The implausible green star hunter

None of us will ever forget the day we saw it.

Though we may live to regret having done so.

We weren’t looking for it, as such – naturally not: why would one deliberately try to find something that can’t exist?

What we had been doing was cataloguing the stars, systematically and methodically, day after day, year after year; and, all the while, honing our technology, techniques and devices to reach farther and faster.

Hunting for some proof that we weren’t alone in this vast universe.

We’d been scanning the sky for decades.

And then, one day, we saw it.

Or, rather, I saw it.

A green star.

In case you don’t know, I should explain. There are red stars, blue stars, and white stars. You might think, since the three primary colours of light are red, green, and blue, that there should be green stars, too: but you’d be wrong. Green stars aren’t just incredibly rare: the nature of reality forbids their very existence.

I could prove that to you if I had more time. But I don’t, because they’re coming. Somehow, they knew that I’d seen this impossible thing. Within minutes, I heard them – in my mind. At first, I thought it was just a dream… but it soon became clear that everyone in the world heard them, too.

The message was very polite, very friendly. It was quite long, but it boiled down to:

“Greetings! So glad to meet you, at last. Our ambassadors are on their way and will be with you tomorrow.”

Excuse me, I have to go now, I have so much to do to prepare for their arrival. The President has to be briefed, my budlings need to be fed and watered – as does my pet Zeek. And the stress of the last few hours has brought on a case of epidermal shock; my skin is in dire need of exfoliation, it’s more sickly yellow than healthy green right now, and, as ‘The Discoverer’, I want to look my best. There are bound to be photographers.

Oh, I do hope that I still have enough time to get my ears repointed.

Word count: 360; Reading time: 1 min 19 sec (numbers courtesy of wordcounter.net)

---

This work of fiction was inspired by:

The Star That Can’t Exist, by Cool Worlds

‘The Star That Can’t Exist’
presented by Professor David Kipping
(See below for full transcript)

As placing this video’s transcript here would make for a long scroll, I’ve moved it to the foot of the post – because I didn’t want to risk you missing the finale:

---

Kermit sings “It’s not easy being green”

It’s not easy being green.
Having to spend each day
the color of the leaves
when I think it might be nicer
being red
or yellow
or gold
or something much more colorful like that.

It’s not easy being green.
It seems you blend in
with so many other ordinary things
and people tend to pass you over
because you’re not standing out
like flashy sparkles in the water,
or stars in the sky.

But,
green is the color of spring.
And green can be cool
and friendly like.
And green can be big,
like a mountain,
or important,
like a river,
or tall like a tree.

When green is
all there is to be,
it could make
you wonder why,
but, why wonder?
Why wonder?

I’m green,
it’ll do fine,
it’s beautiful.

And I think it’s
what I want to be.

The transcript above was made with the help of Sonix, which did most of the donkey work for a tiny fee (I did have to spend some time tidying it up). Note that I do not have the copyright owner’s permission to publish this transcript here. I’ve investigated the copyright rules regarding transcriptions (more about that here), and one thing I’ve learned is that it’s no defence to make a disclaimer like “these aren’t my words, no copyright infringement intended.” However, I offer the transcription here as a service to society (especially the deaf community). I do hope the copyright owner won’t object. And I hope that you find this video as interesting as I did.

---

… and here, as promised, is the transcript of the earlier video:

The Star That Can’t Exist, by Cool Worlds

Narrated by Professor David Kipping

This video is sponsored by Brilliant.

The universe is peppered with a zoo of breathtaking astronomical objects: everything from quasars to icy moons, from tidal streams to magnetars. Time and time again, nature reminds us that her imagination can easily exceed our own. Yet, amongst this menagerie of phenomena, there is one simple type of object which is bizarrely absent; a case where our imagination indeed wins out: a green star.

The physics of light teaches us that green is one of the three primary additive colors, along with red and blue. Mix these three colors together and you can make any other color you want. And so, when we first learn about stars, it’s perhaps not remotely surprising that some stars are red and some stars are blue, and yet there are no green stars. At first, you might think that perhaps the answer to this is that there are, in fact, green stars out there somewhere; just that they’re incredibly rare. After all, in infinite space, surely all possibilities eventually happen. It’s just a question of travelling far enough to find one.

