Summary of post main sequence evolution of sun like stars
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0. Summary of Post-Main-Sequence Evolution of Sun-Like Stars. Core collapses; outer shells bounce off the hard surface of the degenerate C,O core. Formation of a Planetary Nebula. Fusion stops at formation of C,O core. C,O core becomes degenerate. M < 4 M sun. 0.

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Summary of Post-Main-Sequence Evolution of Sun-Like Stars

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Summary of post main sequence evolution of sun like stars

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Summary of Post-Main-Sequence Evolution of Sun-Like Stars

Core collapses; outer shells bounce off the hard surface of the degenerate C,O core

Formation of a Planetary Nebula

Fusion stops at formation of C,O core.

C,O core becomes degenerate

M < 4 Msun


The remnants of sun like stars white dwarfs

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The Remnants of Sun-Like Stars: White Dwarfs

First example:

Sirius B (Astrometric binary; discovered 1862)

  • M ≈ 1 M0

  • L ≈ 0.03 L0

  • Te ≈ 27,000 K

  • R ≈ 0.008 R0

  • r ≈ 3x106 g/cm3


White dwarfs

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White Dwarfs

Degenerate stellar remnant (C,O core)

Extremely dense:

1 teaspoon of WD material:

mass ≈ 16 tons!!!

Chunk of WD material the size of a beach ball would outweigh an ocean liner!

Central pressure:

Pc ~ 3.8*1023 dynes/cm2 ~ 1.5x106 Pc,0

for Sirius B


Summary of post main sequence evolution of sun like stars

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Thin remaining surface layers of He and H produce absorption lines;

DB (Broad He abs. lines)

DA (Broad H abs. lines)

(ZZ Ceti Variables; P ~ 100 – 1000 s)

Low luminosity; high temperature => Lower left corner of the Herzsprung-Russell diagram.


Degenerate matter

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Degenerate Matter

Dx ~ n-1/3

Heisenberg Uncertainty Principle:

(Dx)3 (Dp)3 ~ h3 => (Dp)3min ~ n h3

Non-degenerate matter (low density or high temperature):

Number of available states

Electron momentum distribution f(p)

e-E(p)/kT

Electron momentum p


Degenerate matter1

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Degenerate Matter

Dx ~ n-1/3

Heisenberg Uncertainty Principle:

(Dx)3 (Dp)3 ~ h3 => (Dp)3min ~ n h3

Degenerate matter (High density or low temperature):

Fermi momentum

pF = ħ (3p2ne)1/3

Electron momentum distribution f(p)

e-E(p)/kT

Number of available states

Electron momentum p


Degeneracy of the electron gas in the center of the sun

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Degeneracy of the Electron Gas in the Center of the Sun


The chandrasekhar limit

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The Chandrasekhar Limit

The more massive a white dwarf, the smaller it is.

RWD ~ MWD-1/3 => MWD VWD = const. (non-rel.)

WDs with more than ~ 1.44 solar masses can not exist!

Transition to relativistic degeneracy


Temperature and degree of degeneracy as a function of radius in a white dwarf

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Temperature and Degree of Degeneracy as a Function of Radius in a White Dwarf


Cooling curve of a white dwarf

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Cooling Curve of a White Dwarf

Nuclei settling in a crystalline structure, releasing excess potential energy


White dwarfs in binary systems

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White Dwarfs in Binary Systems

X-ray emission

T ~ 106 K

Binary consisting of WD + MS or Red Giant star => WD accretes matter from the companion

Angular momentum conservation => accreted matter forms a disk, called accretion disk.

Matter in the accretion disk heats up to ~ 1 million K => X-ray emission => “X-ray binary”.


Nova explosions

Nova Explosions

Hydrogen accreted through the accretion disk accumulates on the surface of the WD

  • Very hot, dense layer of non-fusing hydrogen on the WD surface

Nova Cygni 1975

  • Explosive onset of H fusion

  • Nova explosion


Recurrent novae

Recurrent Novae

In many cases, the mass transfer cycle resumes after a nova explosion.

T Pyxidis

R Aquarii

→ Cycle of repeating explosions every few years – decades.


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