Quiz 3
Chapter 11
The Doppler Shift of Pulsars
The Doppler shift describes how a wave is stretched or compressed as the source of the wave moves toward us or away from us. A pulsar can have a Doppler shift.
We can think of the pulses as peaks of a wave; we just don’t have the rest of the wave. And those peaks will be shifted by any motion.
Measuring Doppler Shift
We can measure a Doppler shift from a pulsar—sort of
The rub is that with atoms and molecules, we have a clearly defined rest frequency set by quantum physics. We can measure velocity directly because we know the rest frequency.
Demonstration
You can measure the Doppler shift of the ticks from any clock. To do this, find a small portable clock that gives off loud ticks. Tie it to a meter-long string and whirl it around your head.
You will hear a steady beat because the rotational period can be the clock is not changing its distance anything from seconds to from you, but someone standing milliseconds. All we can see nearby will hear the increase and measure is the observed decrease of the clock tick rate as the period, which is the clock on the string approaches the combination of its rest period and then recedes from them and any Doppler shift.
Doppler Shift
The terms “period” and “frequency” describe the same thing— namely, some sort of repetitive phenomenon—but they are the inverse of each other. Something that happened 10 times a second has a frequency of 10 hertz and a period of 0.1 seconds. Something that happens every 2 seconds has a period of 2 seconds and a frequency of 1/2 hertz.
The Doppler shift is in play for every pulsar in the sky, only we can’t use it because we don’t know the actual period of the pulsar. We can’t use the Doppler shift unless we see the period change.
In fact, the period we observe of every pulsar changes all the time because we’re observing pulsars from a moving platform—the Earth—which spins on its axis toward the east and away from the west. So, as we observe a pulsar rising, we see that its period increases, and as it sets, its period decreases.
The Earth also goes around the Sun at 30 kilometers per second or so. If we measure a pulsar in the spring of the year and then later in the fall, we will have seen a change in its period because of the Earth’s revolution around the Sun.
But we can correct for all of these motions and measure the Doppler shift of pulsars so precisely that we even need to make corrections to pulse arrival times because Earth’s motion is influenced by the gravity of the planet Jupiter.
This Doppler effect is stronger in some parts of the sky than others. Because we know the Earth’s velocity very accurately, this Doppler shift can be used to locate the position of pulsars quite precisely.
How Do We Measure Pulsars So Precisely?
There is radio noise in all of our measurements, and it comes from our electronic equipment, the galactic nonthermal background, the atmosphere, and other sources. The challenge of radio astronomy is how to dig the signal out of the noise.
But we have one important thing going for us: Noise is truly random. It fluctuates from instant to instant. If you average 2 noisy signals, the noise in one tends to cancel the noise in the other.
The amplitude of the noise—that is, the height of the noisy signal— decreases as the square root of the number of samples that you have. If you average 4 noisy signals, the noise in the average has decreased by a factor of 2.
We are able to detect pulsars, and almost every other signal in radio astronomy, because as we add data and average, the noise level decreases while the signal stays constant.
We can look at the pulsar and measure the pulse and average down the noise in time, but because pulsar radio emission is broadband, we can also measure it at a number of frequencies and average over frequency as well as time.
Because of interstellar dispersion, the pulses arrive at slightly different times at different frequencies. We have to shift the samples before adding them lest we blur out the signal. But we can measure the dispersion quite accurately, and the shift is easy.
Using signal-averaging techniques, we can also measure the period derivative, which is the technical name for the spin-down rate, and also the dispersion measure. This allows us to predict the arrival time of pulses many months into the future.
But how do we determine the period in the first place? One way is to average the data using a guess for the period. If we are off, the pulse is blurred because data taken at different times do not add in phase. If we are spot-on, the pulse appears at its sharpest. In detecting new pulsars and measuring their rotational periods, quite a lot of this searching goes on, and it’s computationally intensive.
Confirming Einstein’s Theory of Relativity
In 1972, Joseph Taylor, a young faculty member at the University of Massachusetts in Amherst, wrote a proposal to the National Science Foundation seeking funds to search for new pulsars using Puerto Rico’s Arecibo radio telescope, which is 1000 feet across and has no rival in its sensitivity to pulsars.
At the time of Taylor’s proposal, there were about 100 known pulsars, but no pulsar had been found in a binary system. Taylor got the grant, began to buy the hardware necessary to build a digital pulsar detection system, and recruited a graduate student, Russell Hulse, as a collaborator.
They did their search at frequencies around 400 megahertz. At every point in the sky where they took data, their programs searched more than 500,000 combinations of period, dispersion, and pulse shape seeking a detection.
If you take enough samples of random noise, every once in a while the noise combines to look like something real. But it’s not. Given that each spot on the sky would be analyzed in half a million different ways, Hulse set his threshold for detection at 7 standard deviations.
This means that a signal would have to be 7 times the expected noise level before the computer would flag it as possibly being real.
