STAR CLUSTERS Lecture 3 Kinematic Propertiesmtrenti/Site/slides/Star... · 2016-10-26 · Nora Lützgendorf, KAS16 / 51 1. Star Formation •from gas clouds, fragmentation •Initial

STAR CLUSTERS

Lecture 3 Kinematic Properties

Nora Lützgendorf (ESA)

Nora Lützgendorf, KAS16 / 51

1. Star Formation • from gas clouds, fragmentation • Initial mass function (IMF): multiple power laws, changes

with time 2. Multiple Stellar populations

•Photometric evidence: Multiple sequences in CMD •Spectroscopic evidence: Na-O anti-correlation •Explanations:

1. Polluters + 2nd Generation 2. Polluters

•Problems: Mass budget problem (must have lost 90% of their mass??…), and many more…

2

LECTURE 2


Outline

1. The Gravitational N-body problem 2. Dynamic Equilibrium 3. Negative Heat Capacity 4. Core Collapse 5. Equipartition of energies 6. Mass Segregation


Outline



Gravitation

~Fi =NX

j=1,j 6=i

Gmimj~rj � ~ri|~rj � ~ri|3

mi

mj

~rj �~ri

mj�1

mj�2

mj+1


~̈ri = �GNX

j=1,j 6=i

mj~rj � ~ri|~rj � ~ri|3

6

Gravitation

mi

mj

~rj �~ri

mj�1

mj�2

mj+1


~̈ri = �G2X

j=1,j 6=i


7

Gravitation - N = 2

mi

mj

~rj �~ri


e=0e=0.5

e=1

e=2

Gravitation - N = 2

r(✓) =a(1� e2)

1 + 2 cos(✓)


Gravitation - N = 2


~̈ri = �G3X

j=1,j 6=i


mj�1

10

mi

mj

~rj �~ri

Gravitation - N = 3


Gravitation - N = 3


Gravitation - N = 3


~̈ri = �G3X

j=1,j 6=i


mj�1

13

mi

mj

~rj �~ri

Gravitation - N = 3

CHAOS!BUT…


CHAOS!BUT…

~̈ri = �G3X

j=1,j 6=i


mj�1

14

mi

mj

~rj �~ri

Gravitation - N = 3


Gravitation - N = 3

L1 L2L3

L4

L5


Explanations - Problems

L2

WIND

SOHO

LISAPATHFINDER

HERSCHEL

JWST

GAIA


~̈ri = �GNX

j=1,j 6=i


17

Gravitation - N > 3

mi

mj

~rj �~ri

mj�1

mj�2

mj+1

CHAOS!



18

Outline


Dynamic Equilibrium

EQUILIBRIUM


Dynamic Equilibrium

COLD (v = small or 0)


Dynamic Equilibrium

COLD (v = small or 0)


Dynamic Equilibrium

HOT (v = large)


Dynamic Equilibrium

HOT (v = large)


Dynamic Equilibrium - Definition

EQUILIBRIUM:‣No EXPANSION, and no CONTRACTION, even though all particles are in MOTION


E = W +K = const.

W = �G1

2

NX

i=1

NX

i 6=j

mimj

|~ri � ~rj |

K =1

2

NX

i=1

mi~v2i

25

Virial Theorem

KINETIC ENERGY

POTENTIAL ENERGY

VIRIAL THEOREM

CONSERVATION OF ENERGY

W = �2K



26

Outline


“Temperature”

Like in a gas: ‣Particles move fast system is HOT

‣Particles move slow system is COLD

1

2mv̄2 =

3

2kBT

K =3

2NkBT̄


Heat Capacity

W = �2K

C ⌘ dE

dT̄

K =3

2NkBT̄

= �3

2NkB

E = W +K

= �K

= �3

2NkBT̄

VIRIAL THEOREM


GETS COLDER

C = negative

Heat Capacity

GETS HOTTERC = positive

29

ENERGY

C ⌘ dE

dT̄= �3

2NkB


GETS HOTTER

GETS COLDER

C = negative

Heat Capacity

C = positive

30

ENERGY

C ⌘ dE

dT̄= �3

2NkB


C = negative

C = positive

Heat Capacity


Heat Capacity

ENERGYV1

V2 V2 > V1HOTTER COLDER



33

Outline


Core Collapse

Cluster of stars with equal mass:

Stars deeper in the potential move faster (hot)


Core Collapse

Cluster of stars with equal mass:

Stars deeper in the potential move faster (hot)


Core Collapse

Encounters of fast and slow stars:

Slow star gets faster, fast star gets slower

~

P = M1 · ~v1 +M2 · ~v2 = const.

ENERGY


Core CollapseFast star: looses energy ⇒ sinks deeper in the potential well ⇒ gains speed ⇒ becomes even faster (hotter)

Slow star: gains energy ⇒ climbs out of the potential well, ⇒ looses speed ⇒ becomes even slower (colder)


Core Collapse


Core Collapse


Core Collapse


Core Collapse


Core Collapse


Core Collapse

M15

M28


Core Collapse

M15

M28

Distance

DistanceSu

rface

Brig

htne

ssSu

rface

Brig

htne

ssCore Collapsed



45

Outline


Equipartition of Energies

Cluster of stars with UN - equal mass:


~

P = M1 · ~v1 +M2 · ~v2 = const.

ENERGY

Low-mass star gets faster, high-mass star gets slower

Encounters of high-mass and low-mass stars:

Kinetic energies become more equal


Ki ⇠Mi

2v2i



When all stars (at radius R) have the same kinetic energy

High-mass stars are slow, low-mass stars are fast

EQUIP

ARTIT

ION

V ~ 1/

sqrt(M

)

NO EQUIPARTITION

Anderson & van der Marel, 2010



50

Outline


Mass Segregation

Equipartition of energies:

High-mass stars sink to the centerLow-mass stars rise to the outskirts


Mass Segregation

Mass gradient from center to the outskirts

log

N

log M

Dynamical Mass Loss


Summary - 1

1. The Gravitational N-body problem •N=2: exactly solvable •N=3: approximately solvable •N>3: only numerical solvable

2. Dynamic Equilibrium •No EXPANSION or CONTRACTION of the system

3. Negative Heat Capacity •Remove energy —> hotter •Gain energy —> colder


Summary - 2

4. Core Collapse •Very condensed core, steep light profile

5. Equipartition of Energies •All the stars (at radius R) have the same kinetic energy •High-mass stars: slow, low-mass stars: fast

6. Mass Segregation •Mass gradient from center to the outskirts

Documents

STAR CLUSTERS Lecture 3 Kinematic Propertiesmtrenti/Site/slides/Star... · 2016-10-26 · Nora Lützgendorf, KAS16 / 51 1. Star Formation •from gas clouds, fragmentation •Initial