Clocks in the Sky

Ever since the dawn of humanity, we have been awed by the mysteries of time. Over the millennia, our concept of time has changed radically. Although we seem to have an inborn concept of what we mean by the passage of time, it is almost impossible to define it, without referring to itself! It is by no means clear that our concept of a “tick-tock” of a clock is all there is to it. In fact, Einstein discovered that the nature of time is inextricably linked to space, and the two “coordinates” MUST be clearly stated together to avoid error in either our measurement of space or time. Thus, “here” and “now” become relative concepts, to be resolved only by considering our universe as the realm of spacetime.

But putting these fascinating issues aside for now, we focus our attention on simpler questions: how do we tell time? What sort of devices do we need in order to “tell time”? Consideration quickly leads one to the idea of some repetitive event or phenomenon that can be counted. This defines a notion of an “elapsed interval of time”. This simple idea has led us in eras gone by to use devices such as sand filled hourglasses and sundials to measure the progress of time.

At the age of 17, Galileo observed that a lamp, suspended from the ceiling of the cathedral at Pisa, swayed back and forth in a time interval that was independent of the size of the swing. In the language of physics, we say that the period of oscillation is independent of the amplitude. He had discovered the law of the pendulum, and worked on using this principle to design clocks. He invented the modern day escapement, which converts this continuous back and forth motion into the tick-tock we still see on many grandfather clocks today.

On Earth, we have been able to relate many “clocks” to real physical processes, and thus have gained insight into the workings of our World and solar system. For example, we have divided our “day” into 24 equal hours, and have come to understand (with surprising difficulty!) that this results from the spinning of the Earth on its axis of rotation. Similarly, the regular 365-day “seasons” which we identify with an earthly year (along with day/night duration variations and changes in the elevation of the Sun in the sky) can be attributed to the revolution of the Earth about the Sun.

But many other, more subtle clocks abound in our environment. For example, there is a 13-hour periodicity in our tides, which can be linked to the Moon’s apparent revolution about the Earth. Even though this period is about 29 days, the linkage of this to the earthly day yields this strange 13-hour interval between successive high (or low) tides. The linkage of the 365 day “year” with the 24 hour “day” leads to the observed fact that the stars in the sky repeat their positions every 23h 56m (the “sidereal” day). Thus, the stars rise about 4 minutes earlier each day and seem to slowly drift westward through the seasons. So Orion seems to rise near sunset in December, but appears low in the western sky near sunset in April (as seen by observers in the temperate or equatorial latitudes).

Even more complicated periodicities have been uncovered. It turns out that our Earth wobbles on its axis, just like a top. Remarkably, this wobble takes about 26,000 years to complete one cycle. Even more remarkably, Hipparchus, a Greek astronomer living over 2000 years ago, was able to discover this! Incidentally, this phenomenon, called the precession of the equinoxes, causes the shifting of the Sun’s position within the Zodiac as the centuries elapse, and is directly responsible for the “dawning of the Age of Aquarius”.

Another example is that the circumstances for similar total solar eclipses recur at intervals of 18 years, 11 1/3 days. (Lest you think that the 1/3-day is almost irrelevant to the total, consider the fact that because of that 1/3 day, the eclipse in question occurs 1/3 of the way around the world from the previous one!). The discovery of this is credited to the ancient Babylonians, almost 2500 years ago. (Let’s not forget that these people had no telescopes, no satellites. Only their naked eyes and superlative minds were brought to bear on these very subtle phenomena).

Our Sun has its own set of interesting clocks. For example, if you observe a sunspot near the Sun’s equator, it takes about 25 days for the spot to go once around. Thus, the Sun apparently rotate once every 25 days on its axis. But if you observe a feature near the pole of the Sun, you find that it takes about 30 days to complete one cycle. We say that the Sun rotates “differentially”, not like a solid object such as the surface of the Earth.

With all these clocks surrounding our daily lives, it is perhaps not surprising that far-off cosmic objects exhibit periodic behavior as well. One of the most astonishing discoveries of the 20^th century occurred in the late 1960’s, when Jocelyn Bell, then a graduate student in Cambridge, England, noticed that a source of radio waves in the sky seemed to be changing its brightness every 1.337 seconds. Such a precise celestial clock was unheard of, and people jokingly referred to the new signals as originating from Little Green Men. However, soon thereafter, many such sources were discovered, and the LGMs 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 PSR 1937+214 has been measured to be: P=0.00155780644887275 seconds, a measurement that challenges the accuracy of the best (atomic) clocks we have here on Earth.

How can something change its brightness almost 1000 times each second?? It turns out these objects are not “pulsating” at all, but are incredibly dense neutron stars that ROTATE 1000 times each second. These stars are so compact that one thimbleful of material from their surface would weigh as much as 6 million full sized African elephants! Their extremely large gravitational fields prevents them from breaking apart and their light variations are due to beacons similar to those of lighthouses that beam radiation in a searchlight fashion as they rotate. (For further details, refer to the “CRAB NEBULA” piece...)

