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What effect do the magnetic fields of stars have on one another:do they tend to repel or attract one another?

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2 Answers 2

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They behave just as other magnetic fields do - whether the force is attractive or repulsive would depend on the relative orientation of the fields. But magnetic forces are negligible compared with other (gravitational) forces in terms of accelerating the stars as a whole.

A model for the large scale magnetic field of a star could be that of a magnetic dipole (like a short bar magnet). If so, then the magnetic field strength falls off as the inverse cube of distance. The magnetic potential energy associated with the interaction of two magnetic fields is proportional to the product of the magnetic field due to one of the stars and the magnetic dipole moment of the other, so also falls as the third power of their separation, and the apparent force between them (whether attractive or repulsive, depending on how the stars' magnetic fields are oriented with respect to each other) is the (negative) gradient of this potential energy and so falls as the fourth power of their separation.

This means that magnetic forces rapidly become totally negligible compared with gravitational forces that only fall as the inverse square of separation.

As a rough order of magnitude calculation - imagine two sun-like stars separated by a distance $r$. Each will have a magnetic dipole moment equivalent to a field of about $10^{-4}$ T at the solar photosphere; in SI units $p \simeq 10^{29}$ T m$^3$. The mutual magnetic potential energy between the two stars will be of order $$ U \simeq \left(\frac{\mu_0}{4\pi}\right) \left(\frac{2 p_1 p_2}{r^3}\right) = \frac{\mu_0 p^2}{2\pi r^3}$$ and the force between them (see here for example) is $$ F_{\rm mag} \simeq \pm \frac{3\mu_0 p^2}{2\pi r^4}\ ,$$ where the sign is positive of negative depending on whether the magnetic dipoles are aligned or anti-aligned (the magnitude of the force would be less if it were somewhere in between).

The ratio of gravitational forces to magnetic forces is therefore $$ \frac{F_{\rm grav}}{F_{\rm mag}} \sim \frac{2\pi G M^2}{3\mu_0 p^2} r^2 \, ,$$ where $M$ is the mass of each star.

Putting in the numbers for a pair of one solar-mass stars separated by say $r = 10R_\odot$ then $F_{\rm grav}/F_{\rm mag} \sim 10^{18}$.

That is not to say that the interaction of the magnetic fields of a star and their surroundings are always negligible. If material is ionised, then the Lorentz forces on that material due to a stellar magnetic field can be dominant over gravitational forces - e.g. magnetically, funnelled accretion. The two magnetic fields of stars in a binary system (or the magnetic field of a star and a close-in exoplanet) may also interact, releasing some fraction of the stored magnetic potential energy in the form of flares or heating of plasma, although direct evidence for this happening is sparse.

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It's also interesting to consider "more magnetic" stars - some white dwarfs have magnetic fields at their surface of about 10 T (about $10^5$ times the solar dipole field) and neutron stars can have surface fields of up to $\sim 10^{9}$ T. However, these stars are also much smaller by factors of $10^2$ and $10^5$ in radius and and since the magnetic dipole moment scales as surface field multiplied by volume, their magnetic dipole moments are not that much higher than the Sun's. They can get much closer to each other of course, but not close enough that magnetic forces ever get close to those of gravity.

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    $\begingroup$ while "it's too small to care about" might be a popular answer, suppose an explicit (neglecting forces other than those associated with the stars' magnetic fields) were added. I wonder if interstellar material provides a degree of shielding at large distances, or if it's pure -4 all the way until the observable universe effects set it? $\endgroup$
    – uhoh
    Commented May 22, 2023 at 8:51
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Ugh, another magnet-mania musing. “F*ing magnets, how do they dork?”

The hype about magnets and magnetism is … hype. The Sun’s overall (static) magnetic field is irrelevant at, let’s say, Mercury (hard to draw a line in the sand on such a question). Solar effects are primarily from storms such as CMEs and the larger (X-class) flares, which are not the same thing as the general IMF. As already stated, the force then falls by the inverse fourth power, which makes it really tiny, really quickly.

The solar wind, with or without help/hindrance from photolysis (ionospheres), is far more relevant. But the person on the street- the nonscientist, scientism-swallower- doesn’t grasp the ionosphere and plasma physics, so we never hear that bit from YouTube and its regurgitators.

Of course, it’s hard to generalize about the universe… the _entire universe _ . One could always kluge together some bizarro example involving, say, a Giant in a globular cluster, doing a close pass by … another giant, while flaring. I don’t need to indulge bizarro kludges.

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