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I am working on a solar system for a world where I intend to place my stories. This world should work by the laws of physics as we understand them so that, even though magic is a thing that exists in this world, the world doesn't need magical hand waving.

Here is info on the system that is immutable right now:

The solar system is a binary system made of up a main sequence star with a mass of .5 solar masses and a radius of 556,560 km and a white dwarf star with a mass of .5 solar masses and a radius of 9,500 km. This is orbited by double planet in which each planet is approximately the same mass as the Earth. This causes tidal forces of 3x that of the Moon on the Earth.

This brings me to my two questions:

  1. Would slight accretion of matter onto the white dwarf via the corona of the main sequence star cause enough radiation that life would be impossible?
  2. And if so, how would placing their orbital separation large enough that the white dwarf would be outside the corona of the other star affect the temperature of the planets as one of the stars would always be significantly closer to the planet than our sun is to us on Earth?

In reference to the second question to be outside of the corona, the stars would have to have a constant separation of at least 8,046,720 km with an orbit eccentricity of 0 meaning that one of the stars will always be between 0 km to 4,023,360 km closer which would mean at the higher scale about 2.7% closer to the planet than the Sun is. With that orbital separation they would have an orbital period of 4.8 days. Also that question assumes that having a total luminosity equal to the sun for the binary stars. So individually they would have about 2.6e26 for the main sequence star and 1.1e26 for the white dwarf.

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    $\begingroup$ You're essentially describing a cataclysmic variable system, albeit one with low activity. You should probably be concerned about large outbursts. $\endgroup$ – HDE 226868 Jun 6 '17 at 13:47
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    $\begingroup$ The Roche Lobes of these two stars would be hugely smaller than that of their orbital seperation and as such shouldn't see major acretion. At that distance it should be occasional small ones. $\endgroup$ – Adrienne Jun 6 '17 at 13:52
  • $\begingroup$ .5 solar masses is way too small for a white dwarf. Your numbers need some rework $\endgroup$ – steverino Jun 6 '17 at 14:50
  • $\begingroup$ Adrienne - Ah, I see. Thank you. I was wrong about the separation. @steverino .5 solar masses is actually pretty normal for a white dwarf. $\endgroup$ – HDE 226868 Jun 6 '17 at 16:21
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This largely answers your questions: Habitability of binary star systems

As for radiation, the size, composition, and activeness of the planet's core can determine the strength of its magnetosphere. Which is the invisible shield exerted by the planet that can deflect cosmic radiation.

As for life itself, some life is better than others at resisting the effects of radiation. Extraterrestrial life itself could be structured differently to be more impervious to radiation. Human advancement alone may be able to solve this problem some day as well.

Answers: If your planet has a P-type orbit any accretions between the 2 stars should be largely harmless to your planet. If your planet has an S-type orbit the distance between the stars necessary to maintain that orbit would be great enough that accretions shouldn't be to much of an issue....... however, as with all cosmic disasters, if it's large enough and hits just the right spot it's all over.

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If each planet is approximately the same size as Earth, but tidal forces are only three times those caused by the Moon, then they are separated by a distance of approximately 1,154,527 kilometers, or about 3 times the distance between the Earth and the Moon, with an angular size of about 0.287 degrees- for comparison, the Moon has an angular size in the sky of about half a degree. They will have an orbital period about each other (or "month") of about 101 days.

From all that, we can conclude that the double planets will have no significant effect on the amount of light or radiation they each receive, and we can treat them as separate, individual planets as far as habitability in relation to the stars is concerned. That's kind of too bad, because if it was a close binary planet, then we could rely on the shadowing effect to reduce the problematic effects of the white dwarf.

A main sequence star of 0.5 solar masses will have a luminosity of around 6-7% that of the Sun (the luminosity of a compact white dwarf should be negligible), so to get the same insolation as Earth the double planet system will have to orbit much closer- about 37,400,000 kilometers. That's a little over 9 times the separation between the two stars, so the orbit should be stable. The year would then be 45.65 days- less than half the length of a month!

It seems likely that such planets would be tidally locked to each other, though certainly not necessary. If they are, the month is equal to the sidereal day, and each one will be fixed in position in the other's sky. That would make the solar day equal to

$\frac{L_{Year} L_{Month}}{L_{Year} - L_{Month}} = ~-83.27 Earth days$

assuming prograde rotation of the double planet (where the negative sign indicates the sun crosses the sky in the opposite direction from what you normally expect), or $~31.44 Earth days$ for retrograde rotation. Ignoring the effects of the sun wobbling back and forth due to its own orbit around its binary partner, anyway.