Because these compact objects are small and have intense gravitational fields, they can accelerate material 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.

One of the most beautiful examples of what we can find out about these objects was discovered about 30 years ago. Cen X-3 was observed in the X-rays to be changing its brightness every 4.8 seconds. Furthermore, the source would go completely away for about 12 hours, every 2 days. Because the clock was so accurate, we could actually tell that the source of x-rays was moving around another star. As the x-ray source moved away from our line-of-sight as it went around its companion, the 4.8-second period became slightly longer (a Doppler “red” shift). Then, as it came back towards us on the other side of its orbit around the companion, the period got a bit shorter (Doppler “blue” shift).

Using all this data, we can reconstruct the entire system. We can determine the size of the orbit of the neutron star, the size of the companion star, the luminosity of the source (about 100,000 times brighter than the Sun!) and much more.

Not only can we tell the size of objects using the clocks, sometimes we can also deduce their ages. These objects are like huge flywheels, storing vast quantities of rotational energy. As they radiate, their energy stores get depleted, and they tend to slow down. Thus, the slower pulsars tend to be older.

These pulsars are seen in several different environments. One is in a “binary” system, such as we discussed in Cen X-3. Another is in the center of a supernova remnant, such as the Crab nebula or Cas-A. In this case, there is only a single object surrounded by the exploded material that was once a normal star. The neutron star “engine” that typically powers the SNR tells us much about the explosion itself. (This can now link the “cosmic recycling centers” piece about SNRs...)

Let’s look in detail at Cen X-3, and see how we can piece together this fascinating puzzle….

Activity 1: Loading Centaurus X-3 and seeing the periodicities….

Start DS9, connect to the Virtual Observatory and click on the link that says: “Load the Cen X-3 image”. Now you see a very unusual picture; a black spot surrounded by bright light, and streaks going off on either side. These streaks are because this observation uses the Chandra gratings, which act like prisms to break up the x-ray light into their component x-ray “colors”, much like a rainbow breaks up sunlight into visible light colors. The central black spot results because (paradoxically enough) Cen X-3 is so bright that the satellite collects more photons than the detectors can comfortably handle; we call this phenomenon “pile-up” and for advanced calculations, we can do different analyses to reconstruct the image. We won’t worry about that here.

Now, let’s construct a light curve, to see how Cen X-3 behaves over time. Go to the “analysis” drop-down menu, and select “FTOOLS/Light Curve”. Click “OK”. After a few seconds, the light curve will appear! It looks like a thick black forest, and you can see that the source varies dramatically from about 25 counts/sec to well over 100 counts/sec. Now, let’s ZOOM in and see what’s happening over a small time interval. Place your cursor near the base of the curve (but in the actual plot, NOT below where the time_bin is labeled), near the mark 30000, and left click. While holding down the button, drag the cursor into a skinny tall box about a quarter of an inch wide, going from the bottom of the plot to the top. (Note: it is NOT important exactly where you select the data from; you just want to isolate a small portion of the curve.) After you have selected your box, left click again, and see the “new” curve. Do this again, and after one or two more tries, you will see that you have zoomed in on a portion of the curve where individual “pulses” can be easily seen. (If you make a mistake, or just want to try again, all you have to do is right click on the curve to go back to the original.) You can now easily see how often the x-ray light from Cen X-3 varies up and down. It looks like it’s doing this about every 5 seconds or so, right?

Activity 2: The Power Spectrum

Of course, we really want to see ALL the data at once, and do this we do what we call a power spectrum analysis. This is nothing more than trying to fit a sine curve to all the data, and see which periods emerge. For example, if we looked at plotted the brightness of daylight, as a function of time, we would find that a sine curve of period 24 hours would provide a reasonable fit to the data. Or, if you plotted when a grandfather clock chimed, you would that a one-hour sine curve would work, as well as one with a period of 15 minutes, if the clock chimed every quarter hour as well. This is a very powerful way to see quite accurately how some data might be varying over time.

So, go to the analysis menu and click on “FTOOLS/Power Spectrum”. After about half a minute, the power spectrum will appear! Notice that the plot consists of what appears to be a few sharp lines, indicating that only a few periods are present in the data. The highest peak is at about 0.2 Hz. This is 0.2 cycles per second, or 1 cycle about every 5 seconds, as you found out by looking at the data by eye. The second smaller peak is at exactly twice this frequency. This is just like the overtones present in a musical instrument; other frequencies that make a guitar playing a “G” sound different from a piano playing the “same” note.

Zoom in on the biggest peak, until you get a plot mostly of data, instead of blank space. This will be showing frequencies from about .2075 to .2085 Hz. Notice that the frequencies are not sharp; they appear to be changing slightly. How can that be?

