It is actually of tremendous good, because we can turn the tables and use general relativity to weigh the system! If we assume that general relativity is correct, then the predicted periastron advance depends on only one unmeasured variable, the total mass of the two bodies. Therefore, the measured periastron advance tells us what the total mass must be in order for the predicted and measured values to agree. From the fall 1974 observations, the inferred total mass was about 2.6 solar masses. Eventually, the periastron advance could be measured so accurately, 4.226585 degrees per year, that the total mass of the system was pinned down to 2.8284 solar masses. This was a triumph for general relativity. Here, for the first time, the theory was used as an active tool in making an astrophysical measurement, in this case the determination of the total mass of a distant system to high precision.
The relativists’ intuition that this system would be a new laboratory for Einstein’s theory was confirmed. But there was more to come.
During the first few months of observations of the pulsar, it was realized that this was a very unusual pulsar, over and above it being in a binary system. Once the strange variations in its observed pulse period were seen to be due to Doppler shifts resulting from its orbital motion, these variations could be removed from the data, allowing the observers to examine the intrinsic pulsing of the object, as if it were at rest in space. Its intrinsic pulse period was 0.05903 seconds, but if it was slowing down, as do other pulsars, it was doing so at an unbelievably low rate. It took almost an entire year of observation to detect any change whatsoever in the pulse period, and when the data were finally good enough to measure a change, it turned out to be only a quarter of a nanosecond per year. This was 50,000 times smaller than the rate at which the Crab pulsar’s period changed. Clearly, any friction that the spinning neutron star was experiencing was very, very small, a fact that was consistent with the observation that its radio signal is so feeble that Hulse almost missed it. At this rate, the pulsar would change its period by only half a percent in a million years. The steadiness and constancy of this pulsar made it one of the best timepieces the universe had ever seen! In later years, many rapidly spinning but very steady pulsars would be detected; we will return to them in Chapter 9.
This remarkable steadiness made it possible for the observers to change how they made the measurements. Instead of measuring pulse periods (the difference in time between adjacent pulses) and the changes induced in the periods by the Doppler shift and various relativistic effects, they were able to measure the arrival times of individual pulses. The pulsar was so steady that Taylor and his colleagues could keep track of the radio pulses as they came into the telescope, and even when they had to interrupt the observations for long periods of time, while they returned to their home universities for such “mundane” duties as teaching, or while the telescope was used for other observing programs, they could return to the telescope after such breaks and pick up the incoming train of pulses without losing track of a single beep. To see why this leads to a big improvement in accuracy, consider a simple example. Suppose you can measure arrival times to a basic accuracy of a hundredth of a second. If the pulse period is 1 second, that implies that you can measure the period to 1 percent. But now if you measure the arrival time of pulse number 1 to a hundredth of a second, and then wait 50 seconds and measure the arrival time of pulse number 51 to the same precision, you will have measured the combined period of 50 pulses to a hundredth of a second, or that of a single pulse to one part in 5,000. How do you know that it was pulse 51 and not pulse 39 or 78? Because knowing the period to one part in 100, you know that the error in arrival time after 50 seconds is less than a whole pulse period, and so the pulse that arrives can’t be anything but number 51.
Eventually, this arrival-time technique allowed them to determine the characteristics of the pulsar and the orbit with accuracies that began to boggle the mind: for the intrinsic pulsar period, 0.059030003217813 seconds; for the rate at which the intrinsic pulse period was increasing, 0.272 nanoseconds per year; for the rate of periastron advance, 4.226585 degrees per year; for the orbital period, 27906.9795865 seconds. Because the pulsar period changes by the quoted amount in the last three digits each year, when scientists refer to a measured pulsar period they must also refer to a specific date when that value would be true; in this case, the conventional date is 11 December 2003.
There was more to this accuracy than just an impressive string of significant digits. It also yielded two further relativistic dividends. The first of these was another example of applied relativity, or relativity as the astrophysicist’s friend. Beside the ordinary shift of the pulses’ arrival times caused by the varying orbital position of the pulsar, there are two other phenomena that can affect it, both relativistic in nature. The first is the time dilation of special relativity: because the pulsar is moving around the companion with a high velocity, the pulse period measured by an observer foolish enough to sit on its surface (he would, of course, be crushed to nuclear density) is shorter than the period observed by us. In other words, from our point of view the pulsar clock slows down because of its velocity. Because the orbital velocity varies during the orbit, from a maximum at periastron to a minimum at apastron, the amount of slowing down will be variable, but will repeat itself each orbit. The second relativistic effect is the gravitational redshift, a consequence of the principle of equivalence, as we have already seen in Chapter 2. The pulsar moves in the gravitational field of its companion, while we the observers are at a very great distance; thus, the period of the pulsar is redshifted, or lengthened, just as the period (or the inverse of the frequency) of a spectral line from the Sun is lengthened. This lengthening of the period is also variable because the distance between the pulsar and the companion varies from periastron to apastron, and it also repeats itself each orbit.
