Both the magnetic field strength and charged particle flux fall off proportional to the square of the distance from the planet / star respectively, so I doubt it gets much of anything even with a strong magnetic field unless it’s also near a star.
I’d also point out that the particles aren’t really attracted by the earths magnetic field, we’re just in the pathway, and the magnetic field funnels them to the poles. It’s more guidance than attraction.
If the rogue planet is truly all alone in space, you’re definitely right. 4 million times is a lot, but space is really, really big, and solar radiation falls off with 1/r^2.
Let’s assume the auroras are proportional to the size of the magnetic field. That’s probably not true, it’s probably actually proportional to the square root of the magnetic field because field strengths fall off with 1/r^2, but let’s give it the best possible chance of having huge auroras. That would mean that a planet with 4x the magnetic field of Earth would have the same Aurora brightness at 2x the distance. So, something with 4 million times the magnetic field would have the same brightness at sqrt(4,000,000) the earth-to-sun distance, or 2000 the distance. If it were in our solar system, or even just near our solar system, it would be bright. But, space is big.
Since the earth is about 500 light-seconds from the sun, 2000 earth-distances is about 1 million light seconds, or about 11.5 days. By comparison, the closest star to Sol is Proxima Centauri at 4 light years. So, these Auroras would only be earth-like if the rogue planet were very close to some star. It wouldn’t have to necessarily be in orbit of that star, but it would have to be pretty close. If it were out in the space between the stars, there’s just nothing there for the magnetic field to interact with.
I dont think you’re quite understanding how big 6 orders of magnitude is. 4000000/r2 still falls off way slower than 1/r2.
Also the funnel diagram of the earth’s magnetic field you’re referring to is a near field effect. In the far field regime the only field components that stay strong enough to be relevant are those parallel to the axis of the dipole; a dipole is functionally identical to a bar magnet if you’re measuring it from far enough away. If my understanding of solar wind is correct and the aurora refers to an interaction that occurs between the earth’s magnetic field and particles near the sun, we’re definitely in the far field regime
I don’t think you’re quite understanding the distances involved in what I’m getting at. The particle flux is minuscule, and it’s not the magnetic field that’s attracting particles. It’s only guiding the particles that were already headed towards the planet.
This planet would have great aurorae if it were near a star, but it’s not, so the magnetic field strength is kind of a moot point.
The absolute distance is strictly irrelevant given this is a relative comparison between two magnetic fields. The one that is 6 orders of magnitude higher will maintain that 6 orders of magnitude difference exactly the same at a distance of 100m as it will at a distance of 100au. That means that the stronger field will maintain the minimum strength required to “guide” particles towards the dipole at a greater distance than the weaker magnetic field would. I feel you if you’re only trying to argue that it would still need to be within some neighborhood of some star to produce an aurora, but your posts read like you’re claiming 6 orders of magnitude on the magnetic field makes no difference on how close that object would need to be to produce an aurora, which is flatly incorrect.
Both the magnetic field strength and charged particle flux fall off proportional to the square of the distance from the planet / star respectively, so I doubt it gets much of anything even with a strong magnetic field unless it’s also near a star.
I’d also point out that the particles aren’t really attracted by the earths magnetic field, we’re just in the pathway, and the magnetic field funnels them to the poles. It’s more guidance than attraction.
If the rogue planet is truly all alone in space, you’re definitely right. 4 million times is a lot, but space is really, really big, and solar radiation falls off with 1/r^2.
Let’s assume the auroras are proportional to the size of the magnetic field. That’s probably not true, it’s probably actually proportional to the square root of the magnetic field because field strengths fall off with 1/r^2, but let’s give it the best possible chance of having huge auroras. That would mean that a planet with 4x the magnetic field of Earth would have the same Aurora brightness at 2x the distance. So, something with 4 million times the magnetic field would have the same brightness at sqrt(4,000,000) the earth-to-sun distance, or 2000 the distance. If it were in our solar system, or even just near our solar system, it would be bright. But, space is big.
Since the earth is about 500 light-seconds from the sun, 2000 earth-distances is about 1 million light seconds, or about 11.5 days. By comparison, the closest star to Sol is Proxima Centauri at 4 light years. So, these Auroras would only be earth-like if the rogue planet were very close to some star. It wouldn’t have to necessarily be in orbit of that star, but it would have to be pretty close. If it were out in the space between the stars, there’s just nothing there for the magnetic field to interact with.
I dont think you’re quite understanding how big 6 orders of magnitude is. 4000000/r2 still falls off way slower than 1/r2.
Also the funnel diagram of the earth’s magnetic field you’re referring to is a near field effect. In the far field regime the only field components that stay strong enough to be relevant are those parallel to the axis of the dipole; a dipole is functionally identical to a bar magnet if you’re measuring it from far enough away. If my understanding of solar wind is correct and the aurora refers to an interaction that occurs between the earth’s magnetic field and particles near the sun, we’re definitely in the far field regime
I don’t think you’re quite understanding the distances involved in what I’m getting at. The particle flux is minuscule, and it’s not the magnetic field that’s attracting particles. It’s only guiding the particles that were already headed towards the planet.
This planet would have great aurorae if it were near a star, but it’s not, so the magnetic field strength is kind of a moot point.
The absolute distance is strictly irrelevant given this is a relative comparison between two magnetic fields. The one that is 6 orders of magnitude higher will maintain that 6 orders of magnitude difference exactly the same at a distance of 100m as it will at a distance of 100au. That means that the stronger field will maintain the minimum strength required to “guide” particles towards the dipole at a greater distance than the weaker magnetic field would. I feel you if you’re only trying to argue that it would still need to be within some neighborhood of some star to produce an aurora, but your posts read like you’re claiming 6 orders of magnitude on the magnetic field makes no difference on how close that object would need to be to produce an aurora, which is flatly incorrect.
From how far could the planet guide particles into its aurora?