Radiation Levels and Effects on Planet with 27 Suns

Question

Other posts from this thread will be posted here:

How to make an Earth with 27 suns work (Closed as a duplicate of the follow up, Attempt Two)

How To Make an Earth with 27 Suns Work, Attempt Two: Orbital Stability

(Will be updated as more are posted.)

Info

I finally figured out how to make a planet with 27 suns work: By setting the stars into (mainly) binary orbit pairs several levels deep. Now, in that question, I handwaved the effect of the radiation of the suns on a single, Earth-sized planet (along with the visibility of the suns, which will be enhanced for distance). But now I want to understand what the radiation would do, so I can figure out how to protect the planet in the future.

Let's start listing how the system works:

I'm ignoring most of the stars and focusing on the ones closest to my planet:

The planet, XV, is in orbit around star 5. (Star 5 is in a 5/6 binary pair, the pair of which is in orbit of star 7, which orbits star 1, which is in the binary pair 1/2.)

XV is 1 AU from 5. 5 is 10 AU from 6. the 5/6 pair orbits 7 at a distance of 25 AU. 7 is a distance of 30 AU from 1.

Star magnitude/type:

Star 1 is a class O2 ($\geq\text{16}{\small{M}}_\odot$).

Star 7 is a class A7 ($\text{1.4–2.1}{\small{M}}_\odot$)

Star 5 is a class G2 ($\text{0.8–1.04}{\small{M}}_\odot$)

Star 6 is a class G1 ($\text{0.8–1.04}{\small{M}}_\odot$)

To simplify, the planet orbits 5, which is in a binary with 6, and together they orbit 7, which orbits 1, which is in a binary with 2.

The star and planets formed (in geological time) extremely quickly, and cooled quickly (see the previous question), so imagine that the planet has cooled from molten and that nothing will be going supernova ( due to extended lifespans of stars.)

Question

What would the effects of the radiation of 27 suns be? Criteria:

• List the energy, in Joules, per day, of the solar radiation.

• List the effects of this solar radiation on the planet's atmosphere and surface.

• Use the same magnetic field Earth has.

It's okay if

• The planet is fried vaporized. The substance of the planet is, of course, unobtanium. The purposes of this question are to understand the effects of this stellar environment on a potential planet.
• The magnetic field is stripped away with the atmosphere. While that's sad, I don't mind as long as I am told that the magnetic field is stripped away.

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Thank you to all in the Sandbox who helped me develop this question.

Answer 1

Let's look at two key equations: $$F_i=\frac{L_i}{4\pi r_i^2},\quad \lambda_{\text{max,i}}=\frac{b}{T_i},\tag{1, 2}$$ For a given star with luminosity $L_i$ and surface temperature $T_i$ a distance $r_i$ from the planet, these equations give you the flux from the star ($F_i$) and the wavelength at which its emission is the strongest, according to Wien's law. I've adopted some reasonable values for $M_i$, $L_i$ and $T_i$ based on spectral type. I've also taken $r_i$ to be a mean radius from each of the stars, given that the distances change wildly. Let's take a look at the results (here, Here, $F_s$ is the solar constant): $$ \begin{array}{|c|c|c|c|c|c|c|}\hline \text{Star} & M_i (M_{\odot}) & L_i (L_{\odot}) & T_i (\text{K}) & r_i \text{ (AU)} & F_i(F_s) & \lambda_{\text{max,i}}\text{ (nm)}\\\hline 1 & 16 & 500000 & 20000 & 30 & 1750 & 145\\\hline 5 & 1 & 1 & 5800 & 1 & 1 & 502\\\hline 6 & 0.9 & 0.7 & 5300 & 10 & 0.007 & 547\\\hline 7 & 1.5 & 10 & 7000 & 25 & 0.016 & 414\\\hline \end{array} $$ We have a problem.

Stars 6 and 7 won't contribute as much as Star 1 - note the low fluxes. Star 1, on the other hand, will make life miserable. It's luminous and it's not too far away. Also, its peak emission lies in the ultraviolet, meaning your planet is going to need one heck of an ozone layer to have any hope of surface life. Even at its furthest distance from the planet, Star 1 will still maintain a large surface flux.

Oh, I should note that I went against your wishes and picked values for Star 1 as if it were an O7 star - less massive, less luminous, and cooler. In other words, I essentially chose the best-case spectral type here. If you stick with an O2 star, things will be . . . bad. Really, really, really bad. Specifically, we'd be looking at $M\sim40M_{\odot}$, $L\sim10^6L_{\odot}$, $T\approx50000\text{ K}$, $F\approx3510F_s$, and $\lambda_{\text{max,i}}\approx58\text{ nm}$, all of which are much worse for your planet.

For fun, let's elaborate on this calculate the effective surface temperature, $T_{eff}$. If we assume that the main source of flux is Star 1, then $$T_{eff}=\left(\frac{L_1(1-a)}{16\pi\sigma r_1^2}\right)^{1/4}=\left(F_1\frac{1-a}{4\sigma}\right)^{1/4}$$ Plugging in our values - assuming $a=0.3$ - gives us $T_{eff}\approx1647\text{ K}$. That's much, much worse than Venus - and we haven't even taken the contributions from the other stars into account!

In chat, you talked about how you were wondering how bad stellar activity would be. Fortunately, the O-type star likely isn't a problem here. While O stars have strong stellar winds - and I wrote about that last month - they're usually pretty quiet when it comes to stellar flares and coronal mass ejections. Why? Well, unlike the majority of stars, very few O-type stars have magnetic fields, and magnetic fields are the main force behind this sort of stellar activity.

Conditions in the core of an O star simply aren't ripe to produce a magnetic field by normal means; for decades, both theory and observations indicated that no O-type main sequence stars had magnetic fields. In recent years, a small number of counterexamples have been discovered - $\theta^1$ Ori C is a well-known case - and it's thought that a small fraction of the population do indeed have magnetic fields. However, most don't, and so odds are good that your O star won't be a source of flares or CMEs. The other stars, maybe. But M-type red dwarfs are really the only flare stars, and you don't have any red dwarfs among this subgroup in your system.