The combined effect of these two phenomena is a periodic up and down variation in the observed arrival times, over and above that produced by the orbital position. But whereas the orbital motion changed the pulse period in the fifth decimal place, these effects, being relativistic, are much smaller, changing the pulse period only beginning at the eighth decimal place. It is extremely difficult to measure such a small periodic variation, given the inevitable noise and fluctuations in such sensitive data, but within four years of continual observation and improvement in the methods, the effect was found, and the size of the maximum variation was 184 nanoseconds in the pulse period. Again, as with the periastron, this observation does not test anything, because the predicted effect turns out to contain another unknown parameter, namely the relative masses of the two bodies in the system. The periastron advance gives us the total mass, but not the mass of each body. Therefore we can once again be “applied relativists” and use the measured value of this new effect to determine the relative masses. The result was 1.438 solar masses for the pulsar, and 1.390 solar masses for the companion, good to about 0.07 percent. The understanding and application of relativistic effects here played a central role in the first precise determination of the mass of a neutron star.
These results for the masses of the two bodies were also interesting because they were consistent with what astrophysicists thought about the companion to the pulsar. Because it has never been seen directly, either in optical, radio or X-ray emission, we must use some detective work to guess what the companion might be. It certainly cannot be an ordinary star like the Sun, because the orbital separation between the pulsar and the companion is only about a solar radius. If the companion were Sun-like, the pulsar would be plowing its way through the companion’s outer atmosphere of hot gas, and this would cause severe distortions in the radio pulses that must propagate out of this gas. Such distortions are not seen. Therefore, the companion must be much smaller, yet still have 1.4 times the mass of the Sun. Such astronomical objects are called “compact” objects, and astrophysicists know of only three kinds: white dwarfs, neutron stars and black holes.
The currently favored cand
idate for the companion is another neutron star, based on computer simulations of how this system might have formed from an earlier binary system of two massive stars that then undergo a series of supernova explosions to leave two neutron-star cinders. The fact that both masses turn out to be almost the same is consistent with the observation that in these computer models, the central core of the pre-supernova star tends to have a mass close to 1.4 solar masses. After the outer shell of each star is blown away, the leftover neutron stars each have about this mass. This mass is called the Chandrasekhar mass, after the astrophysicist Subrahmanyan Chandrasekhar, who determined in 1930 that this value was the maximum mass possible for a white dwarf (this discovery earned “Chandra” a share of the Nobel Prize in Physics in 1983). Because a pre-supernova core is similar in many respects to a white dwarf, it is not surprising that this special mass crops up here as well.
According to these models, the pulsar that Hulse detected was formed in the first supernova explosion, which left a spinning pulsar with a strong magnetic field but without really affecting the companion star. But the fate of such a pulsar in isolation is to spin down, causing its magnetic field to weaken to such a degree that it no longer generates a detectable pulsar beam. This pulsar followed this track. Meanwhile, the massive companion star evolved toward its own inevitable supernova explosion, but first it underwent an expansion of its gaseous atmosphere, a common occurrence in the evolution of massive stars. The pulsar skimmed across this atmosphere, getting spun up to a rapid rotational speed, just as a beach ball spins up as it skims across water. It ended up as a weakly magnetized, rapidly spinning pulsar with a weak pulsar beam, pretty much as Hulse detected. The companion star finally exploded, leaving a second pulsar, again without affecting the first pulsar, and eventually the companion pulsar spun down enough that its beam was too weak to detect. The final system, then, is an old neutron star “recycled” as a fast pulsar (the one Hulse detected), and a young neutron star but “dead” pulsar (the one Hulse did not detect).
But the biggest payoff of the binary pulsar was yet to come.
General relativity predicts that binary star systems emit gravitational radiation. We will devote most of Chapter 7 to a discussion of the history and nature of gravitational waves. For our purposes here, the main thing we need to know is that by 1974, gravitational radiation was an active subject, and relativists were dying to find some. Even though Joseph Weber of the University of Maryland had claimed detection of waves as early as 1968, later experiments by other workers had failed to confirm his results, and the general feeling was that gravitational waves had not yet been found. Therefore, when the binary pulsar was discovered, and it was seen to be a new laboratory for relativistic effects, it seemed like a godsend. The binary pulsar could be used in the search for gravitational waves.
But not in the obvious sense. Because the binary pulsar is 29,000 light years away, the gravitational radiation that it emits is so weak by the time it reaches the Earth, and is of such low frequency (about 6 cycles per day), that it is undetectable by any detectors of today or the foreseeable future. On the other hand, general relativity predicts that gravitational waves carry energy away from the system, and therefore the system must be losing energy. How will that loss manifest itself? The most important way is in the orbital motion of the two bodies, because after all, it is the orbital motion that is responsible for the emission of the waves. A loss of orbital energy produces a speed-up of the two bodies and a decrease in their orbital separation. This seemingly contradictory statement can be understood when you realize that the total orbital energy of a binary system has two parts: a kinetic energy associated with the motion of the bodies, and a gravitational potential energy associated with the gravitational force of attraction between them. So although a speed-up of the bodies causes their kinetic energy to increase, a decrease in separation causes their potential energy to decrease by about twice as much, so the net effect is a decrease in energy. The same phenomenon happens, for example, when an Earth satellite loses energy because of friction against the residual air in the upper atmosphere; as it falls toward Earth it goes faster and faster, yet its total energy is declining, being lost in this case to heat. In the case of the binary pulsar, the speeding up combined with the decreasing separation will cause the time required for a complete orbit, the orbital period, to decrease.
