Video: Redshift

In this video, we will learn how to calculate the radial velocity of a star or galaxy using the amount by which absorption lines in the spectrum of light from it are shifted.

17:03

Video Transcript

We may have heard the fact that our universe is expanding, that too, at an ever-accelerating rate. In other words, our universe is getting bigger faster and faster. But the question is, how do we know this. What evidence do we have regarding this fact? In this video, we will be learning about redshift. But in order to do this, we first need to learn about absorption spectra.

One way that we measure the chemical compositions of distant stars, as well as distant galaxies, is by collecting the light coming from them and passing it through a prism. This way, the light from the star, initially white, ends up splitting into all the colours of the rainbow. Now, in this particular spectrum, we can see the longer wavelengths down the right end and the shorter wavelengths down the left end. Where, of course, we use the Greek letter 𝜆 to represent the wavelength of light.

Now, interestingly, in this spectrum of light that we’ve gathered from the star, we don’t see a complete spectrum. In fact, we can see some black bands here, here, here, and here in this diagram. These bands are caused because even though the star itself emits white light, or in other words, all possible wavelengths of visible light, there are certain chemicals in the star itself, for example in the atmosphere of the star, that absorb very specific wavelengths of light. So, even though the star is emitting white light, some wavelengths of light get absorbed, and so they don’t reach us at Earth. Therefore, at the positions of those wavelengths of light, we see black bands.

So, we said that there are chemicals in this star that absorb some light. Now, these chemicals are most commonly just hydrogen gas or helium gas. But there are other possible elements that the star could contain that would absorb different kinds of light. But interestingly, each element has its own signature in terms of what wavelength of light it absorbs. And so, based on this fact, if we can work out which wavelengths of light each element absorbs, then we can look at the spectrum coming from a star or from a galaxy and work out what elements are present in that star or galaxy.

Now, this is all well and good theoretically speaking, but practically, it gets a little bit more complicated. It turns out that when we conduct experiments in a laboratory to try and figure out which wavelengths of light a particular element absorbs. So, let’s say, for argument’s sake, we took a sample of hydrogen and we found that hydrogen absorbed these particular wavelengths of light. Now, we’re not saying that this is necessarily the absorption spectrum of hydrogen, but we’re saying, for argument’s sake, let’s imagine that it was. So, if we figure out in the laboratory that these are the wavelengths that hydrogen absorbs, then that means that if we see black lines in the spectrum from a star or a galaxy at these particular positions, then we can be confident that the star or galaxy in question contains hydrogen.

However, in many cases, what we end up seeing is that in the spectrum from the star or the galaxy, we see the same pattern of black lines in the spectrum but that each spectral line has been shifted towards the right side of this diagram, or towards the red end of the spectrum. In other words, towards a longer wavelength. Now, this phenomenon, this shifting of the spectral lines, is known as redshift because each spectral line has shifted to the red end of the spectrum.

What this means in practice is that the hydrogen in our laboratory on Earth absorbs this particular wavelength for example and the hydrogen in the star or the galaxy absorbs the same wavelength but then all of the light gets redshifted, shifted towards the right, as it comes towards Earth. And the spectral lines get shifted too. Because, remember, longer wavelengths are to the right of this diagram and shorter wavelengths are to the left. And this is true for each one of the spectral lines. Each one of them is redshifted.

So, why does redshift occur? Well, to answer this question, we first need to think about how we’re actually gathering the light from the distant star in this case. So, let’s say we’ve got the distant star here and we’ve got the Earth here with all its scientists and all its telescopes and all its cameras. So, we know that the star emits white light in all directions. And we know that this is a combination of all wavelengths of visible light. For simplicity, though we’re just going to be thinking about one of these wavelengths that the star emits.

So, let specifically think right down the middle of the spectrum. Let’s think about some of the green light that the star emits. And we’re specifically thinking about the light emitted in the direction of the Earth. Now, of course, we have to note that these wavelengths and star sizes and Earth sizes are not drawn to scale here. But anyway, so, we see that the distant star is emitting green light towards the Earth, as well as all of the wavelengths of light. But like we said earlier, we’re only focusing on the green light here.

Now, if the star is not moving relative to the Earth, then the Earth would just pick up green wavelength light coming towards it. Now, to make our next point more clearly, what we’re going to do is to draw our diagram from this perspective. Imagine placing our eyeball here. And additionally, if we imagine some more of the green light being emitted in another direction, then what we’re going to do is to label all the peaks of the light emitted by the star with a line. And so, what we’re going to see are concentric circles around the star where each circle is an outward spreading peak of green light. So, let’s do that. Let’s modify our diagram now.

So, here’s what the diagram looks like once we’ve shifted our perspective. Looks pretty similar but we’re looking at it from above now, remember. And as well as this, we said that we would label every peak of green light coming from the star with a line. And these lines form concentric circles, or more accurately concentric spheres. Because, remember, the star emits light in all directions.

But anyway, so, let’s now imagine that the time it takes for one peak of the green light to move to where the next peak is, because, remember, this light is spreading outwards, let’s say that this time is one second. So, what we’re actually saying is that the period of this light is one second. Now, of course, the period of green light is not actually one second, but we’re just saying that for argument’s sake here, just to make our numbers simpler and our life easier.

