February 29, 2020 0

5.3 Pulsars [Astronomy: State of the Art]

What’s left behind when a massive star collapses
at the end of its life? In particular, when the core is massive enough that it can overcome
electron degeneracy pressure, so the endpoint is not a white dwarf. The disruptive explosion
leading to a supernova—in principle—could detonate the entire material obliterating the star,
and sending it all into space, and leaving nothing behind. Thats one possible outcome, but more likely, in terms of theoretical calculations, is that a compressed state of matter will
be left behind—far eclipsing the density of a white dwarf. If the core is more than about one
and a half times the mass of the sun but less than about three times the mass of the sun,
the new collapse state, consisting of pure neutron material, because the protons and electrons coalesced in a reverse version of the beta decay process. The pure neutron material will be supported by neutron degeneracy
pressure. The fact that neutrons are unable to occupy exactly the same quantum states
as predicted by Ferme. This is a standard part of quantum theory so although neutron matter
may sound very exotic, its physical properties are relatively well understood. So in this
situation, where the core is more massive than a white dwarf, it will collapse to the state
equivalent to a large atomic nucleus, with an atomic number of 10^54, a phenomenal
state of matter, you can almost imagine the neutrons sitting next to each other like grains
of sand touching, or eggs in an egg box. The density of matter is the same as the density
of matter in the atomic nucleus—a trillion grams per cubic centimeter, in this situation
a star more massive than the sun has squashed by gravity to a diameter of ten or twenty
kilometers—the size of a small city. As the star collapses it entrains magnetic
field, trapping it within the plasma and just as by conservation of energy, the star must heat
up when it collapses. The star also must increase the density of its magnetic field lines as
it collapse and they are squeezed in the shrinking plasma. So in principle, a collapsed stellar
remnant will have a phenomenally high magnetic field. By conservation of angular momentum,
the spin rate will also increase dramatically. So the object maybe spinning much faster than
it was as a normal main sequence star. The properties of these objects—called neutron stars were predicted in the 1930s much of the work was done by Robert Oppenheimer who went on later, to become architect of the Manhattan project, and then suffered an ugly end to his career when
he was black listed for political reasons and banned from doing government sponsored
research. Oppenheimer was a brilliant theorist, one of the best in physics in the last century.
This was an era before computers. All his calculations on the state of neutron stars were done with
pure mathematics and physics. He predicted that there should be stars situated in space
with the density equivalent to that of an atomic nucleus, spinning, perhaps, as fast as
one or more times per second, and with magnetic fields trillions of times more than the magnetic
fields of the Earth. The Earth’s magnetic field is about one gauss. For comparison,
a refrigerator magnet is about 100 gauss, and a sunspot is threaded by a magnetic field
of about 1,000 gauss. White dwarf is a fairly compact state of a star, but it’s
magnetic field is about 1,000,000 gauss. Neutron star magnetic fields are a million
times larger—several trillion gauss. For several decades the idea and prediction of
neutron stars just sat in the literature. There was no way to test it. How could you
possibly see a tiny remnant of a star, emitting no energy—no obvious way of detecting it. In fact, observers essentially dismissed the prediction of neutron stars as some esoteric piece of theory
that couldn’t be possibly be tested. We flash forward thirty years to the University of
Cambridge, where a young graduate student, Jocelyn Bell, is taking radio observations of
several regions of the sky, trying to map out radio sources. As she’s observing with this
early radio antenna, she observes a radio source in the constellation Vulpicula. Unlike most radio
sources, it’s pulsing and when she checks it against the standard atomic clock that they
have access to, she’s amazed to discover that it’s a more precise timekeeping object than
the atomic clock itself. The radio trace of the pulse shows that the intensity varies
from one pulse to the next, but the period is absolutely lock steady. It’s an astronomical metronome more accurate than one part in a trillion. She talked to her research advisor, Tony Hewish, and they puzzled over this. They called it a pulsar, but they had no idea what it was. In fact,
the regularity of the pulses was so confusing that they jokingly referred to the first few
found as LGM 1, LGM 2, LGM 3—meaning little green men. The supposition being that only
an intelligent civilization far beyond Earth could generate radio signals with this accurate
a frequency. Jocelyn Bell followed a classic scientific method pursuing her discovery.
As the number of pulsars found with that radio telescope increased, she tracked down and ruled
out alternative sources of the emission. In particular, since the sources rose and set four minutes
earlier each day, it’s clear that they were keeping sidereal, or star time, rather than terrestrial
time. But she went further, ruling out other possible sources of radio emission, such as
faulty alternators on nearby cars, or other radio equipment in nearby villages. Eventually she and her advisor were convinced that they discovered something important, but they were still puzzled as to
what it might be. Then Tony Hewish, her advisor, made the connection, with the long forgotten
papers in the theoretical literature on the prediction of neutron stars. Here could be
a star rotating that rapidly, in a collapsed state. Were pulsars the long sought after speculated neutron stars? The answer turns out to be: yes. In particular it’s now thought that most neutron
stars are indeed completely invisible, and emit no radiation of any kind, but the small
set of neutrons stars have imperfections on their crusts, where at the surface cyclotron
emission is generated. This is the low frequency radiation resulting from electron spiral in
the intense magnetic field of the neutron star. This radio emission, resulting from electrons