Here was a way to detect gravitational radiation, albeit somewhat indirectly, and a number of relativists pointed out this new possibility in the fall of 1974, soon after the discovery of the binary pulsar. As we will see in Chapter 7, the effects of gravitational radiation are exceedingly weak, and this was no exception. The predicted rate at which the 27,000 second orbital period should decrease was only on the order of some tens of microseconds per year. Although this was an exciting possibility, the small size of the effect was daunting, and some thought it would take ten to fifteen years of continual observation to detect it.
Now flash forward just four years, to December 1978: the Ninth Texas Symposium on Relativistic Astrophysics, this time in Munich, Germany (Munich is in the state of Bavaria, sometimes considered the Texas of Germany). Joe Taylor was scheduled to give a talk on the binary pulsar. Rumor had it that he had a big announcement, and only a few insiders knew what it was. Cliff knew because he was scheduled to follow Taylor to present the theoretical interpretation of his results. A press conference had been set up for later in the day. In a succinct, fifteen-minute talk (a longer, more detailed lecture was scheduled for the following day), Taylor presented the bottom line: after only four years of data taking and analysis they had succeeded in detecting a decrease in the orbital period of the binary system, and the amount agreed with the prediction of general relativity, within the observational errors. This beautiful confirmation of an important prediction of the theory was a fitting way to open 1979, the centenary year of Einstein’s birth.
It turned out that the incredible stability of the pulsar clock, together with some elegant and sophisticated techniques for taking and analyzing the data from the Arecibo telescope that Taylor and his team had developed, resulted in such improvements in accuracy that they were able to beat by a wide margin the projected timetable of ten years to see the effect. These improvements at the same time allowed them to measure the effects of the gravitational redshift and time dilation, and thereby measure the mass of the pulsar and of the companion separately. This was important because the prediction that general relativity makes for the energy loss rate depends on these masses, as well as on other known parameters of the system, so they needed to be known before a definite prediction could be made. With the values of about 1.4 solar masses for both stars, general relativity makes a prediction of 75 microseconds per year for the orbital period decrease. The most recent analysis of the data shows agreement with the prediction to better than 0.2 percent. The 1993 Nobel Prize in Physics was awarded to Hulse and Taylor for the discovery of the system and for the confirmation of the existence of gravitational radiation.
These results triggered intensive searches for more binary pulsars at the world’s largest radio telescopes, resulting in an explosion in the number of known pulsars. More than 2,600 pulsars are currently known. What was once “the” binary pulsar has now joined around 290 other pulsars in binary systems. Most are utterly uninteresting for general relativity because they are so widely separated that the effects of the theory are unimportant or undetectable. A few pulsars are known to have planets, presumably not particularly habitable. Only about a hundred of the binaries have orbital periods shorter than a day, which makes them potential fodder for relativity. Some have white dwarf companions, while others appear quite similar to the original Hulse–Taylor binary pulsar. Two systems stand out, however.
The first was discovered in 2003 by Marta Burgay and collaborators using the Parkes 64 meter radio telescope in Australia. This system turned out to be full of surprises. The pulsar’s orbital period was a factor of three shorter than that of the Hulse–Tay
lor binary, making it even more compact and relativistically interesting. The measured periastron advance was a remarkable 17 degrees per year, indicating a total mass of about 2.6 solar masses. A few months after the discovery, followup observations detected weak pulses from the companion! This was the first (and so far the only) double pulsar detected. In fact the two pulsars fit the same theoretical profile as the Hulse–Taylor system: pulsar A was evidently an old recycled pulsar, spun up to a spin period of only 23 milliseconds, while pulsar B, with a longer spin period of 2.8 seconds and a very feeble pulsed signal, was an almost dead, younger pulsar.
Because the variations of the pulses of both pulsars could be tracked, the two orbits could be fixed with more certainty than was the case for the Hulse–Taylor system. From these observations, along with the periastron advance, it was possible to determine the two masses directly: 1.338 and 1.249 solar masses for the main pulsar and the companion pulsar respectively. This in turn could be shown to imply that the orbit was almost perfectly edge-on relative to the line of sight. As a consequence, once per orbit, the signal from the main pulsar would pass close to the companion neutron star, and would therefore experience the Shapiro time delay in its propagation. This delay was measured, and the results agreed completely with the predicted delay, based on the measured mass of the companion. The same effect presumably occurred for the signal from the companion passing by the primary, but the companion’s pulsed signal was too weak and ragged to be useful for measuring such tiny effects. The effect of time dilation and the gravitational redshift on the primary’s observed pulse period was measured, and agreed with the prediction of general relativity. The decreasing orbit period was also measured, and it too agreed with the theory’s prediction for gravitational radiation energy loss, with a precision today even better than that for the Hulse–Taylor pulsar.
Is Einstein Still Right? Page 15
