The structure equations of contact binaries

Kahler, H.

doi:10.1051/0004-6361:20021337

Cited by 16 publications

(18 citation statements)

References 15 publications

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“…Because the radiative energy is so small that it can be neglected relative to gravitational energy and heat energy, the accretion luminosity due to accreting mass is Here, ψ i and s i are, respectively, the gravitational potential and specific entropy at the surface of the component is the rate of mass accretion of the secondary, and β is a coefficient which describes the efficiency of heating of the photosphere by a shock wave region. Kähler (2002a) took the parameter β to be 1.0, i.e. he thought that the bulk kinetic energy gained by falling through the potential is completely transformed into thermal energy and, together with the thermal energy carried by infalling matter, it is regarded as an energy source in the outermost layer of the gainer without energy loss.…”

Section: Contact Condition and Luminosity Transfermentioning

confidence: 99%

Structure and evolution of low-mass W Ursae Majoris type systems - III. The effects of the spins of the stars

Han

Zhang

2005

Monthly Notices of the Royal Astronomical Society

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In a previous paper, using Eggleton's stellar evolution code, we have discussed the structure and evolution of low‐mass W Ursae Majoris (W UMa) type contact binaries with angular momentum loss owing to gravitational radiation or magnetic braking. We find that gravitational radiation is almost insignificant for cyclic evolution of low‐mass W UMa type systems, and it is possible for angular momentum to be lost from W UMa systems in a magnetic stellar wind. The weaker magnetic activity shown by observations in W UMa systems is likely caused by the lower mass of the convective envelopes in these systems than in similar but non‐contact binaries. The spin angular momentum cannot be neglected at any time for W UMa type systems, especially for those with extreme mass ratios. The spin angular momenta of both components are included in this paper and they are found to have a significant influence on the cyclic evolution of W UMa systems. We investigate the influence of the energy transfer on the common convective envelopes of both components in detail. We find that the mass of the convective envelope of the primary in contact evolution is slightly more than that in poor thermal contact evolution, and that the mass of the convective envelope of the secondary in contact evolution is much less than that in poor thermal contact evolution. Meanwhile, the rate of angular momentum loss of W UMa type systems is much lower than that of poor thermal contact systems. This is indeed caused by the lower masses of the convective envelopes of the components in W UMa type systems. Although the models with angular momentum loss for W UMa systems exhibit cyclic evolution, they seem to show that a W UMa system cannot continue this type of cyclic evolution indefinitely, and it might coalesce into a fast‐rotating star after about 1200 cycles of evolution (about 7.0 × 109 yr).

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Section: Contact Condition and Luminosity Transfermentioning

confidence: 99%

Structure and evolution of low-mass W Ursae Majoris type systems - III. The effects of the spins of the stars

Han

Zhang

2005

Monthly Notices of the Royal Astronomical Society

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“…In a preceding paper (Kähler 2002, hereafter K1) the structure equations of contact binaries have been discussed. Serious uncertainties have been shown to concern only the energy transfer by circulation currents from the primary to the secondary.…”

Section: Introductionmentioning

confidence: 99%

On the structure of contact binaries

Kahler

2002

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Abstract. In a preceding paper a simple model for contact binaries has been proposed, based on the usual assumption that the energy sources/sinks caused by the interaction of the components occur only in the secondary's/primary's outer layers. Here the model is applied to a typical late-type system. First we imposed the restriction that the fractional extent in mass of the sources/sinks in the layers above the critical surface is the same in both components, and found solutions evolving in thermal cycles. If the energy transfer is assumed to be sufficiently effective, loss of contact is avoided. Otherwise the cycle consists of a long quiet phase in good contact and a short violent phase with rapid changes between contact, semidetached, and detached configurations. In both cases there are cycles in which the temperatures of the components are similar in the largest part of the time. Other observational tests are also passed. Next we removed the restriction. In the resulting model with three free parameters we found (besides cycles) a large range of solutions in stable thermal equilibrium which are compatible with the observations. From a theoretical viewpoint however all these solutions are unsatisfactory since suffering from several inconsistencies. This result shows that the usual assumption on the energy sources and sinks is too restrictive. We are led to look for modifications of the model which remove the inconsistencies. This will be done in a forthcoming paper.

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“…Because the radiative energy is so small that it can be neglected relative to gravitational energy and heat energy, the accretion luminosity due to accreting mass is where ψ i and s i are, respectively, the gravitational potential and specific entropy at the surface of the component is the rate of mass accretion of the secondary and β is a coefficient that describes the efficiency of heating of the photosphere by the shock wave region. Kähler (2002a) took the parameter β to be 1.0, i.e. he thought that the bulk kinetic energy gained by falling through the potential is completely transformed into thermal energy and, together with the thermal energy carried by infalling matter, it is regarded as an energy source in the outermost layer of the gainer without energy loss.…”

Section: Contact Condition and Luminosity Transfermentioning

confidence: 99%

“…The luminosity transferred by circulation currents from the primary to the secondary adopted by Kähler (2002a) is where σ ex,i is the source (when positive) or sink (when negative) of energy per unit of mass caused by interaction of the components. Although the luminosity increment is applied in the adiabatic portion of the envelope of each star by most previous investigators, according to the energy transfer model (Robertson 1980) there is no essential distinction between convective and radiative envelopes.…”

Section: Contact Condition and Luminosity Transfermentioning

confidence: 99%

Structure and evolution of low-mass W Ursae Majoris type systems - II. With angular momentum loss

Li¹,

Han²,

Zhang³

2004

Monthly Notices of the Royal Astronomical Society

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In a previous paper, using Eggleton's stellar evolution code we have discussed the structure and evolution of low‐mass W Ursae Majoris (W UMa) type contact binaries without angular momentum loss (AML). The models exhibit cyclic behaviour about a state of marginal contact on a thermal time‐scale. Part of the time of each cycle is spent in contact and part in a semidetached state. According to observations, W UMa systems suffer AML. We present the models of low‐mass contact binaries with AML due to gravitational wave radiation or magnetic stellar wind (MSW). We find that gravitational radiation cannot prevent the cyclic evolution of W UMa systems, and the effect of gravitational radiation on the cyclic behaviour of contact binary evolution is almost negligible. We also find that the most likely AML mechanism for W UMa systems is magnetic braking, and that magnetic braking effects can increase the period of the cyclic evolution and shorten the fraction of the time spent in the poor thermal contact state exhibiting EB light curve. If W UMa stars do not undergo cyclic evolution, and their AML is caused simultaneously by MSW of both components, we find that the value of the parameter, λ, should be taken as about 3.8 for W UMa systems, which is larger than the largest value of similar single stars derived from observations. This indicates that the AML efficiency in W UMa systems may be lowered in comparison with non‐contact stars because of less mass contained in the convective envelopes of the components in W UMa systems or some feedback mechanism which may have an effect on W UMa systems. If W UMa systems lose their angular momentum at a constant rate, an angular momentum rate of d ln J/dt≈ 1.6 × 10−9 yr−1 can prevent the cyclic behaviour of the model, and the model can keep in good contact with an essentially constant depth of contact.

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The structure equations of contact binaries

Cited by 16 publications

References 15 publications

Structure and evolution of low-mass W Ursae Majoris type systems - III. The effects of the spins of the stars

Structure and evolution of low-mass W Ursae Majoris type systems - III. The effects of the spins of the stars

On the structure of contact binaries

Structure and evolution of low-mass W Ursae Majoris type systems - II. With angular momentum loss

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