In this video, our topic is classifying stars by brightness and temperature. When we think about the billions and billions of stars in our galaxy alone, it makes sense we would want to come up with a way of organising or classifying them. Two ways of doing this are considering the brightness of a star as well as its temperature. And as we’ll see later on, the temperature of a star is related to the color of light that it gives off.
As we look into how to classify stars using these standards, let’s start by considering the brightness of a star. On one hand, the brightness of a star can seem like a pretty straightforward thing. As we look up into the sky at night, some stars just look brighter. That is, more light seems to be coming from them than from other stars. It’s important to realise though that this assessment, that one star is brighter than another, is based on observing these stars from a particular perspective. That is, it’s based on the viewpoint that our eye has while we’re on the surface of the Earth looking up at the sky.
When we think about star brightness this way, then sometimes appearances can be deceiving. For example, consider this scenario. Let’s say that we’re on the surface of the Earth looking up at the sky. And we see a couple of stars. As we look at these two stars, this one here and this one much farther away, based on our perspective and our vantage point, we make an assessment of which star looks to be brighter. From where we’re standing and looking, it seems as though this closer star is giving off more light. And so we would naturally say that this star is brighter than the one farther away.
We can see, though, that this assessment of relative star brightness would change if our eye was positioned somewhere else. For example, let’s say we were somehow able to observe these two stars from over here. Well, in that case, this closer star would now look brighter to our eye than the one farther away. And so we might conclude that this star is the brighter of the two. So we can see that when our assessment of star brightness depends on our perspective, the particular place from which we’re looking at the stars, those assessments could disagree. From one perspective, this star looks brighter. And from another, another one looks brighter.
What we’d really like is an assessment of star brightness that doesn’t depend on our particular viewpoint. The name for this is the absolute magnitude of a star’s brightness. This measure of star brightness is called absolute because it only depends on the stars themselves and how much light they give off. It’s got nothing to do with where or how we look at a star. Measured on the scale of absolute magnitude then, we can get an objective reading of a star’s brightness. For example, the absolute magnitude of the brightness of our Sun is a little bit less than five, 4.83. And note that this number has nothing to do with how we look at the Sun, whether we’re near to it or far away, whether we view it from an angle or straight on. This value indicates the intrinsic brightness of the Sun in and of itself.
Now, an interesting thing about the absolute magnitude scale is that it’s an inverse scale. This means that the lower our absolute magnitude gets, the brighter a star it indicates. Consider, for example, two other stars beside our Sun, Sirius and Betelgeuse. The absolute magnitude of the brightness of Sirius is 1.4. And that of Betelgeuse is negative 7.2. And because of the way that this measurement scale works, these stars are actually brighter than the Sun, even though these numbers are lower. And of all three stars, Betelgeuse is the brightest because it has the lowest absolute magnitude.
By the way, here we can see an example where the absolute magnitude of a star’s brightness is a negative number, which may seem confusing since we’re calling it an absolute magnitude. Keep in mind, though, that this word absolute refers to the fact that this is a measure of the star’s intrinsic brightness, rather than its brightness with respect to any particular vantage point. So a lower absolute magnitude number indicates a brighter star. This is one way of classifying stars.
Another approach is to organise stars by their temperature. Now, when we talk about the temperature of a star, we need to be careful to indicate which temperature we’re talking about. Recall that, for a large portion of their lifetime, stars, in their core, have a process called nuclear fusion going on. The conditions required for this process tell us that the core of a star is often very hot. For example, the core of our sun is at about 15 million degrees Celsius. A star’s core temperature can be very different from the temperature of its surface. The surface temperature of our Sun, for example, is thousands of times cooler than the temperature of its core. And when we see light coming from a star, that light is indicative of the temperature of the surface, rather than an interior layer of the star. All this to say, when we look at the light that comes from a star and work back from that to solve for the temperature of the star, we’re talking about its surface temperature.
Now, earlier on, we said that we can tell something about the temperature of a star by looking at the color of the light that comes from it. At first though, this idea may seem a bit strange. After all, when we look up at the night sky, don’t all the stars we see appear basically white? Does this mean they all have the same temperature? That they’re all basically like our Sun? Well, it turns out that this perception, that all stars are white in color, has more to do with our eyes than the actual light coming from the star. The way our eyes work, they’re much more sensitive to brightness than they are to color. So if we see a very dim source of light, like the light coming from a distant star, our eyes are able to tell if there’s some light there. But we’re not able to see any color in it. As a result, it looks like that light is white.
The way to get around this limitation of our eyes is to increase the relative brightness of these light sources. One way to do that is to look through an optical device, like a pair of binoculars or a telescope. When we do this and look at a particular star, it’s not uncommon to see the light from that star, take on a color other than white. So just like in the case of star brightness, when we look at the color of light coming from a star, we need to be careful to keep our perspective in mind. From now on, when we talk about the color of light a star gives off, we’ll be speaking of the true color, the one that doesn’t depend on our perspective. And when we know that true color, we can tell something about the temperature of the star’s surface.
We can better understand this connection between star temperature and star color by looking at the colors of light our eyes can see. Recall that the name for this is the visible spectrum. And we can remember further that the visible spectrum is just one small chunk of what’s called the electromagnetic spectrum, the collection of all possible electromagnetic waves. This spectrum is organised by wavelength, where, towards one end, the wavelength is very small. And then, as we move towards the other end, the wavelength gets progressively larger. Now, interestingly, if wavelength gets larger as we move from right to left, then the energy of a wave gets smaller as we move that direction. Or another way to say it, wavelength and energy work in opposite directions. As one increases, the other decreases and vice versa.
