Secular dynamics of S-type planetary orbits in binary star systems: applicability domains of first- and second-order theories

We analyse the secular dynamics of planets on S-type coplanar orbits in tight binary systems, based on first- and second-order analytical models, and compare their predictions with full N-body simulations. The perturbation parameter adopted for the development of these models depends on the masses of the stars and on the semimajor axis ratio between the planet and the binary. We show that each model has both advantages and limitations. While the first-order analytical model is algebraically simple and easy to implement, it is only applicable in regions of the parameter space where the perturbations are sufficiently small. The second-order model, although more complex, has a larger range of validity and must be taken into account for dynamical studies of some real exoplanetary systems such as \(\gamma \) Cephei and HD 41004A. However, in some extreme cases, neither of these analytical models yields quantitatively correct results, requiring either higher-order theories or direct numerical simulations. Finally, we determine the limits of applicability of each analytical model in the parameter space of the system, giving an important visual aid to decode which secular theory should be adopted for any given planetary system in a close binary.     

Polar orbits around binary stars

Oks proposes the existence of a new class of stable planetary orbits around binary stars, in the shape of a helix on a conical surface whose axis of symmetry coincides with the interstellar axis, and rotates with the same orbital frequency as the binary pair. We show that this claim relies on the inappropriate use of an effective potential that is only applicable when the stars are held motionless. We also present numerical evidence that the only planetary orbits whose planes are initially orthogonal to the interstellar axis that remain stable on the time scale of the stellar orbit are ordinary polar orbits around one of the stars, and that the perturbations due to the binary companion do not rotate the plane of the orbit to maintain a fixed relationship with the axis.     

On the determination of double star orbits

It is proposed to improve the convergence of the determination of the elements of the orbits of visual binaries by using not only first, but second-order derivatives in the development of the appropriate equations of condition. Also, some improvements of the Kowalsky-Seeliger method are suggested which improve the accuracy of the orbit used as first approximation.     

Stability of planetary orbits in binary systems

The possible existence of stable orbits is investigated in binary systems using Hill's method. Analytical stability conditions are established for satellites, for inner planets and for outer planets, allowing arbitrary values for the mass-ratio of the binary.Presented at the Symposium Star Catalogues, Positional Astronomy and Celestial Mechanics, held in honor of Paul Herget at the U.S. Naval Observatory, Washington, November 30, 1978.     

Stability of resonant planetary orbits in binary stars

This paper contains a numerical study of the stability of resonant orbits in a planetary system consisting of two planets, moving under the gravitational attraction of a binary star. Its results are expected to provide us with useful information about real planetary systems and, at the same time, about periodic motions in the general four-body problem (G4) because the above system is a special case of G4 where two bodies have much larger masses than the masses of the other two (planets). The numerical results show that the main mechanism which generates instability is the destruction of the Jacobi integrals of the massless planets when their masses become nonzero and that resonances in the motion of planets do not imply, in general, instability. Considerable intervals of stable resonant orbits have been found. The above quantitative results are in agreement with the existing qualitative predictions     

Possible orbits for a third star in the Sirius system

A number of possible sightings of a third star in the Sirius system were reported in the 1920s. Astrometric observations have recently ruled out the presence of a very close companion to either Sirius A or B; however, a third star could exist at large distances. The stability of possible orbits of such a third star was investigated and it was found that the shortest stable orbital period is 275 years.     

Stochasticity of planetary orbits in double star systems. II

Cosmogonical theories as well as recent observations allow us to expect the existence of numerous exo-planets, including in binaries. Then arises the dynamical problem of stability for planetary orbits in double star systems. Modern computations have shown that many such stable orbits do exist, among which we consider orbits around one component of the binary (called S-type orbits). Within the framework of the elliptic plane restricted three-body problem, the phase space of initial conditions for fictitious S-type planetary orbits is systematically explored, and limits for stability had been previously established for four nearby binaries which components are nearly of solar type. Among stable orbits, found up to distance of their sun of the order of half the binarys periastron distance, nearly-circular ones exist for the three binaries (among the four) having a not too high orbital eccentricity. In the first part of the present paper, we compare these previous results with orbits around a 16 Cyg B-like binarys component with varied eccentricities, and we confirm the existence of stable nearly-circular S-type planetary orbits but for very high binarys eccentricity. It is well-known that chaos may destroy this stability after a very long time (several millions years or more). In a first paper, we had shown that a stable planetary orbit, although chaotic, could keep its stability for more than a billion years (confined chaos). Then, in the second part of the present paper, we investigate the chaotic behaviour of two sets of planetary orbits among the stable ones found around 16 Cyg B-like components in the first part, one set of strongly stable orbits and the other near the limit of stability. Our results show that the stability of the first set is not destroyed when the binarys eccentricity increases even to very high values (0.95), but that the stability of the second set is destroyed as soon as the eccentricity reaches the value 0.8.     

An electrically powered binary star?

We propose a model for stellar binary systems consisting of a magnetic and a non-magnetic white dwarf pair which is powered principally by electrical energy. In our model the luminosity is caused by resistive heating of the stellar atmospheres arising from induced currents driven within the binary. This process is reminiscent of the Jupiter–Io system, but greatly increased in power because of the larger companion and stronger magnetic field of the primary. Electrical power is an alternative stellar luminosity source, following on from nuclear fusion and accretion. We find that this source of heating is sufficient to account for the observed X-ray luminosity of the 9.5-min binary RX J1914+24, and provides an explanation for its puzzling characteristics.     

