Pulsar properties Duncan Lorimer West Virginia University Basic

Pulsar properties Duncan Lorimer (West Virginia University) • Basic properties – – Neutron star properties The lighthouse model Pulses and profiles Radio spectra • Pulsar statistics – The P-Pdot diagram – Binary pulsars – Evolutionary scenarios Links to basic physics Gravity Conservation laws Radiation Time transfer

Formation of neutron stars

Neutron star properties • Extremely dense objects – 100, 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 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?

Mind’s-eye view

The sounds of pulsars (google “sounds of pulsars”)

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

Example of profile stabilization

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 and observer would result in this? • What would we see for an aligned rotator? – What would its pulse shape look like? • How do you think pulse width depends on period? – No change, increase with period, decrease with period? – Hint: Recall the previous definition of the light cylinder

Profile widths with frequency

Pulsar intensity and frequency Discuss: Jy, spectral indices, rollovers, breaks, mechanisms

Discussion questions • What fraction of all pulsars can we see? – Assume simple geometry and calculate the fraction of a sphere covered by both 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)?

Time for a break

Pulsar statistics and demography

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 Planets Black holes Maybe you guys will find the first one…

Binary and millisecond pulsars

The first binary pulsar

Ultimate fate of a double neutron star binary system Google John Rowe Animations

Astronomers are looking for these events in other Galaxies

Formation of a double neutron star binary system… Start with two main sequence stars and wait for them to go bang…

Revisiting the “P-Pdot” diagram The millisecond and binary pulsars occupy the lower left part of the diagram. . 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 – – Supernovae Mass transfer X-rays 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

PSR J 1903+0327 Spin = 2. 15 ms Binary = 95 days e = 0. 44 ! M = 1. 74 Msun ! Champion et al. (2008) Science in press An eccentric binary pulsar

Summary • 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 and evolutionary history Whether any have black-hole companions These are some of the motivations for searching