The perturbation caused by planet-moon binarity on the time-of-arrival signal of a pulsar with an orbiting planet is derived for the case in which the orbits of the moon and the planet-moon ...barycenter are both circular and coplanar. The signal consists of two sinusoids with frequency and, where image and image are the mean motions of the planet and moon around their barycenter, and the planet-moon system around the host, respectively. The amplitude of the signal is the fraction image of the system crossing time image, where image and image are the masses of the planet and moon, r is their orbital separation, R is the distance between the host pulsar and planet-moon barycenter, I is the inclination of the orbital plane of the planet, and c is the speed of light. The analysis is applied to the case of PSR B1620-26b, a pulsar planet, to constrain the orbital separation and mass of any possible moons. We find that a stable moon orbiting this pulsar planet could be detected, if its mass were >5% of its planet's mass, and if the planet-moon distance were image2% of the planet- pulsar separation.
Mass transfer in eccentric binary stars Regős, Enikő; Bailey, Vernon C.; Mardling, Rosemary
Monthly notices of the Royal Astronomical Society,
April 2005, Letnik:
358, Številka:
2
Journal Article
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The concept of Roche lobe overflow is fundamental to the theory of interacting binaries. Based on potential theory, it is dependent on all the relevant material corotating in a single frame of ...reference. Therefore if the mass losing star is asynchronous with the orbital motion or the orbit is eccentric, the simple theory no longer applies and no exact analytical treatment has been found. We use an analytic approximation whose predictions are largely justified by smoothed particle hydrodynamic simulations (SPH). We present SPH simulations of binary systems with the same semi-major axis a = 5.55 R⊙, masses M1 = 1 M⊙, M2 = 2 M⊙ and radius R1 = 0.89 R⊙ for the primary star but with different eccentricities e = 0.4, 0.5, 0.6 and 0.7. In each case the secondary star is treated as a point mass. When e = 0.4 no mass is lost from the primary while at e = 0.7 catastrophic mass transfer, partly through the L2 point, takes place near periastron. This would probably lead to common-envelope evolution if star 1 were a giant or to coalescence for a main-sequence star. In between, at e ⩾ 0.5, some mass is lost through the L1 point from the primary close to periastron. However, rather than being all accreted by the secondary, some of the stream appears to leave the system. Our results indicate that the radius of the Roche lobe is similar to circular binaries when calculated for the separation and angular velocity at periastron. Part of the mass loss occurs through the L2 point.
The dynamical stability of quadruple-star systems has traditionally been treated as a problem involving two `nested' triples which constitute a quadruple. In this novel study, we employed a machine ...learning algorithm, the multi-layer perceptron (MLP), to directly classify 2+2 and 3+1 quadruples based on their stability (or long-term boundedness). The training data sets for the classification, comprised of \(5\times10^5\) quadruples each, were integrated using the highly accurate direct \(N\)-body code MSTAR. We also carried out a limited parameter space study of zero-inclination systems to directly compare quadruples to triples. We found that both our quadruple MLP models perform better than a `nested' triple MLP approach, which is especially significant for 3+1 quadruples. The classification accuracies for the 2+2 MLP and 3+1 MLP models are 94% and 93% respectively, while the scores for the `nested' triple approach are 88% and 66% respectively. This is a crucial implication for quadruple population synthesis studies. Our MLP models, which are very simple and almost instantaneous to implement, are available on GitHub, along with Python3 scripts to access them.
The scattered disk is a vast population of trans-Neptunian minor bodies that orbit the sun on highly elongated, long-period orbits. The stability of scattered disk objects is primarily controlled by ...a single parameter - their perihelion distance. While the existence of a perihelion boundary that separates chaotic and regular motion of long-period orbits is well established through numerical experiments, its theoretical basis as well as its semi-major axis dependence remain poorly understood. In this work, we outline an analytical model for the dynamics of distant trans-Neptunian objects and show that the orbital architecture of the scattered disk is shaped by an infinite chain of \(2:j\) resonances with Neptune. The widths of these resonances increase as the perihelion distance approaches Neptune's semi-major axis, and their overlap drives chaotic motion. Within the context of this picture, we derive an analytic criterion for instability of long-period orbits, and demonstrate that rapid dynamical chaos ensues when the perihelion drops below a critical value, given by \(q_{\rm{crit}}=a_{\rm{N}}\,\big(\ln((24^2/5)\,(m_{\rm{N}}/M_{\odot})\,(a/a_{\rm{N}})^{5/2})\big)^{1/2}\). This expression constitutes a boundary between the "detached" and actively "scattering" sub-populations of distant trans-Neptunian minor bodies. Additionally, we find that within the stochastic layer, the Lyapunov time of scattered disk objects approaches the orbital period, and show that the semi-major axis diffusion coefficient is approximated by \(\mathcal{D}_a\sim(8/(5\,\pi))\,(m_{\rm{N}}/M_{\odot})\,\sqrt{\mathcal{G}\,M_{\odot}\,a_{\rm{N}}}\,\exp\big-(q/a_{\rm{N}})^2/2\big\). We confirm our results with numerical simulations and highlight the connections between scattered disk dynamics and the Chirikov Standard Map. Implications of our results for the long-term evolution of the distant solar system are discussed.
Mass transfer in eccentric binary stars Regös, Enikö; Bailey, Vernon C.; Mardling, Rosemary
Monthly notices of the Royal Astronomical Society,
04/2005, Letnik:
358, Številka:
2
Journal Article
We have introduced self-consistent spin, tidal and dynamical equations of motion into REBOUNDx, a library of additional effects for the popular N-body integrator REBOUND. The equations of motion used ...are derived from the constant time lag approximation to the equilibrium tide model of tidal friction. These effects will allow the study of a variety of systems where the full dynamical picture cannot be encapsulated by point particle dynamics. We provide several test cases and benchmark the code's performance against analytic predictions. The open-source code is available in the most recent release of REBOUNDx.
We present two approaches to determine the dynamical stability of a hierarchical triple-star system. The first is an improvement on the Mardling-Aarseth stability formula from 2001, where we ...introduce a dependence on inner orbital eccentricity and improve the dependence on mutual orbital inclination. The second involves a machine learning approach, where we use a multilayer perceptron (MLP) to classify triple-star systems as `stable' and `unstable'. To achieve this, we generate a large training data set of 10^6 hierarchical triples using the N-body code MSTAR. Both our approaches perform better than previous stability criteria, with the MLP model performing the best. The improved stability formula and the machine learning model have overall classification accuracies of 93 % and 95 % respectively. Our MLP model, which accurately predicts the stability of any hierarchical triple-star system within the parameter ranges studied with almost no computation required, is publicly available on Github in the form of an easy-to-use Python script.
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