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.

posted over 5 years ago

HDE 226868‭

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