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An introduction to…
Pulsars!
Paulo César C. Freire
Cornell University / Arecibo Observatory
In this talk:

1930s: Neutron star basics.

The Crab Nebula.

1967: The discovery of the first pulsar.

1968: The discovery of the Crab Pulsar.
White dwarfs * The
Chandrasekhar limit * The neutron * Neutron stars in
supernovae.
Supernovae * M1 * What powers the
Crab nebula? * Pacini’s idea.
Emission
characteristics * Propagation effects * What is a pulsar?
The
discovery of the Crab pulsar * Pulsars are rotating neutron
stars! * The basic pulsar emission model.
In this talk (continued):

Pulsar Timing.

1974: The discovery of PSR B1913+16.

1982: The discovery of PSR B1937+21.
Energy emission * Characteristic ages *
Magnetic Fields * Glitches and timing noise.
discovery of the binary pulsar * pulsars as gravitational
laboratories.
The
Discovery of PSR B1937+21 * Millisecond pulsars as probes of
the equation of state * Formation of millisecond pulsars * Timing
accuracy.
Not in this talk:

Pulsar signal detection.

Pulsar surveys. Avoiding dispersion and scattering *

Historical surveys. The Hulse-Taylor surveys * Arecibo

Applications of timing of millisecond pulsars.
Filter banks * auto-correlators
* baseband systems * incoherent de-dispersion * coherent dedispersion.
Optimal survey parameters * Dedispersion and Fourier
transforms * Harmonic folding * Confirmation observations *
Accelerated surveys.
high-latitude surveys * The Molonglo survey * 20-cm surveys of
the Galactic plane * Globular cluster surveys.
In this talk:

1930s: Neutron star basics.

The Crab Nebula.

1967: The discovery of the first pulsar.

1968: The discovery of the Crab Pulsar.
White dwarfs * The
Chandrasekhar limit * The neutron * Neutron stars in
supernovae.
Supernovae * M1 * What powers the
Crab nebula? * Pacini’s idea.
Emission
characteristics * Propagation effects * What is a pulsar?
The
discovery of the Crab pulsar * Pulsars are rotating neutron
stars! * The basic pulsar emission model.
1930’s: Neutron stars!
The Helix Nebula,
450 light-years away
in Aquarius.

At the end of the lives of most stars, the outer layers of the star
are expelled and form a Planetary Nebula. The core of the star
remains bound, and forms a white dwarf.
Neutron stars!
Sirius B (arrow), the first white
Dwarf discovered, orbits the much
brighter Sirius A with an orbital
period of 50 years.
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
These Earth-sized objects have incredible densities, of the
order of several ton/cm3.
In the 1920’s, using Pauli’s exclusion principle for electrons,
astronomers finally understood that white dwarfs are held
against gravity by degeneracy pressure.
Neutron stars!
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
In 1931, S. Chandrasekhar
(1910-1995) predicts that
above a mass of 1.4 solar
masses, the gravitational field
of a white dwarf star should
make it collapse! (Ap.J., 74,
81-82). He was awarded the
1983 Nobel Prize in Physics for
this fundamental prediction!
This happens because
relativistic electrons behave
like photons!!!
Neutron stars!

Polytropic equation
of state (EOS):
p(r) = k. ρ(r) Γ


For non-relativistic
electrons, Γ = 5/3
For relativistic
electrons, Γ = 4/3,
as for photons.
Mass-radius relation for white dwarfs.
Neutron stars!
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What happens to a white dwarf with a mass over 1.4 solar
masses? Does it just keep collapsing until it forms a black hole?
…Or does it form something else?
In 1932, James Chadwick, then at the Cavendish Laboratory in
Cambridge, England, discovers the neutron. He got the Nobel
physics prize in 1935 for this discovery.
Neutron stars!
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In 1934, Walter Baade and Fritz Zwicky proposed on a paper
about supernovae that extensive stellar collapse of a heavy star
during a supernova event should lead to the formation of a
dense core of neutrons (a neutron star!) at the center of the
SN remnant.
The neutrons form through INVERSE BETA DECAY, which is
possible under the enormous pressures in the collapsing core.
This produces extreme amounts of neutrino emission!!!
Neutron stars!