Yet, the absence of green stars isn’t merely some issue of insufficient data: it’s far deeper than that. It turns out to be an intrinsic rule of our universe. Green stars simply cannot exist. It’s as if somebody wrote into the rules of our universe that, ‘yes, you can have red stars and blue stars, but our universe doesn’t deserve to enjoy the restful, pale light of a tranquil green star’. But, why? Well, to understand this, we have to cover what gives a star its color.

Stars are essentially nuclear engines, converting lighter elements, primarily hydrogen, into heavier elements, primarily helium, deep within their core. The thermal energy released keeps the inner core incredibly hot – over 10 million Kelvin. The outer, inert, layers absorb some of this heat, too, through radiation and convection, and the outermost layer of the Sun is about 6,000 Kelvin. Almost all of the atoms inside a star have been ionized because of the high temperatures involved. So, what this means is that the protons and the electrons have been separated to form this kind of plasma soup. Now, photons, as they try to pass through this plasma, will strongly interact with the ions, so much so that the plasma is essentially opaque to visible light. So, that means that we can’t actually see the inner layers of the Sun. The outer layer fully blocks our view and has no transparency. Thus, when we look at a star, its appearance, including its color, is completely governed by that outermost layer, known as the photosphere. So really, rather than saying there are no green stars, we should really say there are no green photospheres, since that is the only part of the star that we can actually see. Ok, fine, but what gives photospheres their color then? Or, really, I guess a more precise way of framing this would be to ask, “in what ways does light get released from this photosphere layer?”

There’s three basic ways in which light can be released from a given strata of matter: transmission, reflection and emission. Now, we’ve already discussed how stars are mostly a plasma, which means that they have negligible transparency and reflection. Light just gets absorbed by the ionized material, so that leaves us with emission only. Molecules can release radiation through all sorts of interesting processes, such as transitions between different vibrational modes within the molecule. But a star is just too hot for any of that; the extreme heat just rips apart these molecules into their constituent atoms. Now, atomic transitions, they can still occur, but the vast majority of a star’s energy is released through the most basic process: thermal radiation.

To an excellent approximation stars just emit in the same way that an idealized blackbody would. That means that the distribution of how much high energy and low energy photons are produced, known as the emission spectrum, is conveniently governed by a single parameter, its temperature. This curve, known as the Planck or blackbody function, is one of those topics that our Columbia [University] physics students get to wrestle with in their freshman year. It’s an incredibly important physics concept, but sadly one that we just don’t have time to dive into deeply today. However, a great way to learn more about this concept is through our sponsor, Brilliant.

Brilliant is an online learning platform that promotes education by problem solving and practical examples rather than just memorization. Brilliant’s interactivity allows you to develop your intuition of otherwise abstract concepts by exploring intuitive examples. By watching how outcomes change as initial conditions are modified, you experience the principles of science first hand. The astrophysics course on Brilliant includes a section on radiation and the blackbody function, as well as additional sections on atomic spectra and how energy is produced inside stars. All topics that I’ve only been able to touch on briefly in this video. Brilliant have poured a lot of energy into the optimization of education here, making learning a richly enjoyable experience. So, you can subscribe and help us out by using the link brilliant.org/CoolWorlds, and the first 200 of you to use that link will get 20% off the annual premium subscription.

Now, for the purposes of this video, the most important thing about the Planck function is that no matter what temperature we choose, it always has the same basic shape. It starts from zero, rises up to some peak and then slowly drops back down again. This immediately tells us that blackbodies, and thus photospheres, and thus stars do not emit light at just one wavelength, one color of light. No, they emit at many colors simultaneously. And yet more; most of the wavelengths are completely invisible to us. Our eyes can’t see x-rays and ultraviolet, nor can they see infrared and radio waves. What we see, the color, is governed by the shape of the blackbody curve within this tiny little sliver corresponding to the visible band. The overall basic shape of the Planck function is really always the same, except that it shifts over to higher energies as the object’s temperature rises.

