Okay, gang, let's roll. As I have emphasized before, we astronomers have some tremendous problems on our hands. We cannot just vary our experimental domain. We have to accept the universe as given to us. But it is quite remarkable that nonetheless, we can find out so much about the cosmos that we inhabit. We have seen that just being able to find out where objects are in the sky and how far they are away from us was an extraordinary achievement, especially for X-ray astronomy. Certainly a next logical step, would be to find out how these objects are moving. To do this requires some knowledge about their velocities. And this is what we shall explore here. Let's consider a moving object. And, let's imagine that the object is emitting something periodically. It could be light waves. It could be sound waves. Or, it could be just some ticking of a clock. A moment's thought will show that you are, if you are in front of the object, and therefore the object is approaching you, you will see the phenomenon a bit more frequently than if the object were stationary. This is because if the object is moving towards you, each pulse or wave will have less distance to travel to get to you, because the object's motion will be decreasing the distance between you. Hence, the time interval that you measure between the pulses will be shortened. This is easy to see via the little animation shown here. You can see that the pulses sort of bunch up in front of the object and seem to be more spread out behind. So if you measure the time of arrival of these pulses, they will be more frequent if the object is approaching you and less frequent if it is moving away. Furthermore, you can see that the faster the object is moving, the more the frequency will change. Here, you see a comparison of two objects, the top one of which is moving faster than the bottom. Let's see if we can do some experiments to detect this phenomenon, which is known as the Doppler shift in honor of the Austrian physicist Christian Doppler, who proposed it as a possibility way back in 1842. In the following video, I set up a microphone on top of my hummingbird feeder, and waited for the birds to come. Can you hear any changes in the pitch of the sounds that the birds emit? [NOISE] Now, I'm sure you're all chafing at the bit with all sorts of problems with an experiment of this kind. What are some of the problems, and how can we solve them? This would be a good topic for exploration in the forums. So let's try again with something a bit different. Look at this video of a train passing by a camera and microphone. [NOISE] What do you hear, and why? And how does this experiment solve some of the hummingbird problems? A remarkable property of the Doppler shift is that for speeds that are small compared to the propagation speed, c, which is the speed of sound in the case of sound, the speed of light in the case of light, the changes that occur have the same mathematical form even though the nature of sound and light are quite different. In all of these cases, you get the following. Delta lambda over lambda is equal to v over c. If you are measuring the wave length of sound or light. The change in frequency over the stationary frequency is the same, v over c, but with a minus sign, because frequency and wavelength are inversely proportional. So this is what you would use if you were measuring the frequency of light or the pitch of a sound. And delta t over t is v over c if you are measuring the time of arrival of a sound pulse or a flash of light. In all these cases, v is positive if receding from you. And in all cases, v has to be much, much less than the velocity of propagation. But there's one problem with this. If the velocity is across your line of sight, instead of towards you or away from you, you get nothing, nada, zero. So we must amend this and realize that it is only radial motion that exhibits this phenomenon. So let's just put a little v sub r here to show that it's only back and forth motion that the Doppler shift can tell us about. This is another possible bummer. You might think, now, this is useless. If, for example, we have a binary star whose orbit is in the plane of the sky, then the motion will be invisible to us. So if a star is going around another star like so, the motion will not be visible. But now, sometimes we get lucky. Imagine the plane of an orbit which is perpendicular to the plane of the sky. This might look like this. Where our central object is here and our orbiting object kind of goes around like this, and may be receding in this direction here and approaching in this direction here. And now you can see that the motion of the star revolving around its companion exhibits a maximal effect at the sides, with one side approaching and one side receding from us. And when it is moving across our line of sight, we should see no effect at all. We should observe just the same thing as if the object were not moving. Does this ever happen? Well, fortunately for us, a lot of X-ray sources are binary stars with very short orbital periods. Remember Kepler's law that said the square of the period of revolution is proportional to the cube of the distance between the objects. Small t means the distance between the stars is relatively small, and that means that there is a good probability that some, we might catch some edge on enough to undergo an eclipse. If they are edge-on, then the velocity we measure at the extremes of its motion towards or away from us is a good approximation to the circular velocity throughout the orbit. How can we detect this possibility? Well, look at this video clip and see. It is pretty easy to visualize that when the orbiting object is directly behind or directly in front of the companion, the Doppler shift should be zero, because it is moving across our line of sight, with a zero component of velocity towards or away from us. When it is approaching more rapidly, here depicted on the leftmost part of the orbit, the light should be blue shifted towards higher frequency. Or if it is a light pulse we are seeing, the frequency should be at its highest there. At the extreme right, with the object moving away from us, we should see light red shifted or a light pulse with its frequency at a minimum. And we have other information as well. Look at the light curve below this orbit. With some luck we might see an eclipse. And that should happen at the time when the Doppler shift is equal to zero. So we can verify what is going on if this occurs. Potentially, we have a goldmine here. Can we plumb its depths? The answer is a resounding yes. In the early 1970s, using data from Uhuru, the first dedicated satellite devoted to X-ray astronomy, Ethan Schreier and his coworkers discovered a remarkable X-ray source that brought together almost all the ideas that we have studied to date. By looking at power spectra, light curves, energy spectra and other aspects of the data, we were able to construct a model positively breathtaking in its completeness. We learned so much about this object with such exquisite accuracy that you would have thought that it resided around the corner from you, instead of at a distance of about 30,000 light years. Thus the X-ray light that Uhuru collected from this object in the 1970s began its lonely trip to the Earth some 30,000 years ago, and in the following lectures, we will explore it. So stay tuned for our Journey to Cen X-3, one of the most exciting X-ray sources in the sky.
