dynamical analyses support the membership of the young thin-disk population system IM Mon to the Ori OB1a association dynamically. Finally, we derived the distance, age, and metallicity information of Ori OB1a sub-group using information of the IM Mon parameters.

Structures and oscillations of rotationally and tidally distorted polytropic models of stars in the presence of the Coriolis force

The problems of equilibrium structures and periods of oscillations of rotationally and/or tidally distorted polytropic models of stars in binary systems have been studied previously. In the studies, only the effects of gravitational and centrifugal forces while obtaining the Roche equipotential of such stars were considered. The Coriolis force were not considered. In the present study, we have included the effects of the Coriolis force also. The objective of this study is to investigate as to how the inclusion of the Coriolis force in the Roche equipotential affects the equilibrium structures and periods of oscillations of rotationally and/or tidally distorted stars. The results of our study show that the Coriolis force has no appreciable effect on the equilibrium structures and periods of small oscillations of polytropic models of stars in binary systems. The present study also confirms the earlier conclusions that uniform rotation decreases the eigenfrequencies of various modes of oscillation.

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

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.

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

Kopal (Adv. Astron. Astrophys. 9:1–65, 1972) introduced the concept of Roche equipotentials to incorporate the effects of rotation and tidal distortions on the equilibrium structure and periods of small oscillations of rotating stars and stars in binary systems. However his expression for the Roche equipotential accounts for only the effects of centrifugal and gravitational forces and does not take into account the effect of Coriolis force. In this paper we have suitably modified Kopal’s expression for Roche equipotentials to incorporate into it the effect of Coriolis force as well. The modified expression for the Roche equipotential has then been used to compute the equilibrium structures and shapes of polytropic models 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

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.

Equilibrium Structures of Rotationally and Tidally Distorted Polytropic Models of Stars

We propose suitable modifications in the concept of Roche equipotentials to account for the effect of mass distribution inside a star. The Kippenhahn and Thomas (1970) approach is used to incorporate the effects of rotational and tidal forces in the equations of stellar structure. The proposed method is applied to compute structures of certain rotationally and tidally distorted polytropic models.

Equilibrium Structures of Differentially Rotating and Tidally Distorted White Dwarf Models of Stars

In this paper we present a method for computing the equilibrium structures and various physical parameters of a primary component of the binary system assuming that the primary is more massive than the secondary and is rotating differentially according to the law of the w2 = b0 + b1 × s2 + b2 × s4, w being the angular velocity of rotation of a fluid element distant s from the axis of rotation and b0, b1, b2 suitably chosen numerical constants. This method utilizes the averaging approach of Kippenhahn and Thomas (1997) and the concept of Roche equipotentials in a manner earlier used by Mohan et al. (1997) to incorporate the effects of rotation and tidal distortions on the equilibrium structures of certain rotationally and tidally distorted stellar models. The use of the method has been illustrated by applying it to obtain the structures and some observable parameters of certain differentially rotating and tidally distorted binary systems whose primary component is assumed to be a white dwarf star.

The Structure of Close Binaries in Two Dimensions

The structure and evolution of close binary stars has been studied using the two-dimensional stellar structure algorithm developed by Deupree. We have calculated a series of solar composition stellar evolution sequences of binary models in which the mass of the two-dimensional model is 8 M☉ with a point-mass 5 M☉ companion. We have also studied the structure of the companion in two dimensions by considering the zero-age main sequence (ZAMS) structure of a 5 M☉ model with an 8 M☉ point-mass companion. This result suggests that treating the 5 M☉ star as a point source for the 8 M☉ evolution is reasonable. In all cases, the binary orbit was assumed to be circular and corotating with the rotation rate of the stars. We considered binary models with three different initial separations, a = 10, 14, and 20 R☉. These models were evolved through central hydrogen burning or until the more massive star expanded to fill its critical potential surface or Roche lobe. The model with a separation of 20 R☉ will be expected to go through case B-type mass transfer during the shell H-burning phase. The 14 R☉ model is expected to go through mass transfer much earlier, near the middle of core hydrogen burning, and the 10 R☉ model is very close to this situation at the ZAMS. The calculations show that evolution of the deep interior quantities is only slightly modified from those of single-star evolution. Describing the model surface as a Roche equipotential is also satisfactory until very close to the time of Roche lobe overflow, when the self-gravity of the model about to lose mass develops a noticeable aspherical component and the surface timescale becomes sufficiently short, so that it is conceivable that the actual surface is not an equipotential.

Equilibrium structure of stars obeying a generalized differential rotation law

In the present paper we have considered the problem of determining the equilibrium structure of differentially rotating stars in which the angular velocity of rotation varies both along the axis of rotation and in directions perpendicular to it. For this purpose, a generalized law of differential rotation of the typeω2 =b0+b1s2+b2s4+b3z2+b4z4+b5z2s2 (here ω is a nondimensional measure of the angular velocity of a fluid element distants from the axis of rotation andz from the plane through the centre of the star perpendicular to the axis of rotation, andb's are suitably chosen parameters) has been used. Whereas Kippenhahn and Thomas averaging approach has been used to incorporate the rotational effects in the stellar structure equations, Kopal's results on Roche equipotentials have been used to obtain the explicit form of the stellar structure equations, which incorporate the rotational effects up to second order of smallness in the distortion parameters. The method has been used to compute the equilibrium structure of certain differentially rotating polytropes. Certain differentially rotating polytropes. Certain differentially rotating models of the Sun have also been computed by using this approach.

