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Astrophysics & Cosmology

Erik Elfgren Lecture 7 Compact objects

Simulated view of a small black hole in front of the Compact objects Stars deaths’

When there is no more combustible material in the core of the star, compresses the core and the star’s outer layers are shed Compact objects Degeneracy . Quantum states with the same energy are called degenerate

. The number of states with identical energy are called the degeneracy

. According to the Pauli principle two identical fermions cannot occupy the same quantum state simultaneously

. Attempting to force particles closer together will force the particles to attain higher energy levels, effectively producing a counterforce, called degeneracy pressure Compact objects Degenerate objects . In the leftover core of a dead star degeneracy pressure supports the star against the crush of gravity

. A degenerate star which is support by: . degeneracy pressure is called a . neutron degeneracy pressure is called a

. If the remnant core is so massive that the force of gravity is greater than neutron degeneracy pressure the star collapses under its own gravity and becomes a black hole Compact objects White dwarfs . The collapse of the center of a heats the core

. The star has not enough mass to reach the temperatures required for carbon fusion

. Gravity is stopped by the electron degeneracy pressure Globular cluster M4 . The star is now a stable white dwarf Compact objects White dwarfs . Mass: 0,5–1,4 M IK Pegasi A  . Size: Like the

. : 1018 kg/m3

-4 . : 10 –100 L IK Pegasi B . Temperature: 8–30×103 K (record: 4–150×103 K)

The . No energy generation . Life time: > 13×109 Compact objects White dwarfs . The luminosity of the star comes from the residual heat from its compression

. They can be very hot but due to their tiny size their remain small

. They slide down the HR- diagram as the radiate their heat into space, becoming cooler and fainter Compact objects White dwarfs . White dwarfs should be very common (as the remnant of normal )

. Relatively few are detected due to their low luminosity

. No “black dwarfs” yet Compact objects White dwarfs . Most white dwarf stars are composed mostly of carbon and

. Some white dwarfs have passed carbon burning but not burning. These are composed oxygen, neon and

. A few white stars composed principally of helium also exist due to mass loss in binary systems Compact objects White dwarfs . White dwarfs are believed to crystallize

. Lucy is a crystallized white dwarf 50 light-years away in Centaurus

. Lucy is the most massive pulsating white dwarf observed so far

. It’s the largest diamond known with 1033 carats Compact objects White dwarfs

. Degenerate behaves oddly

. The more mass the star has, the smaller it becomes

. More mass more gravity more density more degeneracy pressure Compact objects White dwarfs . Subrahmanyan Chandrasekhar formulated the laws of degenerate matter (Nobel prize 1983)

. He predicted that gravity will overcome the electron degeneracy if a white dwarf has

a mass > 1,4 M

. Energetic , which cause the pressure, reach relativistic speeds Compact objects White dwarfs Chandrasekhar limit . Pauli exclusion principle: Only one fermion can occupy a given quantum state

. The Fermi energy is the energy that divides occupied and unoccupied quantum states at 0 K: 2 2/3  2 Z F 3 2me A mH . The Fermi energy is independent of temperature Compact objects White dwarfs Chandrasekhar limit . Pauli exclusion principle along with the Heisenberg uncertainty principle: x p  / 2 and the classical pressure P m v2 N /V gives the electron degeneracy pressure: 5/3 3 2 2/3 2 Z P 5 me A mH which only depends on the density and not the temperature Compact objects White dwarfs Chandrasekhar limit . For a completely degenerate star of constant density: MV = const

. If you pile mass on the star the volume go towards zero and according to the Heisenberg principle the velocities must therefore go toward infinity

. This is in contradiction with Compact objects White dwarfs Chandrasekhar limit . Inclusion of special relativity leads to smaller velocities thereby contributing to less pressure so the volume will be even smaller than previously predicted and for a certain mass range, the volume even goes to zero

. The relativistic expression for the pressure is 4/3 3 2 1/3 Z P c 4 A mH . The Chandrasekhar mass limit is 2 3 2 c 3/ 2 Z 1 M Ch 8 G A mH

. More complete calculation gives MCh ≈ 1,44 M Compact objects White dwarfs Chandrasekhar limit Compact objects Neutron stars . Leftovers from explosions

. If the core has < 3 M, it will stop collapsing due to the neutron degeneracy pressure

. Density: 1017 kg/m3

1,5 M radius ~ 10 km

. Period: ms – 4 seconds

. Magnetic field: 1013 times that of the Earth Compact objects Neutron stars . If a white dwarf exceeds the Chandrasekhar mass

limit (1,4 M) it collapses until neutron degeneracy pressure takes over

. A neutron star with a mass at the Chandrasekhar limit has a radius of 10–15 km and consists of 1057 RCW 103 neutrons

