Fictional Exoplanet creation

Linguofreak

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In the total energy balance yes, but not per wavelength. What you say is true for line emission, but that's not the mechanism we're dealing with here - we have line absorption but broad blackbody emission.
My understanding is that it is per wavelength: insofar as a body failsto be a perfect absorber it fails to be a perfect blackbody radiator, and at the same wavelengths. I was first made aware of this in a discussion on the vulnerability of spacecraft radiators in combat: you can't protect them from laser fire by making them reflective or transparent, because they'll fail to emit in the affected wavelengths to the exact same degree as they'll fail to absorb. I remember that the discussion specifically covered wavelength specific effects on blackbody radiation.

After doing a bit of research,


gives the equation

\[ \alpha_\lambda = \epsilon_\lambda \]

which, given the lambda subscript, and if I read the article correctly, I believe bears out that absorbtivity and emissivity are equal per wavelength.
 

Thorsten

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My understanding is that it is per wavelength

That is in explicit contradiction to your basic idea of a photosphere having a given temperature though.

Let's clear up the terms so that we see what law applies where.

The relevant issue is - how do we excite states in the molecules? And how do we de-excite them?

In the case of aurorae for instance, the solar wind coming in excites molecules. Since they're 100 km and more up, the atmosphere is very rarefied, and so they can stay in excited states for tens or even hundreds of seconds, and their only way to de-excite is line emission - they have to emit a photon to go down a specific energy level. Thus, Northern Lights do not have a blackbody spectrum, you see colors because the air molecules radiate at specific wavelength only, and the upper atmosphere doesn't get a temperature from the process, because it is highly off-equilibrium.

In the case of Greenhouse, the atmosphere is much denser. So rather than remaining undisturbed by any collisions, excited molecules bump into others all the time, and so the vast majority of them ends up doing thermal de-excitation - the energy ends up not being emitted as photons at specific wavelength but as kinetic energy of other molecules. And these, while bumping into each other, emit photons now and then - in a broad distribution of blakbody radiation (pretty much like the solar photosphere in fact). This process is in thermal equilibrium and hence we an assign a temperature to the atmosphere.

However, this isn't how we feed energy into the atmosphere, because the atmosphere isn't 'black' or 'opaque' throughout - so it doesn't receive energy like a black body would do. It receives energy by doing wavelength specific absorption only (in the limit that the whole atmosphere is opaque, you can reason using thermal equilibrium and just do a simple diffusion equation).

The situation is that the way we feed into the atmosphere is a non-equilibrium process, we have to do the line physics, but once the molecules get excited they thermalize the received energy quickly, and the process by which the energy is radiated away is in thermal equilibrium.

This difference between off-equilibrium and in-equilibrium process is not accounted for in your reasoning. Kirchhoff applies to a blackbody receiving and emitting thermal energy in equilibrium - which however isn't what happens, so the law doesn't apply.

Likewise, the interaction cross section for absorption is high at wavelengths where a state excitation is possible - and that is also where emission is high - but that applies to emission and absorption in off-equilibrium - which also isn't what is happening here, so that reasoning doesn't apply either.

Does that give you a better idea?
 

Thorsten

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Up to this point, things were fairly calculable. Now the Fi-part of SciFi starts - I draw a collection of landmasses underneath the climate lines. The distribution should be Earth-like (more water than land) since the Albedo was similar. From there then follows a measure of geology, and ultimately the different ecological niches, but fist, as promised, let's talk about weather.

My arguments here will be more qualitative as I seriously do not have the resources to run a full weather code for a fictional world.

The basic pattern is that air underneath the subsolar point heats and rises. This sucks air from the ice-covered dark hemisphere inward while the warm air reaches the upper atmosphere and migrates outward.

The massive inflow of air at ground level leads to a spinning vortex due to angular momentum conservation (that's a common pattern observed in objects as diverse as bathtubs and black holes), aka we get a super-cyclone. If the air at the subsolar point is moist, the water condenses, releasing latent heat and leading to copious cloud formation and rain - which provides substantial energy to fuel the process - the mechanism is really the same as for tropical storms on Earth.

weather_standard.jpg

Now, as seen above, the whole process is self-quenching, because the cyclone clouds have a high albedo and cool the subsolar point - which means that the highest energy is suddenly next to the subsolar point where there are no clouds and Mime can warm the sea undisturbed.