Some aspects of illuminated model atmosphere theory as applied to close binary systems

Only recently has the use of irradiated stellar atmosphere models become practical in the study of close binary systems. Aspects of this problem, such as geometrical illumination from a finite solid angle, the transport of polarized radiation, and multiple-iterative heating between the stars, must be included for a realistic treatment. These concepts are developed and applied to grids of plane-parallel stellar atmospheres computed on modified Roche equipotentials. The reflection effect between the stars, actually a radiative heating of the outer layers of the atmosphere, is iterated to consistency, and the incident moments of the radiation field are integrated numerically

Equilibrium structure of differentially rotating polytropic models of the stars

In this paper we propose a method for computing the equilibrium structure of differentially rotating polytropic models of the stars. A general law of differential rotation of the type ω2=b0+b1s2+b2s4, which can account for a reasonably large variety of possible differential rotations in the stars has been used. The distortional effects have been incorporated in the structure equations up to second order of smallness in distortion parametersb0,b1, andb2 using Kippenhahn and Thomas' averaging approach in conjunction with Kopal's results on Roche equipotentials in manner similar to the one earlier used by Mohan and Saxena for computing the equilibrium structure of polytropes having solid body rotation. Numerical results have been obtained for various types of differentially rotating polytropic models of stars of polytropic indices 1.5, 3, and 4. Certain differentially rotating models of the Sun which are possible with such a type of law of differential rotation, have also been computed.

On the interior structure of contact binaries and the light-curve paradox

view Abstract Citations (18) References (19) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS On the Interior Structure of Contact Binaries and the Light-Curve Paradox Tassoul, Jean-Louis Abstract A simple, hydrodynamical model for energy transfer between the components of a contact binary is presented. The dominant feature of the model is the nonuniform heating of the base of the common envelope, which is due to the unequal emergent luminosities at the inner Roche lobes. Expansions in Roche coordinates are used to show how to obtain steady baroclinic solutions for both the large-scale flow and the temperature field. The baroclinic temperature field, which can be expanded in terms of Roche harmonics, is determined mainly by the 3D radiative transfer within the common envelope, the lateral flux being steadily maintained by the temperature differences on each Roche equipotential. The baroclinic model proposed provides a new way to resolve the light-curve paradox for the contact binaries while providing consistent interior structures. Publication: The Astrophysical Journal Pub Date: April 1992 DOI: 10.1086/171212 Bibcode: 1992ApJ...389..375T Keywords: Eclipsing Binary Stars; Hydrodynamic Equations; Light Curve; Radiative Heat Transfer; Stellar Interiors; Stellar Luminosity; Stellar Structure; Baroclinity; Coriolis Effect; Eddy Viscosity; Ekman Layer; Navier-Stokes Equation; Stellar Envelopes; Stellar Rotation; Astrophysics; HYDRODYNAMICS; STARS: BINARIES: CLOSE; STARS: INTERIORS; STARS: ROTATION full text sources ADS |

Eigenfrequencies of small adiabatic barotropic modes of oscillations of rotationally and tidally-distorted stars

In this paper a method is proposed for computing the eigenfrequencies of small adiabatic barotropic modes of oscillations of rotationally and tidally-distorted stars. The method utilizes Kippenhahn and Thomas approach and concepts of Roche equipotentials to incorporate up to second-order the effects of rotation and tidal distortion terms on the eigenfrequencies. The proposed method has also been used to compute the eigenfrequencies of certain barotropic modes of oscillation of some rotationally and tidally distorted models of 10M⊙, and 2.5M⊙ Main-Sequence stars.

Equilibrium structures of rotationally and tidally distorted stellar models

In this paper we present a method for computint the equilibrium structures of rotationally distorted stars as well as rotationally and tidally distorted primary components of the stars in binary systems. The method is based on the averaging technique of Kippenhahn and Thomas (1970) and utilizes the concepts of Roche equipotentials (Kopal, 1972). The method takes into account terms up to second-order of smallness in the rotational and tidal distortion parameters. The use of the method in obtaining the equilibrium structures of certain rotationally and (or) tidally distorted models of Main-Sequence stars is also illustrated.

Effects of rotation and tidal distortions on the periods of adiabatic oscillations of composite models of stars

Mohan and Saxena's approach of using the averaging technique of Kippenhahn and Thomas in conjunction with Kopal's method of evaluating various parameters on the Roche equipotentials has been used to compute the effects of rotation and tidal distortions on the periods of small adiabatic radial and nonradial modes of oscillations of a series of composite models of stars. In these stars the density decreases slowly in the core from the centre to the interface and then falls of rapidly in the envelope from the interface to the outer surface.

Effects of rotation and tidal distortion on the periods of small adiabatic oscillations of the polytropic models of the stars

The averaging technique of Kippenhahn and Thomas (1970) has been used in conjunction with Kopal's method of evaluating various parameters on the Roche equipotentials to determine the effects of rotation and tidal distortions on the periods of small adiabatic radial and nonradial modes of oscillations of polytropic models of the stars.

Effect of rotation and tidal distortions on the structure of polytropic stars

The averaging technique of Kippenhahn and Thomas has been used in conjunction with Kopal's method of evaluating various parameters on the Roche equipotentials, to determine the effects of rotation and tidal distortions on the shapes and structures of the polytropic models of the stars.

A possible mechanism for mass transfer in X-ray binary systems with OB supergiant companions

We have studied the ''beginning Roche lobe overflow'' phase of mass transfer. We find that before the primary fills its Roche lobe, radiation-driven density waves generated in the atmosphere produce a sufficient mass outflow rate to power a compact X-ray source. In particular, for a model of Cygnus X-1, if the radius of the photosphere is between 82 and 86 percent of the radius of the Roche equipotential, large-amplitude density waves with irregular periods of a few days are observed. These density waves, which are generated by radiation pressure effects, pass through the inner Lagrangian point with velocities approx.100 km s/sup -1/, and can easily provide sufficient material to power the compact X-ray source. (AIP)