This prediction has now
been verified! The SN
1987A event created a
shower of neutrinos in
the world’s detectors.
This accounts for 99%
of the energy of the
supernova!
Neutron stars!
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No one knows what happened to the remnant of the star that
exploded as SN 1987 A (Sanduleak –69 202). Was a neutron star
formed? Should we be able to see it?
Landau (1938) and Oppenheimer and Volkoff (1939) calculated the
radius of these objects. They predicted radii of the order of 10 km!
Such small objects should be undetectable by any telescope at the
vast distances to the nearest supernova remnants (normally many
thousands of light-years).
Neutron stars!

The exact relation between mass and radius of a neutron star
depends on the Equation of State for cold matter. This is still not
very well known…
In this talk:

1930s: Neutron star basics.

The Crab Nebula.

1967: The discovery of the first pulsar.

1968: The discovery of the Crab Pulsar.
White dwarfs * The
Chandrasekhar limit * The neutron * Neutron stars in
supernovae.
Supernovae * M1 * What powers the
Crab nebula? * Pacini’s idea.
Emission
characteristics * Propagation effects * What is a pulsar?
The
discovery of the Crab pulsar * Pulsars are rotating neutron
stars! * The basic pulsar emission model.
The Crab Nebula


This was discovered in
Taurus by John Bevis in
1731.
Charles Messier looked at
it and thought he had
found comet Halley in its
1758 return. To prevent
such further occurrences,
he compiled a list of all
nebulosities known to him.
For this reason, the Crab
Nebula is also known as
M1.
The Crab Nebula
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In the 1940’s, it was found that the supernova event that
resulted in the Crab Nebula was witnessed by Chinese
astronomers in the year 1054.
Radio emission from the Crab nebula was first detected by
Bolton, Stanley and Slee (1949). It is one of the most powerful
radio sources known, with a flux of 1000 Jy at 1 GHz. Apart
from M1, it is also known as Taurus A, 3C144 and G184.6-5.8.
The Crab nebula was the first known extra-solar X-ray source
detected (Bowyer et al. 1964). It is used as an X-ray calibrator…
Total emitted power at all wavelengths: 100,000 times the solar
luminosity!!!
Where does all this energy come from?
The Crab Nebula
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In 1942, Walter Baade identified a star with a peculiar spectrum
near the center of the remnant; he proposed that such a star
could be the power source of the nebula.
Radio scintillation studies led Hewish and Okoye (1964) to
propose the existence of a compact radio source near the center
of the nebula, with a steep spectrum.
Pacini (1967) proposed the existence of a highly magnetized,
rapidly spinning neutron star as the power source of the nebula.
This would radiate a very powerful EM wave with the rotational
frequency of the star. This is below the plasma frequency of the
nebula, therefore all this energy will be absorbed and reradiated by the plasma of the nebula.
The Crab Nebula
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
The neutron star should be spinning fast due to conservation of
angular momentum from the parent stellar core!
It should be highly magnetized due to conservation of magnetic
flux from the parent stellar core.
In this talk:

1930s: Neutron star basics.

The Crab Nebula.

1967: The discovery of the first pulsar.

1968: The discovery of the Crab Pulsar.
White dwarfs * The
Chandrasekhar limit * The neutron * Neutron stars in
supernovae.
Supernovae * M1 * What powers the
Crab nebula? * Pacini’s idea.
Emission
characteristics * Propagation effects * What is a pulsar?
The
discovery of the Crab pulsar * Pulsars are rotating neutron
stars! * The basic pulsar emission model.
1967: The discovery of
PSR B1919+21


In August 1967, Jocelyn Bell,
then a graduate student at
Cambridge, finds a radio signal
in the constellation Sagitta (the
Little Arrow) pulsating with a
period of 1.33 seconds. She
found this to appear 4 minutes
earlier every day, indicating a
sidereal source.
For this discovery, Anthony
Hewish earns the Nobel Prize in
Physics 1974.
PSR B1919+21
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The emission temperatures
for pulsars are of the order
of 1030 K! Emission
definitely not thermal, it
must be coherent.
The pulses were soon found
to be arriving with extreme
regularity, although no two
individual pulses are alike.
The average pulse, however,
does not change with time.
Soon other pulsars were
found, some with repetition
periods as small as 0.25 s.
PSR B1919+21
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All pulsars display different
integrated pulse profiles!
These pulse profiles are
characteristic of the
frequency being used to
make the observation.
PSR B1919+21

The pulsed signal has no
line features, except those
resulting from absorption.
It is normally stronger at
about 100 MHz, decreasing
with higher radio
frequencies. No two pulsar
spectra look alike!
PSR B1919+21

The radio signal can be highly polarized, mainly at low
frequencies.

