One of the common tropes in astronomy is a comparison of our Sun to other stars. It’s a great way of showing just how tiny we are. Betelgeuse, for example, has a radius more than 1,100 times that of the Sun. In an image comparing stars, our Sun is easily reduced to a tiny pixel among giants. But such an image is also a bit misleading. While the relative sizes of these images are typically accurate, they ignore the more important aspect of a star, which is its mass.

Since Betelgeuse has a radius 1,100 times that of the Sun, it has a volume about 1.3 billion times larger than the Sun. But its mass is only about 8 – 20 times the Sun. This means the density of Betelgeuse is much, much lower than the Sun. The density of a star isn’t uniform, and increases with depth, but very roughly the average density of the Sun is about 1.4 grams/cc, or about 1.4 times the density of water. That might not seem like much, but it’s pretty high for an object that is mostly hydrogen and helium. The average density of Betelgeuse is about 12 billionths of a gram/cc, which is about a million times less dense than Earth’s atmosphere at sea level. That’s about the same as a vacuum found in an insulating Thermos bottle.

Basically, a star like Betelgeuse is a red hot vacuum.

You might think that such a hot, low-density star isn’t sustainable long term, and you’d be right. Betelgeuse is in its red giant stage, where it makes a last ditch effort to fuse heavier elements to keep going. Most of what we see as the star is in fact its outer layers being expanded to near vacuum by the hot core. Eventually it will lose its battle with gravity and explode as a supernova (though it poses no threat to us).

So the next time you see a comparison of stars, keep in mind that most of the largest stars are basically hot vacuums. In terms of mass the largest stars are only about 200 times that of the Sun. If they had the same density as our home star, even the most massive stars would only be about 6 times larger than the Sun.

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When you look at an image of the Sun, you might notice that it’s edge appears slightly dimmer than its center. This is an effect known as limb darkening, and its actually quite useful to astronomers.

Our line of sight means we see light from different depths. Credit: Wikipedia

It all has to do with our line of sight to the Sun. When we view the middle of the Sun, we are looking directly into the Sun. When we view the edge of the Sun, we see light coming at a glancing edge through the Sun. Because of the density of the Sun’s atmosphere, the light we observe always comes from about the same distance through the upper layer of the Sun. So in the middle we see to a certain depth into the Sun, but on the edge we see light from a more shallow depth. The depth we observe can be determined by simple geometry, so by looking across the Sun, we are actually seeing to a varying depth at different points.

The reason the Sun appears dimmer near the edge is because the Sun gets hotter the deeper you go. This makes sense, but with limb darkening we can prove it. In fact, with detailed measurements of limb darkening, we can determine just how the temperature of the Sun varies with depth.

Limb darkening seen on Betelgeuse. Credit: NASA/Hubble

A similar effect occurs with other stars. There are only a few stars where we can resolve this directly, but Betelgeuse is a good example. In the case of Betelgeuse, the darkened region is much wider than that of the Sun, which indicates Betelgeuse has a much thicker atmosphere. This is typical of red giant stars, which, while larger than the Sun, are much cooler and less dense.

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When we look at stars in the night sky, it is clear that some stars are brighter than others. When early astronomers started measuring the brightness of stars, they used a designation known as apparent magnitude. Early on, apparent magnitude was as basic as “These stars look the brightest, so we will say they are magnitude 1. Those are the next brightest, so they are magnitude 2.” and so forth. As we got better at measuring stellar brightness, the process was formalized, but the basic idea is still the same. The brighter the object, the smaller its magnitude. We can even carry it into negative numbers for planets and the Sun. For example, the maximum magnitude of Jupiter is about -1.6, while the Sun has a magnitude of about -27.

Since apparent magnitude was based on how bright an object appears to our eyes, it isn’t a linear scale. If star A gives off twice as much light as star B (and assuming they are the same distance away from us) star A does not appear twice as bright as star B. Our eyes see on a kind of logarithmic scale. It is what allows us to see things that are very bright and very dim. As a result, a magnitude 1 star is about 2.5 times brighter than a magnitude 2 star. A magnitude 2 star is 2.5 times brighter than a magnitude 3 one, etc.

Of course just because a star looks brighter, that doesn’t mean it actually is brighter. Another aspect of light is that things appear dimmer the farther away they are. If two stars give off the same amount of light, but one is twice as far away, the closer star will appear 4 times brighter than the more distant star.

To account for this, we’ve defined another type of magnitude known as absolute magnitude. The absolute magnitude of a star is defined as what it’s apparent magnitude would be if it were 10 parsecs (about 32 light years) away. For example, the sun has an apparent magnitude of -27, but an absolute magnitude of 4.8, which is actually pretty dim.

Absolute magnitude allows us to compare stars on an equal footing. It also allows us to play with “what if” scenarios. For example, what if a recent supernova in M95 had happened in our neighborhood? Recent observations may have found the star that exploded in older Hubble images, and it appears to have been a red giant about 10 times more massive than our sun. The apparent magnitude of the supernova peaked at about 13. Since M95 is about 37 million light years away, its absolute magnitude is about -17.

In our night sky, perhaps the most famous red giant is the star Betelgeuse. At some point in the next several millennia Betelgeuse will go supernova itself. Betelgeuse is only 650 light years away, so when it goes off, what might we see? Given the absolute magnitude of the recent supernova, if Betelgeuse exploded with the same brightness it would have an apparent magnitude of about -11. That is brighter than any star or planet in our sky, but it isn’t quite as bright as a full moon.

So even if Betelgeuse does explode in the near future, it won’t be the end of the world. It will just be a short lived beacon in our night sky, casting shadows on moonless nights.

Shadows from a supernova. How cool would that be!

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