Clocks in the Sky Ever since the dawn of humanity, we have been awed by the mysteries of time. Over the millenia, 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 sun-dials 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, that can be shown to 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 sucessive 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, is responsible for 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 sun-spot 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 20th 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 (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. (More details??) Not only can we tell the size of objects using the clocks, 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...)