No one knows what causes the radio emission!
PSR B1919+21


The the pulses arrive at the
Earth first at higher
frequencies, then at the lower
frequencies, with delays of
many milliseconds (after
traveling thousands of years in
space).
This delay can be described by
a single quantity, the Dispersion
Measure, or DM, which is
simply a measure of the column
density of electrons between
the telescope and the pulsar.
PSR B1919+21

The delay at a given frequency is given by:
Where

It is because of this effect that we need spectrometers to
observe pulsars!
PSR B1919+21
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Scintillation is a quasi-random variation of
the intensity of the pulsed signal.
It can be refractive or diffractive. The first
is due to the geometry – if it produces
amplification, it is because the interstellar
medium is acting as a magnifying lens.
Example: the caustics seen at the bottom
of a pool .
The second results from the interference
of the waves from the pulsars with
themselves. Example: star twinkling. A
distinguishing feature of this scintillation is
its wavelength dependence – it affects
color.
PSR B1919+21
Scintillation is what Hewish
was looking for, and that is
what was found...
PSR B1919+21
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
Faraday rotation: the different
polarization angles at different
frequencies (caused by the different
velocities at which waves
perpendicular and parallel to a
magnetic field propagate in a plasma)
indicate the strength and orientation
of the magnetic field of the Galaxy
along the line of sight.
Scattering, or multi-path propagation.
This is akin to “ghosts” in a TV image,
caused, for instance, by reflection of
the radio wave in a building. The
“ghost” always arrives later than the
original signal.
PSR B1919+21
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These five propagational effects (dispersion, refractive and
diffractive scintillation, scattering and Faraday rotation) are very
useful probes of the interstellar medium!
Hence, pulsars would be useful even if nothing else was known
about them.
The question now is: WHAT ARE PULSARS?
PSR B1919+21
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
They are Galactic radio sources, as they are found mostly in the
Galactic disk.
Pulsars also present proper motions that are on average much
larger than those of stars (velocities are 100 times the Earth’s
escape velocity!).
Evolution of 100 pulsars
in the Galactic gravitational
field over 200 Myr. Lateral
view, 30 x 10 pc.
PSR B1919+21
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
•
•
•
•
•
•
The repetition rates imply that the source is very compact. A
star pulsating with a period of 0.25 seconds cannot be larger
than 0.25 x c (of 75.000 km).
This is confirmed by radio scintillation: extended objects do not
scintillate, pulsars scintillate a lot.
Is the fundamental periodicity caused by…
White dwarf vibration?
White dwarf rotation?
White dwarf orbits?
Neutron star vibration?
Neutron star rotation?
Neutron star orbit?
PSR B1919+21
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•
•
•
•
•
•
If the periodicity was caused by some sort of orbital motion,
then this should be decreasing in time, because of emission of
gravitational waves. This is not observed!
Also, the orbital period for two white dwarfs in contact is about
one second. Pulsars are observed with periods shorter than
that.
White dwarf vibration?
White dwarf rotation?
White dwarf orbits? NO!
Neutron star vibration?
Neutron star rotation?
Neutron star orbit? NO!
PSR B1919+21
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•
•
•
•
•
•
The vibration periods of neutron stars are predicted to be a
fraction of a millisecond.
The lower limits for white dwarf vibration and rotation periods
are of the order of a second. So perhaps those might be an
explanation... Except that the 0.25 second period is quite
short…
White dwarf vibration? Perhaps, if you push it…
White dwarf rotation? Perhaps, if you push it…
White dwarf orbits? NO!
Neutron star vibration? NO!
Neutron star rotation?
Neutron star orbit? NO!
PSR B1919+21

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
In 1968, Tommy Gold writes that pulsars must be rotating
neutron stars. He predicts a very slow and steady spin-down for
these objects, based on the fact that they must be losing
rotational energy due to their large EM emission.
If the pulsations were due to vibration, then the intensity of the
oscillation should decrease, and the vibration period (a
characteristic of the vibrating object) should remain constant.
He also predicts that faster pulsars might be found, “because
the rotation rates of neutron stars are capable of going up to
more than 100/s, and the observed periods would seem to
represent the slow end of the distribution.”
In this talk:

1930s: Neutron star basics.

The Crab Nebula.

1967: The discovery of the first pulsar.