Activity 3: Doppler shifts and orbital velocities

Other observations show a remarkable feature. Every 2.1 days the x-rays disappear for about 0.4 days. Then when they reappear, the pulses move towards higher frequencies, then move towards lower frequencies, back and forth, every 2 days. What we are apparently seeing is the x-ray source moving towards us (giving us a higher frequency Doppler shift) and then moving away from us, on the other side of the orbit (giving us lower frequencies). Our clock is telling us about the nature of the orbit of the x-ray source! The exact way the frequencies chance tell us that the orbit is essentially a circular one, with the x-ray source moving rapidly about another object. How fast? Use the Doppler shifts to find out (in a way similar to the analysis for 3C273).

Ans: The relative velocity of the source can be found by looking at extremes of the power spectrum. When it’s moving directly towards us, the frequency is 0.20835 Hz. When it’s moving directly away, 0.2078 Hz (approximately). So:

Change in frequency/frequency = v/c

(0.20835-0.2078)/2 = change in frequency = .00028

Why the factor of 2? Because with the two frequencies listed, we are finding out the velocity from one side of the orbit to the other; we want the velocity of the source around its center.

So: .00028/.208 = v/c or v= 400 km/sec.

We have found out how fast this object is moving, without leaving the Earth!

Activity 4: How big is the orbit?

Since we know that the x-ray source is eclipsed every two days, we can use the above answer to find out the radius of the orbit. Here we must assume that the orbit is “edge on”, i.e. we are seeing the source moving directly toward and away from us, not tilted. This is probably a good assumption, because if the orbit were tilted, the x-ray source would not have eclipses; it would just go around and around, like a yo-yo in a vertical loop, never obscured by your hand in the center. Find the size of the orbit.

Ans: C=2 * pi* r = v * Period (of orbit)

So, r= P/6.28 * 400 km/sec

r= 1.15 x 10**7 km

Compare this to the size of the Earth’s orbit around the Sun.

Activity 5: How bright is the x-ray source

As you may remember from previous activities, to do this we need to obtain the distance to the object. This can only be done accurately by getting an optical identification for the object. After much intensive work, an object was located in the approximate location of Cen X-3, and it was found that it too had very slight variations in intensity every 2.1 days. Named Krzeminski’s star, after its discoverer, it was found to be quite distant, about 10 kpc away. Now, you may use the light curve you found earlier and estimate Cen X-3’s peak luminosity. Hint: go back to activity 3 for 3C273 and find how to convert counts/sec to luminosity

Ans: the peak luminosity is about 125 counts/sec.

So,

Luminosity=4*pi*r**2 * 125 * 10**-11 ergs/sec (where r=distance to the object)

L= 4*3.14*10**45*125*10**-11 ergs/sec= 1.5 x 10**37 ergs/sec.

Note that this is LESS than the true value, since we are missing those “pile-up” photons mentioned earlier. But what is really important is that despite this, the number is about 10,000 the entire energy output of the Sun. How does this object do it?

Conclusion

It is truly remarkable that such a simple set of analyses from a single observation can tell us so much about the nature of the binary star system, Cen X-3. But we still have not found out how it works. Now, we must use our imagination and knowledge of astronomy and physics to come up with a model of the system.

First, we need to figure out what type of object can radiate such a prodigious amount of x-rays. This problem was solved in the 1960’s, when “pulsars” were first discovered. Only a neutron star can do this; an object so dense that the entire mass of the Sun would be compacted into a volume no bigger than Manhattan. But why would it vary every five seconds?

If an object has an intense magnetic field, millions of times more powerful than that of the Earth, particles streaming in from the companion star could be trained into a powerful stream of material that would be concentrated at the magnetic poles. This is very similar to what happens when aurorae (the “Northern Lights”) are produced on the Earth. The Sun spews forth particles from a solar storm, and the Earth catches them, and focuses them along the magnetic field lines towards the poles, where they give off the eerie light of an aurora. Now, if this magnetic field in the neutron star is not lined up with the rotation axis of the star, the “hot spots” at the magnetic poles would fly past our sight every revolution of the star, much like a lighthouse beacon illuminates the shoreline as it spins around.

So our picture is this: there are two stars in the system, a tiny dense one that is responsible for the x-rays we see, and a companion, which in this case turns out to be a supergiant star (one that would swallow up the Sun, Mercury, Earth and Mars if it were placed in the center of our solar system!) They revolve around each other every 2.1 days. The supergiant companion provides the “fuel” that the neutron star catches in its intense gravitational field. Then the magnetic field takes over, and funnels the material toward the magnetic poles of the neutron star. As these poles come into view, the intense x-rays emitted from the hot material are seen as “pulses” of radiation every 4.8 seconds.

So are we done? Not really. How did these diverse stars come to be associated with each other? The neutron star is at the end of its evolutionary path, but the supergiant is a very young star. How can exist at the same time, in the same place in the sky? As is usual with our probing of the mysteries of the Universe, as soon as we answer one question, another one pops into view, even more fascinating than the first. But for now, we must be content with our new found understanding of Cen X-3, and leave for another day the story about the evolution of these strange “clocks in the sky”.