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Chapter 10
Chapter 11
Chapter 12
Chapter 14
Chapter 16
A stellar model
P
k
mT
rrr
m
rr
rGm
r
P
B
u
)(π4d
d
)()(
d
d
2
2
32 π16
)( 3
d
d
Trca
rL
r
T
π4 d
d
2r
r
L
ad3
B
)(
)(
π16
3
Trm
rL
mGca
k
u
4.0ad Pd
Td
ln
ln
A stellar model (II)
Evolution before the main sequence
• Interstellar gas cloud – gravitational
instability
• Heating of gas via collaps
• Then reach hydrostatic equilibrium
• Temperature and density reach a level
where fusion will begin
• The star reaches energy equilibrium
Star formation
T=10 K
Hydrostatic equilibrium
T=10 K
Star formation
Gravitational instability
Star formation
Star formation
3RM
Star formation
3RM
R
MG
TkB
Potential:
Kinetic energy of
a hydrogen atom
Star formation
3RM
R
mMGTkE B
utot
hydrogen
Star formation
R
mMGTkE B
utot
0tot E
Unstable if:
E(kin) E(pot)
R
mMGTkE B
utot
E(kin) E(pot)
TkR
mMG
R
mMGTk
B
B
u
u0
Unstable if:
TkR
mMGB
u
TkR
mMGB
u
3RM
u
2
u
3
mG
TkR
TkR
mRG
B
B
u
22 π
mG
TkRR B
J
Jeans length
u
π
mG
TkRR B
J
3π
3
4JJ RMM
Jeans mass
sunJ MT
MM
2/13
10105
T = 10 K, ρ=10 g/cm³ -22
3π
3
4JJ RMM
Jeans mass
sunJ MT
MM
2/13
10105
T = 10 K, ρ=10 g/cm³ -22
M = 1.5 10 M 3
● О
3π
3
4JJ RMM
Jeans mass
sunJ MT
MM
2/13
10105
T = 10 K, ρ=10 g/cm³ -14
M = 1.5 10 M -1
● О
sunJ MT
MM
2/13
10105
101010 log5.0log5.1log TCM J
CMT J 101010 log3
2log
3
1log
NCNC14131312
n
AaT
TXX
0
0
20
0
0
T
TXZ
T ~ 20 mill. K
NCNC14131312
log ρ g/cm³
log T
K
4
9
8
7
6
5
-2 0 2 6 4 8
EOS
Ideal gas
Earth
Solar model
Radiation pressure
M(max) = 50 M(sun)
M(min) = 0.08 M(sun)
Simulation made by
Matthew Bate
University of Exeter
Bate (2010; MNRAS
404, L79) )
Simulating star formation
See http://www.astro.ex.ac.uk/people/mbate/Animations/Stellar/
ZAMS Zero-Age Main Sequence
Zero-Age Main Sequence
Zero-Age Main Sequence
Jupiter
MR MR
Zero-Age Main Sequence
2/1MR 5ML
3ML
42
effTRL 42
effTRL
MR
Small mass Large mass
2/1MR 5ML
3ML
4
effTML 42
effTML
MR
Small mass Large mass
2/1MR 5ML
3ML
4
effTML
34MTeff
24MTeff
42
effTML
MR
Small mass Large mass
2/1MR 5ML
3ML
4
effTML
MTeff 3/4 MTeff
2
42
effTML
MR
Small mass Large mass
2/1MR 5ML
3ML
4
effTML
MTeff 3/4 MTeff
2
3.5
effTL 6
effTL
42
effTML
MR
Small mass Large mass
ZAMS Zero-Age Main Sequence
0.9 M • O •
O 0.9 M
•
ad3
B
)(
)(
π16
3
Trm
rL
mGca
k
u
ad3
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)(
)(
π16
3
Trm
rL
mGca
k
u
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