Taylor and Hulse took their system to the Arecibo telescope and began searching the sky for new pulsars. The observations were performed on and off for more than a year. In the end, they found 40 new pulsars. One in particular caught their eye. It had a period of around 60 milliseconds, which made it the second-fastest pulsar then known, second only to the Crab pulsar.
When Hulse re observed this particular pulsar several times, the pulsar’s period couldn’t be pinned down. He set up a new data analysis scheme with faster time sampling of the incoming signal. The new data showed that this pulsar’s period seemed to be changing in a regular way.
Then, Hulse realized that the changes could arise from a changing Doppler shift of the pulsar, which meant that it must be in orbit around another star—a pulsar in a binary system.
In short order, Joe Taylor arrived at Arecibo carrying new equipment that made study of this pulsar much easier. Here’s what we now know about this amazing system.
There are 2 neutron stars in orbit around each other. Both have about 1.4 times the mass of the Sun, and one of them is a pulsar with its radio beam intersected by Earth. They are quite close together; at their closest, they are only a few times farther apart than the Earth and Moon. They orbit around each other every 7.7 hours. That rapid orbit produces a large Doppler shift in pulse arrival times.
In classical physics, there is nothing to keep 2 objects from orbiting each other forever. But Albert Einstein changed all that with his theory of relativity. Under this theory, space is curved around massive objects, and as they interact gravitationally, they radiate gravitational waves. Eventually, the 2 neutron stars will merge as their orbit decays through radiation of gravitational waves.
The pulsar found by Hulse and Taylor confirmed this theory and provided direct experimental proof that changes in gravity travel at the speed of light. For this, they were both awarded the Nobel prize in Physics in 1993.
Pulsars can be used to probe the curvature of space predicted by Einstein’s theory of relativity. Every object distorts the space around it at least a little. When the pulsar is nearly exactly behind the star, its pulses have to travel an extra distance because of the distortion of space. When the pulsar is behind its companion, the pulses are delayed by the extra path they need to travel. This is a direct measurement of the curvature of space.
Chapter 10
Blobs in the Earth’s turbulent atmosphere act like little lenses or prisms, and the wind blows them past the star, making the star dance and twinkle. The technical term is scintillation.
The Moon, Sun, and planets don’t scintillate, because they have too large an angular size. The light from one point of the planet scintillates, but the light from another part of the planet scintillates in a different way, and all the different scintillations add up to a fairly smooth image, though a bit fuzzy.
It takes 2 things to make a radio source scintillate. First, the radio source has to have a small angular size. It doesn’t have to be small itself, but if it is big it has to be very far away to appear small in the sky. Objects with a negligible angular size are referred to as point sources. They appear in the sky as a point without any structure. A type of radio galaxy called a quasar is very bright and very distant and can look like a point source to us.
The second thing you need to make a point source scintillate is lumps of ionized gas to refract the radio waves and bend them. The signal from a quasar is turned into a lumpy image, and as the ionized gas clouds move around, we alternately see bright and then faint radio emission. That’s the signal of scintillation—a change in brightness with time as the radio source is focused and defocused on our telescope.
At radio wavelengths, the strength of scintillation increases with the wavelength squared. Longer wavelengths (lower frequencies) scintillate much more than higher frequencies. There are many regions of ionized gas between us and a distant quasar, but close to home there’s a pretty powerful lumpy ionized medium that radio waves have to traverse: the solar wind.
The Sun is putting out ionized gas every moment, and it flows past Earth. This is the solar wind. It arises from magnetic storm on the surface of the Sun. It has lumps, an while most of the time it doesn’t affect our radio measurements, at low frequencies it can make point radio sources scintillate
Hewish’s Telescope
Antony Hewish built a telescope to discover quasars by their scintillation from blobs in the solar wind. At the time, in the mid- 1960s, quasars were mysterious beasts, and they still are in many ways.
If you’re trying to understand the properties of something, you need large samples of objects or phenomena to separate the general from the particular. Hewish wanted to discover lots and lots of quasars, and in the process, he and his team discovered something else quite unexpected.
Because the scintillation is strongest at low frequencies, Hewish designed his telescope to work around 80 megahertz, at a wavelength of 3.7 meters, just below the FM band in the United States.
Hewish ended up covering about 4.5 acres—nearly 60 tennis courts—with his antennas. The antennas were just copper wire, strung between wooden poles.
Hewish’s graduate student, Jocelyn Bell Burnell, was involved in the construction and operation of the telescope.
When the Hewish telescope was finished, the observations began
The data were recorded on a chart with pen and ink. Because the scintillations are rapid, the paper moved fast and the pen could record fluctuations as short as 1/10 of a second. The telescope produced 4 beams on the sky in different directions, and the data were filtered in various ways, so there were about 100 feet of chart recording that came out every day—and had to be examined every day, by hand.
The Discovery of Pulsars
Radio telescope sidelobes can be reduced but not eliminated entirely, even from big modern dishes. The result is that radio telescopes have some sensitivity to signals coming from all directions, not just where the main beam is pointed.