So, what we’re actually saying, once again to recap, is that our green light is spreading outwards at a rate of one peak per second, or one complete cycle of green light per second. Now, if we just think about the light moving towards the Earth, then what this means in practice is that if the star is not moving relative to the Earth, then the Earth will receive one peak every second. In other words, at this point in time, the Earth is receiving this peak. One second later, it will receive this peak. Two seconds later, it will receive this peak, and so on and so forth.

And so, that’s all well and good. The star is emitting green light at a rate of one cycle per second and the Earth is receiving green light at a rate of one cycle per second. However, let’s now imagine what would happen if the star is moving away from Earth. So, at this point in time, the star emits green light outwards. And then, we can imagine what would happen one second later. We can imagine that the green light that we just saw being emitted spreads outward about the point at which the star was centred when that light was emitted. But then, at this point the star itself has moved slightly. The new centre of the star is here. Because, remember, we’re saying that the star is now moving away from Earth.

And so, at this point, the star emits a peak of light again. Because, remember, it’s one second later. But this time the light emitted is centred about the current centre of the star. And so, now, we can think about what happens one second after this point in time. The original peak of light that we saw being emitted is still going to spread outwards. And it’s going to continue spreading outwards about the centre of the star when the light was emitted. And the same is true for this peak of light. It’s going to spread outwards but about the centre of the star when the light was emitted. So, one second later the star’s centre has shifted yet again. And in fact, the whole star itself has shifted. And it emits light at this point again.

So, what we’re now seeing is not a pattern of concentric circles with their centres aligned, but rather each circle representing the peak of light emitted is centred about the point at which the star was when that light wave was emitted. And in practice, what this means is that the distance between peaks on the left-hand side of the star as we’ve drawn it is much shorter than before.

If there was an observer standing here, then they would receive a peak of light at a time interval shorter than one second. In other words, they might receive a peak of light every half a second, say. Whereas any observer on this side of the star, such as for example our Earth, will receive a peak of light at a time interval of greater than one second. In other words, it will be more than one second between when the Earth receives this peak and when it receives this peak. And that is all due to the motion of the star away from Earth.

Now, up until this point, we’ve been drawing these peaks as green to represent green light. Because we said earlier that green light was equivalent to one cycle of light every second, just for argument’s sake. However, from the point of view of the observer, such as the Earth, we’re receiving one cycle of light at a time interval of more than one second. And as we can visibly see, the distance between two peaks, which in other words is the wavelength of this light, has increased. There is a larger gap between peaks, and so the wavelength is larger.

And this means that we will no longer receive this light as green light. We might receive it as a long-wavelength light such as yellow light for example, or even red light if this shift in wavelength is extreme. And so, that is why redshift occurs. It occurs when there’s relative motion between the source of light, in this case the star, and the receiver of light, in this case the Earth. Redshift specifically occurs when the source is moving away from the receiver or the receiver is moving away from the source.

The flip side of this is that if we had an observer on the other side such that the star, or the source of light, was moving towards the observer, then the wavelength of light shrinks. And this is known as blueshift. In other words, then, if a source of light is either moving towards you or you are moving towards the source, then the light you receive will be blueshifted. Whereas if the relative motion between the source and the observer is that they are moving away from each other, then the light you receive will be redshifted.

And interestingly, from comparing these two diagrams, we can even see that if the source is moving relatively slowly, then the change in wavelength is not massive. Whereas if the source is moving really quickly, in other words covering a large distance per unit time, then the shift in wavelength is large. In other words, then, the faster the source is moving away from the observer, the larger the redshift.

Now, as it turns out, when we look at most of the galaxies in the sky, we see that the light coming from them is redshifted. In other words, we find the spectrum of light coming from them, and we realise that, for example, a certain galaxy might contain the same pattern of absorption lines as hydrogen’s absorption spectrum, but that each of these spectral lines have been shifted to the red end of the spectrum.

And we see that this is true for the majority of galaxies that we look in in our universe. Only a very small proportion of galaxies are blueshifted. So, what this is telling us is that the majority of galaxies in our universe are moving away from us. And what’s even more interesting is that the galaxies that are further away from us are moving away from us even faster. Because the light from the further galaxies is redshifted more.

Now, Earth is not in a special position. It’s not like everything is moving away from us specifically. It turns out that all galaxies are moving away from each other. But because we are on Earth, it seems like everything is moving away from us specifically. But anyway, so, all galaxies are moving away from each other on average. And what’s more is that further galaxies are moving away from us faster than nearer galaxies. And so, what this tells us is that the universe is expanding. This must be true because all galaxies seem to be moving away from Earth as well as away from each other. And so, the universe is getting bigger.

But more interestingly, like we said earlier, further galaxies are moving away faster than nearer galaxies. And this means that the expansion of the universe is accelerating. It’s getting faster. It seems like the larger of the universe gets, the faster it is expanding. Now, there is actually a mathematical relationship that we can apply here which links the speed of the source of light to how much the light coming from it is redshifted.

