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

B

)(

)(

π16

3

Trm

rL

mGca

k

u