Here, I’m showing you what the disc of a star would look like as we change its stellar temperature. On the right, I’m showing you the location of the star’s color on an RGB color wheel. As you can see, the increasing temperature changes the star’s color from red to white to blue, but, gracefully, it avoids green. With what we’ve discussed so far, we’re actually ready to get some understanding as to why green stars don’t exist, indeed why they can’t exist. The visible part of the spectrum can be further subdivided into three colors: red, for the low energy end, then green in the middle and then finally blue at the highest energy. Now, in this visible region, the blackbody spectrum can really just do one of three things. If we have a very hot star, then the spectrum is shifted over to the high energy side and thus, within the visible region, we will be looking at the declining tail part of the Planck function. Ok, so, what does that mean? Well, it means that we have a little bit of red, a bit more green and lots of blue. So, hot stars tend to look more blue than anything else. Alternatively, let’s take a very cool star. Now, the peak occurs in the low energy region, and thus the part of the Planck function falling within the visible band is the rising portion. So, this means that we have lots of red, some green, but hardly any blue. Thus, overall, red wins, and we get a reddish looking star.

Ok, so that’s two very different possibilities and yet still no green star. But perhaps you might be thinking that there is some middle ground here. Perhaps we can tune this to create, finally, our harmonious green hue. Let’s try setting the peak of this curve right in the middle of the green band: that would correspond to a star whose photosphere was about 5,400 Kelvin. Now, as we can see here, it peaks in the green, but it’s still overall pretty flat in the visible region. That means that there’s still quite a bit of red and blue light mixed in here. In fact, with a bit of math, we can calculate that the star produces about 15% of its total light in the green band, but 13% in the red and 13% in the blue. And if you add roughly equal amounts of red, green and blue together, well, then you get white light. In fact, this is indeed the case for our Sun. It peaks close to green light here, but still appears white to us, at least if you’re in space. That’s because of this contaminating contribution of the red and blue components. The only way that we can make a star genuinely appear green would be if we could keep the peak of this function in the middle of the green band, but simultaneously compress it down, kind of squish that function so it peaks more heavily in the green wavelengths.

But, of course, with the Planck function, as we’ve already discussed, there is only one controlling parameter: the temperature. There’s just nothing else that we can change here to possibly create that desired ‘squishing’ effect. Remarkably, that statement is true, even if we try to change the constants of the universe itself. In the Planck function, we have the following three constants that we could consider varying; these are fundamental constants of the universe. In 1893, Wilhelm Vien showed that the peak of the Planck function occurs at this wavelength, so let’s impose that this must equal 530 nanometres, that’s the center of the green band. The width of the Planck function is a bit trickier; that’s characterized by its standard deviation. Remember, we want to try and shrink this down to something like 10 nanometers or smaller to create our vivid green star. With a bit of math, we find that the standard deviation of the Planck function is this, which, recall, we’re going to try and set to be below 10 nanometers. Look, don’t worry about the details here; the important thing is that the second term looks familiar because it’s already in our other equation for the peak, so we can do a little substitution here to conveniently remove this.

Finally, we can multiply through these numbers here to get our final simplified inequality. Remember that this represents our requirement for a universe to create a green star. It states that we need 900 nanometers to be smaller than 10 nanometers, but, of course, it’s not. In fact, it’s almost 100 times bigger. And note that I didn’t even choose constants of the universe here; they all just canceled out. It’s somewhat staggering, then, that there aren’t just no green stars in our universe: there are no green stars, even in a multiverse of differing physical constants.

Is there any way then to create a star which appears green? Well, clearly trying to change the constants of nature doesn’t work, nor indeed is trying to add different stars together. If I take a red star and a blue star and I kind of merge them almost on top of one another, well, that would just create a whitish blob of light again; not a green star. There is one way that we could create a green appearing star, but it’s really just an optical illusion that only happens when we view stars through a planetary atmosphere. Our Sun provides a clear example of this through the famous green flash effect. As the Sun sets on the horizon, light has to travel through more atmosphere than when the Sun is overhead. The atmosphere preferentially scatters blue light, hence, why the sky is blue. And so at sunset and sunrise, the Sun’s blue light component gets almost totally removed. And so that leaves us with a reddish looking sun. Now, to get green, we have to combine this scattering effect with another effect called refraction. As the Sun dips below the horizon, light from the Sun can actually still reach us: it can bend through the air via refraction and thus continue to reach our eyes. But crucially, red light doesn’t bend, doesn’t refract, as strongly as green light does. So, what that means is that there’s a certain angle at which the red light isn’t bending enough: it gets blocked off by the horizon, thus leaving us just with the green light component. In practice, the Sun dips behind the horizon pretty quickly, and so this effect doesn’t last very long, sometimes just a few seconds, hence the name the green flash.

