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Pulsar properties
Duncan Lorimer
(West Virginia University)
• Basic properties
Neutron star properties
The lighthouse model
Pulses and profiles
• Pulsar statistics
– The P-Pdot diagram
– Binary pulsars
– Evolutionary scenarios
Links to basic physics
Conservation laws
Neutron star properties
• Extremely dense objects
– 100,000,000,000,000,000 kg m-3
– Next thing down from a black hole
Neutron star properties
• Extremely rapid spin
– Rotation rates in excess of 700 Hz
– Speed at surface ~ significant fraction of c
Neutron star properties
• Extreme magnetic fields
– 1,000,000,000,000 x Earth’s field
Neutron star properties
• High space velocities
– Up to 1000 km s-1!
– Signature of a violent birth
Discussion questions
• What’s the escape velocity of a neutron star?
– How does it compare to Earth?
• What are the tidal forces like on a neutron star?
– Difference in g-force between head and your feet
• Apply conservation of angular momentum
– Start with Sun rotating once a month (R ~ 7 x 105 km)
– What is the final rotation period if R = 10 km?
In more detail
Size of emission region is
bounded by the so-called
`light cylinder’ - this is an
imaginary surface that co-rotates
with the neutron star.
Einstein asserts the co-rotation
speed cannot be greater than the
speed of light, c.
This sets a fundamental size
for the emission region.
Q: Formula for light
cylinder radius? What is
its value for P=1 s vs 1 ms?
Individual pulses are very erratic
…but average behavior is stable
Modeling pulse morphology
A hybrid containing features of both models works well…
BUT we are still far from understanding how it all works!
Discussion questions
• What’s with the main pulse + interpulses?
– What configurations of the star/observer needed?
• What would we see for an aligned rotator?
– What would its pulse shape look like?
• What fraction of all pulsars can we see?
– Assume simple geometry and calculate the fraction of a
sphere covered by the north and south magnetic poles.
• How does viewing probability change?
– Is an aligned pulsar illuminating more or less sky than an
inclined one (for a given beam size)?
Pulsar distances
We measure DMs in pc cm-3.
Can use measured DMs to estimate
distances to pulsars!
Black and yellow points are pulsars
discovered at two different survey
frequencies. Which color is the
higher one??
Pulses are scattered as they
traverse irregularities in the
interstellar medium. The
effect is strongly frequency
dependent as shown. In the
extreme case, a pulse can be
rendered undetectable!
Scattering strongly
correlates with distance/DM
The “P-Pdot” diagram
Pulsars are losing rotational
kinetic energy as they radiate!
Their rotation periods are
gradually INCREASING.
In addition to measuring a
spin period, P, we measure
a rate of change of period.
This is known as the `spin
period derivative’ or Pdot
The diagram on the right shows
spin period versus spin period
derivative for known pulsars.
Discuss: Age, Bsurf, Edot
and the pulsar “graveyard”
Binary and millisecond pulsars
• A separate population?
– Shorter spin periods
– Lower magnetic field strengths, higher ages
– Significant fraction of binary companions
• What orbiting companions are known?
Other neutron stars
White dwarfs
Main sequence stars
Black holes
Maybe you guys will find the first one…
Revisiting the “P-Pdot” diagram
The millisecond and binary pulsars
occupy the lower left part of the
Discuss possible evolutionary
scenario from normal to MSP
There are in fact two types
Of “recycled pulsars”
•P<30 ms with circular orbits
•P>20 ms with eccentric orbits
It is thought that these evolve from
Low-mass X-ray binary systems and
High-mass X-ray binary systems
Evolution in a binary system
• Ingredients
Mass transfer
Tidal forces
• Things it explains
– MSP-WD binaries
– NS-NS binaries
– Isolated P=50 ms
• Things it doesn’t
– Isolated MSPs
– Eccentric MSPs
– Pulsar planets
A millisecond pulsar X-ray binary
Association with
VLA source
VLA source is a
quiescent LMXB!
Orbital period
measured from
timing seals the
link… providing
new insights into
pulsar evolution!
Archibald et al. (2009) Science
P=1.69 ms
4.7 hr binary
• Concepts to get across
– Pulsars are extreme objects
– Can be investigated with high-school physics
– Can also be investigated pictorially
• We don’t know all there is to know yet…
– How they radiate
– How fast they spin
– How many there are and evolutionary history
– Whether any have black-hole companions
– These are some of the motivations for searching
See also