Masses of binary stars for general orbits

The masses of a pair of stars in the visual binary system have been estimated. The angle between the orbital plane of the stars and the plane of the sky has been taken into account. Inclination of the major axes of the orbits of the stars with the line of interaction between the orbital plane and the plane of the sky has also been considered. These two inclinations are also computed in terms of the observed quantities. Major and minor axes of actual orbits of the stars are determined.     

Ephemrides of visual binaries in universal variables

In this paper, universal formulations of the two‐body problem are established for ephemerides of visual binary systems, whatever the type of their orbits may be. A computational algorithm is also given and applied to the binaries ADS 9159, ADS 2959 and ADS 11632 as typical examples of elliptic, parabolic and hyperbolic binaries, respectively.     

On the analytic calculation of visual double star orbits

This article studies the existence of periodic Keplerian orbits for visual double stars whose corresponding apparent orbits are to pass through three selected points. The analytical results provide the basis for a new method of calculating orbits which does not require prior calculation of the areal constant. This method is applied to the binary 04404 N 4313.     

Radio precursors to neutron star binary mergings

We discuss a possible generation of radio bursts preceding final stages of binary neutron star mergings which can be accompanied by short gamma-ray bursts. Detection of such bursts appear to be advantageous in the low-frequency radio band due to a time delay of ten to several hundred seconds required for radio signal to propagate in the ionized intergalactic medium. This delay makes it possible to use short gamma-ray burst alerts to promptly monitor specific regions on the sky by low-frequency radio facilities, especially by LOFAR. To estimate the strength of the radio signal, we assume a power-law dependence of the radio luminosity on the total energy release in a magnetically dominated outflow, as found in millisecond pulsars. Based on the planned LOFAR sensitivity at 120 MHz, we estimate that the LOFAR detection rate of such radio transients could be about several events per month from redshifts up to z∼1.3 in the most optimistic scenario. The LOFAR ability to detect such events would crucially depend on exact efficiency of low-frequency radio emission mechanism.     

The near-contact binary star RZ Dra revisited

This paper presents the absolute parameters of RZ Dra. New CCD observations were made at the Mt. Suhora Observatory in 2007. Two photometric data sets (1990 BV and 2007 BVRI) were analysed using modern light-curve synthesis methods. Large asymmetries in the light curves may be explained in terms of a dark starspot on the primary component, an A6 type star. Due to this magnetic activity, the primary component would appear to belong to the class of Ap-stars and would show small amplitude with δ Scuti-type pulsations. With this in mind, a time-series analysis of the residual light curves was made. However, we found no evidence of pulsation behaviour in RZ Dra. Combining the solutions of our light curves and Rucinski et al. (2000)’s radial velocity curves, the following absolute parameters of the components were determined: M₁ = 1.63 ± 0.03 M_⊙, M₂ = 0.70 ± 0.02 M_⊙, R₁ = 1.65 ± 0.02R_⊙, R₂ = 1.15 ± 0.02 R_⊙, L₁ = 9.72 ± 0.30 L_⊙ and L₂ = 0.74 ± 0.10 L_⊙. The distance to RZ Dra was calculated as 400 ± 25 pc, taking into account interstellar extinction. The orbital period of the system was studied using updated O–C information. It was found that the orbital period varied in its long-period sinusoidal form, superimposed on a downward parabola. The parabolic term shows a secular period decrease at a slow rate of 0.06 ± 0.02 s per century and is explained by the mass loss via magnetized wind of the Ap-star primary. The tilted sinusoidal form of the period variation may be considered as an apparent change and may be interpreted in terms of the light-time effect due to the presence of a third body.     

Planetary system formation through binary star merging

A scenario is considered for the formation of a planetary system through the merging of a binary star comprised of low-mass (0.5–1 M _⊙) stars in the stage of contracting towards the main sequence. According to our previous computations (Sirotkin and Karetnikov, 2006), under certain conditions, the destruction of the more massive component can result in the formation of a central star, an accretion disk, and an extended arm. The extended arm is fragmented to form clouds of planetary masses (<5M _J). The formed disk and clouds rotate in the same direction as the central star. The clouds are in elongated orbits (e > 0.3) lying in the orbital plane of the initial binary system. To test these earlier results, we repeated computations for the same system parameters but with higher accuracy. The new computations confirmed the earlier results and gave new information about the cloud and disk structure.     

Stable planetary orbits around one component in nearby binary stars

Numerical simulations are made within the frame of the elliptic planar restricted three-body problem, in order to search if stable orbits exist for planets around one of the two components in double stars. The values taken for the binary's mass ratio and eccentricity correspond to real nearby double and multiple systems; the Centauri and Sirius systems are investigated here. Large stable planetary orbits, already known to exist through a systematic exploration of the circular model and for the Sun-Jupiter elliptic case, are found to exist around Centauri A and Centauri B, as well as around Sirius A, up to distances from each star of the order of more than half the binary's periastron separation. Similar studies for other nearby well-known double and multiple systems will follow.