Bell Burnell and Hewish’s telescope ran day and night, 7 days a week, and Bell Burnell had to sort through all that data. She discovered scintillating sources, which meant new quasars, and also lots of examples of terrestrial interference. There was also a strange faint signal—some “scruff” on the chart recordings—that didn’t look like scintillation and didn’t look like interference.
After a while, Bell Burnell recognized that one particular patch of scruff had reappeared several times from about the same fixed direction in space. That was peculiar. Something was producing regular radio pulses. It didn’t seem fixed to the Earth but appeared earlier each day, like something fixed to the stars.
Could this be some signal from another civilization? They looked at it with another radio telescope at Cambridge, and after a few fumbles detected it. So, it was not being generated in their own equipment.
Study of thousands of feet of charts showed a few other directions with pulsing radio sources. They had discovered something new: pulsars.
They reported their results in a paper in February 1968. By late spring, more pulsars had been discovered. Pulsars were not only real, but there seemed to be quite a lot of them. But what were they?
We now understand that a pulsar is the remnant of a massive star that exploded as a supernova at the end of its life. In order for a star to become a supernova, it has to have times the mass of the Sun.
These massive stars are short-lived, and upon exploding, their interior collapses and forces electrons onto protons to form neutrons, thus producing a neutron star.
A cubic inch of a neutron star—about This ball of matter is incredibly the size of a sugar cube—contains dense—as dense as matter can the same mass as Mount Everest
A neutron particle left by itself in free space decays in just a few minutes into a proton and electron, but bound up in a bundle with others, it’s quite stable.
The neutron star has a diameter of just a few kilometers. It has a mass between 1 and 2 times the mass of the Sun, so that’s a lot of matter compressed into a tiny volume
A star has a magnetic field, just as the Earth does. That magnetic field is threaded through the interior of a star, and when the star collapses, it drags the field down with it, amplifying it enormously. We’re left with a collapsed stellar core that’s rotating rapidly because of conservation of angular momentum.
Earth’s north magnetic pole is not at the North Pole. It’s the same for a neutron star; a neutron star’s magnetic pole can be offset from its rotational pole. The magnetic field produces strong radio emission, and if the magnetic pole sweeps past us, we see it as a radio pulse. And we call it a pulsar.
The pulses from a pulsar are extremely regular. The first pulsars that were detected had periods of about 1 second, meaning that the neutron star was spinning around about once a second. But now we have pulsars whose periods span from a few seconds to a few thousandths of a second.
The pulsars are losing energy as they rotate, so they are slowing slightly, but very predictably. Pulsars slow down and eventually die.
The discovery of pulsars initiated a flurry of observations around the world. Although pulsars were discovered in observations at 80 megahertz, in modern times they’re most commonly observed between 300 megahertz and 3 megahertz using large single dishes.
In a typical pulsar pulse, there’s a main pulse and sometimes a secondary pulse, or interpulse. If we think about the pulsar as having 2 magnetic poles, then it makes sense that sometimes we see emission from both. The average pulse shape is very stable, but any one individual pulse may show large variations in intensity and shape from the average.
How do pulsars produce radio radiation in narrow beams? Nearly 50 years after their discovery, there’s still lots of mystery about the basic pulsar emission mechanism. The emission is certainly nonthermal. It’s broadband, and its intensity increases rapidly to lower frequencies, opposite of the Planck curve—a clear sign of nonthermal emission. But what exactly makes it?
We know that energetic particles in magnetic fields produce nonthermal emission. Pulsars have very strong magnetic fields, far in excess of anything that we could produce on Earth. All we need is particles. It’s likely that charged particles from the neutron star’s surface are accelerated by intense electric fields.
Spiraling in the magnetic fields, these particles emit high-energy photons, which in turn are converted into electrons and positrons by the intense magnetic field. It is these electrons and positrons that produce the radio emission we observe. This sounds plausible, but many details still don’t fit this picture.
The first observers of pulsars discovered that the arrival time of pulses depended on the frequency that was observed. A given pulse arrived first at the higher frequencies and then progressively later at lower and lower frequencies. But all frequencies left the pulsar at the same time. The delay comes from interstellar electrons.
Ionized gas between us and the pulsar delays the pulse arrival. The size of the delay increases as frequency decreases. This process is called dispersion. It depends on the amount of ionized gas between us and the pulsar.
This is important for 2 reasons. First, man made signals from Earth don’t travel through the interstellar medium to reach us, so their pulses are not dispersed unless they’re transmitted that way. Looking for the signature of dispersion gives us one way to discriminate between pulses from space and terrestrial interference.
Second, the amount of dispersion gives us an estimate of the distance to the pulsar. The farther the pulsar, the more it should be dispersed. There are many uncertainties, but it’s so difficult to get distances in radio astronomy that anything that gives us something, even approximating a distance, is grasped like a lifesaver.