. A neutron star is like an enormous nucleus

ρ ≈ 2.9 ρnuclear Compact objects Neutron stars . The force of gravity is very strong: GM g 1,8 1012 m/s 2 R2

.An object dropped from a height of 1 m would hit the surface at a velocity 0,5% the speed of light

. Must use relativity to model correctly Compact objects Neutron stars Structure Outer crust

. Heavy nuclei in a fluid ocean or solid lattice

. Fe-56 nearest the surface

. More neutron rich elements further down Compact objects Neutron stars Structure Inner crust

. Mixture of neutron rich nuclei

. Superfluid free neutrons

. Relativistic electrons Compact objects Neutron stars Structure Outer core

. Primarily superfluid neutrons

. A few superfluid, superconductive protons

. Relativistic degenerate electrons Compact objects Neutron stars Structure Inner core

. Uncertain conditions

. Pion condensates?

. Lambda hyperons?

. Delta isobars?

. Quark-gluon plasmas? Compact objects Neutron stars Rotation . Conservation of angular momentum: L I MR 2 2 i Pf R f

f Pi Ri

. Neutron stars are ~ 500 times smaller than white dwarfs of the same mass, -5 Pf/Pi ~ 10

. PWD ~ 20 min PNS ~ 1 ms Compact objects Neutron stars Luminosity . Blackbody luminosity of a

1,4 M neutron star with T ~ 106 K: 2 4 L 4 R Te 25 7,1 10 W 0.2L .

9 max b /T 3 10 m

Chandra X-ray Image of . This is a X-ray Crab Nebula and difficult to detect Compact objects Neutron stars

. For a neutron star to have a magnetic field it also needs some scattered protons Compact objects Neutron stars Pulsars . The discovery of pulsars in the 1960s stimulated interest in neutron stars

. Radio source some 300 pc away with regular on-off- on cycle of exactly 1,3373011 s

. Was baptized LGM-1, for Vela pulsar "little green men“

. Later named pulsar Compact objects Neutron stars Pulsars . First thought to be white dwarfs, but the period is too low

. Pulsars are rapidly spinning neutron stars

. The pulsar in the Crab nebula indicated that they had something do to with supernovæ

Crab Nebula Compact objects Neutron stars Pulsars

The light house model . A wobbling (precession) of the magnetic field explains the pulses from a neutron star Compact objects Neutron stars Pulsars

Crab Nebula Compact objects Neutron stars Pulsars

Crab Nebula Compact objects Neutron stars Pulsars . Pulsar slow down grad- ually due to energy loss

. The Crab pulsar is slowing 3×10-8 s per day

. Electrons moving in a circular path at relativistic speeds release energy, so called synchrotron Crab pulsar radiation

. We can calculate a pulsar’s age from its period Compact objects Neutron stars Pulsars . Neutron stars seem to have a solid crust overlying a sea of neutrons that can flow with zero friction (called superfluidity)

. Young pulsars sometimes speed up, glitch, probably caused by and instability in a slowing crust with a rapidly rotating interior Compact objects Neutron stars Magnetar . A neutron star with a huge magnetic field

. The decay of the magnetic fields powers the emission of copious amounts of high-energy electromagnetic radiation, particularly X-rays and

. Quakes give gamma- rays burts Compact objects Black holes Mass limit . The upper mass limit of a neutron star is due to . Degenerate nature of neutrons . Strong nuclear force holding neutrons together

. If the mass exceeds 3M even photons cannot escape the star’s gravity and the object becomes a black hole Compact objects Black holes Binary systems . Black holes cannot be seen because they do neither emit not reflect light

. Black holes in binary systems might be possible to detect

. As material is sucked towards a black hole, it heats and emits X-rays

Gamma rays from the galactic center Compact objects Black holes

. A non-rotating black hole only has a “center” and a “surface”

. The black hole is surrounded by the event horizon wherein no light an escape

. The distance between the center and the event horizon is called the Schwartzschild radius: 2 RSch = 2GM/c Compact objects Black holes A black hole can be described completely by three numbers:

. Mass As measured by the black hole’s effect on orbiting bodies . Total electric charge As measured by the strength of it’s electric force (probably small). It can have no magnetic field.

. Angular momentum From the star Compact objects Black holes Rotation . A rotating black hole is called a Kerr black hole

. In the ergosphere, nothing can remain at rest as spacetime here is being pulled around the black hole Compact objects Black holes . Seen from the outside, falling into a black hole is an infinite voyage as gravitational tidal forces pull spacetime in such a way that time becomes infinitely long

. Seen from the inside, the universe seem to speed up, while the trip down to oblivion takes “normal time” Compact objects Black holes Evaporation

. The strong gravitational field causes pair creation . Hawking radiation . The mass loss is less for larger black holes