# On the Kinematic Star Groups in the Pleiades

On the Kinematic Star Groups in the Pleiades —The paper analyzes the estimates of the parameters of wide binary stars (BSs) in the Pleiades open star cluster, obtained in 2020 from Gaia DR2 data. To this end a model of a gravitating system was used, consisting of two stars connected in the total force field of these stars and a homogeneous gravitating sphere simulating a star cluster. The existence of two “tidal” distances \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{r}_{{1,2}}}$$\end{document} between the components of the BS is shown for its distances from the center of the cluster sphere greater than a certain critical value. The lesser of the “tidal” distances \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{r}_{{1,2}}}$$\end{document} decreases with increasing distance from the center of the cluster sphere, since the force of attraction to the center of a homogeneous cluster sphere within its limits increases with distance from its center. The larger of the “tidal” distances \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{r}_{{1,2}}}$$\end{document} is due to the difference in the magnitudes of the cluster force field at the location points of the BS component stars and increases with increasing distance of the BS from the cluster center, reaching values of several parsecs at the periphery of the cluster sphere. The condition for gravitational coupling of wide BSs with zero relative velocities of their components in the common force field of a moving BS and the cluster sphere has been written down and investigated. It is shown that the decay of wide BSs can occur mainly in the direction perpendicular to the direction towards the center of the cluster. This slows down the decay of wide BSs observed in the nearest open clusters. In the case of the cluster sphere mass equal to the total mass of the member stars of the Pleiades cluster with magnitudes \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{m}_{G}} \leqslant {{15}^{{\text{m}}}}$$\end{document}, estimates were obtained for the decay time \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{\tau }_{d}}$$\end{document} and the formation of wide BSs for characteristic Pleiades values of the oscillation parameters of the regular cluster field (at \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{r}_{{1,2}}} = 0.7$$\end{document} pc, the values of \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{\tau }_{d}}$$\end{document} decrease from 1.25 to \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$0.45$$\end{document} Myrs as the distance of the BSs from the center of the cluster sphere increases from 0.34 to 0.45 pc). Estimates of the “tidal” distances \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{r}_{{1,2}}}$$\end{document} between the BS components in the model of an inhomogeneous cluster also show the existence of two values of \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{r}_{{1,2}}}$$\end{document} at the cluster periphery for BS distances from the cluster center greater than a certain critical value. It is shown that changes in the regular force field in the core of a collapsing cluster destroy wide BSs more actively than their encounters with groups of several stars. Estimates of the distances of the kinematic groups of stars from the center of the cluster in the Pleiades were obtained. Kinematic groups of three stars are located mainly at distances \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$r \simeq 1.5$$\end{document}–\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$2.4$$\end{document} pc and \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$r \simeq 3.1$$\end{document}–\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$6.7$$\end{document} pc from the center of the cluster. Kinematic groups of four stars in the Pleiades are located near the distances \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$r \simeq 2$$\end{document} pc and \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$r \simeq 4$$\end{document} pc from the center of the cluster. Possible mechanisms of formation for such groups in the Pleiades are discussed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Astrophysical Bulletin Springer Journals

# On the Kinematic Star Groups in the Pleiades

, Volume 76 (3) – Jul 1, 2021
17 pages

Publisher
Springer Journals
Copyright © Pleiades Publishing, Ltd. 2021. ISSN 1990-3413, Astrophysical Bulletin, 2021, Vol. 76, No. 3, pp. 269–285. © Pleiades Publishing, Ltd., 2021. Russian Text © The Author(s), 2021, published in Astrofizicheskii Byulleten’, 2021, Vol. 76, No. 3, pp. 328–346.
ISSN
1990-3413
eISSN
1990-3421
DOI
10.1134/s1990341321030056
Publisher site
See Article on Publisher Site

### Abstract

—The paper analyzes the estimates of the parameters of wide binary stars (BSs) in the Pleiades open star cluster, obtained in 2020 from Gaia DR2 data. To this end a model of a gravitating system was used, consisting of two stars connected in the total force field of these stars and a homogeneous gravitating sphere simulating a star cluster. The existence of two “tidal” distances \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{r}_{{1,2}}}$$\end{document} between the components of the BS is shown for its distances from the center of the cluster sphere greater than a certain critical value. The lesser of the “tidal” distances \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{r}_{{1,2}}}$$\end{document} decreases with increasing distance from the center of the cluster sphere, since the force of attraction to the center of a homogeneous cluster sphere within its limits increases with distance from its center. The larger of the “tidal” distances \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{r}_{{1,2}}}$$\end{document} is due to the difference in the magnitudes of the cluster force field at the location points of the BS component stars and increases with increasing distance of the BS from the cluster center, reaching values of several parsecs at the periphery of the cluster sphere. The condition for gravitational coupling of wide BSs with zero relative velocities of their components in the common force field of a moving BS and the cluster sphere has been written down and investigated. It is shown that the decay of wide BSs can occur mainly in the direction perpendicular to the direction towards the center of the cluster. This slows down the decay of wide BSs observed in the nearest open clusters. In the case of the cluster sphere mass equal to the total mass of the member stars of the Pleiades cluster with magnitudes \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{m}_{G}} \leqslant {{15}^{{\text{m}}}}$$\end{document}, estimates were obtained for the decay time \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{\tau }_{d}}$$\end{document} and the formation of wide BSs for characteristic Pleiades values of the oscillation parameters of the regular cluster field (at \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{r}_{{1,2}}} = 0.7$$\end{document} pc, the values of \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{\tau }_{d}}$$\end{document} decrease from 1.25 to \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$0.45$$\end{document} Myrs as the distance of the BSs from the center of the cluster sphere increases from 0.34 to 0.45 pc). Estimates of the “tidal” distances \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{r}_{{1,2}}}$$\end{document} between the BS components in the model of an inhomogeneous cluster also show the existence of two values of \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{r}_{{1,2}}}$$\end{document} at the cluster periphery for BS distances from the cluster center greater than a certain critical value. It is shown that changes in the regular force field in the core of a collapsing cluster destroy wide BSs more actively than their encounters with groups of several stars. Estimates of the distances of the kinematic groups of stars from the center of the cluster in the Pleiades were obtained. Kinematic groups of three stars are located mainly at distances \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$r \simeq 1.5$$\end{document}–\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$2.4$$\end{document} pc and \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$r \simeq 3.1$$\end{document}–\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$6.7$$\end{document} pc from the center of the cluster. Kinematic groups of four stars in the Pleiades are located near the distances \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$r \simeq 2$$\end{document} pc and \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$r \simeq 4$$\end{document} pc from the center of the cluster. Possible mechanisms of formation for such groups in the Pleiades are discussed.

### Journal

Astrophysical BulletinSpringer Journals

Published: Jul 1, 2021

Keywords: stars: kinematics and dynamics—open clusters and associations