The equation that we’re looking for is this one here. This one tells us that 𝜆 subscript source, that’s the wavelength of, let’s say, a particular spectral line in the spectrum of light coming from a star or a galaxy. Minus 𝜆 sub Earth, which is the wavelength of that same spectral line when taken on Earth, or in other words when stationary relative to the observer. Divided by that same value of 𝜆 Earth. Is equal to 𝑉 divided by 𝐶, where 𝑉 is the speed at which the source, let’s say a star or a galaxy, is moving away from the observer, which usually is the Earth. And 𝐶 is the speed of light.

So, in practice, then, let’s say that this is the spectrum for hydrogen taken on Earth because this means that the hydrogen is stationary relative to the observer. And we see the same spectral lines, the spectral lines for hydrogen, in the spectrum from a distant star. So, we know that this distance star must contain hydrogen, but we see that each one of these spectral lines is redshifted.

Based on this redshift, we can figure out the velocity at which the star is moving away from Earth. And to do this, we find 𝜆 subscript source for a particular spectral line, for example, minus 𝜆 subscript Earth, the wavelength of that same spectral line when taken in a spectrum stationary relative to the observer. Divided by that same value of 𝜆 sub Earth. And when we find that fraction, it is equal to 𝑉, the speed at which the source is moving away from the observer, divided by 𝐶, the speed of light. So, now that if we’ve understood what redshift is and taken a look at this equation here, let’s attempt an example question.

An astronomer looks at the absorption lines in the spectrum of light coming from a distant galaxy. He identifies the absorption lines of hydrogen, which makes up most of the galaxy. He then compares these lines to the same absorption lines from a laboratory sample. His results are shown in the diagram. How is the galaxy moving in relation to Earth?

Okay, so, what we’ve been told in this question is that the scientist has two spectra to compare. One is an absorption spectrum taken from a sample of hydrogen in the laboratory. And the other is the spectrum taken from a distant galaxy. Now, we’ve been told that the astronomer identifies the absorption lines of hydrogen in the spectrum from the distant galaxy. And we can see that this is true because these are the absorption lines of hydrogen as seen in the laboratory. And we see the same pattern of absorption lines in the spectrum from the galaxy, except that each spectral line has been shifted towards the right slightly, or towards the red end of the spectrum.

In other words, then, the wavelength of each hydrogen spectral line in the spectrum from the galaxy is longer than the wavelength of that same spectral line in the spectrum from the hydrogen taken in the laboratory. Now, let’s recall that the reason for this is that in the laboratory, of course, the hydrogen is not moving relative to the Earth. And so, we find a particular set of wavelengths that represent the spectral lines of hydrogen. However, in the spectrum from the galaxy, each spectral line is shifted in wavelength because the galaxy is moving relative to Earth.

And we can recall that if this here is the Earth, and this here is the distant galaxy, and if the Earth and the galaxy are not moving relative to each other, then the light emitted by the galaxy will be received by Earth with the same time period, or in other words, the same amount of time between peaks, as when the light was emitted by the galaxy itself. But if we’ve got the Earth here, and we’ve got the galaxy initially here, and the galaxy is moving away from Earth, then we can see that as the galaxy moves away, the wavelength of light received by Earth will be longer than if the galaxy was stationary relative to Earth.

And that’s exactly what we’re seeing in the two spectra. Each spectral line is shifted to the red end of the spectrum towards the right. And so, the wavelength of each spectral line has increased. The reason for this is because the light has been redshifted. And this occurs because the galaxy is moving away from Earth. And therefore, the light reaching Earth has a stretched wavelength. And hence, we’ve found the answer to our question. We can say that the galaxy is moving away from Earth.

Okay, so, now that we’ve had a look at an example question, let’s summarise what we’ve talked about in this lesson. We firstly saw that redshift is the shifting of light to the red end of the spectrum, or towards longer wavelengths, when the source of light is moving away from the observer. Or, of course, when the observer is moving away from the source. Basically, the relative motion between the two must be that they are moving apart from each other.

Next, we saw that there’s an equation which links the amount of redshift, represented by this fraction on the left-hand side, to the velocity at which the source of light is moving away from the observer. And we saw that 𝜆 subscript source represents the wavelength of, for example, a spectral line in the spectrum of light from the source. And 𝜆 subscript observer is the wavelength of that same spectral line in a spectrum taken from something that was stationary relative to the observer.

However, it doesn’t have to apply to spectral lines. If we know, for example, that a specific wavelength of light in a stationary source is shifted to another wavelength in a moving source, then we can still calculate the velocity of the source relative to the observer using this equation. Where, of course, 𝐶 is the speed of light.

And finally, we saw that redshift provided the first real evidence for the expansion of the universe. This is because we observe that light coming from almost all galaxies was redshifted. And this suggested that all of those galaxies were moving away from us, but also away from each other. And therefore, the universe is expanding. And even more interestingly, it seems like the further galaxies are from us, the faster they are moving away from us. And this means that the expansion of the universe is accelerating. In other words, the larger the universe gets, the faster it expands.

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