effect

binary star magnetic braking

Magnetic braking slows the orbital decay of binary star systems through electromagnetic interactions.
21 related articles · 2 formulas

Description

Magnetic braking in binary star systems is a process where the orbital motion of the two stars is slowed down due to electromagnetic interactions. In a close binary system, if one star has a strong magnetic field and a stellar wind, the wind particles are forced to co-rotate with the star out to a large distance, carrying away angular momentum. This loss of angular momentum from the star's rotation also affects the orbital motion of the binary, causing the stars to spiral closer together over time. This mechanism is particularly important for the evolution of cataclysmic variable stars and other compact binaries, as it drives them toward mass transfer and eventual merger.

History

The concept of magnetic braking was proposed in 1966 by Ludwig Biermann and Rolf Kippenhahn, who suggested that stellar winds in magnetic stars could remove angular momentum. The application to binary star evolution was developed in the 1970s and 1980s, notably by Bohdan Paczyński and others, to explain the period gap in cataclysmic variables.

How it works

The magnetic field of a star, such as a low-mass main-sequence star, extends into space and interacts with the ionized stellar wind. The wind is forced to rotate with the magnetic field lines out to the Alfvén radius, where the magnetic energy density equals the kinetic energy density of the wind. Beyond this radius, the wind escapes, carrying with it angular momentum that is extracted from the star's rotation. In a binary system, the star's rotation is tidally locked to the orbital period, so the loss of rotational angular momentum is transferred to the orbit, reducing its separation and period. This process is most effective for stars with strong magnetic fields and high mass-loss rates.

In practice

Magnetic braking is used in models of binary star evolution to predict the orbital periods of systems like cataclysmic variables and to understand the formation of compact binaries that eventually merge, producing gravitational waves detectable by observatories like LIGO.

Fun fact

Magnetic braking is so effective that it can shrink the orbit of a binary system by a factor of two over a few billion years, dramatically altering its future evolution.

Concept graph →

Formulas

$$t \propto P^2 B^{-2}$$
Timescale for pulsar spin-down due to magnetic dipole radiation.
What is in the formula
tvariableSpin-down timescale — time second
PvariableRotation period — time second
BvariableMagnetic field strength at the surface — magnetic flux density tesla
t_{\rmns,spd}\simeq6.3*10^{4}{\rmyr}*(\frac{p_0}{0.2{\rms}})^2(\frac{b_0}{10^{12.5}{\rmg}})^{-2} · 2607.17556v1
t'_{\rmhs,spd}\sim12.7{\rmyr}*(\frac{p_{\rmhs}}{0.28{\rms}})^2(\frac{b_{\rmhs}}{10^{15}{\rmg}})^{-2} · 2607.17556v1
$$\Delta\Omega = \frac{4\pi\chi}{(1-e^2)^{3/2}} \left(\frac{r_g}{a}\right)^{3/2}$$
Frame-dragging causes precession of orbital nodes.
What is in the formula
\Delta\Omegavariableprecession rate of orbital nodes — angular velocity radian per second
\chivariabledimensionless spin parameter of central body — dimensionless spin parameter
evariableorbital eccentricity — eccentricity
r_gvariablegravitational radius of central body — length metre
avariablesemi-major axis of orbit — length metre
δω_{\rmlt}=\frac{4πχ}{(1-e^2)^{3/2}\sini}(\frac{r_g}{a})^{3/2}\sinβ\sinλ · 2607.24931v1

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