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Imagine an earthlike planet in the habitable zone of Alpha Centauri B. Call it ACBc (although I am not sure ACBb has been confirmed). When ACA and ACB are closest to one another, they are about 11 AU apart (similar to the distance from Saturn to the sun). Rounding to 10 AU, this means that the irradiance from ACA on our hypothetical ACBc is about 1% of what it would be if ACA and ACBc were one AU apart, like the sun and the earth. Since ACA has 1.5 times the sun's luminosity, that would work out to about 1.5% of the sun's apparent brightness from the earth.

But, when ACA and ACB are farthest apart (which is a larger part of the time because they are moving more slowly then), the distance is more than 3.5 times as great, so the apparent brightness is more than ten times smaller.

This means that, for maybe ten consecutive earth-years out of every 79, ACBc would be getting an extra 1-1.5% irradiance, averaged over the surface of the planet. By comparison, the sun's apparent brightness is about 3.4% greater when the earth at perihelion than at aphelion. This does warm the earth slightly near perihelion, but the effect is swamped at most locations by the tilt of the earth's axis. Perihelion is during the northern winter, when it is coldest for many of the planet's inhabitants.

Still, the effect is not zero, and it would accumulate over several years. Has anyone done any modeling for how that would affect the climate for that period of time when ACA and ACB are near minimum distance? Is there a rule of thumb for solar forcing to suggest how much the average temperature would increase per year over those years?

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    $\begingroup$ "That's less than half the difference between northern winter and summer from the sun on the earth": There must be an arithmetical error somewhere, or a most regrettable confusion between irradiance (which is a momentary value) and irradiation (which is its integral over time). Where I live, at 45° northern latitude, the average day length in summer is about 14 hours, and the average day length in winter in about 10 hours; there is a 40% difference in irradiation right there. Moreover, the sun is higher in the sky in summer than in winter, almost doubling the difference in total irradiation. $\endgroup$
    – AlexP
    Oct 26, 2023 at 20:59
  • $\begingroup$ I was unclear. Hopefully my revision conveys better what I meant. $\endgroup$ Oct 26, 2023 at 21:24
  • $\begingroup$ Relevant question: Planets orbiting Alpha Centauri. Note that, somewhat by definition, a planet orbiting ACB within its habitable zone must account for the effects of ACA. Thus, the only practical affect ACA would have on the weather of a planet orbiting ACB would be to cause the summers and winters (mostly summers) to be more extreme, but still survivable (or it's not in a habitable zone...). Remember that 11AU is a long honking distance, so the effect will likely be small. However, I wonder if we have any hard science to prove that. $\endgroup$
    – JBH
    Oct 27, 2023 at 15:35
  • $\begingroup$ Greetings, why don't you put your setup in something like Universe Sandbox and observe, what happens. I actually find a lot of enjoyment in setting up mostly strange solar systems with it and try to sneak in an habitable planet/moon somewhere unexpected. But be aware, that this simulation can still be a bit off reality... at the other hand, it would take a very dedicated astrophysicist to find flaws in a setup made this way. $\endgroup$ Nov 27, 2023 at 7:10

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You've done most of the hard work already. The effective temperature of a planet is given by:

$T_{eff} = (aI)^\frac{1}{4}$

Where $a$ is a constant based on properties of the planet (Albedo, rotation rate, and emissitivity) and $I$ is the irradiance. If it is indeed the case that irradiance is increased by 1.5%, the increase in temperature should be $1.015^\frac{1}{4} = 1.0037$, i.e. a 0.37% increase in temperature at the minimum distance between stars. Assuming the same effective temperature as Earth of 254 K, we're looking at an increase of a whopping one Kelvin.

Earth is significantly hotter than its effective temperature because of greenhouse gases, and as you mention in your original question and AlexP in a comment, the dominating factor on climate temperature is axial tilt and latitude, by a long shot, but yes indeed the temperature variation on this 79 year cycle would be measureable and attributable to the binary parter star.

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