# Could a bipolar nebula be produced by a time gradient?

M2-9 is an example of a bipolar nebula that resembles two back-to-back rocket nozzles. Is it possible that this shape (somewhat unusual for an explosion) is the result of a time gradient? A rotating neutron star having collapsed and preserved its angular momentum with an equatorial velocity of relativistic proportions would be at a significantly different time than the poles of the star. Frame dragging would spread this effect out from the equator to neighboring space. A nova exploding under these conditions would be constrained outward at the poles since the relativistic time gradient puts the space near the equator in the future, relative to the poles, and would not share the same "now," making that space inaccessible to the expanding explosion. Something rotating at much slower speed would explode in a more spherical manner.

Is this a plausible reason for the shape of bipolar nebulae?

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Well, the equatorial velocity of a neutron star isn't more than $9 \times 10^7 \text{ m/s}$, which gives a $\gamma$ factor of $\sim 1$ (it's actually $1.08$, but that doesn't make a large difference to time dilation effects).

I'm not too clear about how exactly frame dragging works, but it seems like a small time dilation effect wouldn't have a significant impact on how spherical the nebula is. A recent hypothesis is that this could be the effect of strong magnetic fields which originated in the star that created the nebula. Even though the star may not be "active" anymore, stellar interiors are thought to be highly conductive, so it is extremely hard for currents to dissipate, leading to extremely long lifetimes for magnetic fields.

Since these nebulae are largely charged particles (electrons/positrons/protons), they'd be trapped in a magnetic field and forced to travel along the field lines. So even if initially they had a strong velocity component perpendicular to the magnetic field, as they rotated around the field they would radiate and loose energy, and therefore start rotating closer and closer to the magnetic field line. This has the advantage of explaining several shapes via the same process, since this largely depends on the shape of a magnetic field (which need not always be dipolar).

There have only been (as far as I know) a few confirmations of planetary nebulae which are in a magnetic field, but I suspect that it'll be the hypothesis that's proven valid.

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