Timing is everything. Our ancestors' very survival depended upon it. Knowing when to plant crops, when to move their living quarters to lower elevations. Or when animals they hunted began the migration to different feeding grounds. When the earliest humans realized that certain recurring star patterns at night prestaged the return of spring and the planting season or the onset of fall and the harvest season. They had discovered in effect that the Earth makes a trip around its parent Sun once every 365 or so sunrises. Many cultures divided this year into smaller units based on the recycling of phases of the moon. And then into still smaller ones, such as our presently used weeks and hours. Galileo and his contemporaries learned to use pendulums and water clocks to fine-tune timing to units of seconds. Their successors in today's modern laboratories have created atomic clocks that can pin down time intervals. That are smaller than a nanosecond. 10 to the minus 9 seconds. And just as there are clocks in the sky that have long periods like the Sun, the Earth, and moon motions that govern the year, the day and the month, there are other celestial clocks which have much smaller periods. These clocks were only discovered by astronomers after the construction and perfection of short period clocks on Earth. Some stars pulsate expanding and contracting regularly with periods that are only minutes long. Others take years to complete one cycle. All stars rotate just as the Earth does which, with periods that range from milliseconds to months. Binary system contains two stars that mutually orbit in regular period of days to years. Clocks indeed can be find in almost every variety through out the sky. One of the most astonishing discoveries of the 20th Century along these lines, occurred in the late 1960's when Jocelyn Bell, then a graduate student in Cambridge England, discovered a source of radio waves in the sky that seemed to be changing its brightness every 1.337 seconds. Furthermore, the period of the brightness variation was precisely repetitive to better than one part in 10,000,000. Such a stable celestial clock was unheard of. And the discovers, the discoverers jokingly referred to the new signals, as originating from little green men. However, soon thereafter, many such sources were discovered, and the LGM's seemed to be begging for another explanation. Renamed pulsars, they are among the most intriguing cosmic sources of radiation we know. They have extremely well-defined periods, making exceptionally accurate clocks. For example, the period of pulsar 1937+214 has been measured to be 0.00155780644887275 seconds, a measurement that challenges the accuracy of the best atomic clocks we have here on the Earth. How can something change its brightness almost 1000 times each second? It turns out that these objects are not pulsating at all, but are incredible stars that rotate 1,000 times each second. These stars are so dense and compact, that one thimble full of material from their surface would weigh as much as millions of full sized African elephants. Their extremely large gravitational fields prevent them from breaking apart and their light variations are due to beacons somewhat similar to those of light houses that beam radiation in a search light fashion as they rotate. Because these compact objects are small and have intense gravitational fields, they can accelerate materials to very high speeds. When this material collides with some neighboring gas, the object can heat up to millions of degrees. This leads to emission of x-rays, and indeed, some of the most exciting discoveries concerning the nature of white dwarves, neutron stars, and black holes, have been made by looking at x-radiation using satellites such as Chandra. Let's look at one of these sources in depth. Cen X-3, discovered more than 30 years ago, beautifully illustrates the process of astronomical discovery, and is a representative of an object of this kind. Using x-ray and optical data, we can reconstruct the contents, properties, and behavior of the entire system. We can determine that Cen X-3 is a binary system. That it contains a neutron star, and a companion much larger and more massive. We can find the rotation period of the neutron star. The orbit size of the neutron star. The size and mass of the companion star. The luminosity of the source, which turns out to be thousands of times brighter than the sun, and much more. Not only can we tell the size of the objects using clocks, sometimes we can also deduce their ages. These objects are like huge fly wheels, storing vast quantities of rotational energy. Let's look in detail at Cen X-3 and see how we can piece together the observations to understand this fascinating system. So we connect to DS9 and the Virtual Observatory. Rutgers Primary MOOC Analysis Server, scroll down' til we see the EXOSAT Cen X-3 Observation. Look at the light curve. Let's get our analysis stuff over here. And our Chandra Ed analysis tools over here. And the first thing we're going to look at is the F-tools light curve. We want to plot that. And, by the way, the reason you don't see anything in this box is because this is a non-imaging observation. And here we have it. First, look at the x axis. This is in seconds from 0 to well over 100,000. This observation is about one and a half days long. Things seem to be varying wildly between, oh, about 250 counts per second to over 100 counts per second. And yet, we have a region here, about 40,000 seconds long, In which the x-rays seem to disappear. We'll deal with the nothing happening part first. Let's form some theories. What could this dearth of x-rays be due to? Well, maybe it's just space junk. Stuff out in space, occulting our detector which makes the x-rays disappear. What else could it be? Well maybe somebody just flipped the switch. You know Cen X-3's out there, you just go click, on and off. And there is the end of the x-rays for 40,000 seconds or so. Something else might be, satellite malfunction. The satellite had a problem. You can see, OK? That it is our job as scientists to eliminate some of these maybe silly possibilities and for others, come up with plausible, detailed mechanisms that can be tested with predictions. Why don't you try to come up with your own theories, and then go about trying to falsify them. Here are some more clues that will help us home in on something more reasonable. It turns out that every 2.09 days, the same thing happens. Like clockwork. Cen X-3 disappears in x-rays, for about 40,000 seconds. So let's just write that period on the blackboard. And for our second hint, let's zoom in on a small portion of that light curve, where we have x-rays, and let's see what's going on. Let's zoom in on the light curve. We left-click, and just drag a little box here. Release and there you see the zoomed in part of the light curve. Still can't tell what's going on, though. It looks just kind of going up and down. Let's zoom in again. Let's just make another little rectangle. And now you can start seeing things a little bit better. Let's do it one more time. And now you can see what Cen X-3 seems to be doing. About every five seconds, it seems to be marching up and down. Kind of erratically, but there definitely seems to be some sort of periodic set of peaks in the light curve of Cen X-3. Can we quantify that a little bit more? Well, we can, and the way we do that is by running a power spectrum. This tells us precisely what components of time variability we will see. So we plot the power spectrum and let's see what we get. Here it is. And we have a tremendous peak at 0, and that's because Cen X-3 is very bright. But look at this little, it looks like a little teeny tiny thing over here at about 0.2 cycles per second. But let's rescale this so that we can see what's going on. We'll do a range, and our y-axis will go from 0 to 200,000. Un-check automatic, go OK, and now you can see things a little bit more reasonably in the Power Spectrum. Let's look at this 0.2 second periodicity, or 0.2 cycles per second, periodicity. Let's just zoom in, and see what's happening. Let's do it again. Now you can see something very, very intersting. It's not really just one period, it's a set of periods. Do one more zoom, and then we'll return to the blackboard. Here you can see, the frequency seems to be, starting about here. And going out to here, it's centered around all about 0.2071 cycles per second.