In the same way, then, we can imagine that a bright Sun-like star, but not the Sun itself, that is setting on the horizon, could also appear green via the same effect. But remember, this is just a temporary optical illusion. In deep space, dust clouds can sometimes interact with light, too, but it’s difficult to imagine how such clouds could conspire to create the same effect in a persistent way. It really does seem as if nature prohibits green stars to grace our skies.

Now, in a way, this actually presents kind of an interesting opportunity because, look, we have established that to the best of our knowledge of the laws of physics, as we know them, nature cannot produce green stars; it simply can’t do that. And so, if we ever did see a green star out there in the universe, well, it cannot be natural. It would have to be an artificial effect. Somebody must have done that to that star. And look, it’s not even that technically difficult to imagine how that would happen. We can make light sources appear green all the time; you just grab a green filter, and you stick it in front of the light source. So, we could imagine a advanced civilization perhaps wrapping their star up in a kind of bubble of semi-transparent material to create the illusion of their star appearing green.

Of course, building a filter this large would be an outrageous engineering project, one only possible by a highly advanced civilization. But, in principle, this bubble, which might remind you of a Dyson sphere, could just sit around the star for billions of years, making the star appear green and thus artificial. For billions of years, anyone looking at that star would immediately be able to tell us something was very wrong with it, that someone must have done that deliberately. But, why would somebody do this? Well, who knows, but maybe it’s nothing more complicated than a cosmic art piece made by a highly advanced civilization which thinks nothing of wrapping stars up in giant bubbles for their own amusement. Or, maybe it’s made by a civilization which is trying to use it as a beacon, as a signal, that somebody lives here in this neck of the woods. After all, what we have here is an effect which is non-natural; an effect which is viewable from afar just by the color alone; it could persist for potentially billions of years, and it is effectively a completely passive beacon, requiring no active power source to maintain.

Whenever astronomers come across possible non-natural phenomena like this, we call it a ‘technosignature’. Narrowband radio communication is perhaps the most famous example of this. What makes this a green star effect, an interesting technosignature, I think, is that it’s incredibly easy to look for. We can trivially measure the color of a star, and indeed we regularly do so for billions of them. Now, I bet when you started this video, a video about why we don’t see green stars in the universe, you didn’t expect it to lead to technosignatures. But I think this little journey that we’ve taken together here kind of illuminates how astronomers often come up with technosignatures in the first place. You start with a simple question about the nature of the universe; you then consider through a possible natural exceptions to this behavior: you estimate how observable this effect might be, and, in the end, you might be left with something potentially interesting to go after.

Whether a civilization would actually go to the enormous trouble of doing this: who knows? I have to admit I’m rather skeptical about that. But, on the other hand, xenopsychology is complete speculation. So, perhaps so. The real point here, and ultimately the strength of any technosignature, is that this effect is incredibly easy for us to check out. Many stars have already had their colors measured and catalogued online, available through services like SIMBAD. And, if we find a green star and it turns out not to be an alien civilization after all, then you’ve just discovered the very first example of a completely new phenomenon anyway.

So there you have it. Green stars can’t naturally exist, not in our universe or indeed within a broader multiverse of varying physical constants. But, despite that, perhaps they are out there: beacons of artificial construct, monuments to a civilization’s mastery of the cosmos. But, more importantly, I hope this illustrates how sometimes asking simple questions, the kind of questions that a child might pose, can lead to profound and fascinating insights. Never dismiss those simple questions, because sometimes pulling on those threads can unravel the very sense of our place in the universe. So, until the next video, stay thoughtful and stay curious.

Thank you so much for watching this video, everybody. If you liked it, then be sure to click the subscriber link down below [assumes YouTube], so of course, you get access to all of our future videos too. And if you really want to help us out, then you can become a regular supporter of our research group, the Cool Worlds Lab, by clicking the link up above [assumes YouTube] where you get access to special perks as a member of our team. Thanks for sticking to the end on this one and until next time, have a cosmically awesome day.

The transcript above was made with the help of Sonix, which did most of the donkey work for a tiny fee (I did have to spend some time tidying it up). Note that I do not have the copyright owner’s permission to publish this transcript here. I’ve investigated the copyright rules regarding transcriptions (more about that here), and one thing I’ve learned is that it’s no defence to make a disclaimer like “these aren’t my words, no copyright infringement intended.” However, I offer the transcription here as a service to society (especially the deaf community). I do hope the copyright owner won’t object. And I hope that you find this video as interesting as I did.