Theres a famous star that I'm sure you've seen in the sky. Its name is Betelgeuse, and you can find it in the Orion constellation, where it marks Orion's right shoulder. If you want to call it “Beetlejuice,” I'm fine with that so long as you don't say it three times.
But something is going on up there. This red supergiant has dimmed repeatedly in the past few years, which could mean that it's ready to go full supernova quite soon—and by “soon” we mean within the next 10,000 years. Actually, since it's some 500 light-years away, it's possible that it already exploded and we just don't know it yet. It could show up tomorrow.
One thing's for sure: If Betelgeuse does blow, it will be the brightest supernova ever witnessed by humans. Just how bright are we talking? Could you see it during the day? Would it be dangerous? I'm going to show you how to figure all this out with just some very basic physics.
What Is a Supernova?
In most stars, the core is composed of hydrogen and helium, the two lightest elements—but only the positively charged nuclei of those atoms, since it's too hot for the electrons to stay put. Under immense gravity and temperatures, these nuclei can fuse into heavier elements, releasing massive amounts of energy in the process. (This nuclear fusion is where our sun gets its energy.)
For a stable star like our sun, there's a balance between two opposing forces. The mass of all the matter in the star produces a gravitational force that tends to collapse the star. However, this is countered by the outward-pushing force from the core, so the star remains fairly constant in size, even though it's not a solid object like a planet.
But as a star ages, it gradually uses up its hydrogen and helium and starts producing heavier elements like carbon, oxygen, silicon, and finally iron. And that's as far as it goes—fusing elements heavier than iron takes energy instead of creating it, so the star essentially runs out of fuel and collapses in on itself.
In some cases, this collapse can be very severe—so severe that it rapidly increases the pressure and temperature in the core of the star. The star then goes boom. Big boom. Well, big silent boom, since explosions make no sound in the vacuum of space.
But this produces A LOT of light energy. For comparison, our sun has a luminosity, or power output, of 3.8 x 1026 watts. A supernova that was observed in 2015 (ASASSN-15h) had a peak luminosity of around 2 x 1038 watts. That's more power output than 500 billion suns. It's crazy. Oh, you didn't see that one? Yeah, because it was in a different galaxy. Betelgeuse is in our back yard, astronomically speaking.
Brightness and Luminosity
A long time ago, a Greek philosopher named Hipparchus categorized the stars into six groups, based on how bright they appeared in the night sky. From that, we have developed a classification scheme for “apparent magnitude,” such that a star of magnitude 1 looks very bright, while you probably can't even see a magnitude 6 star through light pollution. Betelgeuse is in the first group.
To be clear, this isn't the actual luminosity of a star—it's how bright it appears from Earth, which depends on (1) how much light it produces and (2) how far away it is. Oh, also (3), magnitude is based on how the human eye sees objects, and it's not linear. A magnitude 1 object has a light intensity (in watts per square meter) that is 100 times greater than a magnitude 6 object.
There can be objects even brighter than magnitude 1, and they would have negative values. For example, the planet Venus is the brightest object in the night sky, aside from the moon, averaging around –4.1, depending on its position.
The Effect of Distance
So here's how we can proceed: If we have the intrinsic luminosity of an object (how much light energy it produces), we can calculate the intensity of the light a given distance away (how much light is received at that point). And then we can convert that to the magnitude scale to describe how bright it appears to the human eye.
For example, say we have a light bulb that puts out 20 watts of light. That's its luminosity. If the light radiates equally in all directions, and you're standing r meters away, you can imagine that the total light is spread over the surface area of a sphere with radius r. As the distance grows, the light is spread over a larger sphere, so there's less in any one spot. Since the surface area of a sphere (A = 4πr2) is proportional to the square of the radius, we call this the inverse square law.
With that, we can write the intensity (I) at a location as a function of luminosity (L) and distance (r):
This means that if we cut the distance in half, the light will be four times as intense. So distance makes a huge difference in the brightness of an object.
It’s Gonna Be Epic
OK, now let's apply this to a Betelgeuse supernova. We can start with a luminosity of 2 x 1038 watts, like that supernova in 2015. For the distance, I'm going to use 500 light-years. (Surprisingly, we don't have a great value for the distance to this star, but this is in the ballpark. If you're curious, here are the methods we use to measure distances in astronomy.)
Of course, to use our formula, we need to convert this distance from light-years to meters. Since light moves at a speed of 300 million meters per second, I get a distance of 4.73 x 1018 meters. With that, the intensity of the light received by Earth would be 0.711 watts per square meter.
Now, to convert that to magnitude, we need a reference star. Let's use Sirius. It's one of the brightest stars in the sky, with an intrinsic luminosity 25.4 times greater than the sun, and it's 8.79 lightyears away. That gives us a magnitude (mr ) of –1.46. Then the magnitude (m) of the Betelgeuse supernova would be calculated as:
Crunching the numbers gives me a brightness magnitude of –18.5—which, holy cow, is pretty awesome. If our guesstimates for luminosity and distance aren't too far off, it will be by far the brightest object in the night sky. For comparison, a full moon has a magnitude of –12.6, so this supernova would also be easily visible even during the day.
With the naked eye, the supernova would still look like just a single point of light—because, hey, it's pretty close for a star, but it's still far away. You wouldn't see a disk as with our own sun or moon, but it would be by far the brightest dot you've ever seen in the night sky, and it would probably last for weeks.
But is it dangerous? Well, this is still a lot lower than the brightness of the sun, which has a magnitude of –26.8. So you wouldn't get sunburned by it, but you also probably shouldn't look at it with an optical telescope. I think it would be fine to take a selfie with the supernova in the background. Your grandchildren are going to want to see that.