If you magically assume that the luminosity and year length are the same as they are for our Earth & Sun, then the solar days assuming the double planets are tidally locked to each other become $~139.68$ and $~79.15$ Earth days, respectively.

The distance from the Earth to the Sun varies between 147,500,000 and 152,600,000 km over the course of a year, a variation of about 1.7% on either side of the mean. Assuming perfectly circular orbits, the change in distance between either lobe of the binary planet and the main sequence star would vary between a minimum of $0.25AU - 4,023,360 km - 577263.5 km = ~0.219AU, ~32,798,844 km$ and a maximum of $0.25AU - 4,023,360 km - 577263.5 km = ~0.281AU, ~42,000,091 km$ for the low-luminosity, close in orbit, giving a variation of 12.3% about the mean; or between $1AU - 4,023,360 km - 577263.5 km = ~0.969AU, ~144,997,247 km$ and $1AU + 4,023,360 km + 577263.5 km = ~1.03AU, ~154,198,494 km$, for a variation of about 3.1% about the mean.

Insolation in the temperate latitudes varies by much more than 12% between summer and winter solstices, so I'd say even the most extreme option here should still be survivable, although there would be notable planet-wide seasons with not-very-straightforward sum-of-sinusoids patterns induced by these variations, on top of whatever you might get from inclination of the double planet with respect to its orbit around the suns. Expanding the orbit a bit might be a good idea as well, since these sum-of-sinusoids variations in distance will result in more equal time in the hot vs. cold regimes, and thus more time in the hot regime, than the Earth experiences due to orbital eccentricity.

So, the only thing you really need to worry about is radiation from the white dwarf, and the effects of eclipses of each star by the other. Most of the time, the white dwarf will just be a bright speck in the sky that contributes little to the warmth of the double planet, but slightly increases the UV and X-ray load. That should be quite survivable with a sufficiently thick atmosphere. Occasionally, you'll get a break from the excess UV due to eclipse by the main sequence star. The low luminosity of a white dwarf means we can pretty much ignore the small reduction in insolation due to its eclipse. And, since white dwarfs are tiny, transits of the main sequence star by the white dwarf should also have negligible impact on the insolation the planets receive.

This is, however, a cataclysmic binary. It's on the outer edge of being such, but it's likely to have recurrent nova events with a frequency on the order of decades- maybe centuries. If a nova event occurs while the white dwarf is in view of one of the planets, it's going to be sterilized. And not just the side of the world facing the star- thousands of times solar luminosity is going to mess up the entire planet. So, we need to figure out what the probability is that the white dwarf will be eclipsed from the point of view of the binary planet at any given time. That's rather complicated to do precisely, but we really just need an order of magnitude, so we'll consider just one lobe of the binary planet at a time.

For the 1AU orbit, the average angular size of the main sequence star is about 0.4272 degrees, and the total angular deflection of the white dwarf is about 3.08 degrees. In reality, it will spend more time at the edges of its travel, out of eclipse, than it will in alignment with the main sequence star, but we'll be generous for order-of-magnitude estimation purposes and assume it spend equal time in all angular positions. Half of the time it overlaps with the main sequence star, it will be in eclipse, which works out to about 7% of the time. That means that, for any given nova event, there is more than a 93% chance that one half of the binary planet will be sterilized, and much more (because the events are not uncorrelated) than an 87% chance that both will be sterilized. If novas occur on a timescale of approximately once per century, that means there is an expectation value of about 115 years before all life in this system is destroyed.

Bummer.

For the closer, low-luminosity orbit, the angular size of the main sequence star is about 1.7 degrees, while the angular deflection of the white dwarf will be about 12.28 degrees. That gives a rough 13% chance of being in eclipse, which still leads to a generous expectation value of 132 years before all life is wiped out.

In summary: Most of the time, accretion and variations in orbital distance should be within ranges that are conducive to life, assuming that the planets otherwise have good conditions. But the occasional outbursts of nova radiation from the white dwarf due to long-term accretion would indeed make life impossible.

To fix this, you will want to give the binary stars an orbital period of much longer than just a few days, to ensure the white dwarf remains quiescent, and as a result you will want a larger and more luminous main sequence star so that you can put the binary planet at a large enough distance that the orbit remains stable and it still gets enough light.

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