near the surface of the neutron star, emerges on hot spots on the crust of the neutron star,
and because this star is spinning, those hot spots project their radiation like a beam
into space that pivots around the sky with a rotation frequency of the neutron star itself. So, as was realized
in 1967, pulsars are the subset of neutron stars where there is radio emission from the surface,
cyclotron emission where the beam goes into space, and as the star rotates, sweeps across
the Earth to be detected by radio telescopes. The pulsing is there for sequentially the
beam passing over the Earth time after time as the star rotates. And because the star is so
dense and small, it rotates rapidly, so the pulses are quite frequent. Radio catalogs
now contain three or more thousand pulsars, mostly in the plane of the Milky Way galaxy, and most within distances of hundreds of light years from the Earth. Every now and then a pulsar is
found where the cyclotron emission extends to higher frequencies, and is visible optically.
There is only a hand full of them, but they include the most famous pulsar of all, the
pulsar at the center if the Crab Nebula, the dying star detonated in 1054 A.D. This
pulsar has a period of exactly a third of a second, and has been observed pulsing in
optical light as well as in radio-waves. In this picture—an animation of the Crab Nebula—we see the neutron star at the center. The surrounding region is detritus from the
supernova the went off a millennium ago. An x-ray telescope, such as the Chandra Observatory, shows that gas glowing, and actually changing its structure from year to year, because of
the changes in density, as the radiation passes through the interstellar medium. It’s worth
taking a moment to let settle in, exactly how exotic and bizarre a neutron star is.
A neutron star is an entire star the size of the sun—a million kilometers—that has collapsed to the size of a city that has magnetic field trillions of times of that of the Earth, and
is spinning hundred of times per-minute. Pulsars with a wide range of frequencies have now
been detected, the early pulsars mostly had periods within a second and about tenth of
a second. The longest pulsars are rarely more than a few seconds in period. The most rapid
pulsars are called millisecond pulsars, because their spin rates are hundreds of times a second. Let’s listen to a sonification of three different pulsars. This is the trace of the
radiowaves, literally turned into a sound wave so that you can hear the frequency of the pulse
passing over the Earth as the nutron star (and pulsar) spin. The first example is a long
period pulsar with a period of about 1.4 seconds, sounding more or less like a metronome (Pulsar sound). The second is a fairly rapid pulsar revolving at 33 revolutions per second—a period
of about thirty milliseconds (pulsar sound) The third example is one of the most rapid
pulsars known. It’s going so fast that it emits a whine—above middle C on the piano (pulsar sound). Again, this is an object the mass of a star, and the size of a city, spinning six hundred
times per second in space. Neutron stars have been studied in sufficient numbers, and in
enough detail to produce other interesting science. Indirect detection gravity waves were
shown when a binary pulsar has its period slowly increasing, energy lost in the binary
system and in the spin down rate of the pulsars matched exactly the prediction from general
relativity of the release of unseen gravity waves from the system. Pulsars are brillant
time keeping peaces—accurate in the best cases to one part in 10^15. They’re natures best
clocks, but they’re not perfect. Occasionally the stresses in the spinning neutron material
adjust or alter the crust, in a form of staquake unique to neutrons stars. In a neutron
starquake the strength of the pulses and their frequency changes abruptly, to form
a new situation as the crust rearranges. This has been observed a number of times. There
is also a very slow, but steady and detectable spin down rate in most pulsars, caused by the release
of gravity waves. In another bizarre consequence that’s a predict of general relativity: if we were
able to stare at a neutron star, we would see more than half of its surface, because light
is bent so much, close to the neutron star, that it passes around the backside—meaning we
could see behind the half of the surface we expect to see. As a last piece of pulsar exotica,
consider this: to be correct, historically, the first exoplanets to be discovered were
not 51 peg, and its neighbors, in 1995; The first exoplanet was found in 1992 orbiting
a pulsar. As the discoverers are happy to point out, the first planets were not found in 1995.
The pulsar 1257 + 12 had slight irregularities in its timing, which were used to infer the
presents of planets. The exquisite precision of the pulsar as a metronome, allowed these
deviations to be modeled as planets. Not just a planet the size of the Earth, but even a planet the size of the
moon. It’s likely that these planets were not given as much attention as the should have been,
because nobody expected planets to be formed around the pulsar, and nobody could image how
there might be life around the dead remnants of a massive star. It’s still a little unclear
how pulsar planets formed, and only a few other examples have been found, but most likely they form out of the debris left over at the end of a star’s life. When a collapsed stellar
remnant is between one and a half and 3x the mass of the sun, it collapses to an exotic
state of matter that is esentually pure neutron material. The density of this is the same
that of an atomic nucleus of an atomic number of 10^54. Neutron stars where predicted,
and for three decades nobody expected to be able to observe them. Until the accidental discovery of pulsars,
the subset of neutron stars where cyclotron emission produces radio waves that sweep across radio telescopes with a spin rate of a neutron star. Several thousand pulsars are known, and
they’re representatives of the much larger unseen population of neutron stars in the galaxy.
Spin rates can be as extreme as six or seven hundred times per second, and the magnetic
fields can exceed a trillion gauss. These are truly extraordinary objects, the size of a
city, but with the mass of the sun.

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