Star Formation

Classifying Stars

• The surface temperature of a star T is compared to a black body.

– Luminosity L

– Radius R

• The absolute magnitude calculates the brightness as if the stars were 10 pc away.

– Related to luminosity

•

• Type Temperature

O 35,000 K

B20,000 K

A 10,000 K

F 7,000 K

G 6,000 K

K 4,000 K

M 3,000 K

424 TRL

72.4)/log(5.2 sunLLM

Stellar Relations

• Some bright stars (class) (absolute magnitude)

– Sun G2 4.8

– Sirius A1 1.4

– Alpha Centauri G2 4.1

– Capella G8 0.4

– Rigel B8 -7.1

– Betelgeuse M1 -5.6

– Aldebaran K5 -0.3

Luminosity vs. Temperature

• Most stars show a relationship between temperature and luminosity.

– Absolute magnitude can replace luminosity.

– Spectral type/class can replace temperature.

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O B A F G K MSpectral Type

Sun

Hertzsprung-Russell Diagram

• The chart of the stars’ luminosity vs. temperature is called the Hertzsprung-Russell diagram.

• This is the H-R diagram for hundreds of nearby stars.

– Temperature decreases to the right

Main Sequence

• Most stars are on a line called the main sequence.

• The size is related to temperature and luminosity:

– hot = large radius

– medium = medium radius

– cool = small radius

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O B A F G K MSpectral Type

1 solar radius

Sirius

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Giants

• Stars that are brighter than expected are large and are called giants or supergiants.

• Betelgeuse is a red supergiant with a radius hundreds of times larger than the sun.

AldebaranCapella

RigelBetelgeusesupergiants

giants

Dwarves

• Stars on the main sequence that dim and cool are red dwarves.

• Small, hot stars that are dim are not on the main sequence and are called white dwarves.

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white dwarves

Interstellar Medium

• Interstellar space is filled with gas (99%) and dust (1%).

• Interstellar gas, like the sun, is 74% hydrogen and 25% helium.

• Interstellar dust, like clouds in the gas giants, are molecular carbon monoxide, ammonia, and water.

• Traces of all other elements are present.

• Atoms are widely spaced, about 1 atom per cm3, a nearly perfect vacuum.

• The temperature is cold, less than 100 K.

Molecular Clouds

• The small mass of atoms creates very weak gravity.

• Gravity can pull atoms and molecules together.

• Concentrations equal to 1 million solar masses can form giant molecular clouds over 100 ly across.

Catalysts for Star Formation

• A cool (10 K) nebula can be compressed by shock waves.

• These shock waves are from new stars and exploding supernovae.

exploding star shock waves nebula with areas of higher density

Gravitational Contraction

• Density fluctuations cause mass centers to appear.

• Mass at a distance will be accelerated by gravity.

• If there is no outward pressure there will be free fall.

– Mass m0 within radius r

– Conservation of energy

– Calculate free fall time

2

)()(

r

rGmrg

r

rdrrrm0

24)()(

0

00

2

2

1

r

Gm

r

Gm

dt

dr

021

0

000

00

22rr

drr

Gm

r

Gmdr

dr

dt

032

3

G

Protostars

• Local concentrations in a nebula can be compressed by gravity. With low temperature they don’t fly apart again.

– Contracting material forms one or more centers

– The contracting material begins to radiate

– These are protostars, called T Tauri stars (G, K, M).

Hydrostatic Equilibrium

• Gravity is balanced by pressure.

– Equilibrium condition

– True at all radii

• The left side is related to average pressure.

– Integrated by parts

• The right side is the gravitational potential energy.

2

)()(

r

rrGm

dr

dP

RR

dmr

rGm

dr

dPr

0 20

3 )(4

gravEVP 3

VPdr

dPr

R34

0

3

V

EP grav

3

Adiabatic Index

• Adiabatic compression is not linear in pressure and volume.

– Parameter is adiabatic index

– Relate to internal energy

• The gravitational energy was also related to the pressure.

– Energy condition for equilibrium

)(1

1PVdPdVdEint

0P

dP

V

dV

V

EP int)1(

V

E

V

Eintgrav )1(

3

0)1(3 intgrav EE

Formation Conditions

• Contraction requires gravitational energy to exceed internal energy.

– Thermal kinetic energy 3kT/2

• The conditions for cloud collapse follow from mass or density.

– Jeans mass, density MJ, J

RmG

kTM

2

3min

intgrav EE

3

2 2

3

4

3

mG

kT

MJ

R

GMfEgrav

2

Fusion Begins

• Initial energy is absorbed by hydrogen ionization.

– D = 4.5 eV

– I = 13.6 eV

• Apply this to hydrostatic equilibrium.

• Continued contraction results in quantum electron gas.

– When degenerate it resists compression

– Sets temperature at core

IH

DH

I m

M

m

ME

2

eV6.2212

1 IDkT

3

23)(

h

kTmm e

342

382

Mh

mmGkT e

Birth of the Sun

• Gravity continues to pull the gas together.

– Temperature and density increases

• If the temperature at the center becomes 5 million degrees then hydrogen fusion begins.

• At this point the star has reached the main sequence.

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1 M

Birth of Other Stars

• Large masses become brighter, hotter stars.

• Gravity causes fusion to start sooner, about 100,000 years.

• Small masses become dimmer, cooler stars.

• Gravity takes longer to start fusion, up to 100 million years.

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10 M

3 M

0.02 M

0.5 M