Tidal Constraints for Wide Binaries in Pleiades

Abstract

—A technique is proposed for estimating the parameters of spatial orientation of the $${{{\mathbf{r}}}_{{1,2}}}$$ vectors of distances between the components in wide binary stars (BS) in open star clusters (OCs). An analysis of the orientation features of these vectors for 36 wide BSs previously discovered in Pleiades based on Gaia DR2 data shows that the largest number of vectors $${{{\mathbf{r}}}_{{1,2}}}$$ of wide BSs in Pleiades are oriented in direction close to the perpendicular to cluster center. This result agrees with earlier estimates that yielded positive total energies for wide BSs in Pleiades and with the conclusion that the disruption of wide binaries can occur mostly in the direction perpendicular to the direction of the cluster center. Two groups are distinguished by the value of their $$\kappa $$ parameter—the ratio of the mass of the component of the binary that is closest to the cluster center to the mass of the more distant component: with $$\kappa < 1$$ and $$\kappa > 1$$, each consisting of 18 stars. Different dependence on the orientation parameters of the vectors $${{{\mathbf{r}}}_{{1,2}}}$$ for these groups is indicative of different tidal constraints from the regular cluster field. Equations are derived for estimating the tidal distances $${{r}_{{c,1,2}}}$$ between the components of wide BSs in OCs in terms of two models of mass density distribution: an OC model with a uniform-density core and density decreasing as $$\rho (r) \sim 1{\text{/}}{{r}^{2}}$$ outside this core, where $$r$$ is the clustercentric distance, and a point-mass cluster model. The equations were derived using the integral of the energy of the system of three gravitating bodies and the condition of the balance of the attraction on the BS component by the cluster and the other two bodies of the system. Tidal constraints on wide BSs in Pleiades are analyzed. It is shown that $${{r}_{{c,1,2}}}$$ in the cluster core is mostly determined by the regular force field of the cluster. Outside the core and at the cluster periphery, the most likely hitherto studied formation mechanism of wide BSs (and hence of the $${{r}_{{c,1,2}}}$$ value) is "pulling" components of such BSs into resonance with oscillations of the regular cluster field. Therefore, the presence of wide BSs in Pleiades can be considered as one of the signs of the nonstationarity of Pleiades in the field of regular forces. Formulas are derived for estimating $${{r}_{{c,1,2}}}$$ for wide BSs moving in circular orbits in a non-uniform cluster, which take into account the effect on $${{r}_{{c,1,2}}}$$ of the cluster mass distributed between the components of the wide BS. The distances $${{r}_{{c,1,2}}}$$ at the cluster periphery ($$r > 3.5$$ pc) are shown to increase by about a factor of three when passing from radial to circular BS orbits.