Orbit and spin evolution of the synchronous binary stars on the main sequence phase

TL;DR

This paper derives and solves equations describing the orbital and spin evolution of synchronous binary stars, showing how their orbits shrink and circularize over time, with applications to the Algol A, B system.

Contribution

It provides analytical solutions for the evolution of synchronous binary stars and applies these to real systems like Algol A, B, offering new insights into their orbital and spin dynamics.

Findings

Semi-major axis shrinks over time

Orbital eccentricity decreases until circularization

Orbital period shortens and primary spin speeds up

Abstract

The sets of the synchronous equations are derived from the sets of non-synchronous equations The analytical solutions are given by solving the set of differential equations. The results of the evolutionary tendency of the orbit-spin are that the semi-major axis shrinks gradually with time: the orbital eccentricity dereacses gradually with time until the orbital circularization; the orbital period shortens gradually with time and the rotational angular velocity of primary component speed up with time gradually before the orbit-rotation achieved the circularization The theoretical results are applied to evolution of the orbit and spin of synchronous binary stars Algol A, B on the main sequence phase The circularization time and life time (age) and the evolutional numerical solutions of orbit and spin when circularization time are estimeted for Algol A, B. The results are discussed and concluded.