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Transcript
Pulsar properties Duncan Lorimer (West Virginia University) • Basic properties – – – – Neutron star properties The lighthouse model Pulses and profiles Distances • Pulsar statistics – The P-Pdot diagram – Binary pulsars – Evolutionary scenarios Links to basic physics Gravity Conservation laws http://relativity.livingreviews.org/lrr-2008-8 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?? Pulse scattering 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 Planets 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 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 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 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 are and evolutionary history – Whether any have black-hole companions – These are some of the motivations for searching See also http://relativity.livingreviews.org/lrr-2008-8