Neutron stars

Lecture 19

University of Naples Federico II, Academic Year 2011-2012Istituzioni di Astrofisica, read by prof. Massimo Capaccioli

Learning outcomes

The student will see:

• xxx

Discovery of neutron stars1967: A. Hewish & J. Bell discovered regularly spaced radio pulses at P = 1.337 s, repeating from same point in sky.

Approx. 1500 pulsarsnow known, with periods on range 0.002< P < 4.3 s.

Discovery of neutron stars

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Crab pulsar - embedded in Crab nebula, which is remnant of supernova historically recorded in 1054AD by the Chinese.

Crab pulsar emits X-ray, optical, radio pulses P = 0.033 s

Spectrum is power law from hard X-rays to the IR

⇒ synchrotron radiation: relativistic electrons spiralling around magnetic field lines.

Neutron stars

If a degenerate core (or white dwarf) exceeds the ( ), it must collapse until neutron degeneracy pressure

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Neutron star

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Neutron stars

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White dwarf

Neutron star

Creation of neutrons

At high densities, neutrons are created rather than destroyed.

The most stable arrangement of nucleons is one where neutrons and protons

are found in a lattice of increasin

Neutroniza

gly neutro

tion.

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ons.

Neutron drip

Nuclei with too many neutrons are unstable; beyond the “neutron drip-line”, nuclei become unbound.

These neutrons form a nuclear halo: the neutron density extends to greater distances than is the case in a well-bound, stable nucleus

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Free neutrons pair up to form bosons.Degenerate bosons can flow without viscosity.

A rotating container will form quantized vortices.

At neutron degeneracy pressure dominates;

nuclei

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issolve

ρ ×

and protons also form a superconducting superfluid.

Superfluidity

Neutron stars: structure

1. Outer crust: heavy nuclei in a fluid ocean or solid lattice.

2. Inner crust: a mixture of neutron-rich nuclei, superfluid free neutrons, and relativistic electrons.

3. Interior: primarily superfluid neutrons.

4. Core: uncertain conditions; likely consist of pions and other elementary particles.

The maximum mass that can be supported by neutron degeneracy is uncertain, but can be no more than 2.2÷2.9 M

�(depending on rotation

rate).

Rotation

Conservation of angular momentum led to the prediction that neutron stars must be rotating very rapidly.

low rotation rate high rotation rate

Sur

face

tem

pera

ture

[K]

Cooling

Internal temperature drops to ~109 K within a few days.

Surface temperature hovers around 106 K for about 10,000 years.

Lum

inos

ity [e

rgs/

s]

Neutron stars: luminosity

Chandra X-ray image of a neutron star

What is the blackbody luminosity of a 1.4 neutron star, with a surface temperature of 1 million K ?

M⊙

Pulsars

Variable stars with very well-defined periods (usually 0.25-2 s).

Some are measured to ~15 significant figures and rival the best atomic clocks on Earth.

Pulsars7

15

The increase very gradually, with characteristic of .

periods lifetime

~10 yr

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Pulsars

time

Pulsar PSR1919+21The shape of each pulse shows substantial variation, though the average pulse shape is very stable.

Franco Pacini

Possible explanations

How to obtain very regular pulsations?

1. Binary stars: such short periods would require very small separations. Could only be neutron stars. However, their periods would decrease as gravitational waves carry their orbital energy away.

2. Pulsating stars.White dwarf oscillations are 100-1000 s, much longer than observed for pulsars.Neutron star pulsations are predicted to be more rapid than the longest-period pulsars.

3. Rotating stars.How fast can a star rotate before it breaks up ?

Pulsars: rapidly rotating neutron stars

Discovery of the pulsar in the Crab Nebula in 1968 (P = 0.0333 s) confirmed that it must be due to a neutron star.

Many pulsars are known to have high velocities (1000 km/s) as expected if they were ejected from a SN explosion.

Pulsar model

• The model is a strong dipole magnetic field, inclined to the rotation axis.

