SLIDE 1
Star-forming region in Carina, NGC 3582, from Astronomy Picture of the Day: http://apod.nasa.gov/apod/ap130611.html
Star-forming region in Carina, NGC 3582, from Astronomy Picture of - - PowerPoint PPT Presentation
Star-forming region in Carina, NGC 3582, from Astronomy Picture of - - PowerPoint PPT Presentation
Star-forming region in Carina, NGC 3582, from Astronomy Picture of the Day: http://apod.nasa.gov/apod/ap130611.html Star-forming region in Cassiopeia , Heart and Soul nebula, IC1805 & IC1848, from Astronomy Picture of the Day:
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SLIDE 3
Star-forming region in Cassiopeia, Heart and Soul nebula, IC1805 & IC1848, from Astronomy Picture of the Day: http://apod.nasa.gov/apod/ap100601.html
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Star-forming region in Cassiopeia, IC1795, from Astronomy Picture of the Day: http://apod.nasa.gov/apod/ap091210.html
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Star-forming region in Carina NGC3372, from Astronomy Picture of the Day: http://apod.nasa.gov/apod/ap100226.html
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Stellar Configurations
- Self gravitating
- Self-consistent solution needed
- Different processes resist collapse
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Planets
- Gravity weak because of small M
- Atomic forces provide balancing pressure
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Jupiter with moons Ganymede (upper) and Io (lower), from Astronomy Picture of the Day: http://apod.nasa.gov/apod/ap130215.html
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Normal Stars
- Gravitational energy starts process
- Fusion then supplies energy
- Plasma of electrons and nuclei
- Kinetic pressure, P = nkT
- Radiation pressure, P = 1
3u(T), helps and domi-
nates above about 10M⊙
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SLIDE 11
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FOUR POSSIBLE END STATES OF STARS
DISPERSED GAS DWARF STAR NEUTRON STAR BLACK HOLE NORMAL STAR INCREASING MASS
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White Dwarf
- Fusion has stopped
- Collapses to a small size, nuclear spacing ∼ 1/100
that of a solid
- Electron degeneracy pressure supports it, P ∝ 1
me n5/3
- White → gray → brown (dead, cold)
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SLIDE 14
Assume uniform density of α++ and e− EK = E(α)
K
small
+E(e)
K
= 3
5 NeǫF = 3 5 Ne ¯ h2 2me
- 3π2(Ne/V )
2/3
V = 4
3πR3
M ≈ Nαmα = (Ne/2)mα ⇒ Ne = 2M/mα EK = 3
5
9π
2
2/3 ¯
h2 me
- M
mα
2/3 1
R2
EP = −3
5 G M2 R
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SLIDE 15
ET R EP EK R
ET = EK + EP MR3
0 = 2(9π)2
¯ h6 G3m3
em5 α
= 0.74 × 1051 kg-m3 R0 ∝ 1/M1/3 Stable for any M.
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X-ray image of Sirius B (brighter) and Sirius A (less bright) , from Astronomy Picture of the Day: http://apod.nasa.gov/apod/ap001006.html
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Sirius B: M = 2.1 × 1030 kg R
- bserved
5.6 × 106 m
- ur model
7.1 × 106 m (good) better model 8.6 × 106 m (⇒ a problem)
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Our model of Sirius B implies ne = 8.6 × 1029 cm−3 ǫF = 4.7 × 10−7 ergs → 3.4 × 109K (Tsurface ∼ 2 × 107 K) But mec2 = 8.2 × 10−7 ergs ⇒ relativity needed
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Dwavevectors(k) = V (2π)3 Dstates(k) = 2V (2π)3 N =
4
3πk3
F
- 2V
(2π)3 ⇒ kF = (3π2N/V )1/3 ǫ = c| k| ⇒ ǫF = c(3π2N/V )1/3
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#(ǫ) =
4 3π k3(ǫ)
- (ǫ/c)3
2V
(2π)3
=
1 3π2V
1
c
3
ǫ3 D(ǫ) = d# dǫ = V π2
1
c
3
ǫ2
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D(ǫ) = aǫ2 N =
ǫF
D(ǫ) dǫ =
ǫF
aǫ2 dǫ = 1
3aǫ3 F
E =
ǫF
ǫD(ǫ) dǫ =
ǫF
aǫ3 dǫ = 1
4aǫ4 F
=
3 4NǫF
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P = −
∂E
∂V
- N,S
- dS=0 at T=0
= −3 4N
∂ǫF
∂V
- N
= 1 4(N/V )ǫF ∝ (N/V )4/3 This pressure rises less steeply with density, (N/V )4/3, than is the case for the non-relativistic gas, (N/V )5/3.
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For a white dwarf composed of α particles and elec- trons, V = 4 3πR3 M ≈ Nαmα = 1 2Nemα ⇒ Ne = 2(M/mα) EK = 3 4NeǫF = 3 4Nec(3π2Ne/V )1/3 = 3 2c( M mα )
9π
2 M mα 1 R3
1/3
= 3 2
9π
2
1/3
c
M
mα
4/3 1
R
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The R dependence of the two contributions to the total energy is straight forward: EK = a/R and EP = −b/R where a and b are known expressions. Then ETOTAL = (a − b)/R which is never stable. The condition a = b is a special case, a dividing line between collapse and infinite expansion.
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c
M
mα
4/3
∼ GM2 c Gm4/3
α
∼ M2/3 M ∼
c
Gm2
α
3/2
mα
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The Chandrasekhar limit for the maximum possible mass of a white dwarf is MCh = 0.20
Z
A
ch
Gm2
p
3/2
mp where Z/A is the average ratio of atomic number to atomic weight of the stellar constituents. Note that it has the same form as our expression. For Z/A = 0.5 (α particles) this gives MCh = 1.4MSun.
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Neutron Star
- p+ + e− → n to lower coulomb energy
- Degeneracy pressure of neutrons
MR3
0 ∝ ¯
h6/G3m8
n
⇒ R0 ∼ 15 km if M = 1.4M⊙
- Nuclear forces also contribute to P
- Rotating neutron stars seen as pulsars
- Also subject to stability limit, M ∼ 2M⊙
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http://chandra.harvard.edu/photo/2006/crab/
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STELLAR CONFIGURATIONS
NORMAL STAR DWARF STAR NEUTRON STAR BLACK HOLE DISPERSED GAS
GRAVITY GAS PRESSURE (+ RADIATION ) ELECTRON DEGENERACY NEUTRON DEGENERACY + NUCLEAR FORCES
1 g/cm3 106 g/cm3 1014 g/cm3
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Artist’s conception of accretion disk around a black hole , from Astronomy Picture of the Day: http://apod.nasa.gov/apod/ap130312.html
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http://commons.wikimedia.org/wiki/File:Cygnus_X-1.png
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