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To my understanding, part of the reason life is able to exist on Earth besides its ozone layer is due to its magnetic field, which protects the planet and its life against solar winds and keeps the atmosphere from being stripped away. Now, I’m aware that Earth’s magnetic field varies a bit in strength at places as well (from 25 to 65 microteslas or 0.25 to 0.65 gauss), but that’s only against Sol’s winds, which vary from around 400 to 750 km/s depending on where the planet receives the flare.

Since many factors have to be taken into account for such a thing, I am sure there is no one formula that guarantees accuracy, though there likely is one that provides an estimation. Star and planet size, distance from one another, possibly the axial tilt of both celestial bodies, and the frequency of flares are all factors I think are appropriate to keep in mind. Essentially, what I am asking for is a way to determine the necessary strength of a planet’s magnetic field to support life using a given formula, using an Earth-like planet about 1.65 AU away from an F8 spectral type star as part of an example.


NOTE: If further information is needed, please ask. I only included what I thought was relevant, so there is a high chance I missed something important.

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    $\begingroup$ We can’t come up with anything that’s anywhere near as definitive as a formula while we have only one example of a life-bearing planet to work from. We think that planets probably need magnetic fields to be hospitable to life, but we won’t have a clear idea how strong those magnetic fields need to be until we have a lot more examples. $\endgroup$ – Mike Scott Aug 20 '18 at 14:19
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    $\begingroup$ Stellar class and flare activity, both in terms of frequency and intensity, are not necessarily correlated, unless the classification is for a "flare star", which makes answering this almost impossible. $\endgroup$ – Ash Aug 20 '18 at 14:19
  • $\begingroup$ @MikeScott That's what I was afraid of, but I thought someone might have an estimation correlated from other factors. Worth a shot either way. $\endgroup$ – Pleiades Aug 20 '18 at 14:22
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The necessary strength is zero

Perhaps not the answer you are looking for, but it is obvious from our solar system that a planet can maintain an atmosphere without a geological magnetic field. Venus has such an atmosphere and no magnetic field (see considerations). Titan likewise has an atmosphere, although there is insufficient evidence to show that it has always had its atmosphere.

Do you count an induced magnetic field?

There are planets that have magnetic fields that are not caused by the action of their molten core, as Earth's is. Venus' atmosphere is so massive that it causes its own induced magnetic field. Europa's sub-surface ocean also causes and induced magnetic field. So you could have a planet with no bare geological magnetic field, but once it acquires are large ocean or atmosphere starts to protect itself.

Other ways to keep an atmosphere

While a magnetic field may protect an atmosphere on a geological scale, gravity can do so as well. If we made Earth more massive but less dense, then the escape velocity of would be larger but surface gravity could be the same. Taken to an extreme, Saturn has a lower surface gravity than Earth, yet an escape velocity almost four times as high. So tinkering with planet mass and composition can help you keep an atmosphere with no magnetic field.

You can also continuously replenish your atmosphere

There is some evidence (from isotope ratios) that most of Titan's atmosphere has been lost over geological time. Therefore there must be some means of replenishing it, since it is still there. This means is not clear, but outgassing from inside the planet is one option, as is addition in the form of extra-planetary debris. While lots of comet strikes might not be good for business on your planet, dropping a planetary ring, broken up icy moon, or asteroid belt onto a planet's surface over geological time could potentially provide a stable atmosphere for hundreds of millions of years.

Conclusion

While not answering the spirit of your question, there are several ways to keep an atmosphere long enough for life to develop without requiring a geological magnetic field. So the direct answer would be that the necessary magnetic field strength is 0 teslas.

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  • $\begingroup$ I appreciate this answer a LOT, but my main concern with magnetic fields was more with protection against high-energy UV rays. I mean there are LOTS of ways to get around that I'm sure, but I honestly just wanted to see how big an aurora borealis I could get away with jamming into a project lol $\endgroup$ – Pleiades Aug 20 '18 at 15:34
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    $\begingroup$ @Pleiades A magnetic field doesn't deflect UV rays, instead it deflects charged particles (mostly protons) that are flying out of the sun at high speed. If those particles hit the atmosphere, they release UV. But, if the atmosphere is thick enough, that UV might not even make to to the surface. Also, there are certain things (Carbon Dioxide and water come to mind) that are better at absorbing UV and other high energy radiation than others. High concentrations of those gasses or thick clouds of them could also block the UV radiation. $\endgroup$ – kingledion Aug 20 '18 at 15:37
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I have recently done a bit of research into this subject myself. I skipped the really difficult mathematical stuff by choosing a planet similar to earth that had the correct specs. Of course, I was looking mainly at the size of the sun, the number of planets in the system, the number of satellites orbiting said planet, where the position of the planet was within the sun's habitable region, and other variables I thought were necessary to support human life. That being said, of the planets in our solar system, only Juptier's moon Ganymede meets similar requirements as it too generates it's own magnetic field. Since it's sibling IO is supposed to be a hot planet I can't see how Ganymede wouldn't be any cooler, judging by it's proximity to Jupiter, although not a sun itself, it is a gas giant. I also took into account the number of days the planet took to rotate around the sun and only chose something within the range of our own planet, assuming that several hundred days give or take was one of the requirements to sustain human life. My planet actually has a slightly longer year than our own but not much more than 400 days. I also chose to have a 26 hour day and an eight day week instead of merely seven, which logically lengthens the span of a month. Hope this helps. P.s. I also took into account that the sun would have to be the same type as our own, in the range of a g-class planet only a few degrees off from Sol. https://en.wikipedia.org/wiki/Sun

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