1968: The discovery of the Crab Pulsar.
White dwarfs * The
Chandrasekhar limit * The neutron * Neutron stars in
supernovae.
Supernovae * M1 * What powers the
Crab nebula? * Pacini’s idea.
Emission
characteristics * Propagation effects * What is a pulsar?
The
discovery of the Crab pulsar * Pulsars are rotating neutron
stars! * The basic pulsar emission model.
1968: The discovery of
PSR B0531+21 (Crab Pulsar)

In 1968, at the height of the “pulsar fever”, giant radio pulses
originating in the Crab Nebula were detected (Staelin and
Reifenstein). These extremely short bursts proved the existence
of a pulsar at the center of the Nebula (PSR 0531+21). This is
the compact radio source detected by Hewish and Okoye in 1964.
PSR B0531+21

Soon, Arecibo observations showed that the repetition period of
the pulsar was only 33 ms! The pulsar showed measurable
rotational slowdown within a single day!
PSR B0531+21
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
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PULSARS ARE NEUTRON STARS!!! No white dwarf can
rotate so fast! And, the pulsar is slowing down, which excludes
any kind of vibration. T. Gold was right!
NEUTRON STARS EXIST!!! The theorists were not just having
a bad trip (although it looked like that…)
PULSARS RESULT FROM STELLAR COLLAPSE IN
SUPERNOVAE!!!! Baade and Zwicky were right!!!!
THE ROTATIONAL ENERGY LOSS OF THE CRAB PULSAR
IS EXACTLY THE SAME AS THE EMISSION OF THE CRAB
NEBULA!!!! Pacini was right, neutron stars are fast, have large
magnetic fields, and one of them powers the Crab Nebula.
However, no one predicted the feature that makes pulsars really
shine, the radio emission.
PSR B0531+21


After this event, the basic model
of pulsar emission becomes
established: pulsars are the radio
equivalent of lighthouses on a
neutron star.
Non-thermal radiation at a variety
of wavelengths is emitted
through the magnetic poles,
which are generally misaligned
with the spin axis. We see a pulse
at the Earth every time this
magnetic axis points towards us.
PSR B0531+21

Radakhrishnan and Cooke’s (1969) rotating vector model,
explains the polarization characteristics of slow pulsars. It
allows a basic determination of the geometry of pulsar
emission!
PSR B0531+21



Baade’s star is found to be
the optical counterpart of the
Crab pulsar. The optical
pulsations have exactly the
same period. This is the first
pulsar seen at optical
wavelengths!
X-ray pulses are also
measured at the same
frequency.
A second pulsar was soon
found in the Vela supernova
remnant, (the Vela pulsar, or
PSR 0833-45) which also
shows optical and X-ray
emission.
Listening…

Let us take a break and listen to some pulsars:
http://www.jb.man.ac.uk/~pulsar/Education/Sounds/
In this talk (continued):

Pulsar Timing.

1974: The discovery of PSR B1913+16.

1982: The discovery of PSR B1937+21.
Energy emission * Characteristic ages *
Magnetic Fields * Glitches and timing noise.
discovery of the binary pulsar * pulsars as gravitational
laboratories.
The
Discovery of PSR B1937+21 * Millisecond pulsars as probes of
the equation of state * Formation of millisecond pulsars * Timing
accuracy.
Pulsar timing



How regularly do pulsars spin?
Can we learn something from this rotation?
For an isolated pulsar, the two main parameters measured by
timing (apart from the position in the sky and the DM) are the
rotational period and its first derivative. From these two
parameters alone, one can learn a lot about a given pulsar.
Pulsar timing

Increase in P results from loss of rotational energy:

Energy is radiated mostly as dipole radiation:

Evolution of spin frequency:
Pulsar timing

The pulsar’s age τ can be estimated, integrating the spindown
and assuming that P >> P0:

Assumptions (n = 3, P >> P0 ) may be wrong, but τ is normally
a good estimator of the age.

For the Crab pulsar, real age is 949 years (in 2003), and τ is
1237 years!
Pulsar timing

The pulsar’s magnetic field can also be estimated:

We assumed: R = 10 km, I = 2/5 M R2 = 1038 kg m2
α = 90 degrees.
Most pulsars have fields of 108 T, i.e., tens of millions of times
more powerful than anything that can be produced on Earth.