• The time-varying electric and magnetic fields form an EM wave that carries energy away from the star as magnetic dipole radiation.

• Electrons or ions are propelled from the strong gravitational field.

As they spiral around B-field lines, they emit radio radiation.

• Details are still very much uncertain!

The Crab Pulsar

This movie shows dynamic rings, wisps and jets of matter and antimatter around the pulsar in the Crab Nebula.

X-ray light (Chandra) Optical light (HST)

The inner ring is ∼1 light year across.

Crab nebula: energy source

We saw that the Crab nebula is expanding at an accelerating rate.

What drives this acceleration?

To power the acceleration of the nebula, plus provide the observed relativistic electrons and magnetic field requires an energy source of 5×1031 W.

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Binary Pulsars

Using the Arecibo 305 m antenna, in 1974 Russell Hulse& Joseph Taylorof Princeton University (both Nobel laureate in 1993) discovered a pulsar, PSR1913+16, with a pulse period of 59 milliseconds.Systematic variation (P = 7.75 hours) in pulses arrival time – sometimes arriving sooner than expected, sometimes later – showed that the neutron star was in a binary system with another star.

The orbit of PSR 1913+16 is inclined at ∼ 45° and oriented in such a way that periastron occurs nearly perpendicular to line of sight.

Binary Pulsar PSR1913+16

The number of pulses per second, P, gives the radial velocity of the pulsar along its orbit (when the pulsar is approaching and is close to its periastron, the pulses should come closer together; the opposite is true when it is moving away from us).

The fact that the negative velocities are larger than the posititive one shows that the orbit is highly eccentric.

Binary Pulsar PSR1913+16 – Doppler effect

The pulsar arrival times also vary as the pulsar moves through its orbit.

When the pulsar is on the orbit’s side closest to Earth, the pulses arrive more than 3 seconds earlier that when on the furthest side.

Difference caused by the shorter distance from Earth to the pulsar when it is on the close side of its orbit.

The difference of 3 light seconds implies that the orbit is ∼1 million kilometers across.

PSR1913+16: varying distance & relativity effects

When the objects are closer together, near apastron, the gravitational field is stronger, so that time (between pulses) is slowed down, just as Einstein predicted.

The pulsar clock is slowed down when it is traveling fastest and in the strongest part of the gravitational field.

The orbit of the pulsar appears to rotate with time; the orbit is not a closed ellipse, but a continuous elliptical arc whose point of closest approach (periastron) rotates with each orbit.

The rotation of the pulsar's periastron is analogous to the advance of the perihelion of Mercury in its orbit.

The observed advance for PSR 1913+16 is ∼ 4.2 degrees per year; the pulsar's periastron advances in a single day by the same amount as Mercury's perihelion advances in a century.

Binary Pulsar PSR1913+16: precession

Relativity predicts that binary system lose energy as orbital energy is converted to gravitational radiation.

In 1983, Taylor and collaborators reported a systematic shift in the observed periastron time relative to expectation for fixed orbital separation.

By 1982 the pulsar was arriving at its periastron more than a second earlier than in 1974.

Because the binary system is losing energy, the orbits are shrinking (∼3.1 mm per orbit), and in ∼ 3×108 years from now the two stars should coalesce, with strong emission of gravitational radiation.

PSR1913+16: tests of General Relativity

Joseph H. Taylor1941-

Irwin I. Shapiro delayWhen the orbital plane is along the line of sight, there is a delay in the pulses due to the warping of space, named after the former director of Harvard-Smithsonian Center for Astrophysics.

Shapiro delay in pulsar PSRJ 1909-3744 due to the gravitational field of its white dwarf companion.

Top panel: configuration of pulsar & companion 1) when pulsar is closest to us (left, minimum delay), 2) it is on the far side (right, maximum delay).

Bottom panel: variation in the Shapiro delay through one complete orbit of the pulsar-white dwarf system.

The size and shape of this delay curve allowed astronomers to precisely calculate the mass of the pulsar using observations with the 64-meter Parkes radio telescope in Australia.

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Irwin I. Shapiro1929-