Pulsars and Supernovae II
7. STRUCTURE AND FORMATION
the structure of neutron stars neutron drip vortex pinning starquakes radio glitches Neutron stars – observed parameters • The exact structure of a neutron star depends critically on the equation of state, relating pressure to density (or mass to radius).
• Binary pulsar timing observations allow us to measure the masses of some neutron stars directly.
• All appear to be close to the GW170817 canonical Chandrasekhar mass of ∼ 1.4 푀⊙
• The theoretical upper mass limit (the Oppenheimer Volkov limit) depends on the equation of state, but is probably ∼ 2푀⊙.
Jim Lattimer
2 7. Structure and formation Neutron star formation • Neutron stars are probably always the remnant of a core-collapse supernova (e.g. Type II).
• Thought not to be formed by accretion-induced collapse of a white dwarf (Type Ia).
• SN rates in the Galaxy are about 1 every 65 y, so maybe 108 to 109 neutron stars in the Galaxy(!)
• Visible supernova remnant is brief, lasting ~105 y (most pulsars are >106 years old).
• Neutron star – speed ~500 km/s, and so may move away from the supernova remnant – surface gravity ~1012 g – surface escape velocity of ~c/2.
Burrows 2000
3 7. Structure and formation The outer structure of neutron stars • The average (mass) density of a neutron star is 휌 ≃ 6.7 × 1017 kg m−3, more than twice nuclear densities.
• The actual density will increase towards the centre.
• Observations of glitches, and their recovery, point at a solid crust and a superfluid interior.
• Crust is compressed iron nuclei in a close-packed lattice and degenerate electrons 휌 ≃ 109 kg m−3 (about a ton per cm3)
• Solid crust contains only 1-2 percent of the moment of inertia, and is ∼ 500 m thick.
• ‘Atmosphere’ ∼ 5 mm thick (and very dense!)
• Electron spins are oriented along B-field, distorting the ‘atoms’ in the outer envelope into cylinders
4 7. Structure and formation The innner structure of neutron stars
• Beneath the crust, the greater pressure allows inverse beta decay and ‘neutron drip’ as the atomic structure eventually dissolves into a sea of superfluid neutrons (and about 5 − percent electrons/protons) . 푝 + ⅇ → 푛 + 휈푒
• The inner crust is a mixture of free degenerate neutrons, degenerate (relativistic) electrons and neutron-rich nuclei.
• The core region depends on the equation of state but probably comprises superfluid neutrons and superconducting electrons and protons.
• Rapid rotation means the neutron star is oblate, with a flattening of about 퐸 휔2푎3 rot ∼ ∼ 10−2 to 10−8. 퐸grav 퐺푀
5 7. Structure and formation The structure of neutron stars
• Gravitational wave observations tell us deviations from this shape are at a very low level (less than 10−7 in some cases (i.e. 0.1 mm!)
• Otherwise the neutron star is a perfect sphere!
6 7. Structure and formation Neutron drip
• The idea of a neutron drip line comes from nuclear physics: the line in the Z-N plane below which nuclei cannot keep hold of neutrons. In a neutron star dripped neutrons come from inverse beta decay: − 푝 + ⅇ → 푛 + 휈푒
Hinde and Dasgupte 2004
7 7. Structure and formation Neutron drip
lasagna spaghetti
Pasta phases (Caplan et al 2013) gnocchi
Chamel Nicolas • At ever increasing pressures, protons and electrons combine to form neutrons (inverse beta decay) and the iron nuclei become neutron-rich. − 푝 + ⅇ → 푛 + 휈푒
• Eventually neutrons are no longer retained, and ‘drip’ out of the distorted nuclei.
8 7. Structure and formation Neutron star structure
NICER/GSFC
9 7. Structure and formation Vortex pinning
• The superfluid core of the neutron star does not rotate simply with the crust.
• When a superfluid is rotated it forms microscopic vortex lines which, because it is a superfluid, can be maintained indefinitely (i.e. without viscous damping).
• These vortices are at the quantum level, carrying ℏ of angular momentum in a size of 10−14 m
• The (area) density of vortices defines the local rotation rate of the material.
• The interior superfluid is rotationally coupled to the crust via the magnetic field, and rotates with it.
10 7. Structure and formation Vortex pinning
• As the neutron star spins down, the angular momentum of the core is lost by allowing these vortices to migrate outwards, away from the spin axis (reducing the vortex density). In equilibrium spin-down these vortices diffuse out to the crust where they dissipate.
• However, the part of the superfluid in the inner crust interacts with the iron nuclei and can get ‘pinned’ in place, unable to migrate, so that this component of the superfluid does not spin down with the star.
• The pinned vortices store angular momentum which is released suddenly if the pinning fails, causing the neutron star to suddenly increase in rotation rate – a glitch. • Slow (days-years) recovery times after a glitch can only be explained by an interior superfluid.
11 7. Structure and formation Radio glitches
• Pulsar glitches appear as a step increase in rotation rate of a pulsar
• We can interpret these as the result of vortex unpinning – a portion of the superfluid vortices, prevented from migrating, have suddenly dislodged and transferred their angular momentum to the bulk of the neutron star, spinning it up.
12 7. Structure and formation Radio glitches • If you remove the mean spin-down, glitches look like this :
• The effective moment of inertial is increasing after a glitch as the unpinning spreads, decreasing the spin- down rate.
Espinosa et al 2017 13 7. Structure and formation Starquakes
• Glitches in the Crab pulsars are rather different, showing a step increase in slowdown rate between glitches that does not recover over time:
It’s hard to see in the raw data…
Lyne at al 1993
14 7. Structure and formation Remove the mean slope…
Lyne at al 1993
15 7. Structure and formation Starquakes
• The dominant mechanism in Crab pulsar glitches seems to be a change in the shape of the neutron star (and therefore a change in its moment of inertia) due to a starquake – a re-adjustment of the shape of the crust. This may be cause by the star spinning down, and therefore having a lower natural spin-induced oblateness. The neutron star hangs on to its old shape as long as it can, but eventually the crust yields and there is a sudden change in shape.
• Starquakes in magnetars (highly magnetised neutron stars) release copious amounts of electromagnetic energy as gamma and X-rays (e.g. SGR 1806-20, Dec 2004– see later!)
16 7. Structure and formation