Pulsar timing




Most pulsars show significant departures from simple, uniformly
slowing rotation. The two main departures are:
Glitches. This corresponds to starquakes, caused by a sudden
shrinkage in the star’s size, with corresponding spin up.
Timing noise. The origin of this phenomenon is unknown.
The younger the pulsar, and the more intense its magnetic field,
the larger are the torques applied to it surface. The phenomena
listed above seem to be related to these torques…
Pulsar timing

The Crab pulsar is a particularly noisy one. For this reason, it
has been monitored daily for more than 30 years. In 1999, it
had already glitched 13 times.
In this talk (continued):

Pulsar Timing.

1974: The discovery of PSR B1913+16.
Energy emission * Characteristic ages *
Magnetic Fields * Glitches and timing noise.
The
discovery of the binary pulsar * pulsars as gravitational
laboratories.

1982: The discovery of PSR B1937+21.
Discovery of PSR B1937+21 * Millisecond pulsars as probes of
the equation of state * Formation of millisecond pulsars * Timing
accuracy.
1974: The discovery of
PSR B1913+16

Russel Hulse and Joe Taylor discovered PSR B1913+16, in the
constellation Aquila (the Eagle), during a systematic 430-MHz
survey of the Galactic plane at Arecibo.
PSR B1913+16


It has a DM of 168.77 cm-3 pc and a rotational period of 59 ms.
This was the second shortest period known at the time.
This was the first binary pulsar to be discovered.
PSR B1913+16

The pulsar and the
companion star are
orbiting the common
center of mass. The
orbital period is 7h 45m
and the eccentricity is
0.61.
PSR B1913+16


When timing pulsars (or
measuring radial velocities
with the aid of spectral
lines) one has access to the
line-of-sight velocity, which
causes a Doppler shift on
the wavelength of the
spectral line or a modulation
on the period of the pulsar.
In the case of pulsar timing,
one can also measure the
range relative to the center
of mass of the binary,
normally with a precision of
the order of 1 km or less.
PSR B1913+16


Five Keplerian parameters can normally be measured from
fitting the velocity (or, preferably, the delay) curves: orbital
period (Pb), projected size of the orbit, in light seconds (x),
eccentricity (e), longitude of periastron (ω) and time of passage
through periastron (T0). A non-changing Keplerian orbit is
exactly what is predicted by Newtonian gravity.
Without access to information on transverse velocities, the
individual masses of the components (m1 and m2) and the
inclination of the system (i) cannot be measured, but…
PSR B1913+16

The mass function, a relation between these three quantities,
can be measured to excellent precision, as it depends on two
observable parameters:
PSR B1913+16
For most binary pulsars, and spectroscopic binaries, there is
no information on the transverse velocities, so this is as far as
we can go.
However, the PSR B1913+16 system is so extreme, and
pulsar timing is so precise, that some effects of general
relativity became detectable!
Three such effects have been measured for PSR B1913+16:



1.
2.
3.
Periastron advance (ώ).
Rotational slowdown due to gravitational redshift and Lorenz
time dilation (Einstein delay, γ).
Orbital decay due to emission of gravitational waves (dPb/dt).
PSR B1913+16


Perihelion advance due to general relativity had been observed for
the orbits of several planets in the solar system, most notably
Mercury.
The periastron of PSR B1913+16 advances 4.226607(7)
degrees/year. The daily periastron advance is the same as
Mercury’s perihelion advance in a century…
PSR B1913+16


The Einstein delay was also measured: γ = 0.004294(1) s. The
pulsar slows down visibly when it is near the companion,
accumulating a delay relative to the prediction of constant rotational
period. General relativity predicts that time itself slows down in an
intense gravitational field (in this case, that of the companion
object).
The pulsar also rotates more slowly due to special-relativistic time
dilation – it is traveling faster near the companion object.
PSR B1913+16

These two effects determine the mass and inclination of the
system! This happens because, according to General relativity,
they depend on the known Keplerian parameters and the
masses of the two objects:
PSR B1913+16


The masses of the
individual components
(and, from the mass
function, the inclination
of the system!) are only
well determined if we
assume that General
relativity is right.
This is the most precise
measurement of any
mass outside the solar
system.
PSR B1913+16



A third relativistic effect is measurable: The orbital period is
becoming shorter.
General relativity predicts this to be due to the loss of energy
caused by emission of gravitational waves. This depends only on
quantities that are already (supposedly) known:
Prediction: the orbital period should decrease –2.40247 x 10-12
s/s (or 75 μs per year!)
PSR B1913+16
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Value observed (after
subtraction of the Galactic
motion of the pulsar) is:
–2.4085(52) x 10-12 s/s.
The agreement is perfect!
GENERAL RELATIVITY
GIVES A SELFCONSISTENT ESTIMATE
FOR THE MASSES OF THE
TWO COMPONENTS OF
THE BINARY!
GRAVITATIONAL WAVES
EXIST!
PSR B1913+16

For this measurement, Hulse and Taylor were awarded the 1993
Nobel Prize in Physics.