So the cyclone will generally go to where it can suck most energy from the sea, and hence 'wobble' around the subsolar point. In addition, because the orbit is eccentric, it will weaken at apoapsis simply because the available energy is less - so a winter pattern will look more like this

weather_winter.jpg

Likewise, the process of cold air flowing in at ground level won't equalize with the high atmosphere outward flow easily, because the upper atmosphere has 1/5 of the density, so it's not easy to transport the same mass that is coming in. There will instead be boundary instabilities at the division line between warm and cold air, with fingers of cold air reaching inward while pockets of cold air being pushed outward - leading to the developments of frontal weather - cold fronts with massive thunderstorms and clear weather in their wake, warm fronts with plenty of snow on the ice shields - here's a coldfront coming in.

weather_coldfront.jpg

Now, the consequence of a massive coldfront is that there's a broad stretch of planet which has a few days of exceptionally fine weather - and if the coldfront reaches up to the subsolar point, there's a massive heating of the ocean and hence a juicy path filled with energy to fuel the cyclone - so it may react and use this energy - and thus detetch from the subsolar point and migrate outward - creating a far-reaching warmfront over the ice (and sucking cold air inward in other places.

weather_super_cyclone.jpg


Finally, just like a hurricane can spawn secondary storms at its fringes, it would be fairly normal that the super-cyclone generates secondary cyclones which migrate outward (they're not much restricted by Coriolis forces, as we've already established these are weak). Again these would move warm and cold air when they reach the boundary between ice and thawed land.

weather_secondary.jpg

So that, in a nutshell, is what I believe the typical weather patterns on this world would be and why.

The consequence is a high variability of weather - when a coldfront moves in, temperatures can easily drop by 20-30 K within a few hours. Winds can reach hurricane-force quickly when a cyclone makes landfall. Precipitation is copious nearly everywhere, especially at the windward side of mountains. All of this shapes the terrain which will have deeply-cut water erosion created canyons. Every lifeform needs to cope with the potential of high windspeeds and sudden freezing.

I'm currently in a discussion with a fellow biologist tossing around ideas what plausible adaptions to these conditions could be for plants and animals, and (with the understanding that this gets more into the Fi-realm) I will eventually present some of that as well.
 

Linguofreak

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Likewise, the process of cold air flowing in at ground level won't equalize with the high atmosphere outward flow easily, because the upper atmosphere has 1/5 of the density, so it's not easy to transport the same mass that is coming in. There will instead be boundary instabilities at the division line between warm and cold air, with fingers of cold air reaching inward while pockets of cold air being pushed outward - leading to the developments of frontal weather - cold fronts with massive thunderstorms and clear weather in their wake, warm fronts with plenty of snow on the ice shields - here's a coldfront coming in.

<image snipped>

Now, the consequence of a massive coldfront is that there's a broad stretch of planet which has a few days of exceptionally fine weather - and if the coldfront reaches up to the subsolar point, there's a massive heating of the ocean and hence a juicy path filled with energy to fuel the cyclone - so it may react and use this energy - and thus detetch from the subsolar point and migrate outward - creating a far-reaching warmfront over the ice (and sucking cold air inward in other places.

View attachment 26764


Finally, just like a hurricane can spawn secondary storms at its fringes, it would be fairly normal that the super-cyclone generates secondary cyclones which migrate outward (they're not much restricted by Coriolis forces, as we've already established these are weak). Again these would move warm and cold air when they reach the boundary between ice and thawed land.

Something I'd heard said would likely be a typcial weather pattern for planets like this, but didn't quite understand the reason for, is a cross-shaped pattern with cold air from the night side coming in from two opposite arms of the cross, and warm air coming from the subsolar point returning to the night side on the other two. I'd gotten the impression that it was supposed to be a coriolis effect of some sort, but when I tried drawing out what coriolis effects would do to the winds, it didn't look like it would produce that kind of pattern (nevermind your point about coriolis effects not being strong enough).

But looking at what you have there, I think I may have misunderstood the argument that was being made. It may have been more along the lines of those boundary instabilities pulling the cyclone off center, creating a situation like that illustrated in the image I left in the quote. With the spawning of secondary cyclones, you might then get a situation where two cyclones got drawn off in different directions by different cold fronts, and ended up creating two copies of the illustrated situation.
 

Thorsten

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I don't know the source you're referring to, but I would assume that the general pattern must be a mixture of

  • inflow to the subsolar point at ground level, outflow in the upper atmosphere and
  • inflow and outflow by 'fingers' of air driven by the boundary instability

It is clear that heat exchange must take place in some form, but the precise balance would depend on factors like whether the subsolar point is over land and water, the general moisture level on the planet (massive storm systems are much easier to maintain over water with the high latent heat release when it rains off), the scale altitude of the atmosphere vs. the presence and location of a stratosphere, that in turn depends on the gas mixture as well as the stellar radiation spectrum,... So I would guess that under different circumstances, on a much drier planet perhaps, the permanent presence of a cyclone is not really obvious and in/outflow patterns could dominate the dynamics most of the time.

(I haven't tried to calculate this though, my weather reasoning is heavily based on Earth as atmosphere conditions on Stormhold are sufficiently similar)
 
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