Now, this fact, that energy increases as we go from left to right across the visible spectrum, is useful to us. It means that if we pick two different colors in the visible spectrum, say we pick yellow and green, then we can tell which of these two colors indicates a more energetic wave of light. It’s green light because that color appears farther to the right on the visible spectrum than yellow light. And if we picked another color, say blue light, we could see that light of that color is more energetic than green or yellow. And again, that’s because it’s farther to the right in the visible spectrum. So we’re now seeing a connection between the color that light has and the energy that it has. But then, where does the energy that we’re talking about come from? Well, it comes from the star, which is giving off light of some particular color. And the more energy that star has, the higher its temperature will be. After all, temperature is an expression of heat energy.
So the color of light coming from a star tells us how energetic that star is, which tells us about its surface temperature. This means that, along with wavelength and energy as they vary in the visible spectrum, we can also write down how temperature varies with color. So here’s what we’re seeing. Hotter stars, those with a higher surface temperature, will have light that’s in the blue-to-violet-to-purple range. And relatively cooler stars will have light that looks red or orange.
At this point, we may wonder about stars which look neither blue nor red in color. For example, what about our Sun, which gives off white light? Well, we know that white light is a combination of all the visible colors. So a star that truly gave off light that was white would be one that has a temperature in the middle range between these hotter, bluer stars and the cooler, redder ones. And so we see how we can connect the wavelength of light coming from a star, that is, the color of light it gives off, with the temperature of that star’s surface.
Knowing all this about classifying stars by brightness and temperature, let’s get a bit of practice with these ideas through an example.
Two stars, A and B, are known to have the same brightness. When observed by an astronomer on Earth, however, star B appears brighter than star A. Which star is farther away from Earth?
Okay, so in this exercise, we have these two stars, star A over here and star B we’ll say is over here. And an important fact about these two stars that we’re told is that they have the same brightness. In other words, they give off the same amount of light. But then, we’re told that when these two stars are observed by an astronomer on Earth, they don’t appear to have the same brightness. But rather, star B appears brighter than star A. Based on this information, we want to figure out which of these two stars is farther away from Earth.
On one level, the two bits of information we have about these star brightnesses seem to contradict one another. At first, we’re told that they’re the same. But then, we’re told that star B appears brighter than star A. What we need to realise though is that these are two different assessments of the star brightness. The first one that tells us they have the same brightness is a measure of what’s called the absolute magnitude of the brightnesses of these stars.
When we talk about absolute magnitude, we’re describing the brightness of a star in terms of the intrinsic properties of the star all by itself. It’s got nothing to do with how the star is looked at or perceived. So the first sentence of our statement is telling us that, in an absolute sense, regardless of how these stars are looked at, they have the same brightness. They give off the same amount of light. But if we introduce an observer, the astronomer on Earth, then it may not appear that these stars have the same brightness.
Our statement tells us that the astronomer, based on Earth, perceives star B to be brighter than star A. And this makes perfect sense if star B is closer to the astronomer than star A is. In that case, more of the light given off by star B, compared to the light given off by star A, would reach the astronomer’s eye. So then, rather than these two pieces of information about star brightness contradicting one another, they actually give us more information about the space relationships of these stars to the astronomer. Since star B appears brighter than star A, that must mean that star A is farther away from the astronomer. And since the astronomer is on Earth, that must mean that star A is also farther away from Earth than star B.
Let’s look now at a second example exercise.
An astronomer looks at the light coming from two stars: star A and star B. Star B is emitting bluer light than star A. Which star is hotter?
Okay, so we have these two stars. Star A we’ll say is over here and star B we’ll say is over here. And we’re told that when an astronomer looks at the light coming from both stars, the light from star B appears bluer than the light coming from star A. The question then is which of these two stars is hotter, that is, higher in temperature. Now, what we’ve been given in this exercise is the information about the color of light that comes from these stars. We want to take that information and make an inference about the relative temperature of these stars. So what does the color of light that comes from a star tell us about its temperature?
To figure this out, it will be helpful to look at all the light our eyes are capable of seeing, called the visible spectrum. For all the light in this spectrum, we know that not only does that light have a color associated with it, but it also has a wavelength. And that as we go from the right side of the spectrum to the left side, that wavelength increases. But we know that, in general, for waves of light as their wavelength grows gets bigger, the amount of energy carried by that wave decreases. This means that while wavelength gets bigger right to left on the spectrum, energy gets bigger left to right. In other words, the most energetic visible waves of light are blue and purple, while the least energetic are red and orange. So we see a connection between the color of light and the energy that it has. But we want to find a connection between color and temperature.
Thankfully, though, we’re not far away because we can recall that the energy in these light waves is supplied by the stars that emit the waves. And the more energy a star has, the hotter that star will be, the higher its temperature will be. So just as energy increases left to right across the visible spectrum, so does star temperature. This is to say that the hottest stars give off light that looks blue or purple. And the coolest ones give off light that looks red or orange.
And knowing that, we can now answer our question. We know that star B is emitting light that is bluer in color than that of star A. This means that the light coming from star B is farther to the right on the visible spectrum than the light coming from star A. And therefore, the light from star B has more energy, which indicates a higher temperature of the star emitting that light. Because the light coming from star B is bluer than that from star A, that means that star B is hotter than star A.
Let’s summarise now what we’ve learned in this lesson about classifying stars by brightness and temperature. Starting off, we saw that stars vary in their brightness, how much light they emit, as well as their temperature. And that these are two ways of classifying or organising stars. We then saw that star brightness is measured using absolute magnitude, an objective brightness scale where lower values indicate greater brightness. And finally, we learned that star color corresponds to star surface temperature, where bluer light indicates hotter stars and red light corresponds to cooler stars.