This is all very fine and beautiful, but are double neutron stars
supposed to exist?
This was originally quite a puzzle…

In this talk (continued):

Pulsar Timing.

1974: The discovery of PSR B1913+16.

1982: The discovery of PSR B1937+21.
Energy emission * Characteristic ages *
Magnetic Fields * Glitches and timing noise.
discovery of the binary pulsar * pulsars as gravitational
laboratories.
The
Discovery of PSR B1937+21 * Millisecond pulsars as probes of
the equation of state * Formation of millisecond pulsars * Timing
accuracy.
1982: The discovery of
PSR B1937+21

In 1982, at an Observatory near you, Don Backer and Shri
Kulkarni found the first millisecond pulsar, PSR B1937+21, in the
constellation Vulpecula (the Little Fox). The object is isolated.
PSR B1937+21



The pulsar was found in a search targeted at the location of a
compact (scintillating) radio source with a steep spectrum in the
radio nebula 4C21.53W.
At first, it was thought to be rotating 1284 times a second! This
was later found to be due to the fact that the profile has a
double peak – the second Fourier component is the strongest!
Still, a rotation of 642 times a second (or a period of 1.57 ms)
implies that the equator is moving at 1/7 the speed of light!
PSR B1937+21




Is that possible? Why doesn’t the star fly apart?
The gravity at the surface of a pulsar is about 1012 times more
powerful than at the Earth’s surface.
The rotational velocity introduces constraints on the equation of
state: radii must be smaller than ~20 km, otherwise the
centrifugal force would be larger than the gravitational force.
Some models of the behavior of nuclear matter at high densities
have already been excluded by the discovery of PSR B1937+21,
as they cannot predict a stable configuration rotating 642 times
a second – such models tend to predict large stellar radii.
PSR B1937+21
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The rotational period
derivative was found to
be extremely small,
which sets this pulsar
completely apart from
other young pulsars with
small periods, like the
Crab pulsar.
The magnetic field is
~1000 times weaker
than that of normal
pulsars, the age is of the
order of billions of years!
More than 100 other
millisecond pulsars have
been found to date!
PSR B1937+21
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The formation of such stars was a mystery at first. In the same
year, Alpar suggested that Millisecond Pulsars are formed in
Low-Mass X-ray Binaries (LMXBs).
Under this suggestion, all MSPs should still be part of pulsar –
white dwarf binaries. While this is true for most MSPs found
since, PSR B1937+21 itself is isolated.
The formation of isolated millisecond pulsars is still not
understood.
PSR B1937+21
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A distinctive feature
of the formation
model for MSP/white
dwarf systems is the
prediction that the
orbits should be
circular. This is
observed to be true.
PSR B1937+21
The rotation of most known millisecond pulsars is perfect, i.e.,
it can be described, to within observational accuracy, as a
perfect, featureless slowdown.
Millisecond pulsars have better long-term stability than atomic
clocks!
Uses are manifold… And have absorbed much time and effort
over the last 21 years, with many delightful results:
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1.
2.
3.
Tests of General Relativity
Search for gravitational waves produced by giant black hole
mergers.
Probe newtonian systems, like planetary systems and Globular
clusters.
PSR B1937+21
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Just an example of the precision
of millisecond pulsar timing: PSR
J1738+0333.
Period is 5.8500957647881(5)
ms, the projected semi-major
axis of the pulsar’s orbit is
102,857,840 +/- 60 m
Difference between semi-major
axis and semi-minor axis of the
pulsar’s orbit: 200 μm, or less
than 1/100 of an inch!
Second most perfect circle
known!
Pulsar 1 kpc away…
Listening to MSPs
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Millisecond pulsars sound decidedly different:
http://www2.naic.edu/~pfreire/47Tuc.html
Thank you for your time!
Contact me at: [email protected], or visit my website at
http://www2.naic.edu/~pfreire/.
The National Astronomy and Ionosphere Center is operated by
Cornell University, under a cooperative agreement with the
National Science Foundation.