D-2: The Gift of Giving

This piece was written by Murmeldjuret as part of the Astroknowledge series and is reproduced here with their permission. It was originally published on the Stellaris forums.

 

Today I will be continuing The Beautiful Void’s astroknowledge series.

Right now you are emitting radiation. So are your walls. Don’t worry it is perfectly normal and won’t kill you. You should actually be glad the walls radiate back to you, if they wouldn’t you would start freezing. The same reason the walls radiate heat to you is the way we find the temperature of suns millions of lightyears away.

All light and heat is created when an electron loses potential energy. It is how lightbulbs, LEDs, x-ray cathodes, and forest fires emit light. Whenever an electron moves from a high energy state to a low energy state it emits the difference as electromagnetic radiation. Short jumps become low energy radio waves, and the longest jumps become gamma rays.

X-ray cathodes work by sending high velocity electrons at a target material, knocking out electrons from their orbit. Higher energy electrons fall into these holes, and emit X-rays while doing so.

Atoms and molecules also have kinetic, rotational, and vibrational energy levels. When they interact with each other, they change their internal energy levels. This is what we see as temperature. Hotter objects have more kinetic, rotational, and vibrational energy. Temperature is their ability to give off this energy to other things. When they touch another colder object, they will lose heat energy and the colder will gain that heat energy. Temperature equalizes because something that is better at giving than something else gives back will lose. This seems natural and is something humans notice quickly. Touching cold objects lowers your temperature, while nobody wants to touch hot coals because they love to give.

Heat has another way of transferring than simple touch, namely as radiation. The side facing a hot fire will become hotter than the side facing away, which is not due to the heat transfer via the air between. The vibrational energy can be transferred via photons, as well as normal matter. All things above absolute zero has vibrational energy and as soon as it interacts with another electron it will change its vibrational energy. Any loss here is emitted as electromagnetic radiation. Much of it is contained inside the object, but anything close to the surface has a fair chance to emit it out of the body.

This is then also related to temperature, or willingness to lose energy. The heat you radiate is absorbed by the walls and their radiation is absorbed by you. Heat radiation is for most parts marginal inside earth’s atmosphere. Air is a better conductor for heat than radiation. This is not the case in space. In space, all heat is exchanged through radiation.

The type of radiation is not dependent on the object, or the shape, or the substance. It is only dependent on temperature, the willingness to give energy. This is Planck’s Law, and describes how much and of what type of radiation an object emits. It is always shaped this way, as the total number of atoms is so incredibly large any oddities get marginalized.
[IMG]
We can from this estimate the peak temperature of emission, and it follows the very simple Wien displacement law. Wavelength = constant/Temperature. It is a good approximationexcept for really cold temperatures.

So what does this mean?
It means that whenever we look at an object in its spectrum, we can accurately give its exact temperature. Below is the sun:
[IMG]
We can say that the surface temperature is 5778K within a few degrees of error. Similarly, we cantake the temperature of any distant object that we can spectrally resolve. It also shows why hot suns are blue, as their peak is to the left of the visible spectrum, and why cold stars are red, as their peak is to the right of the visible spectrum.

For those who wonder why we often call it black-body radiation, it is because the actual formula includes an emissiveness term, as radiation from object to medium isn’t perfect. Low emissiveness works like heat mirrors. The heat is never taken up by the object to be re-emitted. If emissiveness is max, it follows the curve exactly and this is called black-body radiation. On earth, almost nothing has true black-body radiation, but in space everything is close to true black-bodies.

If you look at the Planck law curves above you can see that things at room temperature (300K) would be far to the right of the visible (400-700nm). This places it in infrared, which is why we often talk of infrared as heat radiation. Like any radiation wecan see it. IR cameras can photograph things in room temperature, but this is always tricky as the camera itself gives off radiation.

As things grow hotter, their wavelengths become shorter, and eventually what is normally considered heat radiation in infrared turns into visible radiation. When things grow even hotter than the sun they begin emitting their peak in UV, and eventually the hottest things at millions of Kelvin emit X-rays from heat alone. As things grow colder they become redder to eventually be invisible to our eyes. Below is a piece of iron at my guess around 1300K, or 1000C. You can see the hottest part appear white, and as the metal grows colder it grows redder to eventually be outside thevisible spectrum entirely. Light and heat is also reflecting off the hammer above and the anvilbelow.

Spoiler: Ironworking

[IMG]

So this is how we can say how hot a sun is, regardless of distance, because it is the shape/colour/spectrum of the light, not only thestrength that depends on temperature. The lightfrom distant and nearby stars include an indicator of heat and total luminosity in their light.

Heat is wonderful thing and all it wants to do is give. So when a superhot sun is melting your ships, just know that all it is trying to do is share some of its warmth. And your cold metal shell is unable to give the same warmth back.

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