A Caltech Library Service

Energy optimization in binary star systems: explanation for equal mass members in close orbits

Adams, Fred C. and Batygin, Konstantin and Bloch, Anthony M. (2020) Energy optimization in binary star systems: explanation for equal mass members in close orbits. Monthly Notices of the Royal Astronomical Society, 494 (2). pp. 2289-2298. ISSN 0035-8711. doi:10.1093/mnras/staa850.

[img] PDF - Published Version
See Usage Policy.

[img] PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


Observations indicate that members of close stellar binaries often have mass ratios close to unity, while longer period systems exhibit a more uniform mass-ratio distribution. This paper provides a theoretical explanation for this finding by determining the tidal equilibrium states for binary star systems – subject to the constraints of conservation of angular momentum and constant total mass. This work generalizes previous treatments by including the mass fraction as a variable in the optimization problem. The results show that the lowest energy state accessible to the system corresponds to equal mass stars on a circular orbit, where the stellar spin angular velocities are both synchronized and aligned with the orbit. These features are roughly consistent with observed properties of close binary systems. We also find the conditions required for this minimum energy state to exist: (1) the total angular momentum must exceed a critical value, (2) the orbital angular momentum must be three times greater than the total spin angular momentum, and (3) the semimajor axis is bounded from above. The last condition implies that sufficiently wide binaries are not optimized with equal mass stars, where the limiting binary separation occurs near a₀ ≈ 16R*.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Adams, Fred C.0000-0002-8167-1767
Batygin, Konstantin0000-0002-7094-7908
Bloch, Anthony M.0000-0003-0235-9765
Additional Information:© 2020 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model ( Accepted 2020 March 19. Received 2020 February 9; in original form 2019 November 25. Published: 29 March 2020. We would like to thank Kaitlin Kratter, Darryl Seligman, and Chris Spalding for useful discussions. We also thank the referee for useful input. This work was supported through the University of Michigan, the National Science Foundation, the Air Force Office of Scientific Research, the David and Lucile Packard Foundation, and the Alfred P. Sloan Foundation.
Group:Astronomy Department
Funding AgencyGrant Number
University of MichiganUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
David and Lucile Packard FoundationUNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
Subject Keywords:binaries: close – binaries: spectroscopic – stars: formation
Issue or Number:2
Record Number:CaltechAUTHORS:20200420-104600810
Persistent URL:
Official Citation:Fred C Adams, Konstantin Batygin, Anthony M Bloch, Energy optimization in binary star systems: explanation for equal mass members in close orbits, Monthly Notices of the Royal Astronomical Society, Volume 494, Issue 2, May 2020, Pages 2289–2298,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:102650
Deposited By: Tony Diaz
Deposited On:20 Apr 2020 19:06
Last Modified:16 Nov 2021 18:14

Repository Staff Only: item control page